{ "meta": { "api_version": "v1", "attribution": "lithium-niobate.com data compiled by Wentao Jiang; cite the original sources listed per value.", "count": 344, "data_version": "0.1.0", "documentation": "https://lithium-niobate.com/api/openapi.json", "license": { "id": "CC-BY-4.0", "name": "Creative Commons Attribution 4.0 International", "url": "https://creativecommons.org/licenses/by/4.0/" }, "note": "Canonical terms (data/glossary.yaml, origin canonical) merged with the chapter glossaries (content/chapters/*/glossary.yaml, origin chapter), deduplicated by normalized term." }, "terms": [ { "aliases": [ "+c face", "z+ face", "+z (+c) face", "+c face (+z face)" ], "category": "crystal", "chapters": [ "01-crystal", "04-quirks" ], "id": "plus-z-face", "long": "IRE 1949 (as used in Weis & Gaylord 1985), IRE 1958 (as cited in Volk & Wöhlecke 2009) and IEEE Std 176-1987 (positive d33: tension along Z makes the +Z face positive) give the same +z for LN. The pyroelectric coefficient p3 is negative in this frame. Flipping +z (a 180 deg rotation about x) reverses every odd-rank tensor (e, d, r, chi(2), p3) but leaves the elastic and photoelastic tensors unchanged.", "origin": "canonical", "related": [ "polar-axis", "ieee-176", "pyroelectric-effect", "piezoelectric-effect" ], "short": "The +z (+c) face of LiNbO3 is the c face that becomes negatively charged under compression along c and positively charged on cooling.", "sources": [ { "locator": "pp. 192-193", "source_id": "weis1985" }, { "locator": "p. 22", "source_id": "ieee176" }, { "locator": "p. 2", "source_id": "volk2008" }, { "source_id": "ire1949" }, { "source_id": "weis1985" } ], "term": "+z face (+c face)" }, { "chapters": [ "08-industry" ], "id": "1-6t-3-2t", "long": "Pluggable optical modules with 1.6 or 3.2 Tb/s aggregate rate, e.g. 8 lanes of 200 or 400 Gb/s (DR8 = 8 parallel single-mode lanes).", "origin": "chapter", "short": "Pluggable optical modules with 1.6 or 3.2 Tb/s aggregate rate, e.g. 8 lanes of 200 or 400 Gb/s (DR8 = 8 parallel single-mode lanes).", "sources": [], "term": "1.6T / 3.2T" }, { "aliases": [ "128 deg rotated Y-cut", "128YX LN", "128 Y-X cut" ], "category": "acoustics", "chapters": [ "03-sound", "07-history", "05-making" ], "id": "128-y-x-cut", "long": "Shibayama et al. 1976 reported it as the optimum rotated Y-cut for acoustic-surface-wave filter substrates, and it later became a standard SAW cut. Interdigital transducers on the polished plate launch and detect the surface wave along x.", "origin": "canonical", "related": [ "y-cut", "saw", "idt", "electromechanical-coupling" ], "short": "The 128 deg Y-X cut of LiNbO3 is a substrate orientation whose plate normal is the y axis rotated by about 128 deg about x, with surface waves propagating along x.", "sources": [ { "source_id": "shibayama1976" } ], "term": "128 deg Y-X cut" }, { "chapters": [ "01-crystal" ], "id": "180-deg-domain-wall", "long": "The boundary between antiparallel domains, ideally one to two lattice units wide.", "origin": "chapter", "short": "The boundary between antiparallel domains, ideally one to two lattice units wide.", "sources": [ { "source_id": "gopalan2007" } ], "term": "180 deg domain wall" }, { "aliases": [ "C3v", "point group 3m" ], "category": "crystal", "chapters": [ "01-crystal" ], "id": "point-group-3m", "long": "The point group fixes which tensor components can be nonzero, for example the r tensor with independent r13, r22, r33 and r51. It lacks an inversion center, which allows piezoelectric, Pockels and chi(2) effects, and it is polar (the two ends of the threefold axis are inequivalent), which allows pyroelectricity. Weis & Gaylord 1985 prints the Schoenflies symbol as C6v, a typo; 3m corresponds to C3v. IEEE Std 176-1987 lists LiNbO3 as its example of class 3m.", "origin": "canonical", "related": [ "space-group-r3c", "mirror-plane", "polar-axis", "eo-tensor" ], "short": "3m (Schoenflies C3v) is the point group of ferroelectric LiNbO3: a threefold rotation axis along c with three mirror planes that contain it.", "sources": [ { "locator": "p. 192, Sec. 2.1", "source_id": "weis1985" }, { "locator": "Table 3", "source_id": "ieee176" }, { "source_id": "weis1985" } ], "symbol": "3m", "term": "3m point group" }, { "chapters": [ "02-light" ], "id": "acceptance-bandwidth", "long": "Full width at half maximum of sinc²(Delta k L/2) in the chosen parameter q: 2.783/(L |d Delta k/dq|).", "origin": "chapter", "short": "Range of wavelength, temperature or angle over which phase matching holds.", "sources": [], "term": "acceptance bandwidth" }, { "aliases": [ "AO effect", "acousto-optics" ], "category": "acoustics", "chapters": [ "03-sound", "06-devices" ], "id": "acousto-optic-effect", "long": "Diffraction efficiency scales with the figure of merit M2 = n^6 p² / (rho v³); Weis & Gaylord 1985 tabulates acousto-optic figures of merit for LN. In thin-film LN, acoustic resonators and waveguides give GHz acousto-optic modulators and microwave-to-optical converters (Shao et al. 2019; Sarabalis & et al. 2020).", "origin": "canonical", "related": [ "photoelastic-effect", "saw", "piezo-optomechanics", "microwave-to-optical-transduction" ], "short": "The acousto-optic effect is the modulation or diffraction of light by an acoustic wave through the index changes it carries: photoelastic, plus electro-optic from the accompanying piezoelectric field in LiNbO3.", "sources": [ { "locator": "p. 201", "source_id": "weis1985" }, { "source_id": "shao2019" }, { "source_id": "sarabalis2020" } ], "term": "acousto-optic effect" }, { "chapters": [ "03-sound" ], "id": "acousto-optic-figure-of-merit", "long": "LN, longitudinal wave along X: M2 = 6.99 x 10^-15 s³/kg (status P-comp, Dixon 1967 via Weis & Gaylord 1985).", "origin": "chapter", "short": "Material ranking numbers for acousto-optic devices, e.g. M2 = n^6 p²/(rho v³).", "sources": [ { "source_id": "weis1985" }, { "citation": "R. W. Dixon, \"Photoelastic Properties of Selected Materials and Their Relevance for Applications to Acoustic Light Modulators and Scanners\", Journal of Applied Physics 38 5149-5153 (1967)", "doi": "10.1063/1.1709293", "ref": "03-sound/dixon1967" } ], "term": "acousto-optic figure of merit" }, { "chapters": [ "05-making" ], "id": "analog-provenance", "long": "A reported value taken from a paper other than the one anchoring a process flow, or from LiTaO3, and marked as such.", "origin": "chapter", "short": "A reported value taken from a paper other than the one anchoring a process flow, or from LiTaO3, and marked as such.", "sources": [], "term": "Analog (provenance)" }, { "chapters": [ "06-devices" ], "id": "ao-modulator", "long": "A modulator in which an acoustic wave, launched piezoelectrically, changes the refractive index and modulates or frequency-shifts light.", "origin": "chapter", "short": "A modulator in which an acoustic wave, launched piezoelectrically, changes the refractive index and modulates or frequency-shifts light.", "sources": [], "term": "AO modulator" }, { "aliases": [ "argon ion milling", "physical dry etching" ], "category": "fabrication", "chapters": [ "05-making" ], "id": "ar-milling", "long": "Optimized physical etching produces the smooth, angled sidewalls of low-loss TFLN ridges (Zhu et al. 2021). Ar+ milling of the LN surface has also been reported to alleviate DC drift in TFLN modulators (Shi et al. 2025).", "origin": "canonical", "related": [ "propagation-loss", "dc-bias-drift", "cmp", "duv-lithography" ], "short": "Ar+ milling is physical dry etching in which accelerated argon ions sputter material, the usual way to etch LiNbO3 waveguides because LN resists chemical dry etching.", "sources": [ { "source_id": "zhu2021" }, { "source_id": "shi2025" } ], "term": "Ar+ milling" }, { "aliases": [ "IBE" ], "chapters": [ "05-making" ], "id": "argon-ion-milling-ion-beam-etching", "long": "Physical removal of material by a directed beam of argon ions.", "origin": "chapter", "short": "Physical removal of material by a directed beam of argon ions.", "sources": [], "term": "Argon ion milling / ion beam etching" }, { "chapters": [ "08-industry" ], "id": "atlas-sample", "long": "The curated set of modulator papers in eo-modulator-atlas (233 papers at the pinned commit); counts describe the sample, not the whole field.", "origin": "chapter", "short": "The curated set of modulator papers in eo-modulator-atlas (233 papers at the pinned commit); counts describe the sample, not the whole field.", "sources": [], "term": "atlas sample" }, { "chapters": [ "01-crystal" ], "id": "backswitching", "long": "Spontaneous return of freshly reversed domains to the original direction after a too-short poling pulse.", "origin": "chapter", "short": "Spontaneous return of freshly reversed domains to the original direction after a too-short poling pulse.", "sources": [ { "source_id": "volk2008" } ], "term": "backswitching" }, { "category": "optics", "chapters": [ "02-light" ], "id": "bandgap", "long": "Thierfelder et al. 2010 posed the question directly ('Do we know the band gap of lithium niobate?'). Because the absorption edge also shifts with Li content, an optical gap value needs the composition and the absorption criterion.", "origin": "canonical", "related": [ "uv-absorption-edge", "transparency-window" ], "short": "The band gap of LiNbO3 is usually quoted as about 3.7 eV from optical absorption, while GW calculations place the fundamental quasiparticle gap at least 1 eV higher.", "sources": [ { "locator": "abstract", "source_id": "thierfelder2010" } ], "term": "band gap" }, { "chapters": [ "05-making" ], "id": "bcb", "long": "Benzocyclobutene, a polymer adhesive used to bond early LN films; it limits later annealing temperatures. Maximum 320 C, below the about 800 C needed to restore r33 fully [Andrea Guarino et al. 2007; P].", "origin": "chapter", "short": "Benzocyclobutene, a polymer adhesive used to bond early LN films; it limits later annealing temperatures.", "sources": [ { "source_id": "guarino2007" } ], "term": "BCB" }, { "aliases": [ "back end of line" ], "chapters": [ "08-industry" ], "id": "beol", "long": "The metal interconnect layers of a CMOS process, above the transistors.", "origin": "chapter", "short": "The metal interconnect layers of a CMOS process, above the transistors.", "sources": [], "term": "BEOL" }, { "aliases": [ "double refraction" ], "category": "optics", "chapters": [ "02-light" ], "id": "birefringence", "long": "From the Zelmon et al. 1997 Sellmeier it is -0.0842 at 633 nm, -0.0766 at 1064 nm and -0.0736 at 1550 nm (21 C). It depends on temperature and composition, which permits temperature-tuned birefringent phase matching.", "origin": "canonical", "related": [ "negative-uniaxial", "ordinary-index", "extraordinary-index", "birefringent-phase-matching", "walk-off" ], "short": "Birefringence is the index difference n_e - n_o, which for congruent LiNbO3 is negative, about -0.07 to -0.08 between 633 and 1550 nm.", "sources": [ { "source_id": "zelmon1997" }, { "source_id": "rii" } ], "term": "birefringence" }, { "aliases": [ "critical phase matching", "noncritical phase matching", "90 deg phase matching" ], "category": "nonlinear-optics", "chapters": [ "02-light", "07-history" ], "id": "birefringent-phase-matching", "long": "In negative uniaxial LN, type-I SHG converts an o-polarized fundamental into an e-polarized harmonic. Angle tuning (critical phase matching) incurs walk-off; at theta = 90 deg, temperature tuning gives noncritical phase matching without walk-off (Miller et al. 1965). Because n_e depends on temperature and Li content, the matching temperature shifts with composition.", "origin": "canonical", "related": [ "phase-matching", "walk-off", "negative-uniaxial", "birefringence" ], "short": "Birefringent phase matching cancels material dispersion with the difference between ordinary and extraordinary indices, so that orthogonally polarized waves share the same phase velocity.", "sources": [ { "source_id": "boyd1964" }, { "source_id": "miller1965" } ], "term": "birefringent phase matching" }, { "aliases": [ "BLIIRA", "blue-light-induced infrared absorption" ], "category": "quirks", "chapters": [ "04-quirks" ], "id": "bliira", "long": "Hirohashi et al. 2007 measured picosecond BLIIRA in single-domain and periodically poled ferroelectrics and found it lowest in KNbO3 and MgO:LN, and slightly increased by periodic poling. Like GRIIRA, it adds infrared absorption and heating that degrade high-power frequency conversion.", "origin": "canonical", "related": [ "griira", "polaron", "mgo-doping", "ppln" ], "short": "BLIIRA is the infrared absorption induced in LiNbO3 by blue (or two-photon) excitation through the same light-generated polaron absorption bands.", "sources": [ { "source_id": "hirohashi2007" }, { "source_id": "imlau2015" } ], "term": "BLIIRA (blue-light-induced infrared absorption)" }, { "aliases": [ "ingot" ], "category": "fabrication", "chapters": [ "05-making" ], "id": "boule", "long": "Unless grown at the congruent composition, a boule changes composition along its length as the melt drifts (Carruthers et al. 1971). Composition-sensitive quantities such as the Curie temperature or the UV absorption edge are used to check uniformity.", "origin": "canonical", "related": [ "czochralski-growth", "congruent", "curie-temperature", "uv-absorption-edge" ], "short": "A boule is the as-grown single-crystal ingot from which LiNbO3 wafers are cut after orientation.", "sources": [ { "source_id": "ballman1965" }, { "source_id": "carruthers1971" }, { "locator": "Eqs. (6.2)-(6.6), pp. 140-142", "source_id": "volk2008" } ], "term": "boule" }, { "aliases": [ "Nb_Li^4+" ], "chapters": [ "04-quirks" ], "id": "bound-small-polaron", "long": "Electron trapped on a Nb antisite; absorption band near 1.6 eV; cause of GRIIRA.", "origin": "chapter", "short": "Electron trapped on a Nb antisite; absorption band near 1.6 eV; cause of GRIIRA.", "sources": [ { "citation": "Judith R. M.-L. Schwesyg, \"Interaction of light with impurities in lithium niobate crystals\", Dr. rer. nat. dissertation, Universität Bonn (2011)", "ref": "04-quirks/schwesyg2011" } ], "term": "bound small polaron" }, { "chapters": [ "03-sound" ], "id": "bragg-diffraction", "long": "The diffracted light is shifted in frequency by the acoustic frequency.", "origin": "chapter", "short": "Diffraction of light by a thick acoustic grating at the angle where momentum is conserved: sin(theta_B) = lambda0/(2 n Lambda).", "sources": [], "term": "Bragg diffraction" }, { "aliases": [ "BAW", "bulk acoustic wave" ], "category": "acoustics", "chapters": [ "03-sound", "06-devices" ], "id": "baw", "long": "In congruent LN the measured longitudinal and shear velocities along Z are 7328.20 and 3590.41 m/s (Kushibiki et al. 1999 Table II). BAW resonators confine such a mode between electrodes or free surfaces; thin LN plates support high-coupling shear resonances used in XBARs and mm-wave resonators (Lu 2025).", "origin": "canonical", "related": [ "christoffel-equation", "xbar", "saw", "electromechanical-coupling" ], "short": "A bulk acoustic wave (BAW) is an elastic wave propagating through the volume of a crystal as a quasi-longitudinal or one of two quasi-shear modes.", "sources": [ { "locator": "Table II", "source_id": "kushibiki1999" }, { "source_id": "lu2025" } ], "term": "bulk acoustic wave (BAW)" }, { "aliases": [ "Glass current", "photogalvanic effect", "BPVE" ], "category": "quirks", "chapters": [ "04-quirks", "07-history" ], "id": "bulk-photovoltaic-effect", "long": "Glass et al. 1974 identified it as the driver of photorefraction in LN: in an open-circuit crystal, charge accumulates until conduction balances the current, giving E_sc ~ j_pv / (sigma_d + sigma_ph), which is large in insulating crystals. MgO doping does not reduce the photovoltaic current but raises sigma_ph, collapsing E_sc (Bryan et al. 1984).", "origin": "canonical", "related": [ "photorefraction", "space-charge-field", "photoconductivity", "mgo-doping" ], "short": "The bulk photovoltaic effect is a DC current driven by uniform illumination in a crystal without inversion symmetry, j = kappa alpha I along c in LiNbO3, with no applied field or gradient.", "sources": [ { "source_id": "glass1974" }, { "locator": "abstract", "source_id": "bryan1984" } ], "term": "bulk photovoltaic effect" }, { "aliases": [ "compound annual growth rate" ], "chapters": [ "08-industry" ], "id": "cagr", "long": "The constant yearly growth rate that links a base value to a forecast value; as quoted by each market report.", "origin": "chapter", "short": "The constant yearly growth rate that links a base value to a forecast value; as quoted by each market report.", "sources": [], "term": "CAGR" }, { "aliases": [ "CL-TWE, T-rail electrode" ], "chapters": [ "06-devices" ], "id": "capacitively-loaded-electrode", "long": "A traveling-wave electrode with small T-shaped segments that reach toward the waveguide from wide rails, keeping the field gap small while the current flows in low-loss rails.", "origin": "chapter", "short": "A traveling-wave electrode with small T-shaped segments that reach toward the waveguide from wide rails, keeping the field gap small while the current flows in low-loss rails.", "sources": [], "term": "capacitively loaded electrode" }, { "aliases": [ "coincidence-to-accidental ratio" ], "chapters": [ "06-devices" ], "id": "car", "long": "Ratio of true photon-pair coincidences to accidental coincidences; a pair-source quality figure.", "origin": "chapter", "short": "Ratio of true photon-pair coincidences to accidental coincidences; a pair-source quality figure.", "sources": [], "term": "CAR" }, { "chapters": [ "02-light" ], "id": "cascaded-chi-2", "long": "For |Delta k| L >> 1, up- and down-conversion produce a fundamental phase -eta_norm P L/Delta k; negative (defocusing) for Delta k = k_2w - 2k_w - 2 pi/Lambda > 0.", "origin": "chapter", "short": "A mismatched chi(2) process that acts like a Kerr effect of chosen sign.", "sources": [ { "citation": "R. DeSalvo et al., \"Self-focusing and self-defocusing by cascaded second-order effects in KTP\", Optics Letters 17 28 (1992)", "doi": "10.1364/OL.17.000028", "ref": "02-light/desalvo1992" } ], "term": "cascaded chi(2)" }, { "aliases": [ "coherent driver modulator" ], "chapters": [ "08-industry" ], "id": "cdm", "long": "A packaged IQ modulator with integrated RF drivers for coherent transceivers; HB-CDM is the high-bandwidth class.", "origin": "chapter", "short": "A packaged IQ modulator with integrated RF drivers for coherent transceivers; HB-CDM is the high-bandwidth class.", "sources": [], "term": "CDM" }, { "aliases": [ "coherent driver modulator; high-bandwidth CDM" ], "chapters": [ "07-history" ], "id": "cdm-hb-cdm", "long": "Packaged coherent IQ modulator with integrated RF driver.", "origin": "chapter", "short": "Packaged coherent IQ modulator with integrated RF driver.", "sources": [], "term": "CDM, HB-CDM" }, { "category": "rf", "chapters": [ "06-devices" ], "id": "characteristic-impedance", "long": "Matching Z0 to the driver and termination (usually 50 ohm) avoids reflections. The permittivity of LN raises the capacitance per length, lowering Z0 and the microwave phase velocity together, so Z0, microwave index and RF loss are designed jointly with the optical cross-section.", "origin": "canonical", "related": [ "traveling-wave-electrode", "velocity-matching", "dielectric-permittivity", "eo-bandwidth" ], "short": "The characteristic impedance Z0 = sqrt((R + j omega L) / (G + j omega C)) of a transmission-line electrode is the voltage-to-current ratio of a single traveling wave on it.", "sources": [ { "source_id": "zhang2021" } ], "symbol": "Z0", "term": "characteristic impedance Z0" }, { "chapters": [ "01-crystal" ], "id": "charged-domain-wall", "long": "A domain wall inclined to c, carrying bound charge 2 Ps sin(theta) per area that mobile carriers screen.", "origin": "chapter", "short": "A domain wall inclined to c, carrying bound charge 2 Ps sin(theta) per area that mobile carriers screen.", "sources": [ { "citation": "C. S. Werner, S. J. Herr, K. Buse, B. Sturman, E. Soergel, C. Razzaghi, I. Breunig, \"Large and accessible conductivity of charged domain walls in lithium niobate\", Sci. Rep. 7, 9862 (2017)", "doi": "10.1038/s41598-017-09703-2", "ref": "01-crystal/werner2017" } ], "term": "charged domain wall" }, { "aliases": [ "CMP", "chemo-mechanical polishing", "Chemical mechanical polishing" ], "category": "fabrication", "chapters": [ "05-making" ], "id": "cmp", "long": "In LNOI production it removes split-surface roughness and residual damage and sets the final film thickness (Jia et al. 2021). Combined with laser or photolithographic masks it shapes microresonators and waveguides with very smooth surfaces (Lin et al. 2020).", "origin": "canonical", "related": [ "ion-slicing", "lnoi", "propagation-loss", "ar-milling" ], "short": "Chemical-mechanical polishing (CMP) smooths and thins a surface by combined chemical attack and abrasive polishing with a slurry, used on LiNbO3 films after ion slicing and to pattern low-loss structures.", "sources": [ { "source_id": "lin2020" }, { "source_id": "jia2021" } ], "term": "chemical-mechanical polishing (CMP)" }, { "category": "acoustics", "chapters": [ "03-sound" ], "id": "christoffel-equation", "long": "In piezoelectric LN the stiffness is replaced by the stiffened tensor c_ijkl + (e_pij n_p)(e_qkl n_q) / (eps_pq^S n_p n_q). With the Kushibiki et al. 1999 constants the stiffened longitudinal velocity along Z is 7328.6 m/s, against a measured 7328.20 ± 0.32 m/s (unstiffened: 7102.1 m/s).", "origin": "canonical", "related": [ "elastic-stiffness", "baw", "piezoelectric-coefficients", "saw" ], "short": "The Christoffel equation, det(Gamma_ik - rho v² delta_ik) = 0 with Gamma_ik = c_ijkl n_j n_l, gives the phase velocities and polarizations of the three bulk acoustic waves for propagation direction n.", "sources": [ { "locator": "Table II", "source_id": "kushibiki1999" }, { "source_id": "warner1967" }, { "source_id": "ieee176" }, { "citation": "J. W. Jaeken & S. Cottenier, \"Solving the Christoffel equation: Phase and group velocities\", Computer Physics Communications 207 445-451 (2016)", "doi": "10.1016/j.cpc.2016.06.014", "ref": "03-sound/jaeken2016" } ], "term": "Christoffel equation" }, { "aliases": [ "constant strain", "high-frequency value", "superscript S" ], "category": "electro-optics", "chapters": [ "02-light", "03-sound", "06-devices" ], "id": "clamped", "long": "Clamped EO coefficients of LN exclude the indirect piezoelectric-photoelastic part: r^T_ij = r^S_ij + p_ik d_jk (Weis & Gaylord 1985 Eq. (13)). They apply to GHz modulators: r33^S is close to r33^T, while r22 and r51 are much smaller. Permittivity likewise has eps^S below eps^T (eps11^S = 44.9 versus eps11^T = 83.3, Kushibiki et al. 1999).", "origin": "canonical", "related": [ "unclamped", "eo-tensor", "dielectric-permittivity", "r22", "r51" ], "short": "A clamped coefficient (superscript S) is defined at constant strain, the condition reached at drive frequencies above the mechanical resonances of the sample, where the lattice cannot follow the field.", "sources": [ { "locator": "Eq. (13), p. 199", "source_id": "weis1985" }, { "locator": "Tables IV-V", "source_id": "kushibiki1999" } ], "term": "clamped (constant strain, S)" }, { "chapters": [ "02-light" ], "id": "clamped-s-and-free-t-coefficients", "long": "Clamped (constant strain, S): field frequency above mechanical resonances. Free (constant stress, T): includes the indirect contribution through converse piezoelectric strain and photoelasticity, r^T = r^S + p d.", "origin": "chapter", "short": "Coefficients measured above or below the acoustic resonances.", "sources": [ { "source_id": "weis1985" } ], "term": "clamped (S) and free (T) coefficients" }, { "chapters": [ "03-sound" ], "id": "clamped-and-free-s-and-t", "long": "eps^T = eps^S + d e^t. For LN eps11^T/eps0 = 83.3 and eps11^S/eps0 = 44.9 (Kushibiki et al. 1999, P). The same distinction separates r^T and r^S electro-optic coefficients.", "origin": "chapter", "short": "Mechanical boundary condition: constant strain (clamped, above mechanical resonances) or constant stress (free, below them).", "sources": [ { "source_id": "ieee176" }, { "source_id": "kushibiki1999" }, { "source_id": "weis1985" } ], "term": "clamped and free (S and T)" }, { "chapters": [ "02-light" ], "id": "cln-congruent-ln", "long": "Congruent lithium niobate, about 48.4 to 48.5 mol% Li2O. Standard wafer material. Contrast SLN (near-stoichiometric, about 50 mol%) and MgO-doped LN.", "origin": "chapter", "short": "LN grown at the composition where melt and crystal match; Li-deficient.", "sources": [ { "source_id": "volk2008" } ], "term": "CLN, congruent LN" }, { "aliases": [ "congruent LN; stoichiometric (or near-stoichiometric) LN" ], "chapters": [ "07-history" ], "id": "cln-sln", "long": "CLN is grown at the congruent composition and is Li-deficient; SLN approaches [Li]/[Nb] = 1, grown by double-crucible Czochralski (Kitamura et al. 1992) or made by vapor transport equilibration (Y.S. Luh et al. 1987).", "origin": "chapter", "short": "CLN is grown at the congruent composition and is Li-deficient; SLN approaches [Li]/[Nb] = 1, grown by double-crucible Czochralski (Kitamura et al. 1992) or made by vapor transport equilibration (Y.S. Luh et al. 1987).", "sources": [ { "source_id": "kitamura1992" }, { "source_id": "luh1987" } ], "term": "CLN, SLN" }, { "aliases": [ "coercive field (Ec)", "Ec" ], "category": "ferroelectric", "chapters": [ "01-crystal", "05-making" ], "id": "coercive-field", "long": "Volk & Wöhlecke 2009 Table 7.1 gives about 21 kV/mm for congruent LN at room temperature, 6.0-6.5 kV/mm for near-stoichiometric LN (its text also quotes 2.1-2.5 kV/mm) and an average of 6.0-6.8 kV/mm for 5 mol% MgO LN. Reported congruent-to-stoichiometric ratios range from about 3 to 5 (Volk & Wöhlecke 2009; Gopalan et al. 1998), as the sources measured different crystals.", "origin": "canonical", "related": [ "internal-field", "poling", "stoichiometric", "mgo-doping", "ferroelectric" ], "short": "The coercive field E_c is the field along c needed to reverse the spontaneous polarization of LiNbO3 at a given temperature and field ramp.", "sources": [ { "locator": "Table 7.1, p. 185; p. 118", "source_id": "volk2008" }, { "locator": "abstract", "source_id": "gopalan1998" }, { "source_id": "volk2008" }, { "citation": "Carsten Langrock, \"Classical and low-light-level detection and pulse characterization using optical-frequency mixers\", PhD dissertation, Department of Electrical Engineering, Stanford University (advisor M. M. Fejer) (2007)", "ref": "05-making/langrock2007" } ], "symbol": "E_c", "term": "coercive field" }, { "aliases": [ "coherence length (l_c)" ], "category": "nonlinear-optics", "chapters": [ "02-light", "07-history" ], "id": "coherence-length", "long": "In QPM the sign of d is reversed every L_c, so a first-order grating has period Lambda = 2 L_c = 2 pi / |Delta k|. An m-th order grating (odd m) uses Lambda = 2 m L_c, with efficiency reduced by 1/m².", "origin": "canonical", "related": [ "qpm", "phase-matching", "d-eff", "ppln" ], "short": "The coherence length L_c = pi / |Delta k| is the distance over which the phase mismatch between nonlinear polarization and generated wave reaches pi, after which conversion reverses.", "sources": [ { "source_id": "fejer1992" } ], "symbol": "L_c", "term": "coherence length" }, { "chapters": [ "08-industry" ], "id": "coherent", "long": "Transmission that encodes amplitude and phase on two polarizations and detects them against a local oscillator; used for long reach.", "origin": "chapter", "short": "Transmission that encodes amplitude and phase on two polarizations and detects them against a local oscillator; used for long reach.", "sources": [], "term": "coherent" }, { "chapters": [ "07-history" ], "id": "columbium", "long": "Name given by Hatchett (1801) to the element now called niobium (Hatchett 1802).", "origin": "chapter", "short": "Name given by Hatchett (1801) to the element now called niobium (Hatchett 1802).", "sources": [ { "source_id": "hatchett1802" } ], "term": "columbium" }, { "aliases": [ "CLN", "congruent composition", "congruent lithium niobate", "Congruent composition" ], "category": "defects", "chapters": [ "01-crystal", "05-making", "07-history", "04-quirks" ], "id": "congruent", "long": "Both 48.38 and 48.45 mol% Li2O are in use (Volk & Wöhlecke 2009 uses both and gives [Li]/[Nb] = 0.94). The Li2O-Nb2O5 phase diagram (Reisman & Holtzberg 1958) and stoichiometry studies (Lerner et al. 1968; Carruthers et al. 1971) established the Li deficit. The Nb excess is accommodated largely as Nb_Li antisites, which govern photorefraction, coercive field and Curie temperature.", "origin": "canonical", "related": [ "stoichiometric", "antisite-nb-li", "li-vacancy", "czochralski-growth", "curie-temperature" ], "short": "Congruent LiNbO3 is the Li-deficient composition (about 48.4-48.5 mol% Li2O) at which melt and crystal have the same composition, so Czochralski boules grow uniform.", "sources": [ { "locator": "pp. 4-5, 9, 142", "source_id": "volk2008" }, { "source_id": "reisman1958" }, { "source_id": "lerner1968" }, { "source_id": "carruthers1971" }, { "source_id": "volk2008" } ], "term": "congruent lithium niobate (CLN)" }, { "chapters": [ "08-industry" ], "id": "congruent-ln", "long": "LN grown from the melt composition at which crystal and melt have the same composition; Li-deficient; the standard SAW and optical grade.", "origin": "chapter", "short": "LN grown from the melt composition at which crystal and melt have the same composition; Li-deficient; the standard SAW and optical grade.", "sources": [], "term": "congruent LN" }, { "chapters": [ "01-crystal" ], "id": "congruent-melting-composition", "long": "The composition at which melt and growing crystal are identical, about 48.4-48.5 mol% Li2O for LiNbO3.", "origin": "chapter", "short": "The composition at which melt and growing crystal are identical, about 48.4-48.5 mol% Li2O for LiNbO3.", "sources": [ { "source_id": "volk2008" } ], "term": "congruent melting composition" }, { "chapters": [ "02-light" ], "id": "conoscopy", "long": "Each point of the observed figure corresponds to one propagation direction through the plate; the figure shows isogyres (polarization extinction) and isochromes (constant retardation).", "origin": "chapter", "related": [ "isogyre", "isochrome", "melatope" ], "short": "Viewing a crystal plate in a cone of light between crossed polarizers.", "sources": [ { "citation": "Max Born & Emil Wolf, \"Principles of Optics\" (2019)", "doi": "10.1017/9781108769914", "ref": "02-light/bornwolf" } ], "term": "conoscopy" }, { "chapters": [ "03-sound" ], "id": "constant-e-constant-d", "long": "Elastic constants at constant D are stiffer: c^D = c^E + e^t h (c33^D 249.35, status derived, vs c33^E 234.18 GPa, P, for LN).", "origin": "chapter", "short": "Electrical boundary condition: shorted (E = 0) or open (D = 0).", "sources": [ { "source_id": "ieee176" } ], "term": "constant E, constant D" }, { "chapters": [ "03-sound" ], "id": "constitutive-equations", "long": "IEEE 176 gives four exact forms with independent variables (S, E), (T, E), (T, D), (S, D) and coefficients e, d, g, h. Only the (S, E) form yields the field equations of the unbounded medium; the others suit bodies where some variables are nearly zero.", "origin": "chapter", "related": [ "e-coefficient", "d-coefficient", "g-coefficient", "h-coefficient" ], "short": "Linear relations between stress, strain, electric field and displacement in a piezoelectric.", "sources": [ { "source_id": "ieee176" } ], "term": "constitutive equations" }, { "chapters": [ "02-light" ], "id": "contracted-voigt-index", "long": "1 = xx, 2 = yy, 3 = zz, 4 = yz, 5 = xz, 6 = xy. Factor conventions for strain-like quantities differ between sources (convention of 2s); see chapter 03.", "origin": "chapter", "short": "Shorthand that maps index pairs to 1..6.", "sources": [], "term": "contracted (Voigt) index" }, { "chapters": [ "03-sound" ], "id": "convention-of-2s", "long": "Engineering shear strain S4 = 2 S23. No factor on stress, stiffness c, piezo e, photoelastic p, EO r. Factor 2 on shear strain and on d (and g) for q = 4..6; factors 2 and 4 on compliance s and piezo-optic pi. Checks: c66 = (c11 - c12)/2 but s66 = 2(s11 - s12); d16 = -2 d22.", "origin": "chapter", "short": "Factors of 2 and 4 that appear when tensors are written in Voigt matrices.", "sources": [ { "source_id": "ieee176" }, { "source_id": "weis1985" } ], "term": "convention of 2s" }, { "chapters": [ "03-sound" ], "id": "cooperativity", "long": "Conversion efficiency in p05: eta = eta_e 4C/(1 -+ C)² for red (upper sign) and blue detuning.", "origin": "chapter", "short": "C = 4 g0² n_c/(kappa gamma): ratio of optomechanical coupling to the optical and mechanical loss rates.", "sources": [ { "source_id": "jiang2020" } ], "term": "cooperativity" }, { "aliases": [ "co-packaged optics / near-packaged optics / linear pluggable optics" ], "chapters": [ "08-industry" ], "id": "cpo-npo-lpo", "long": "Ways to place optics close to a switch chip (CPO, NPO) or to drive a pluggable without a retiming DSP (LPO).", "origin": "chapter", "short": "Ways to place optics close to a switch chip (CPO, NPO) or to drive a pluggable without a retiming DSP (LPO).", "sources": [], "term": "CPO / NPO / LPO" }, { "aliases": [ "coplanar waveguide" ], "chapters": [ "06-devices" ], "id": "cpw", "long": "A transmission line with a signal conductor between two ground conductors on one surface.", "origin": "chapter", "short": "A transmission line with a signal conductor between two ground conductors on one surface.", "sources": [], "term": "CPW" }, { "chapters": [ "04-quirks" ], "id": "cte", "long": "Coefficient of thermal expansion.", "origin": "chapter", "short": "Coefficient of thermal expansion.", "sources": [], "term": "CTE" }, { "aliases": [ "continuous-time linear equalizer" ], "chapters": [ "08-industry" ], "id": "ctle", "long": "An analog filter that boosts high frequencies to compensate channel or device roll-off.", "origin": "chapter", "short": "An analog filter that boosts high frequencies to compensate channel or device roll-off.", "sources": [], "term": "CTLE" }, { "aliases": [ "Curie temperature (Tc)" ], "category": "ferroelectric", "chapters": [ "01-crystal", "07-history" ], "id": "curie-temperature", "long": "Volk & Wöhlecke 2009 Table 1.1 gives 1140 C for congruent and 1206 C for near-stoichiometric LN. Linear fits such as T_c = 39.064 c - 746.73 (c in mol% Li2O; Bordui et al. 1992, as given in Volk & Wöhlecke 2009) are used to infer composition. Older values, such as 1165 C in Weis & Gaylord 1985 Table 1, refer to crystals of unstated composition, so T_c values without composition are not comparable.", "origin": "canonical", "related": [ "ferroelectric", "congruent", "stoichiometric", "space-group-r3c", "vte" ], "short": "The Curie temperature T_c is the temperature of the ferroelectric (R3c) to paraelectric (R-3c) transition of LiNbO3, and it rises with Li content.", "sources": [ { "locator": "Table 1.1; Eqs. (6.2)-(6.3), p. 140", "source_id": "volk2008" }, { "source_id": "bordui1992" }, { "locator": "Table 1, p. 197", "source_id": "weis1985" }, { "source_id": "volk2008" }, { "source_id": "smolenskii1966" } ], "symbol": "T_c", "term": "Curie temperature" }, { "aliases": [ "crystal pulling", "Cz growth", "Cz" ], "category": "fabrication", "chapters": [ "05-making", "07-history", "08-industry" ], "id": "czochralski-growth", "long": "BALLMAN 1965 reported Czochralski growth of LN among other piezoelectric and ferroelectric crystals. Growing at the congruent composition keeps melt and crystal compositions equal along the boule (Carruthers et al. 1971); stoichiometric crystals need double-crucible growth with continuous powder supply (Kitamura et al. 1992).", "origin": "canonical", "related": [ "boule", "congruent", "stoichiometric" ], "short": "Czochralski growth pulls a single crystal from a melt on a rotating seed, the standard method for LiNbO3 boules.", "sources": [ { "source_id": "ballman1965" }, { "source_id": "carruthers1971" }, { "source_id": "kitamura1992" }, { "citation": "Wang, Ji, Dai, Shen, Bao, \"The growth and characterization of six inch lithium niobate crystals with high homogeneity\", CrystEngComm 22 794-801 (2020)", "doi": "10.1039/C9CE01761E", "ref": "05-making/wang2020cryst" }, { "citation": "Chen, Zhu, Liu, Xue, \"State of the Art in Crystallization of LiNbO3 and Their Applications\", Molecules 26 7044 (2021)", "doi": "10.3390/molecules26227044", "ref": "05-making/chen2021molecules" }, { "source_id": "czochralski1918" }, { "source_id": "fedulov1965" } ], "term": "Czochralski growth" }, { "chapters": [ "03-sound" ], "id": "d-coefficient", "long": "d = e s^E. Voigt shear entries carry a factor 2 (d16 = -2 d22 for 3m). LN from Kushibiki et al. 1999: d15 66.4, d22 20.3, d31 -1.04, d33 8.69 pC/N (status derived).", "origin": "chapter", "short": "Piezoelectric strain constant, C/N = m/V: charge per unit stress, or strain per unit field.", "sources": [ { "source_id": "ieee176" }, { "source_id": "kushibiki1999" } ], "term": "d coefficient" }, { "category": "nonlinear-optics", "chapters": [ "02-light" ], "id": "d33", "long": "With all waves e-polarized, a first-order QPM grating with 50% duty cycle gives d_eff = (2/pi) d33. Compilations give 34 pm/V at 1.06 µm (Volk & Wöhlecke 2009 Table 1.2, legacy scale); Shoji et al. 1997 indicates that such standard values are overestimated, and Zhu et al. 2021 Table 1 lists -27.0 pm/V without a reference. Values at other wavelengths are commonly scaled by Miller's rule.", "notes": "Not the piezoelectric strain constant d33 (pC/N); see piezoelectric-coefficients.", "origin": "canonical", "related": [ "second-order-susceptibility", "d-eff", "qpm", "ppln", "millers-rule" ], "short": "d33 is the chi(2) component coupling optical fields polarized along c, the largest nonlinear coefficient of LiNbO3 and the one used by PPLN.", "sources": [ { "locator": "Table 1.2, p. 4", "source_id": "volk2008" }, { "locator": "abstract", "source_id": "shoji1997" }, { "locator": "Table 1", "source_id": "zhu2021" } ], "symbol": "d33", "term": "d33 (nonlinear)" }, { "aliases": [ "digital-to-analog converter" ], "chapters": [ "06-devices" ], "id": "dac", "long": "The electronic circuit that generates the multilevel drive waveform; its bandwidth often limits symbol rate in modulator experiments.", "origin": "chapter", "short": "The electronic circuit that generates the multilevel drive waveform; its bandwidth often limits symbol rate in modulator experiments.", "sources": [], "term": "DAC" }, { "aliases": [ "sigma_d" ], "category": "defects", "chapters": [ "04-quirks" ], "id": "dark-conductivity", "long": "For undoped or slightly doped congruent LN at room temperature, extrapolation from high temperature gives about 1e-14 to 1e-16 S/m, protonic, with an activation energy of about 1.1 eV (Volk & Wöhlecke 2009). The Maxwell relaxation time tau = eps eps0 / sigma_d is then about 0.3-29 days for eps33 = 28; Volk & Wöhlecke 2009 p. 159 states 5-500 days. Millisecond-to-hour drift in TFLN modulators therefore points to conduction in claddings, interfaces or contacts rather than bulk LN.", "origin": "canonical", "related": [ "dc-bias-drift", "photoconductivity", "space-charge-field", "hologram-fixing" ], "short": "Dark conductivity is the electrical conductivity of LiNbO3 without illumination, which sets how long space-charge and bias fields persist.", "sources": [ { "locator": "Sec. 3.2.1, pp. 59-60; p. 159", "source_id": "volk2008" }, { "source_id": "holzgrafe2024" }, { "source_id": "volk2008" } ], "symbol": "sigma_d", "term": "dark conductivity" }, { "chapters": [ "04-quirks" ], "id": "dark-trace", "long": "Gray coloration in the visible left by intense pulsed light; stable in congruent LN, decays within minutes in Mg- or Zn-doped crystals above threshold. Also gray track or gray trace.", "origin": "chapter", "short": "Gray coloration in the visible left by intense pulsed light; stable in congruent LN, decays within minutes in Mg- or Zn-doped crystals above threshold.", "sources": [ { "source_id": "volk2008" } ], "term": "dark trace" }, { "aliases": [ "bias drift", "DC drift", "EO relaxation" ], "category": "quirks", "chapters": [ "04-quirks", "06-devices", "07-history" ], "id": "dc-bias-drift", "long": "Mobile charge in LN, claddings and buried oxide, interface and contact traps, photogenerated carriers and pyroelectric charge contribute; a layered RC model with tau = eps rho per layer captures time scales from milliseconds to hours or longer in TFLN (Zhu et al. 2021 Sec. 7.1). Drift was characterized in bulk Ti:LN devices by Yamada & Minakata 1981. Mitigations include LN-metal interface control with annealing (Holzgrafe et al. 2024), Ar+ milling (Shi et al. 2025) and TFLT.", "origin": "canonical", "related": [ "dark-conductivity", "pyroelectric-effect", "mzm", "ar-milling", "tflt", "unclamped" ], "short": "DC bias drift is the slow change of an LN modulator's operating point under constant bias voltage, caused by charge redistribution that screens the applied field.", "sources": [ { "locator": "Sec. 7.1", "source_id": "zhu2021" }, { "source_id": "yamada1981" }, { "source_id": "holzgrafe2024" }, { "source_id": "shi2025" }, { "source_id": "seino1992" } ], "term": "DC (bias) drift" }, { "aliases": [ "DLC" ], "chapters": [ "05-making" ], "id": "diamond-like-carbon", "long": "Hard amorphous carbon film used as an etch mask that erodes slowly under argon ions. 300 nm PECVD from CH4; LN:DLC selectivity up to 3 [Li et al. 2023; P].", "origin": "chapter", "short": "Hard amorphous carbon film used as an etch mask that erodes slowly under argon ions.", "sources": [ { "citation": "Li, Wang, Lihachev, Zhang, Tan, Churaev et al., \"High density lithium niobate photonic integrated circuits\", Nature Communications 14 4856 (2023)", "doi": "10.1038/s41467-023-40502-8", "ref": "05-making/li2023nc" } ], "term": "Diamond-like carbon" }, { "aliases": [ "dielectric constant", "relative permittivity" ], "category": "rf", "chapters": [ "01-crystal", "03-sound", "06-devices" ], "id": "dielectric-permittivity", "long": "Kushibiki et al. 1999 measured eps11^T = 83.3 and eps33^T = 28.5 and fitted eps11^S = 44.9 and eps33^S = 26.7 for congruent LN; the large eps11 gap comes from piezoelectric coupling. Across sources eps11^T spans 83.3-85.2 and eps33^S 23.7-29. Electrodes driven above the acoustic resonances, as in GHz modulators, see eps^S.", "origin": "canonical", "related": [ "clamped", "unclamped", "characteristic-impedance", "velocity-matching", "piezoelectric-effect" ], "short": "The relative permittivity of LiNbO3 is a uniaxial tensor (eps11 perpendicular, eps33 parallel to c) whose value depends on whether the crystal is mechanically free (eps^T) or clamped (eps^S).", "sources": [ { "locator": "Tables IV-V", "source_id": "kushibiki1999" }, { "locator": "Table 1, p. 197", "source_id": "weis1985" } ], "symbol": "eps_ij", "term": "dielectric permittivity (eps^T, eps^S)" }, { "aliases": [ "tau_di" ], "chapters": [ "04-quirks" ], "id": "dielectric-relaxation-time", "long": "Time eps eps0 / sigma over which free charge screens a field in a medium of conductivity sigma; sets photorefractive write, erase, and drift times.", "origin": "chapter", "short": "Time eps eps0 / sigma over which free charge screens a field in a medium of conductivity sigma; sets photorefractive write, erase, and drift times.", "sources": [ { "source_id": "volk2008" } ], "term": "dielectric relaxation time" }, { "aliases": [ "DFG", "difference-frequency generation" ], "category": "nonlinear-optics", "chapters": [ "02-light" ], "id": "dfg", "long": "It is the same three-wave interaction as optical parametric amplification, viewed from the idler. PPLN supports DFG into the mid-IR within the LN transparency window.", "origin": "canonical", "related": [ "sfg", "opa", "phase-matching", "transparency-window" ], "short": "Difference-frequency generation (DFG) is the chi(2) process in which a pump at omega_p and a signal at omega_s generate an idler at omega_i = omega_p - omega_s while amplifying the signal.", "sources": [ { "source_id": "armstrong1962" } ], "term": "difference-frequency generation (DFG)" }, { "chapters": [ "04-quirks" ], "id": "diffusion-field", "long": "Space-charge field set up by diffusion of carriers from bright to dark fringes; independent of intensity and shifted a quarter period from the light pattern.", "origin": "chapter", "short": "Space-charge field set up by diffusion of carriers from bright to dark fringes; independent of intensity and shifted a quarter period from the light pattern.", "sources": [ { "source_id": "volk2008" } ], "term": "diffusion field" }, { "chapters": [ "04-quirks" ], "id": "discharge-layer", "long": "Thin conductive film (for example a few nm of Al) over resist on an insulating substrate that carries away charge during electron-beam lithography.", "origin": "chapter", "short": "Thin conductive film (for example a few nm of Al) over resist on an insulating substrate that carries away charge during electron-beam lithography.", "sources": [ { "citation": "Wentao Jiang, \"Yapping on e-beam lithography\" (2024)", "ref": "04-quirks/blog-ebl-2024" } ], "term": "discharge layer" }, { "chapters": [ "01-crystal" ], "id": "displacive-vs-order-disorder-transition", "long": "Two limiting pictures of a structural phase transition: a soft mode whose frequency goes to zero, or ions hopping among pre-existing wells that become equally occupied above Tc.", "origin": "chapter", "short": "Two limiting pictures of a structural phase transition: a soft mode whose frequency goes to zero, or ions hopping among pre-existing wells that become equally occupied above Tc.", "sources": [ { "source_id": "inbar1996" } ], "term": "displacive vs order-disorder transition" }, { "chapters": [ "04-quirks" ], "id": "domain-inversion-layer", "long": "Surface layer with reversed spontaneous polarization, formed for example on the +c face during Ti indiffusion.", "origin": "chapter", "short": "Surface layer with reversed spontaneous polarization, formed for example on the +c face during Ti indiffusion.", "sources": [ { "citation": "S. Miyazawa, \"Ferroelectric domain inversion in Ti-diffused LiNbO3 optical waveguide\", Journal of Applied Physics 50 4599-4603 (1979)", "doi": "10.1063/1.326568", "ref": "04-quirks/miyazawa1979" } ], "term": "domain inversion layer" }, { "chapters": [ "01-crystal" ], "id": "domain-merging", "long": "Lateral spread of reversed domains beyond the electrode, which widens stripes and changes the duty cycle.", "origin": "chapter", "short": "Lateral spread of reversed domains beyond the electrode, which widens stripes and changes the duty cycle.", "sources": [ { "source_id": "volk2008" } ], "term": "domain merging" }, { "category": "ferroelectric", "chapters": [ "01-crystal", "05-making" ], "id": "domain-wall", "long": "Field switching proceeds by nucleation at electrode edges, forward growth along c and sideways wall motion, which in LN tends to produce hexagonal domains. Point defects pin walls, so switching fields, wall velocity and back-switching differ between congruent and stoichiometric crystals.", "origin": "canonical", "related": [ "ferroelectric-domain", "poling", "coercive-field", "internal-field" ], "short": "A domain wall is the narrow boundary between antiparallel domains in LiNbO3, across which the polarization reverses.", "sources": [ { "source_id": "gopalan2007" }, { "source_id": "chakkoria2025" } ], "term": "domain wall" }, { "chapters": [ "01-crystal" ], "id": "domain-wall-conduction", "long": "Electrical conduction along charged domain walls, more than 13 orders of magnitude above the bulk in MgO-doped LiNbO3.", "origin": "chapter", "short": "Electrical conduction along charged domain walls, more than 13 orders of magnitude above the bulk in MgO-doped LiNbO3.", "sources": [ { "citation": "C. S. Werner, S. J. Herr, K. Buse, B. Sturman, E. Soergel, C. Razzaghi, I. Breunig, \"Large and accessible conductivity of charged domain walls in lithium niobate\", Sci. Rep. 7, 9862 (2017)", "doi": "10.1038/s41598-017-09703-2", "ref": "01-crystal/werner2017" } ], "term": "domain-wall conduction" }, { "aliases": [ "Double-crucible Czochralski" ], "chapters": [ "01-crystal", "05-making" ], "id": "double-crucible-czochralski-dccz", "long": "Growth of near-stoichiometric LiNbO3 from an Li-rich inner melt replenished by stoichiometric powder fed to an outer crucible.", "origin": "chapter", "short": "Growth of near-stoichiometric LiNbO3 from an Li-rich inner melt replenished by stoichiometric powder fed to an outer crucible.", "sources": [ { "source_id": "kitamura1992" } ], "term": "double-crucible Czochralski (DCCZ)" }, { "aliases": [ "dual-polarization quadrature phase-shift keying" ], "chapters": [ "07-history" ], "id": "dp-qpsk", "long": "Coherent format carrying 2 bits per symbol in each of two polarizations; an LN modulator for it, described by Fujitsu as a world first, announced in 2009 (Fujitsu Introduces World's First DP-QPSK LN Modulator for 100Gbps Optical Networks).", "origin": "chapter", "short": "Coherent format carrying 2 bits per symbol in each of two polarizations; an LN modulator for it, described by Fujitsu as a world first, announced in 2009 (Fujitsu Introduces World's First DP-QPSK LN Modulator for 100Gbps Optical Networks).", "sources": [ { "source_id": "fujitsu-2009" } ], "term": "DP-QPSK" }, { "aliases": [ "Duty cycle (poling)" ], "chapters": [ "01-crystal", "02-light", "05-making" ], "id": "duty-cycle", "long": "Ratio of reversed-domain width to period in a periodically poled structure, optimally 0.5 for first-order QPM.", "origin": "chapter", "short": "Ratio of reversed-domain width to period in a periodically poled structure, optimally 0.5 for first-order QPM.", "sources": [ { "source_id": "volk2008" }, { "source_id": "fejer1992" } ], "term": "duty cycle" }, { "aliases": [ "deep-ultraviolet lithography", "DUV stepper" ], "category": "fabrication", "chapters": [ "05-making", "08-industry", "07-history" ], "id": "duv-lithography", "long": "Luke et al. 2020 used DUV lithography to make wafer-scale low-loss LN photonic integrated circuits, and the TFLT platform of Wang et al. 2024 was also patterned with a DUV stepper. Mask-based exposure repeats the same layout on every die, which wafer-level yield data and process design kits rely on.", "origin": "canonical", "related": [ "tfln", "tflt", "ar-milling", "lnoi" ], "short": "Deep-ultraviolet (DUV) lithography patterns resist by projection exposure in steppers or scanners, enabling wafer-scale, foundry-style patterning of TFLN instead of electron-beam writing.", "sources": [ { "source_id": "luke2020" }, { "source_id": "wang2024" } ], "term": "DUV lithography" }, { "chapters": [ "03-sound" ], "id": "e-coefficient", "long": "T = c^E S - e^t E; D = e S + eps^S E. LN (Kushibiki et al. 1999, P): e15 3.655, e22 2.407, e31 0.328, e33 1.894 C/m². No Voigt factor.", "origin": "chapter", "short": "Piezoelectric stress constant, C/m²: stress per unit field at constant strain, or charge per unit strain.", "sources": [ { "source_id": "ieee176" }, { "source_id": "kushibiki1999" } ], "term": "e coefficient" }, { "chapters": [ "05-making" ], "id": "edge-exclusion", "long": "Rim of a wafer left out of measurement or devices because film quality or handling degrades there. 8 mm on 4-inch TFLN [Luke et al. 2020; P].", "origin": "chapter", "short": "Rim of a wafer left out of measurement or devices because film quality or handling degrades there.", "sources": [ { "source_id": "luke2020" } ], "term": "Edge exclusion" }, { "chapters": [ "02-light" ], "id": "effective-area", "long": "Area defined by the nonlinear overlap of the interacting modes; its definition (with or without n_eff, which field components) must be stated with every value. Unit: um².", "origin": "chapter", "short": "Cross-section that sets nonlinear intensity in a waveguide.", "sources": [], "term": "effective area" }, { "category": "optics", "chapters": [ "02-light", "06-devices" ], "id": "effective-index", "long": "In TFLN waveguides n_eff lies between the cladding index and the LN index seen by the mode (n_o or n_e, set by polarization and cut). Phase matching in waveguides uses modal indices; for first-order QPM SHG the period is Lambda = lambda_F / (2 (n_eff,SH - n_eff,F)).", "origin": "canonical", "related": [ "group-index", "phase-matching", "qpm", "overlap-factor" ], "short": "The effective index n_eff = beta / k0 of a waveguide mode is its propagation constant divided by the vacuum wavenumber.", "sources": [ { "source_id": "zhu2021" } ], "symbol": "n_eff", "term": "effective index" }, { "aliases": [ "d_eff" ], "category": "nonlinear-optics", "chapters": [ "02-light" ], "id": "d-eff", "long": "For an e + e -> e interaction in PPLN, an m-th order grating with duty cycle D gives d_eff = (2/(m pi)) d33 sin(m pi D), which reduces to (2/pi) d33 for first order and D = 0.5. Conversion efficiency at low power scales as d_eff².", "origin": "canonical", "related": [ "d33", "qpm", "ppln", "coherence-length" ], "short": "The effective nonlinear coefficient d_eff is the projection of the d tensor onto the polarizations of the interacting waves, including any reduction by a QPM grating.", "sources": [ { "source_id": "fejer1992" } ], "symbol": "d_eff", "term": "effective nonlinear coefficient" }, { "aliases": [ "electronic integrated circuit" ], "chapters": [ "08-industry" ], "id": "eic", "long": "The driver or receiver chip paired with a photonic chip.", "origin": "chapter", "short": "The driver or receiver chip paired with a photonic chip.", "sources": [], "term": "EIC" }, { "aliases": [ "elastic constants", "stiffness tensor" ], "category": "acoustics", "chapters": [ "03-sound" ], "id": "elastic-stiffness", "long": "Kushibiki et al. 1999 gives c11 = 198.86, c12 = 54.67, c13 = 67.99, c14 = 7.83, c33 = 234.18 and c44 = 59.85 GPa, with c66 = (c11 - c12)/2 = 72.09 GPa; resonant ultrasound (Ogi et al. 2002) agrees within about 1% except c14 (8.7 GPa). c14 is positive in the IEEE/IRE frame. At constant D, piezoelectric stiffening makes c^D larger than c^E.", "origin": "canonical", "related": [ "christoffel-equation", "piezoelectric-coefficients", "voigt-notation", "ieee-176", "baw" ], "short": "The elastic stiffness tensor c_IJ^E (GPa) of LiNbO3 relates stress to strain at constant electric field, with six independent components for 3m: c11, c12, c13, c14, c33 and c44.", "sources": [ { "source_id": "kushibiki1999" }, { "source_id": "ogi2002" }, { "locator": "Table 6, p. 200", "source_id": "weis1985" } ], "symbol": "c_IJ^E", "term": "elastic stiffness c^E" }, { "aliases": [ "3-dB EO bandwidth", "3 dB EO bandwidth" ], "category": "electro-optics", "chapters": [ "06-devices" ], "id": "eo-bandwidth", "long": "Papers differ in convention (3 dB or 6 dB, electrical or optical scale), so values need the definition. In traveling-wave LN modulators it is limited by electrode microwave loss, microwave-optical velocity mismatch and impedance mismatch. Micro-structured (segmented) electrodes reduce RF loss and relax the voltage-bandwidth trade-off (Kharel et al. 2021).", "origin": "canonical", "related": [ "traveling-wave-electrode", "velocity-matching", "characteristic-impedance", "vpi" ], "short": "The electro-optic bandwidth of a modulator is the modulation frequency at which its EO response has fallen by a stated amount, usually 3 dB, from its low-frequency value.", "sources": [ { "source_id": "zhang2021" }, { "source_id": "kharel2021" } ], "term": "electro-optic bandwidth" }, { "aliases": [ "EO comb", "resonant EO comb" ], "category": "electro-optics", "chapters": [ "02-light", "06-devices" ], "id": "eo-comb", "long": "In a resonant EO comb, a TFLN microring whose free spectral range matches the drive frequency recirculates light through the phase modulation, cascading sidebands over many resonances (Zhang et al. 2019). Span is limited by drive strength, loss and dispersion (Parriaux et al. 2020).", "origin": "canonical", "related": [ "microring", "kerr-soliton-microcomb", "pockels-effect", "group-index" ], "short": "An electro-optic (EO) frequency comb is a set of equally spaced optical lines produced by strong phase or intensity modulation at a microwave frequency, which sets the line spacing.", "sources": [ { "source_id": "zhang2019" }, { "source_id": "parriaux2020" } ], "term": "electro-optic frequency comb" }, { "chapters": [ "02-light", "06-devices" ], "id": "electro-optic-frequency-shifter", "long": "In TFLN, two coupled rings (photonic molecule) with supermode splitting 2 mu driven at Omega = 2 mu transfer light between supermodes, shifting it by Omega.", "origin": "chapter", "short": "Device that moves light to a new frequency with a microwave drive.", "sources": [ { "source_id": "hu2021" } ], "term": "electro-optic frequency shifter" }, { "chapters": [ "02-light" ], "id": "electro-optic-tensor", "long": "Third-rank tensor in contracted 6 x 3 form. Point group 3m has four independent coefficients: r13, r22, r33, r51 (r42 = r51). Unit: pm/V.", "origin": "chapter", "short": "The table of coefficients r_Ij linking field to index change.", "sources": [ { "source_id": "weis1985" } ], "term": "electro-optic tensor" }, { "aliases": [ "Pockels tensor", "r tensor" ], "category": "electro-optics", "chapters": [ "02-light" ], "id": "eo-tensor", "long": "For LN (3m, x perpendicular to a mirror) the nonzero components are r13 = r23, r33, r22 = -r12 = -r61 and r42 = r51. Each has a clamped (S) and an unclamped (T) value, related by r^T_ij = r^S_ij + p_ik d_jk (Weis & Gaylord 1985 Eq. (13)). Signs depend on the +z and +y convention, and most tables list magnitudes.", "origin": "canonical", "related": [ "pockels-effect", "r33", "r13", "r22", "r51", "voigt-notation" ], "short": "The electro-optic tensor r_Ij (pm/V) relates the change of optical impermeability to the applied field, Delta B_I = r_Ij E_j, with I = 1-6 in Voigt notation.", "sources": [ { "locator": "Table 4 and Eq. (13), p. 199", "source_id": "weis1985" } ], "symbol": "r_ij", "term": "electro-optic tensor r_ij" }, { "chapters": [ "03-sound" ], "id": "electromechanical-coupling-factor", "long": "Material factors (IEEE 176 Table 10), e.g. k33² = d33²/(s33^E eps33^T); thickness factors k_t = e33/(c33^D eps33^S)^(1/2). LN (status derived): k_t 0.247, k15 0.600. For surface waves, k² approx 2 (v_free - v_met)/v_free.", "origin": "chapter", "short": "Dimensionless k: the fraction of stored energy that converts between mechanical and electrical form, as k².", "sources": [ { "source_id": "ieee176" }, { "citation": "K. A. Ingebrigtsen, \"Surface Waves in Piezoelectrics\", Journal of Applied Physics 40 2681-2686 (1969)", "doi": "10.1063/1.1658060", "ref": "03-sound/ingebrigtsen1969" } ], "term": "electromechanical coupling factor" }, { "aliases": [ "k^2", "K^2", "k_t^2", "coupling coefficient", "electromechanical coupling coefficient" ], "category": "acoustics", "chapters": [ "03-sound", "07-history" ], "id": "electromechanical-coupling", "long": "For SAW it is estimated as K² = 2 (v_free - v_metallized) / v_free. Large k² in LN allows wide-band filters, and cut angles are chosen to maximize k² of the wanted mode (Shibayama et al. 1976). Thin LN plates in XBARs reach high coupling for a laterally excited shear mode (Plessky et al. 2019).", "origin": "canonical", "related": [ "saw", "idt", "xbar", "piezoelectric-coefficients", "128-y-x-cut" ], "short": "The electromechanical coupling coefficient k² measures the fraction of energy converted between electrical and mechanical form in a given piezoelectric mode, e.g. k_t² = e33² / (c33^D eps33^S) for a thickness mode.", "sources": [ { "source_id": "shibayama1976" }, { "source_id": "plessky2019" }, { "source_id": "yamanouchi1972" } ], "symbol": "k^2", "term": "electromechanical coupling k^2" }, { "aliases": [ "EBL" ], "chapters": [ "05-making" ], "id": "electron-beam-lithography", "long": "Writing a pattern into resist point by point with a focused electron beam. Write time t = dose x area / current; 7600 µC/cm² at 100 nA takes 21.1 h per cm² (derived from [Kaufmann et al. 2023]).", "origin": "chapter", "short": "Writing a pattern into resist point by point with a focused electron beam.", "sources": [ { "citation": "Kaufmann, Finco, Maeder, Grange, \"Redeposition‐free inductively‐coupled plasma etching of lithium niobate for integrated photonics\", Nanophotonics 12 1601-1611 (2023)", "doi": "10.1515/nanoph-2022-0676", "ref": "05-making/kaufmann2023" } ], "term": "Electron-beam lithography" }, { "chapters": [ "01-crystal" ], "id": "empty-octahedral-site", "long": "The structurally vacant octahedron in the sequence Nb, empty, Li along +c, distinct from a Li vacancy, which is a defect.", "origin": "chapter", "short": "The structurally vacant octahedron in the sequence Nb, empty, Li along +c, distinct from a Li vacancy, which is a defect.", "sources": [ { "source_id": "volk2008" } ], "term": "empty octahedral site" }, { "chapters": [ "04-quirks" ], "id": "eo-hysteresis", "long": "Persistent change of DC electro-optic response magnitude and linearity after long biasing; reversible with zero or reverse bias.", "origin": "chapter", "short": "Persistent change of DC electro-optic response magnitude and linearity after long biasing; reversible with zero or reverse bias.", "sources": [ { "citation": "Matthew Yeh et al., \"Hysteresis and Trap Emission in dc-Biased Integrated Lithium Niobate Electro-optic Modulators\", Nano Letters 26 13450-13456 (2026)", "doi": "10.1021/acs.nanolett.6c03406", "ref": "04-quirks/yeh2026" } ], "term": "EO hysteresis" }, { "chapters": [ "02-light" ], "id": "eo-overlap-factor", "long": "Gamma = (g/V) integral_LN E^RF |E|² dA / integral |E|² dA. Power-normalized perturbation theory replaces n_e³ by n_e^4/n_eff, which matters when n_eff is well below n_e.", "origin": "chapter", "short": "Fraction of the ideal field-mode coupling a real electrode achieves.", "sources": [], "symbol": "Gamma", "term": "EO overlap factor" }, { "aliases": [ "electro-optic small-signal transmission" ], "chapters": [ "06-devices" ], "id": "eo-s21", "long": "The modulator's measured response, optical modulation amplitude per unit RF drive, versus frequency, usually in dB relative to a low-frequency reference.", "origin": "chapter", "short": "The modulator's measured response, optical modulation amplitude per unit RF drive, versus frequency, usually in dB relative to a low-frequency reference.", "sources": [], "term": "EO S21" }, { "chapters": [ "06-devices" ], "id": "er-lnoi", "long": "Erbium-doped LNOI; provides optical gain near 1530 nm when pumped near 980 or 1480 nm.", "origin": "chapter", "short": "Erbium-doped LNOI; provides optical gain near 1530 nm when pumped near 980 or 1480 nm.", "sources": [], "term": "Er:LNOI" }, { "chapters": [ "05-making" ], "id": "etch-selectivity", "long": "Ratio of the etch rate of the target material to that of the mask.", "origin": "chapter", "short": "Ratio of the etch rate of the target material to that of the mask.", "sources": [], "term": "Etch selectivity" }, { "chapters": [ "08-industry" ], "id": "evidence-grade", "long": "The site's label for how a claim was checked: F (primary source read), V (vendor claim), T (trade press read), C (snippet only), LG (low-grade), E (site estimate), S (speculation).", "origin": "chapter", "short": "The site's label for how a claim was checked: F (primary source read), V (vendor claim), T (trade press read), C (snippet only), LG (low-grade), E (site estimate), S (speculation).", "sources": [], "term": "evidence grade" }, { "chapters": [ "06-devices" ], "id": "extinction-ratio", "long": "Ratio of maximum to minimum output power of a modulator, in dB, static (DC sweep) or dynamic (eye).", "origin": "chapter", "short": "Ratio of maximum to minimum output power of a modulator, in dB, static (DC sweep) or dynamic (eye).", "sources": [], "term": "extinction ratio" }, { "category": "optics", "chapters": [ "02-light" ], "id": "extraordinary-index", "long": "For congruent LN, n_e = 2.2028 at 632.8 nm and 24.5 C (Weis & Gaylord 1985 Table 2), and the Zelmon et al. 1997 Sellmeier gives 2.1376 at 1550 nm and 21 C. n_e rises with temperature (dn_e/dT about 3.3e-5 to 3.8e-5 /K near 1.5 µm) and with Nb excess, so QPM design needs a temperature- and composition-dependent model. r33 modulates n_e.", "origin": "canonical", "related": [ "ordinary-index", "thermo-optic-coefficient", "sellmeier-equation", "r33" ], "short": "The extraordinary index n_e is the refractive index of LiNbO3 for light polarized parallel to the c axis.", "sources": [ { "locator": "Table 2, p. 197", "source_id": "weis1985" }, { "source_id": "zelmon1997" }, { "source_id": "jundt1997" }, { "locator": "Table 6.1, p. 145", "source_id": "volk2008" } ], "symbol": "n_e", "term": "extraordinary index" }, { "aliases": [ "Fe:LN", "iron-doped lithium niobate" ], "category": "defects", "chapters": [ "04-quirks", "07-history" ], "id": "fe-doping", "long": "Light excites electrons from Fe2+; they move by bulk photovoltaic current, drift and diffusion and retrap at Fe3+ in darker regions, building a space-charge field. Fe:LN combined with thermal fixing gave long-lived holograms. Transition-metal impurities also cause residual absorption in nominally undoped crystals, up to 0.04 cm⁻¹ between 400 and 2000 nm as grown (Schwesyg 2011).", "origin": "canonical", "related": [ "photorefraction", "hologram-fixing", "space-charge-field", "bulk-photovoltaic-effect" ], "short": "Iron doping supplies Fe2+/Fe3+ deep traps in LiNbO3 that act as photorefractive donors and acceptors, making Fe:LN a holographic recording medium.", "sources": [ { "source_id": "volk2008" }, { "locator": "abstract; Sec. 3.1, 3.3", "source_id": "schwesyg2011" }, { "source_id": "staebler1971" }, { "source_id": "peterson1971" }, { "source_id": "mok1993" } ], "term": "Fe doping (Fe:LN)" }, { "aliases": [ "domain" ], "category": "ferroelectric", "chapters": [ "01-crystal", "05-making" ], "id": "ferroelectric-domain", "long": "Domains in LN were revealed by acid etching, which attacks the two polar faces at different rates (Nassau et al. 1965). Inverting a domain reverses the sign of d33 and r33 but leaves the refractive indices unchanged, which QPM gratings exploit. Domain stability and wall motion depend strongly on composition and defects (Gopalan et al. 2007).", "origin": "canonical", "related": [ "domain-wall", "poling", "qpm", "ppln", "coercive-field" ], "short": "A ferroelectric domain is a region of uniform spontaneous polarization; LiNbO3 has only 180 deg domains, with P_s along +c or -c.", "sources": [ { "source_id": "nassau1965" }, { "source_id": "gopalan2007" }, { "source_id": "volk2008" } ], "term": "ferroelectric domain" }, { "aliases": [ "ferroelectric" ], "category": "ferroelectric", "chapters": [ "01-crystal", "07-history" ], "id": "ferroelectric", "long": "Matthias and Remeika reported ferroelectricity in LiNbO3 and LiTaO3 in 1949, describing them as ilmenite-type; the 1966 structure work established the distinct R3c LN structure. The polar phase persists up to the Curie temperature (about 1140 C for congruent LN), and reversal at room temperature needs about 21 kV/mm in congruent crystals.", "origin": "canonical", "related": [ "spontaneous-polarization", "curie-temperature", "coercive-field", "ferroelectric-domain", "space-group-r3c" ], "short": "LiNbO3 is ferroelectric: it has a spontaneous polarization along c that a sufficiently strong applied field can reverse.", "sources": [ { "source_id": "matthias1949" }, { "source_id": "abrahams1966" }, { "locator": "Table 1.1; Table 7.1, p. 185", "source_id": "volk2008" }, { "source_id": "volk2008" } ], "term": "ferroelectricity" }, { "chapters": [ "08-industry" ], "id": "ferroniobium", "long": "An iron-niobium alloy, the main traded niobium product, used to make high-strength steel.", "origin": "chapter", "short": "An iron-niobium alloy, the main traded niobium product, used to make high-strength steel.", "sources": [], "term": "ferroniobium" }, { "chapters": [ "02-light" ], "id": "finesse", "long": "F = FSR / linewidth = pi sqrt(r)/(1 - r) for round-trip amplitude transmission r.", "origin": "chapter", "short": "Resonance spacing divided by resonance width.", "sources": [], "term": "finesse" }, { "chapters": [ "05-making" ], "id": "fluence", "long": "Number of implanted ions per unit area, in cm^-2. 4 x 10^16 cm^-2 He+ [Andrea Guarino et al. 2007; P]; 7.0 x 10^16 cm^-2 H+ for LiTaO3 [Wang et al. 2024; P].", "origin": "chapter", "short": "Number of implanted ions per unit area, in cm^-2.", "sources": [ { "source_id": "guarino2007" }, { "source_id": "wang2024" } ], "term": "Fluence" }, { "aliases": [ "fiber-optic gyroscope" ], "chapters": [ "08-industry" ], "id": "fog", "long": "A rotation sensor that measures the Sagnac phase between counter-propagating light in a fiber coil; LN integrated optical circuits split and modulate the light.", "origin": "chapter", "short": "A rotation sensor that measures the Sagnac phase between counter-propagating light in a fiber coil; LN integrated optical circuits split and modulate the light.", "sources": [], "term": "FOG" }, { "chapters": [ "01-crystal" ], "id": "forward-and-reverse-poling", "long": "Reversal from the virgin single-domain state (forward) and back to it (reverse); forward needs the larger field in congruent crystal.", "origin": "chapter", "short": "Reversal from the virgin single-domain state (forward) and back to it (reverse); forward needs the larger field in congruent crystal.", "sources": [ { "source_id": "volk2008" } ], "term": "forward and reverse poling" }, { "chapters": [ "08-industry" ], "id": "foundry", "long": "A company that manufactures chips to customers' designs; a pure-play foundry makes no products of its own.", "origin": "chapter", "short": "A company that manufactures chips to customers' designs; a pure-play foundry makes no products of its own.", "sources": [], "term": "foundry" }, { "aliases": [ "Nb_Nb^4+" ], "chapters": [ "04-quirks" ], "id": "free-small-polaron", "long": "Electron self-trapped on a regular Nb site; absorption band near 1.0 eV.", "origin": "chapter", "short": "Electron self-trapped on a regular Nb site; absorption band near 1.0 eV.", "sources": [ { "citation": "Judith R. M.-L. Schwesyg, \"Interaction of light with impurities in lithium niobate crystals\", Dr. rer. nat. dissertation, Universität Bonn (2011)", "ref": "04-quirks/schwesyg2011" } ], "term": "free small polaron" }, { "chapters": [ "02-light" ], "id": "free-spectral-range", "long": "FSR = c/(n_g L_rt) for round-trip length L_rt. Unit: Hz.", "origin": "chapter", "short": "Frequency spacing between adjacent ring resonances.", "sources": [], "term": "free spectral range" }, { "chapters": [ "03-sound" ], "id": "g-coefficient", "long": "g = beta^T d. LN (status derived, Kushibiki et al. 1999): g15 0.090, g22 0.0275, g33 0.0345 V m/N.", "origin": "chapter", "short": "Piezoelectric voltage constant, V m/N: field per unit stress at constant D.", "sources": [ { "source_id": "ieee176" }, { "source_id": "kushibiki1999" } ], "term": "g coefficient" }, { "aliases": [ "heralded second-order correlation at zero delay" ], "chapters": [ "06-devices" ], "id": "g2-0", "long": "Measures multi-photon contamination of a heralded single photon; 0 is ideal.", "origin": "chapter", "short": "Measures multi-photon contamination of a heralded single photon; 0 is ideal.", "sources": [], "term": "g2(0)" }, { "aliases": [ "gigabaud" ], "chapters": [ "06-devices", "07-history" ], "id": "gbd", "long": "Symbol rate in 1e9 symbols per second; bit rate = symbol rate x bits per symbol.", "origin": "chapter", "short": "Symbol rate in 1e9 symbols per second; bit rate = symbol rate x bits per symbol.", "sources": [], "term": "GBd" }, { "aliases": [ "k_G" ], "chapters": [ "04-quirks" ], "id": "glass-constant", "long": "Scalar coefficient in j_pv = k_G alpha I linking photovoltaic current density to absorbed intensity.", "origin": "chapter", "short": "Scalar coefficient in j_pv = k_G alpha I linking photovoltaic current density to absorbed intensity.", "sources": [ { "source_id": "volk2008" } ], "term": "Glass constant" }, { "chapters": [ "01-crystal" ], "id": "glide-plane", "long": "A mirror reflection combined with a translation along the plane; in R3c the mirrors of 3m are c-glide planes.", "origin": "chapter", "short": "A mirror reflection combined with a translation along the plane; in R3c the mirrors of 3m are c-glide planes.", "sources": [ { "source_id": "hsu1997" } ], "term": "glide plane" }, { "aliases": [ "GRIIRA", "green-induced infrared absorption" ], "category": "quirks", "chapters": [ "04-quirks", "01-crystal" ], "id": "griira", "long": "During SHG to the green it adds absorption at the infrared fundamental, heating the crystal and detuning phase matching. Furukawa et al. 2001 assigned it to the Nb_Li bound polaron and found that its MgO threshold equals that of photorefraction.", "origin": "canonical", "related": [ "bliira", "polaron", "antisite-nb-li", "mgo-doping", "shg" ], "short": "GRIIRA is the transient infrared absorption induced in LiNbO3 by green light, caused by light-generated small polarons.", "sources": [ { "source_id": "furukawa2001" }, { "source_id": "imlau2015" } ], "term": "GRIIRA (green-induced infrared absorption)" }, { "category": "optics", "chapters": [ "02-light", "06-devices" ], "id": "group-index", "long": "In traveling-wave modulators the optical group index must match the microwave index of the electrode for modulation to accumulate along the device. n_g also sets the free spectral range of a ring resonator, FSR = c / (n_g L), and links intrinsic Q to loss.", "origin": "canonical", "related": [ "effective-index", "velocity-matching", "traveling-wave-electrode", "microring", "q-factor" ], "short": "The group index n_g = n_eff - lambda dn_eff/dlambda gives the speed c/n_g at which an optical pulse envelope, or a modulation imprinted on it, travels in a waveguide.", "sources": [ { "source_id": "zhu2021" }, { "source_id": "zhang2021" } ], "symbol": "n_g", "term": "group index" }, { "chapters": [ "02-light" ], "id": "group-velocity-mismatch", "long": "Difference of inverse group velocities, (n_g2 - n_g1)/c; bulk CLN e-polarized 1550/775 nm: 302 fs/mm. Unit: fs/mm.", "origin": "chapter", "short": "Pulses at two wavelengths travel at different speeds.", "sources": [], "term": "group-velocity mismatch" }, { "aliases": [ "ground-signal-ground / ground-signal-signal-ground" ], "chapters": [ "06-devices" ], "id": "gsg-gssg", "long": "Electrode layouts for single-ended (GSG) or differential (GSSG) traveling-wave drive.", "origin": "chapter", "short": "Electrode layouts for single-ended (GSG) or differential (GSSG) traveling-wave drive.", "sources": [], "term": "GSG / GSSG" }, { "chapters": [ "03-sound" ], "id": "h-coefficient", "long": "h = beta^S e. LN (status derived): h15 9.19, h22 6.06, h33 8.01 x 10^9 V/m.", "origin": "chapter", "short": "Piezoelectric stiffness-voltage constant, V/m: field per unit strain at constant D.", "sources": [ { "source_id": "ieee176" } ], "term": "h coefficient" }, { "aliases": [ "Vpi", "half-wave voltage", "V_pi" ], "category": "electro-optics", "chapters": [ "06-devices", "02-light" ], "id": "vpi", "long": "For a lumped phase shifter of length L, V_pi = lambda g / (n_e³ r33 Gamma L), with g the electrode gap and Gamma the field-mode overlap factor; push-pull drive halves it. RF V_pi rises with frequency through electrode loss and velocity mismatch, so DC and RF values differ. TFLN brought V_pi to CMOS-compatible levels at high bandwidth (Wang et al. 2018).", "origin": "canonical", "related": [ "vpil", "overlap-factor", "push-pull", "mzm", "r33" ], "short": "The half-wave voltage V_pi is the drive voltage that produces a pi phase shift in a phase modulator, or switches an MZM from maximum to minimum transmission.", "sources": [ { "source_id": "wang2018" }, { "source_id": "zhang2021" }, { "source_id": "alferness1982" } ], "symbol": "V_pi", "term": "half-wave voltage V_pi" }, { "chapters": [ "05-making" ], "id": "hard-mask", "long": "An inorganic layer patterned first and then used to protect material during a harsher etch. SiO2, a-Si, Cr, HSQ, and DLC have been used on LN (manuscript 5.7).", "origin": "chapter", "short": "An inorganic layer patterned first and then used to protect material during a harsher etch.", "sources": [], "term": "Hard mask" }, { "chapters": [ "03-sound" ], "id": "heralded-microwave-photon", "long": "A microwave photon whose creation is signalled by the detection of a partner optical photon.", "origin": "chapter", "short": "A microwave photon whose creation is signalled by the detection of a partner optical photon.", "sources": [ { "citation": "W. Jiang et al., \"Optically heralded microwave photon addition\", Nature Physics 19 1423-1428 (2023)", "doi": "10.1038/s41567-023-02129-w", "ref": "03-sound/p17" }, { "citation": "W. Jiang et al., \"Optically heralded microwave photon addition\", Zenodo (2023)", "doi": "10.5281/zenodo.7903643", "ref": "03-sound/zenodo7903643" } ], "term": "heralded microwave photon" }, { "aliases": [ "unit cell", "lattice constants" ], "category": "crystal", "chapters": [ "01-crystal" ], "id": "hexagonal-cell", "long": "Lattice constants depend on composition: Volk & Wöhlecke 2009 lists a = 515.0 pm, c = 1386.4 pm for congruent and a = 514.7 pm, c = 1385.6 pm for near-stoichiometric LN. Synchrotron data (Hsu et al. 1997) give a_R = 5.493 A and alpha = 55.89 deg, consistent within uncertainty. Quoting lattice values without the cell setting is a common error.", "origin": "canonical", "related": [ "space-group-r3c", "congruent", "stoichiometric" ], "short": "The R3c structure of LiNbO3 can be described by a hexagonal cell (a = 5.148 A, c = 13.863 A at room temperature) or by the primitive rhombohedral cell (a_R = 5.494 A, alpha = 55.867 deg).", "sources": [ { "locator": "pp. 193-194, Eq. (1)", "source_id": "weis1985" }, { "locator": "Table 1.1, p. 3", "source_id": "volk2008" }, { "source_id": "hsu1997" } ], "term": "hexagonal and rhombohedral cells" }, { "chapters": [ "01-crystal" ], "id": "hexagonal-setting", "long": "Description of the trigonal lattice by a hexagonal prism cell with a = 5.148 A, c = 13.863 A and six formula units.", "origin": "chapter", "short": "Description of the trigonal lattice by a hexagonal prism cell with a = 5.148 A, c = 13.863 A and six formula units.", "sources": [ { "source_id": "hsu1997" } ], "term": "hexagonal setting" }, { "aliases": [ "hole polaron", "O^-" ], "chapters": [ "01-crystal", "04-quirks" ], "id": "hole-polaron-o", "long": "A hole trapped on an oxygen ion next to a cation defect such as a Li vacancy, absorbing broadly near 500 nm.", "origin": "chapter", "short": "A hole trapped on an oxygen ion next to a cation defect such as a Li vacancy, absorbing broadly near 500 nm.", "sources": [ { "source_id": "volk2008" }, { "citation": "Judith R. M.-L. Schwesyg, \"Interaction of light with impurities in lithium niobate crystals\", Dr. rer. nat. dissertation, Universität Bonn (2011)", "ref": "04-quirks/schwesyg2011" } ], "term": "hole polaron (O^-)" }, { "aliases": [ "thermal fixing" ], "category": "quirks", "chapters": [ "04-quirks", "07-history" ], "id": "hologram-fixing", "long": "In thermal fixing (Amodei & Staebler 1971) the crystal is heated during or after recording so that mobile ions drift to compensate the electronic grating; after cooling, uniform illumination redistributes the electrons and reveals the ionic copy. It followed the demonstration of holographic storage in LN (Chen et al. 1968) and made long-lived Fe:LN holograms possible.", "origin": "canonical", "related": [ "photorefraction", "fe-doping", "space-charge-field", "dark-conductivity" ], "short": "Hologram fixing converts a photorefractive electronic charge grating in LiNbO3 into a stable ionic grating, so that reading light no longer erases it.", "sources": [ { "source_id": "staebler1971" }, { "source_id": "chen1968" }, { "source_id": "volk2008" } ], "term": "hologram fixing" }, { "chapters": [ "05-making" ], "id": "hsq", "long": "Hydrogen silsesquioxane, a negative EBL resist that becomes silicon oxide and serves as an etch mask or cladding. FOx-16, about 500 nm, 85 deg resist sidewall after development [Kaufmann et al. 2023; P].", "origin": "chapter", "short": "Hydrogen silsesquioxane, a negative EBL resist that becomes silicon oxide and serves as an etch mask or cladding.", "sources": [ { "citation": "Kaufmann, Finco, Maeder, Grange, \"Redeposition‐free inductively‐coupled plasma etching of lithium niobate for integrated photonics\", Nanophotonics 12 1601-1611 (2023)", "doi": "10.1515/nanoph-2022-0676", "ref": "05-making/kaufmann2023" } ], "term": "HSQ" }, { "chapters": [ "05-making" ], "id": "icp-rie", "long": "Inductively coupled plasma reactive ion etching, where a coil sustains a dense plasma and a separate bias sets ion energy. Ar 10 sccm, 1 mTorr, 300 W, 600 V gives 24 nm/min on LN [Kaufmann et al. 2023; P].", "origin": "chapter", "short": "Inductively coupled plasma reactive ion etching, where a coil sustains a dense plasma and a separate bias sets ion energy.", "sources": [ { "citation": "Kaufmann, Finco, Maeder, Grange, \"Redeposition‐free inductively‐coupled plasma etching of lithium niobate for integrated photonics\", Nanophotonics 12 1601-1611 (2023)", "doi": "10.1515/nanoph-2022-0676", "ref": "05-making/kaufmann2023" } ], "term": "ICP-RIE" }, { "chapters": [ "05-making" ], "id": "icpcvd", "long": "Chemical vapour deposition in an inductively coupled plasma, allowing films near room temperature. 800 nm SiO2 at 80 C preserved the benefit of annealing [Shams-Ansari et al. 2022; P].", "origin": "chapter", "short": "Chemical vapour deposition in an inductively coupled plasma, allowing films near room temperature.", "sources": [ { "citation": "Shams-Ansari, Huang, He, Li, Holzgrafe, Jankowski et al., \"Reduced material loss in thin-film lithium niobate waveguides\", APL Photonics 7 081301 (2022)", "doi": "10.1063/5.0095146", "ref": "05-making/shamsansari2022" } ], "term": "ICPCVD" }, { "aliases": [ "IEEE 176", "IEEE Standard on Piezoelectricity" ], "category": "crystal", "chapters": [ "01-crystal", "03-sound" ], "id": "ieee-176", "long": "For 3m it takes +Z with positive d33, +Y with positive d22, and X along an a axis perpendicular to a mirror plane, completing a right-handed set. The only frame change from the IRE 1949 standard stated in the document is a 180 deg rotation about Z for quartz (class 32), so the LN frame is the same in both. In this frame c14 is positive (as in Kushibiki et al. 1999 and Smith and Welsh 1971), so a data set reporting c14 < 0 uses a non-standard frame (an inference from the rule texts).", "notes": "Predecessor: IRE 'Standards on Piezoelectric Crystals, 1949', Proc. IRE 37, 1378 (ire1949).", "origin": "canonical", "related": [ "plus-z-face", "mirror-plane", "voigt-notation", "piezoelectric-coefficients" ], "short": "IEEE Std 176-1987, the IEEE Standard on Piezoelectricity, sets axis and sign conventions for piezoelectric crystals and lists LiNbO3 as its class-3m example.", "sources": [ { "locator": "Table 5 (p. 18); Sec. 3.2.5.1; Table 3", "source_id": "ieee176" }, { "source_id": "ire1949" }, { "locator": "Table 6, p. 200", "source_id": "weis1985" }, { "source_id": "ieee176" } ], "term": "IEEE Std 176-1987" }, { "chapters": [ "07-history" ], "id": "ilmenite", "long": "FeTiO3 structure type, centrosymmetric (as noted by Matthias & Remeika 1949). LN was first described as ilmenite-type; its ferroelectric structure is R3c (Abrahams et al. 1966).", "origin": "chapter", "short": "FeTiO3 structure type, centrosymmetric (as noted by Matthias & Remeika 1949).", "sources": [ { "source_id": "matthias1949" }, { "source_id": "abrahams1966" } ], "term": "ilmenite" }, { "aliases": [ "intensity modulation / direct detection" ], "chapters": [ "08-industry" ], "id": "im-dd", "long": "Transmission that encodes data in optical intensity and detects it with a photodiode; used inside data centers.", "origin": "chapter", "short": "Transmission that encodes data in optical intensity and detects it with a photodiode; used inside data centers.", "sources": [], "term": "IM/DD" }, { "aliases": [ "intensity modulation with direct detection; 4-level pulse amplitude modulation" ], "chapters": [ "07-history" ], "id": "im-dd-pam-4", "long": "Data-center link format; PAM-4 carries 2 bits per symbol.", "origin": "chapter", "short": "Data-center link format; PAM-4 carries 2 bits per symbol.", "sources": [], "term": "IM/DD, PAM-4" }, { "aliases": [ "optical indicatrix", "impermeability tensor", "index ellipsoid (indicatrix)" ], "category": "optics", "chapters": [ "02-light" ], "id": "index-ellipsoid", "long": "For unbiased LN, B11 = B22 = 1/n_o² and B33 = 1/n_e², an ellipsoid of revolution about c. The Pockels effect is a linear change Delta B_I = r_Ij E_j; for a field along z, Delta(1/n_e²) = r33 E3, so Delta n_e = -(1/2) n_e³ r33 E3. A field along y changes B11 and B22 by -r22 E2 and +r22 E2 and adds B23 = r51 E2; a field along x adds B12 = -r22 E1 and B13 = r51 E1. Either makes the crystal biaxial and rotates the principal axes.", "origin": "canonical", "related": [ "pockels-effect", "eo-tensor", "optic-axis", "r33", "r51" ], "short": "The index ellipsoid is the surface B_ij x_i x_j = 1, where B = (eps/eps0)⁻¹ is the optical impermeability tensor, whose semi-axes are the principal refractive indices.", "sources": [ { "source_id": "weis1985" }, { "source_id": "zhu2021" }, { "citation": "Max Born & Emil Wolf, \"Principles of Optics\" (2019)", "doi": "10.1017/9781108769914", "ref": "02-light/bornwolf" } ], "symbol": "B_ij", "term": "index ellipsoid" }, { "chapters": [ "03-sound" ], "id": "indirect-photoelastic-effect", "long": "Significant for p13 and p33 in LN (status P-comp): p13(primary) = p13(measured) - 0.043, p33(primary) = p33(measured) - 0.154; depends on acoustic propagation direction.", "origin": "chapter", "short": "Index change from strain via the piezoelectric field and the electro-optic effect.", "sources": [ { "source_id": "weis1985" } ], "term": "indirect photoelastic effect" }, { "chapters": [ "06-devices" ], "id": "insertion-loss", "long": "Optical power lost through a device, either on chip with couplers removed or fiber to fiber with couplers included; the two are not comparable.", "origin": "chapter", "short": "Optical power lost through a device, either on chip with couplers removed or fiber to fiber with couplers included; the two are not comparable.", "sources": [], "term": "insertion loss" }, { "aliases": [ "IDT", "interdigital transducer" ], "category": "acoustics", "chapters": [ "03-sound", "07-history", "04-quirks", "06-devices" ], "id": "idt", "long": "Excitation is strongest when the electrode period (one finger pair) equals the acoustic wavelength, giving a center frequency f0 = v / p. White and Voltmer demonstrated direct piezoelectric coupling to surface waves with IDTs in 1965 (White & Voltmer 1965). The coupling coefficient k² sets the attainable filter bandwidth.", "origin": "canonical", "related": [ "saw", "electromechanical-coupling", "xbar", "128-y-x-cut" ], "short": "An interdigital transducer (IDT) is a pair of interleaved comb electrodes on a piezoelectric surface that converts an RF voltage into a surface acoustic wave and back.", "sources": [ { "source_id": "white1965" }, { "citation": "W. R. Smith et al., \"Analysis of Interdigital Surface Wave Transducers by Use of an Equivalent Circuit Model\", IEEE Transactions on Microwave Theory and Techniques 17 856-864 (1969)", "doi": "10.1109/TMTT.1969.1127075", "ref": "03-sound/smith1969" } ], "term": "interdigital transducer (IDT)" }, { "aliases": [ "internal field (Eint)" ], "category": "ferroelectric", "chapters": [ "01-crystal" ], "id": "internal-field", "long": "Gopalan et al. 1998 reports about 2.5 kV/mm in congruent LN and a vanishing value in near-stoichiometric crystals, tying it to nonstoichiometric defects. Volk & Wöhlecke 2009 Table 7.1 gives about 5 kV/cm (0.5 kV/mm) for 5 mol% MgO LN.", "origin": "canonical", "related": [ "coercive-field", "antisite-nb-li", "stoichiometric", "domain-wall" ], "short": "The internal field is a built-in bias in congruent LiNbO3 that makes the forward and reverse coercive fields unequal, shifting the hysteresis loop along the field axis.", "sources": [ { "locator": "abstract", "source_id": "gopalan1998" }, { "locator": "Table 7.1", "source_id": "volk2008" }, { "source_id": "gopalan1998" } ], "symbol": "E_int", "term": "internal field" }, { "chapters": [ "05-making" ], "id": "inverse-taper-edge-coupler", "long": "Waveguide that narrows toward the chip edge so the mode expands to match a fiber. Below 1.7 dB/facet with a bilayer taper [He et al. 2019; P(abs)].", "origin": "chapter", "short": "Waveguide that narrows toward the chip edge so the mode expands to match a fiber.", "sources": [ { "citation": "He, Zhang, Shams-Ansari, Zhu, Wang, Marko, \"Low-loss fiber-to-chip interface for lithium niobate photonic integrated circuits\", Optics Letters 44 2314 (2019)", "doi": "10.1364/OL.44.002314", "ref": "05-making/he2019ol" } ], "term": "Inverse taper edge coupler" }, { "aliases": [ "crystal ion slicing", "CIS", "Smart Cut", "ion cut", "Crystal ion slicing", "ion slicing", "also crystal ion slicing, Smart Cut" ], "category": "fabrication", "chapters": [ "05-making", "07-history", "08-industry" ], "id": "ion-slicing", "long": "Smart Cut was developed for silicon-on-insulator using hydrogen implantation and bonding (Bruel 1995); Levy et al. 1998 made single-crystal LN films by crystal ion slicing, the basis of LNOI. The implant energy sets film thickness; annealing removes implantation damage and the split surface is polished by CMP (Jia et al. 2021).", "origin": "canonical", "related": [ "wafer-bonding", "lnoi", "cmp", "tfln" ], "short": "Ion slicing (crystal ion slicing, a Smart Cut variant) detaches a sub-micrometre single-crystal layer from a LiNbO3 wafer by light-ion implantation to a set depth, bonding to a handle wafer, and splitting along the implanted plane.", "sources": [ { "source_id": "bruel1995" }, { "source_id": "levy1998" }, { "source_id": "jia2021" } ], "term": "ion slicing (Smart Cut)" }, { "aliases": [ "in-phase / quadrature modulator" ], "chapters": [ "06-devices" ], "id": "iq-modulator", "long": "Two MZMs nested in an outer interferometer with a 90-degree phase offset, used to write amplitude and phase (QAM) onto light.", "origin": "chapter", "short": "Two MZMs nested in an outer interferometer with a 90-degree phase offset, used to write amplitude and phase (QAM) onto light.", "sources": [], "term": "IQ modulator" }, { "aliases": [ "International Quantum Electronics Conference" ], "chapters": [ "07-history" ], "id": "iqec", "long": "Conference where the 1980 MgO:LN abstract appeared (Iqec 1980).", "origin": "chapter", "short": "Conference where the 1980 MgO:LN abstract appeared (Iqec 1980).", "sources": [ { "source_id": "iqec1980" } ], "term": "IQEC" }, { "chapters": [ "02-light" ], "id": "isochrome", "long": "Locus of directions with equal phase retardation Gamma; dark between crossed polarizers in monochromatic light where Gamma = 2 pi m.", "origin": "chapter", "short": "Ring of equal retardation.", "sources": [], "term": "isochrome" }, { "chapters": [ "02-light" ], "id": "isogyre", "long": "Locus of directions whose eigen-polarization azimuth is 0 or 90 deg to the polarizer; forms the dark cross of a uniaxial interference figure.", "origin": "chapter", "short": "Dark brush where an eigen-polarization lines up with the polarizer.", "sources": [], "term": "isogyre" }, { "chapters": [ "04-quirks" ], "id": "ito-buffer", "long": "Indium tin oxide, a transparent conductor, used in place of SiO2 as the buffer layer under modulator electrodes to reduce drift.", "origin": "chapter", "short": "Indium tin oxide, a transparent conductor, used in place of SiO2 as the buffer layer under modulator electrodes to reduce drift.", "sources": [ { "citation": "C. M. Gee et al., \"Minimizing dc drift in LiNbO3 waveguide devices\", Applied Physics Letters 47 211-213 (1985)", "doi": "10.1063/1.96220", "ref": "04-quirks/gee1985" } ], "term": "ITO buffer" }, { "chapters": [ "02-light" ], "id": "kerr-frequency-comb", "long": "Comb formed by cascaded four-wave mixing in a high-Q resonator pumped by a CW laser; a dissipative Kerr soliton is its mode-locked state.", "origin": "chapter", "short": "Equally spaced laser lines generated by four-wave mixing in a ring.", "sources": [ { "citation": "Tobias J. Kippenberg et al., \"Dissipative Kerr solitons in optical microresonators\", Science 361 (2018)", "doi": "10.1126/science.aan8083", "ref": "02-light/kippenberg2018" } ], "term": "Kerr frequency comb" }, { "chapters": [ "06-devices" ], "id": "kerr-soliton", "long": "A stable pulse circulating in a chi(3) microresonator whose spectrum is a frequency comb.", "origin": "chapter", "short": "A stable pulse circulating in a chi(3) microresonator whose spectrum is a frequency comb.", "sources": [], "term": "Kerr soliton" }, { "aliases": [ "dissipative Kerr soliton", "Kerr comb" ], "category": "nonlinear-optics", "chapters": [ "02-light", "06-devices" ], "id": "kerr-soliton-microcomb", "long": "The line spacing equals the resonator free spectral range. The first LN soliton microcombs (He et al. 2019) were self-starting and switched bidirectionally with the help of photorefraction. Monolithic LN circuits combined Kerr comb generation with on-chip EO modulation (Wang et al. 2019).", "origin": "canonical", "related": [ "kerr-effect", "microring", "eo-comb", "photorefraction" ], "short": "A Kerr soliton microcomb is a frequency comb formed by a dissipative Kerr soliton circulating in a high-Q microresonator with anomalous dispersion under CW pumping.", "sources": [ { "source_id": "he2019" }, { "source_id": "wang2019" } ], "term": "Kerr soliton microcomb" }, { "category": "nonlinear-optics", "chapters": [ "02-light" ], "id": "kleinman-symmetry", "long": "For LiNbO3 it adds d15 = d31 to the 3m relations (d24 = d15), leaving three independent coefficients, d33, d31 and d22. Being a low-dispersion approximation, it loses accuracy as any of the interacting frequencies approaches an absorption resonance.", "origin": "canonical", "related": [ "second-order-susceptibility", "d33", "point-group-3m" ], "short": "Kleinman symmetry is the approximate invariance of the chi(2) tensor under any permutation of its Cartesian indices, valid when all frequencies lie far from material resonances.", "sources": [ { "source_id": "armstrong1962" }, { "citation": "D. A. Kleinman, \"Nonlinear Dielectric Polarization in Optical Media\", Physical Review 126 1977-1979 (1962)", "doi": "10.1103/PhysRev.126.1977", "ref": "02-light/kleinman1962" } ], "term": "Kleinman symmetry" }, { "chapters": [ "01-crystal" ], "id": "kolmogorov-avrami-ishibashi-kai-model", "long": "Switched-fraction law X(t) = 1 - exp(-(t/t0)^n) for nucleation-and-growth polarization reversal.", "origin": "chapter", "short": "Switched-fraction law X(t) = 1 - exp(-(t/t0)^n) for nucleation-and-growth polarization reversal.", "sources": [], "term": "Kolmogorov-Avrami-Ishibashi (KAI) model" }, { "chapters": [ "01-crystal" ], "id": "kroeger-vink-notation", "long": "Defect notation giving species, site and charge relative to the host site, with a prime for negative and a bullet for positive excess charge.", "origin": "chapter", "short": "Defect notation giving species, site and charge relative to the host site, with a prime for negative and a bullet for positive excess charge.", "sources": [ { "source_id": "volk2008" } ], "term": "Kroeger-Vink notation" }, { "chapters": [ "07-history" ], "id": "kukhtarev-equations", "long": "Band-transport rate equations for photorefractive recording (N. V. Kukhtarev et al. 1978).", "origin": "chapter", "short": "Band-transport rate equations for photorefractive recording (N. V. Kukhtarev et al. 1978).", "sources": [ { "source_id": "kukhtarev1978a" } ], "term": "Kukhtarev equations" }, { "chapters": [ "04-quirks" ], "id": "kukhtarev-model", "long": "Band-transport rate equations (generation, recombination, drift, diffusion, photovoltaic current, Gauss law) for photorefractive gratings.", "origin": "chapter", "short": "Band-transport rate equations (generation, recombination, drift, diffusion, photovoltaic current, Gauss law) for photorefractive gratings.", "sources": [ { "source_id": "kukhtarev1978a" } ], "term": "Kukhtarev model" }, { "chapters": [ "03-sound" ], "id": "lamb-wave", "long": "Guided wave in a free plate with symmetric (S) and antisymmetric (A) families.", "origin": "chapter", "related": [ "sh0-mode" ], "short": "Guided wave in a free plate with symmetric (S) and antisymmetric (A) families.", "sources": [], "term": "Lamb wave" }, { "chapters": [ "04-quirks" ], "id": "laser-induced-damage", "long": "Irreversible mechanical destruction (optical breakdown) at very high pulsed intensity or fluence; separate from photorefraction.", "origin": "chapter", "short": "Irreversible mechanical destruction (optical breakdown) at very high pulsed intensity or fluence; separate from photorefraction.", "sources": [ { "source_id": "volk2008" } ], "term": "laser-induced damage" }, { "chapters": [ "03-sound" ], "id": "leaky-saw", "long": "Mostly shear-horizontal on rotated Y-X LN near 36 to 64 deg; complex velocity. 64 deg Y-X: 4691.4 m/s open, 4448.2 m/s shorted, k² 10.4% (status derived, Kushibiki et al. 1999; Warner constants give 11.0%). On 41 deg Y-X the open-surface wave sits at the fast-shear bulk velocity, 4750 m/s.", "origin": "chapter", "short": "A surface wave faster than the slow shear bulk wave that slowly radiates energy into the substrate (pseudo-SAW).", "sources": [ { "source_id": "yamanouchi1972" }, { "source_id": "kushibiki1999" }, { "source_id": "warner1967" } ], "term": "leaky SAW" }, { "aliases": [ "Li2O out-diffusion" ], "category": "quirks", "chapters": [ "04-quirks", "05-making", "07-history" ], "id": "li-out-diffusion", "long": "It was used deliberately to form planar waveguides (Kaminow et al. 1973), with its diffusion kinetics studied by Carruthers et al. 1974, and it can accompany other high-temperature steps. In thin films, Li out-diffusion during anneals is one proposed cause of higher coercive fields (Zhu et al. 2021).", "origin": "canonical", "related": [ "li-vacancy", "extraordinary-index", "ti-indiffusion", "coercive-field" ], "short": "Li out-diffusion is the loss of Li2O from the surface of LiNbO3 at high temperature, leaving a Li-poor surface layer with a higher extraordinary index.", "sources": [ { "source_id": "carruthers1974" }, { "source_id": "kaminow1973" }, { "source_id": "zhu2021" } ], "term": "Li out-diffusion" }, { "aliases": [ "lithium vacancy", "Li vacancy (V_Li)" ], "category": "defects", "chapters": [ "01-crystal" ], "id": "li-vacancy", "long": "The model writes the congruent defect structure as Nb_Li^4+ + 4 V_Li^-; a comparative structural study of different compositions (Iyi et al. 1992) supports it over the Nb-site vacancy model (Abrahams & Marsh 1986). Li2O loss at high temperature adds vacancies near the surface.", "origin": "canonical", "related": [ "antisite-nb-li", "congruent", "li-out-diffusion", "polaron" ], "short": "A lithium vacancy (V_Li) is an empty Li site; in the Li-site vacancy model of congruent LiNbO3, four V_Li compensate each Nb_Li antisite.", "sources": [ { "source_id": "iyi1992" }, { "source_id": "abrahams1986" }, { "source_id": "lerner1968" }, { "source_id": "volk2008" } ], "symbol": "V_Li", "term": "Li vacancy" }, { "chapters": [ "01-crystal" ], "id": "li-site-vacancy-model", "long": "Defect model [Li(1-5x) Nb_Li(x) V_Li(4x)] Nb O3, supported by X-ray plus neutron refinement and NMR and commonly accepted.", "origin": "chapter", "short": "Defect model [Li(1-5x) Nb_Li(x) V_Li(4x)] Nb O3, supported by X-ray plus neutron refinement and NMR and commonly accepted.", "sources": [ { "source_id": "iyi1992" } ], "term": "Li-site vacancy model" }, { "aliases": [ "lithium carbonate" ], "chapters": [ "08-industry" ], "id": "li2co3", "long": "The lithium starting powder for LN crystal growth; most lithium is consumed by batteries.", "origin": "chapter", "short": "The lithium starting powder for LN crystal growth; most lithium is consumed by batteries.", "sources": [], "term": "Li2CO3" }, { "chapters": [ "05-making" ], "id": "lift-off", "long": "Patterning metal by evaporating it over a resist pattern and dissolving the resist, leaving metal only where the resist was open.", "origin": "chapter", "short": "Patterning metal by evaporating it over a resist pattern and dissolving the resist, leaving metal only where the resist was open.", "sources": [], "term": "Lift-off" }, { "chapters": [ "06-devices" ], "id": "line-rate-net-rate", "long": "Line rate counts all transmitted bits; net rate subtracts forward-error-correction and other overhead.", "origin": "chapter", "short": "Line rate counts all transmitted bits; net rate subtracts forward-error-correction and other overhead.", "sources": [], "term": "line rate / net rate" }, { "aliases": [ "LNOI", "Lithium niobate on insulator", "lithium niobate on insulator" ], "category": "fabrication", "chapters": [ "05-making", "07-history", "08-industry", "06-devices" ], "id": "lnoi", "long": "Made by ion slicing and bonding (Levy et al. 1998; Rabiei & Gunter 2004) and named in the review of Poberaj et al. 2012, it confines light in sub-micrometre waveguides with high index contrast. 'LNOI' usually refers to the wafer and 'TFLN' to the platform and its devices.", "origin": "canonical", "related": [ "tfln", "ion-slicing", "wafer-bonding", "tflt" ], "short": "LNOI (lithium niobate on insulator) is a layer stack of a thin single-crystal LiNbO3 film on a low-index insulator, usually SiO2, on a handle wafer such as Si, LN or quartz.", "sources": [ { "source_id": "poberaj2012" }, { "source_id": "levy1998" }, { "source_id": "jia2021" }, { "source_id": "rabiei2004" } ], "term": "lithium niobate on insulator (LNOI)" }, { "aliases": [ "lithium niobate, LiNbO3" ], "chapters": [ "07-history" ], "id": "ln", "long": "Ferroelectric oxide crystal, space group R3c; ferroelectricity reported in 1949 (Matthias & Remeika 1949).", "origin": "chapter", "short": "Ferroelectric oxide crystal, space group R3c; ferroelectricity reported in 1949 (Matthias & Remeika 1949).", "sources": [ { "source_id": "matthias1949" } ], "term": "LN" }, { "chapters": [ "03-sound" ], "id": "ln-on-sapphire", "long": "Thin-film LN bonded on sapphire; acoustic waves are guided without suspension.", "origin": "chapter", "short": "Thin-film LN bonded on sapphire; acoustic waves are guided without suspension.", "sources": [ { "citation": "F. M. Mayor et al., \"Gigahertz Phononic Integrated Circuits on Thin-Film Lithium Niobate on Sapphire\", Physical Review Applied 15 014039 (2021)", "doi": "10.1103/PhysRevApplied.15.014039", "ref": "03-sound/p09" }, { "citation": "C. J. Sarabalis et al., \"Acousto-optic modulation in lithium niobate on sapphire\", APL Photonics 5 086104 (2020)", "doi": "10.1063/5.0012288", "ref": "03-sound/sarabalis2020" } ], "term": "LN on sapphire" }, { "aliases": [ "lithium niobate / lithium tantalate on insulator" ], "chapters": [ "08-industry" ], "id": "lnoi-ltoi", "long": "Thin-film wafers for photonics: LN or LT film on buried oxide on a Si, LN, or quartz handle.", "origin": "chapter", "short": "Thin-film wafers for photonics: LN or LT film on buried oxide on a Si, LN, or quartz handle.", "sources": [], "term": "LNOI / LTOI" }, { "chapters": [ "02-light" ], "id": "lnoi-tfln", "long": "Sub-micrometre single-crystal LN film bonded on a silica layer (or other insulator), patterned into waveguides by etching.", "origin": "chapter", "short": "Thin-film lithium niobate on insulator.", "sources": [], "term": "LNOI, TFLN" }, { "chapters": [ "03-sound" ], "id": "love-wave", "long": "Shear-horizontal wave guided by a surface layer slower than the substrate.", "origin": "chapter", "short": "Shear-horizontal wave guided by a surface layer slower than the substrate.", "sources": [], "term": "Love wave" }, { "aliases": [ "lithium tantalate, LiTaO3" ], "chapters": [ "07-history" ], "id": "lt", "long": "Isomorphous sibling of LN; reported ferroelectric with LN in 1949 (Matthias & Remeika 1949); main substrate for phone SAW filters by qualitative industry evidence.", "origin": "chapter", "short": "Isomorphous sibling of LN; reported ferroelectric with LN in 1949 (Matthias & Remeika 1949); main substrate for phone SAW filters by qualitative industry evidence.", "sources": [ { "source_id": "matthias1949" } ], "term": "LT" }, { "chapters": [ "02-light" ], "id": "lugiato-lefever-equation", "long": "Driven, damped nonlinear Schrodinger equation for the intracavity field: d psi/dt = -(1 + i zeta) psi + i |psi|² psi + i (d2/2) d² psi/d theta² + f.", "origin": "chapter", "short": "The equation that models Kerr combs in a ring.", "sources": [ { "citation": "L. A. Lugiato & R. Lefever, \"Spatial Dissipative Structures in Passive Optical Systems\", Physical Review Letters 58 2209-2211 (1987)", "doi": "10.1103/PhysRevLett.58.2209", "ref": "02-light/lugiato1987" } ], "term": "Lugiato-Lefever equation" }, { "aliases": [ "MZM", "Mach-Zehnder interferometer modulator", "Mach-Zehnder modulator" ], "category": "devices", "chapters": [ "06-devices", "07-history" ], "id": "mzm", "long": "Biased at quadrature it gives linear small-signal intensity modulation; biased at null it gives field modulation, and IQ modulators nest two MZMs. Bulk Ti:LN MZMs served long-haul fibre links for decades (Wooten et al. 2000), and TFLN MZMs (Wang et al. 2018) reach lower V_pi at high bandwidth.", "origin": "canonical", "related": [ "vpi", "push-pull", "traveling-wave-electrode", "dc-bias-drift", "tfln" ], "short": "A Mach-Zehnder modulator (MZM) splits light into two arms with EO phase shifters and recombines it, converting the phase difference into intensity, T = cos²(Delta phi / 2).", "sources": [ { "source_id": "alferness1982" }, { "source_id": "wooten2000" }, { "source_id": "wang2018" } ], "term": "Mach-Zehnder modulator (MZM)" }, { "chapters": [ "08-industry" ], "id": "market-teaser", "long": "The free summary page of a paid market report; it shows headline numbers without data or method.", "origin": "chapter", "short": "The free summary page of a paid market report; it shows headline numbers without data or method.", "sources": [], "term": "market teaser" }, { "chapters": [ "04-quirks" ], "id": "maxwell-wagner-relaxation", "long": "Relaxation in a layered dielectric whose layers differ in eps/sigma: voltage moves from capacitive to resistive division with time constant (C1+C2)/(G1+G2).", "origin": "chapter", "short": "Relaxation in a layered dielectric whose layers differ in eps/sigma: voltage moves from capacitive to resistive division with time constant (C1+C2)/(G1+G2).", "sources": [], "term": "Maxwell-Wagner relaxation" }, { "chapters": [ "02-light" ], "id": "melatope", "long": "Center of the isochrome system; one in a uniaxial figure, two in a biaxial figure.", "origin": "chapter", "short": "Point in a conoscopic figure where an optic axis emerges.", "sources": [], "term": "melatope" }, { "chapters": [ "03-sound" ], "id": "metallization-ratio", "long": "Fraction of the IDT period covered by metal fingers.", "origin": "chapter", "short": "Fraction of the IDT period covered by metal fingers.", "sources": [], "term": "metallization ratio" }, { "aliases": [ "MgO:LN", "magnesium doping", "magnesium-oxide-doped lithium niobate" ], "category": "defects", "chapters": [ "01-crystal", "04-quirks", "07-history", "02-light", "05-making" ], "id": "mgo-doping", "long": "Bryan et al. 1984 reported the threshold, an about 100x increase in photoconductivity, a drop of activation energy from 0.5 to 0.1 eV, and a shift of the OH band from 2.87 to 2.83 µm. Mg replaces Nb_Li antisites, which also removes the bound-polaron sites behind GRIIRA (same threshold, Furukawa et al. 2001). MgO also lowers the coercive field: Volk & Wöhlecke 2009 Table 7.1 averages 6.0-6.8 kV/mm for 5 mol% MgO, against about 21 kV/mm for undoped congruent LN.", "origin": "canonical", "related": [ "photorefraction", "photoconductivity", "griira", "antisite-nb-li", "coercive-field", "ppln" ], "short": "MgO doping above a threshold (about 4.5 at.% MgO in congruent LiNbO3) makes the crystal resistant to photorefractive damage by raising its photoconductivity.", "sources": [ { "locator": "abstract", "source_id": "bryan1984" }, { "source_id": "furukawa2001" }, { "locator": "Table 7.1, p. 185", "source_id": "volk2008" }, { "source_id": "bryan1984" }, { "source_id": "zheng2016" }, { "source_id": "iqec1980" } ], "term": "MgO doping" }, { "aliases": [ "ring resonator", "microresonator" ], "category": "devices", "chapters": [ "02-light", "06-devices" ], "id": "microring", "long": "In TFLN, voltage shifts the resonances through the Pockels effect, enabling tunable filters and resonant EO combs (Zhang et al. 2019); monolithic ultra-high-Q rings (Zhang et al. 2017) made such devices practical. With chi(3) and anomalous dispersion, rings host Kerr solitons (He et al. 2019), and with QPM they serve as resonant SHG and OPO devices.", "origin": "canonical", "related": [ "q-factor", "eo-comb", "kerr-soliton-microcomb", "group-index", "photorefraction" ], "short": "A microring resonator is a closed waveguide loop, coupled to a bus waveguide, that resonates where the round-trip phase is a multiple of 2 pi (n_eff L = m lambda).", "sources": [ { "source_id": "zhang2017" }, { "source_id": "zhang2019" }, { "source_id": "he2019" } ], "term": "microring resonator" }, { "chapters": [ "06-devices" ], "id": "microwave-optical-transducer", "long": "A device that converts microwave photons (e.g. from a superconducting qubit) to optical photons and back, via the Pockels effect or a mechanical intermediary.", "origin": "chapter", "short": "A device that converts microwave photons (e.g. from a superconducting qubit) to optical photons and back, via the Pockels effect or a mechanical intermediary.", "sources": [], "term": "microwave-optical transducer" }, { "aliases": [ "microwave-optical conversion", "quantum transduction" ], "category": "devices", "chapters": [ "03-sound", "06-devices" ], "id": "microwave-to-optical-transduction", "long": "LN offers two routes: cavity electro-optics, where a microwave resonator modulates an optical resonator through r33, and piezo-optomechanics, where the microwave drives a mechanical mode piezoelectrically and the mode modulates light photoelastically. Figures of merit are conversion efficiency, added noise and bandwidth (Han et al. 2021).", "origin": "canonical", "related": [ "piezo-optomechanics", "pockels-effect", "microring" ], "short": "Microwave-to-optical transduction converts signals or single quanta between GHz microwave and optical carriers, for example to link superconducting qubits through optical fibre.", "sources": [ { "source_id": "han2021" }, { "source_id": "jiang2020" } ], "term": "microwave-to-optical transduction" }, { "category": "nonlinear-optics", "chapters": [ "02-light" ], "id": "millers-rule", "long": "It is used to scale LN d coefficients measured at one wavelength, e.g. 1.064 µm, to another. Shoji et al. 1997 found the rule 'not so good' for scaling its absolute d values across wavelengths, so scaled values carry extra uncertainty.", "origin": "canonical", "related": [ "second-order-susceptibility", "d33" ], "short": "Miller's rule states that chi(2)(omega3; omega1, omega2) is approximately proportional to the product of the linear susceptibilities at the three frequencies, with a nearly material-independent constant.", "sources": [ { "source_id": "miller1964" }, { "locator": "abstract", "source_id": "shoji1997" } ], "term": "Miller's rule" }, { "chapters": [ "01-crystal" ], "id": "miller-savage-method", "long": "Measurement of domain-wall velocity from the shift of etched wall positions between field pulses.", "origin": "chapter", "short": "Measurement of domain-wall velocity from the shift of etched wall positions between field pulses.", "sources": [ { "source_id": "volk2008" } ], "term": "Miller-Savage method" }, { "category": "crystal", "chapters": [ "01-crystal", "03-sound" ], "id": "mirror-plane", "long": "With x perpendicular to a mirror and y lying in it, the 3m tensor forms place r22, d22 and e22 at fixed positions and give c24 = -c14. A 180 deg rotation about z flips c14, e22, d22, r22, p14 and p41 together, so data sets in different frames cannot be mixed blindly. IEEE 176-1987 removes this freedom by requiring positive d22 along +Y.", "origin": "canonical", "related": [ "point-group-3m", "ieee-176", "voigt-notation", "elastic-stiffness" ], "short": "Each of the three mirror planes of LiNbO3 contains the c axis, and the crystal-physics x axis is chosen perpendicular to one of them.", "sources": [ { "locator": "Sec. 3.2.5; Table 5 (p. 18)", "source_id": "ieee176" }, { "source_id": "weis1985" } ], "term": "mirror plane" }, { "chapters": [ "02-light" ], "id": "mode-hybridization", "long": "Anticrossing of TE- and TM-like modes caused by broken symmetry (slanted sidewalls, asymmetric slab, rotated crystal axes), producing hybrid polarization states.", "origin": "chapter", "short": "TE and TM modes mix where their indices would cross.", "sources": [ { "citation": "Archana Kaushalram et al., \"Mode hybridization analysis in thin film lithium niobate strip multimode waveguides\", Scientific Reports 10 (2020)", "doi": "10.1038/s41598-020-73936-x", "ref": "02-light/kaushalram2020" } ], "term": "mode hybridization" }, { "aliases": [ "multi-project wafer" ], "chapters": [ "08-industry" ], "id": "mpw", "long": "A shared fabrication run in which several customers' designs occupy one wafer, splitting the cost.", "origin": "chapter", "short": "A shared fabrication run in which several customers' designs occupy one wafer, splitting the cost.", "sources": [], "term": "MPW" }, { "aliases": [ "multi-project wafer; process design kit" ], "chapters": [ "07-history" ], "id": "mpw-pdk", "long": "Shared wafer runs among customers; the design rules and component library for a process (luxtelligence-about, TFLN photonic foundry emerges from CSEM spin-off).", "origin": "chapter", "short": "Shared wafer runs among customers; the design rules and component library for a process (luxtelligence-about, TFLN photonic foundry emerges from CSEM spin-off).", "sources": [ { "source_id": "csem-2025" } ], "term": "MPW, PDK" }, { "aliases": [ "modified uni-traveling-carrier photodiode" ], "chapters": [ "06-devices" ], "id": "mutc-photodiode", "long": "A III-V photodiode design in which only electrons transit the depletion region, enabling high bandwidth.", "origin": "chapter", "short": "A III-V photodiode design in which only electrons transit the depletion region, enabling high bandwidth.", "sources": [], "term": "MUTC photodiode" }, { "aliases": [ "optical group index" ], "chapters": [ "06-devices" ], "id": "n-g", "long": "c divided by the optical group velocity in the waveguide; atlas column `ng_opt`.", "origin": "chapter", "short": "c divided by the optical group velocity in the waveguide; atlas column `ng_opt`.", "sources": [], "term": "n_g" }, { "aliases": [ "microwave (RF) effective index" ], "chapters": [ "06-devices" ], "id": "n-rf", "long": "c divided by the microwave phase velocity on the electrode line; atlas column `n_rf`.", "origin": "chapter", "short": "c divided by the microwave phase velocity on the electrode line; atlas column `n_rf`.", "sources": [], "term": "n_RF" }, { "chapters": [ "03-sound" ], "id": "nanobender", "long": "Tens of nm/V actuation vs about 0.01 nm/V for standard piezoelectric coefficients; displacement scales with the square of the aspect ratio; 5 nm/V small-signal optical tuning (p07, status reported).", "origin": "chapter", "short": "A submicron piezoelectric bending beam driven by non-uniform fields from closely spaced electrodes.", "sources": [ { "citation": "W. Jiang et al., \"Nanobenders as efficient piezoelectric actuators for widely tunable nanophotonics at CMOS-level voltages\", Communications Physics 3 156 (2020)", "doi": "10.1038/s42005-020-00412-3", "ref": "03-sound/p07" } ], "term": "nanobender" }, { "aliases": [ "Nb antisite", "Nb_Li" ], "chapters": [ "01-crystal", "04-quirks" ], "id": "nb-antisite-nb-li", "long": "A niobium ion on a lithium site, the main intrinsic defect of Li-deficient LiNbO3.", "origin": "chapter", "short": "A niobium ion on a lithium site, the main intrinsic defect of Li-deficient LiNbO3.", "sources": [ { "source_id": "volk2008" } ], "term": "Nb antisite (Nb_Li)" }, { "chapters": [ "01-crystal" ], "id": "nb-site-vacancy-model", "long": "Defect model [Li(1-5x) Nb_Li(5x)] [Nb(1-4x) V_Nb(4x)] O3, proposed from X-ray occupancies of 4.9% Nb on Li sites.", "origin": "chapter", "short": "Defect model [Li(1-5x) Nb_Li(5x)] [Nb(1-4x) V_Nb(4x)] O3, proposed from X-ray occupancies of 4.9% Nb on Li sites.", "sources": [ { "source_id": "abrahams1986" } ], "term": "Nb-site vacancy model" }, { "aliases": [ "niobium pentoxide" ], "chapters": [ "08-industry" ], "id": "nb2o5", "long": "High-purity niobium oxide, one of the two starting powders for LN crystal growth; 69.904 wt% Nb.", "origin": "chapter", "short": "High-purity niobium oxide, one of the two starting powders for LN crystal growth; 69.904 wt% Nb.", "sources": [], "term": "Nb2O5" }, { "aliases": [ "niobium antisite", "antisite defect" ], "category": "defects", "chapters": [ "01-crystal", "04-quirks" ], "id": "antisite-nb-li", "long": "In the Li-site vacancy model each Nb_Li^4+ is compensated by four Li vacancies (Lerner et al. 1968, supported by Iyi et al. 1992); the alternative Nb-site vacancy model is due to Abrahams & Marsh 1986. Nb_Li traps electrons as bound small polarons and so drives photorefraction and GRIIRA in undoped crystals; MgO above its threshold removes these sites. Defect complexes around Nb_Li are linked to the internal field and high coercive field of congruent LN.", "origin": "canonical", "related": [ "li-vacancy", "polaron", "congruent", "griira", "mgo-doping" ], "short": "An Nb_Li antisite is a niobium ion on a lithium site, the dominant intrinsic defect that accommodates the Li deficit of congruent LiNbO3.", "sources": [ { "source_id": "iyi1992" }, { "source_id": "abrahams1986" }, { "source_id": "volk2008" }, { "source_id": "furukawa2001" } ], "symbol": "Nb_Li", "term": "Nb_Li antisite" }, { "aliases": [ "NSLN", "SLN" ], "chapters": [ "04-quirks", "05-making" ], "id": "near-stoichiometric-lithium-niobate", "long": "Crystal close to the 50:50 Li:Nb ratio, grown from Li-rich or K2O-modified melts or made by vapor transport equilibration.", "origin": "chapter", "short": "Crystal close to the 50:50 Li:Nb ratio, grown from Li-rich or K2O-modified melts or made by vapor transport equilibration.", "sources": [ { "source_id": "gopalan1998" } ], "term": "near-stoichiometric lithium niobate" }, { "category": "optics", "chapters": [ "02-light" ], "id": "negative-uniaxial", "long": "The extraordinary index surface lies inside the ordinary one and touches it on the optic axis, so type-I birefringent phase matching combines ordinary fundamental waves into an extraordinary harmonic (o + o -> e). Requiring n_e < n_o over a Sellmeier model's validity range is a useful check; it exposes the swapped MgO:LN o/e headings in Zelmon et al. 1997, already noted by Gayer et al. 2008.", "origin": "canonical", "related": [ "birefringence", "optic-axis", "birefringent-phase-matching", "sellmeier-equation" ], "short": "LiNbO3 is negative uniaxial: its extraordinary index is smaller than its ordinary index (n_e < n_o).", "sources": [ { "source_id": "zelmon1997" }, { "locator": "p. 348", "source_id": "gayer2008" } ], "term": "negative uniaxial" }, { "chapters": [ "01-crystal" ], "id": "neumann-s-principle", "long": "The symmetry elements of any physical property of a crystal include the symmetry elements of its point group.", "origin": "chapter", "short": "The symmetry elements of any physical property of a crystal include the symmetry elements of its point group.", "sources": [ { "source_id": "weis1985" } ], "term": "Neumann's principle" }, { "chapters": [ "02-light" ], "id": "nonlinear-coefficient-tensor", "long": "Contracted 3 x 6 tensor; in 3m with Kleinman symmetry the independent coefficients are d33, d31, d22. P_i(2 omega) = 2 eps0 sum_l d_il (E E)_l. Unit: pm/V.", "origin": "chapter", "short": "Coefficients d_il that set how strongly light mixes.", "sources": [ { "citation": "Robert W. Boyd, \"Nonlinear Optics, 3rd ed.\", Academic Press (2008)", "doi": "10.1016/b978-0-12-369470-6.00014-9", "ref": "02-light/boyd2008" } ], "term": "nonlinear coefficient tensor" }, { "chapters": [ "02-light" ], "id": "nonlinear-parameter", "long": "gamma = 2 pi n2/(lambda A_eff); nonlinear phase gamma P L. Unit: 1/(W m).", "origin": "chapter", "short": "Kerr phase per watt per metre in a waveguide.", "sources": [], "term": "nonlinear parameter" }, { "category": "nonlinear-optics", "chapters": [ "02-light" ], "id": "n2", "long": "For LiNbO3, DeSalvo et al. 1996 measured 9.33e-20 m²/W at 1064 nm (Z-scan, 30 ps, e-polarization) and 8.25e-19 m²/W at 532 nm (22 ps), as transcribed in refractiveindex.info; Zhu et al. 2021 tabulates 1.8e-19 m²/W without a primary reference. Values depend on wavelength, polarization and pulse duration.", "origin": "canonical", "related": [ "kerr-effect", "kerr-soliton-microcomb" ], "short": "n2 is the nonlinear refractive index coefficient in n = n0 + n2 I, expressed in m²/W.", "sources": [ { "source_id": "desalvo1996" }, { "source_id": "rii" }, { "locator": "Table 1", "source_id": "zhu2021" } ], "symbol": "n2", "term": "nonlinear refractive index n2" }, { "chapters": [ "02-light", "06-devices" ], "id": "normalized-conversion-efficiency", "long": "eta_norm = P_2w/(P_w² L²) in the undepleted, phase-matched, lossless limit; unit %/W/cm². Theory: 8 pi² d_eff²/(eps0 c n_w² n_2w lambda_w² A_eff). Unit: %/W/cm².", "origin": "chapter", "short": "SHG efficiency per watt and per length squared.", "sources": [], "term": "normalized conversion efficiency" }, { "aliases": [ "non-return-to-zero / four-level pulse-amplitude modulation" ], "chapters": [ "06-devices" ], "id": "nrz-pam4", "long": "Intensity formats carrying 1 bit (NRZ) or 2 bits (PAM4) per symbol.", "origin": "chapter", "short": "Intensity formats carrying 1 bit (NRZ) or 2 bits (PAM4) per symbol.", "sources": [], "term": "NRZ / PAM4" }, { "aliases": [ "Optical Fiber Communication Conference; European Conference on Optical Communication", "Optical Fiber Communication Conference / European Conference on Optical Communication" ], "chapters": [ "07-history", "08-industry" ], "id": "ofc-ecoc", "long": "Main annual optical-networking conferences.", "origin": "chapter", "short": "Main annual optical-networking conferences.", "sources": [], "term": "OFC, ECOC" }, { "chapters": [ "01-crystal" ], "id": "oh-stretch-band", "long": "Infrared absorption of OH^- ions near 3480 cm⁻¹ (2.87 µm) whose shape and position track composition and dopant thresholds.", "origin": "chapter", "short": "Infrared absorption of OH^- ions near 3480 cm⁻¹ (2.87 µm) whose shape and position track composition and dopant thresholds.", "sources": [ { "source_id": "volk2008" } ], "term": "OH stretch band" }, { "chapters": [ "02-light" ], "id": "opo-threshold", "long": "For a resonator with energy decay rates kappa_j and coupling g: P_th = hbar omega_p kappa_p² kappa_s kappa_i/(16 g² kappa_p,ex) (all resonant, zero detuning, H = hbar g(a_p^dagger a_s a_i + h.c.)).", "origin": "chapter", "short": "Pump power at which the OPO starts oscillating.", "sources": [], "term": "OPO threshold" }, { "category": "optics", "chapters": [ "02-light" ], "id": "optic-axis", "long": "LN is uniaxial because threefold symmetry makes eps11 = eps22. Light propagating at angle theta to c splits into an ordinary wave (index n_o) and an extraordinary wave with 1/n(theta)² = cos²(theta)/n_o² + sin²(theta)/n_e².", "origin": "canonical", "related": [ "ordinary-index", "extraordinary-index", "birefringence", "negative-uniaxial", "index-ellipsoid" ], "short": "The optic axis of LiNbO3 is the crystal c axis, the single direction along which light of any polarization propagates with index n_o.", "sources": [ { "source_id": "weis1985" }, { "source_id": "zhu2021" } ], "term": "optic axis" }, { "chapters": [ "02-light" ], "id": "optical-impermeability", "long": "B = eps_r⁻¹ = (1/n²)_ij. Electro-optic effect: Delta B_I = r_Ij E_j (contracted index I).", "origin": "chapter", "short": "The inverse dielectric tensor, the quantity the Pockels effect changes linearly.", "sources": [], "symbol": "(1/n^2)_ij", "term": "optical impermeability" }, { "aliases": [ "chi(3)", "third-order nonlinearity" ], "category": "nonlinear-optics", "chapters": [ "02-light" ], "id": "kerr-effect", "long": "In LN it coexists with a large chi(2) and drives self-phase modulation, four-wave mixing and dissipative Kerr solitons in TFLN microrings (He et al. 2019; Wang et al. 2019). Measured n2 values also contain wavelength- and pulse-dependent contributions such as two-photon absorption (DeSalvo et al. 1996).", "origin": "canonical", "related": [ "n2", "kerr-soliton-microcomb", "microring" ], "short": "The optical Kerr effect is the intensity-dependent refractive index n = n0 + n2 I arising from the third-order susceptibility chi(3).", "sources": [ { "source_id": "desalvo1996" }, { "source_id": "he2019" }, { "source_id": "wang2019" } ], "term": "optical Kerr effect" }, { "aliases": [ "OPA", "parametric gain", "optical parametric amplification", "optical parametric amplifier" ], "category": "nonlinear-optics", "chapters": [ "02-light", "06-devices" ], "id": "opa", "long": "Under phase matching the small-signal gain grows exponentially with length, with a gain coefficient proportional to d_eff times the square root of pump intensity. Degenerate, phase-sensitive OPA amplifies one field quadrature and de-amplifies the other, the mechanism behind squeezed-light generation in PPLN waveguides.", "origin": "canonical", "related": [ "opo", "dfg", "d-eff", "ppln" ], "short": "Optical parametric amplification (OPA) is chi(2) gain for a signal at omega_s pumped at omega_p > omega_s, generating an idler at omega_i = omega_p - omega_s.", "sources": [ { "source_id": "armstrong1962" }, { "source_id": "zhu2021" } ], "term": "optical parametric amplification (OPA)" }, { "aliases": [ "OPO", "optical parametric oscillator" ], "category": "nonlinear-optics", "chapters": [ "02-light", "06-devices", "07-history" ], "id": "opo", "long": "The first widely tunable coherent parametric oscillator used LiNbO3 (Giordmaine & Miller 1965), and bulk PPLN OPOs (Myers et al. 1995) became standard mid-IR sources. Output wavelengths follow energy conservation and phase matching and are tuned by temperature, angle or poling period.", "origin": "canonical", "related": [ "opa", "ppln", "qpm", "q-factor" ], "short": "An optical parametric oscillator (OPO) places a parametric amplifier in a resonator so that signal and/or idler build up from noise above a pump threshold.", "sources": [ { "source_id": "giordmaine1965" }, { "source_id": "myers1995" }, { "source_id": "harris1969" } ], "term": "optical parametric oscillator (OPO)" }, { "aliases": [ "ODRI" ], "chapters": [ "01-crystal", "04-quirks" ], "id": "optical-damage-resistant-ion", "long": "A dopant (Mg, Zn, In, Sc, Hf, Zr) that strongly reduces photorefraction above a threshold concentration.", "origin": "chapter", "short": "A dopant (Mg, Zn, In, Sc, Hf, Zr) that strongly reduces photorefraction above a threshold concentration.", "sources": [ { "source_id": "volk2008" } ], "term": "optical-damage-resistant ion" }, { "category": "optics", "chapters": [ "02-light" ], "id": "ordinary-index", "long": "For congruent LN, n_o = 2.2866 at 632.8 nm and 24.5 C (Nelson and Mikulyak, as compiled in Weis & Gaylord 1985 Table 2); the Zelmon et al. 1997 Sellmeier gives 2.2111 at 1550 nm and 21 C. n_o is much less sensitive to Li content and to temperature than n_e.", "origin": "canonical", "related": [ "extraordinary-index", "birefringence", "sellmeier-equation", "negative-uniaxial" ], "short": "The ordinary index n_o is the refractive index of LiNbO3 for light polarized perpendicular to the c axis.", "sources": [ { "locator": "Table 2, p. 197", "source_id": "weis1985" }, { "source_id": "zelmon1997" }, { "locator": "Table 6.1, p. 145", "source_id": "volk2008" } ], "symbol": "n_o", "term": "ordinary index" }, { "chapters": [ "01-crystal" ], "id": "orthohexagonal-crystal-physics-frame", "long": "The right-handed Cartesian x, y, z frame used for tensor properties, with z along c, x along an a axis perpendicular to a mirror plane, and y in a mirror plane.", "origin": "chapter", "short": "The right-handed Cartesian x, y, z frame used for tensor properties, with z along c, x along an a axis perpendicular to a mirror plane, and y in a mirror plane.", "sources": [ { "source_id": "weis1985" } ], "term": "orthohexagonal (crystal-physics) frame" }, { "aliases": [ "Octal Small Form-factor Pluggable; 8-lane, 500 m single-mode interface" ], "chapters": [ "07-history" ], "id": "osfp-dr8", "long": "Pluggable transceiver form factor; DR8 uses eight parallel fiber lanes.", "origin": "chapter", "short": "Pluggable transceiver form factor; DR8 uses eight parallel fiber lanes.", "sources": [], "term": "OSFP, DR8" }, { "aliases": [ "EO overlap", "electro-optic overlap integral", "overlap factor", "Gamma" ], "category": "electro-optics", "chapters": [ "06-devices" ], "id": "overlap-factor", "long": "Gamma = (g/V) * integral_LN(E_z |E_opt|² dA) / integral(|E_opt|² dA), so Gamma = 1 for a uniform field V/g filling the mode. It enters V_pi*L = lambda g / (n_e³ r33 Gamma). In TFLN, cladding, etch depth and electrode placement trade Gamma against metal-induced optical loss.", "origin": "canonical", "related": [ "vpi", "vpil", "effective-index", "traveling-wave-electrode" ], "short": "The electro-optic overlap factor Gamma is the overlap between the applied RF field, normalized to V/g, and the optical mode intensity inside the EO material.", "sources": [ { "source_id": "zhang2021" }, { "source_id": "rao2018" } ], "symbol": "Gamma", "term": "overlap factor Gamma" }, { "chapters": [ "01-crystal" ], "id": "oxygen-octahedron", "long": "The cage of six oxygen atoms around each cation site; in LiNbO3 one third of the octahedra hold Li, one third Nb, one third are empty.", "origin": "chapter", "short": "The cage of six oxygen atoms around each cation site; in LiNbO3 one third of the octahedra hold Li, one third Nb, one third are empty.", "sources": [ { "source_id": "weis1985" } ], "term": "oxygen octahedron" }, { "chapters": [ "04-quirks" ], "id": "pam4", "long": "Four-level pulse amplitude modulation, a line code carrying two bits per symbol.", "origin": "chapter", "short": "Four-level pulse amplitude modulation, a line code carrying two bits per symbol.", "sources": [], "term": "PAM4" }, { "chapters": [ "01-crystal" ], "id": "paraelectric-phase", "long": "The non-polar, centrosymmetric phase above the Curie temperature, in which Li lies in the oxygen layers and Nb at octahedron centres.", "origin": "chapter", "short": "The non-polar, centrosymmetric phase above the Curie temperature, in which Li lies in the oxygen layers and Nb at octahedron centres.", "sources": [ { "source_id": "weis1985" } ], "term": "paraelectric phase" }, { "chapters": [ "03-sound" ], "id": "partial-wave-method", "long": "SAW calculation that superposes bulk-like partial waves decaying into the substrate and enforces the surface boundary conditions.", "origin": "chapter", "short": "SAW calculation that superposes bulk-like partial waves decaying into the substrate and enforces the surface boundary conditions.", "sources": [ { "citation": "J. J. Campbell & W. R. Jones, \"A method for estimating optimal crystal cuts and propagation directions for excitation of piezoelectric surface waves\", IEEE Transactions on Sonics and Ultrasonics 15 209-217 (1968)", "doi": "10.1109/T-SU.1968.29477", "ref": "03-sound/campbell1968" } ], "term": "partial-wave method" }, { "aliases": [ "process design kit" ], "chapters": [ "08-industry" ], "id": "pdk", "long": "The design rules, component library, and models a foundry supplies so customers can design for its process.", "origin": "chapter", "short": "The design rules, component library, and models a foundry supplies so customers can design for its process.", "sources": [], "term": "PDK" }, { "chapters": [ "05-making" ], "id": "pecvd", "long": "Plasma-enhanced chemical vapour deposition, used for SiO2 masks and cladding at a few hundred degrees C. 800 nm at 300 C [Shams-Ansari et al. 2022; P].", "origin": "chapter", "short": "Plasma-enhanced chemical vapour deposition, used for SiO2 masks and cladding at a few hundred degrees C.", "sources": [ { "citation": "Shams-Ansari, Huang, He, Li, Holzgrafe, Jankowski et al., \"Reduced material loss in thin-film lithium niobate waveguides\", APL Photonics 7 081301 (2022)", "doi": "10.1063/5.0095146", "ref": "05-making/shamsansari2022" } ], "term": "PECVD" }, { "chapters": [ "07-history" ], "id": "pelopium", "long": "Name Rose gave in 1846 to a supposed second new metal in Bavarian tantalite, after Pelops; shown to be niobium (Rose 1846, Jean Charles Galissard de Marignac 1866).", "origin": "chapter", "short": "Name Rose gave in 1846 to a supposed second new metal in Bavarian tantalite, after Pelops; shown to be niobium (Rose 1846, Jean Charles Galissard de Marignac 1866).", "sources": [ { "source_id": "rose1846" }, { "source_id": "marignac1866" } ], "term": "pelopium" }, { "chapters": [ "08-industry" ], "id": "per-lane-rate", "long": "Data rate carried by one optical lane (one wavelength on one fiber); 200 G/lane and 400 G/lane are the module generations behind 1.6T and 3.2T.", "origin": "chapter", "short": "Data rate carried by one optical lane (one wavelength on one fiber); 200 G/lane and 400 G/lane are the module generations behind 1.6T and 3.2T.", "sources": [], "term": "per-lane rate" }, { "aliases": [ "PPLN", "PPMgLN", "MgO:PPLN", "periodic poling (PPLN)", "Periodic poling", "periodically poled lithium niobate" ], "category": "nonlinear-optics", "chapters": [ "02-light", "05-making", "06-devices", "07-history", "01-crystal" ], "id": "ppln", "long": "Bulk PPLN is made by electric-field poling through patterned electrodes (Yamada et al. 1993) and became the standard crystal for QPM SHG and mid-IR OPOs (Myers et al. 1995). MgO-doped PPLN reduces photorefraction and GRIIRA. In TFLN, nanophotonic PPLN waveguides combine QPM with sub-micrometre confinement.", "origin": "canonical", "related": [ "qpm", "poling", "opo", "shg", "mgo-doping" ], "short": "Periodically poled lithium niobate (PPLN) is LiNbO3 with a periodic pattern of inverted ferroelectric domains that acts as a QPM grating.", "sources": [ { "source_id": "yamada1993" }, { "source_id": "myers1995" }, { "source_id": "fejer1992" }, { "citation": "Chen, Wang, Tian, Tang, Gu, Qian et al., \"Wafer-Scale Periodic Poling of Thin-Film Lithium Niobate\", Materials 17 1720 (2024)", "doi": "10.3390/ma17081720", "ref": "05-making/chen2024materials" } ], "term": "periodically poled lithium niobate (PPLN)" }, { "category": "nonlinear-optics", "chapters": [ "02-light", "07-history" ], "id": "phase-matching", "long": "For SHG, Delta k = (4 pi / lambda_F)(n_2omega - n_omega); with Delta k not zero the low-power output follows sinc²(Delta k L / 2) and oscillates with period 2 L_c in length. In LN it is achieved by birefringence (angle or temperature tuning), by QPM gratings, or by modal dispersion in thin-film waveguides.", "origin": "canonical", "related": [ "birefringent-phase-matching", "qpm", "coherence-length", "effective-index", "walk-off" ], "short": "Phase matching is the condition Delta k = 0 under which the nonlinear polarization and the generated wave stay in phase, so the generated field grows over the whole interaction length.", "sources": [ { "source_id": "armstrong1962" }, { "source_id": "boyd1964" }, { "source_id": "fejer1992" }, { "source_id": "miller1965" } ], "symbol": "Delta k = 0", "term": "phase matching" }, { "aliases": [ "photonic crystal" ], "chapters": [ "06-devices" ], "id": "phc", "long": "A periodically patterned waveguide or cavity that confines light by a photonic band gap; used for compact, high-Q EO modulators.", "origin": "chapter", "short": "A periodically patterned waveguide or cavity that confines light by a photonic band gap; used for compact, high-Q EO modulators.", "sources": [], "term": "PhC" }, { "chapters": [ "03-sound" ], "id": "phononic-index-guiding", "long": "Used in thin-film LN on sapphire phononic circuits.", "origin": "chapter", "short": "Confinement of an acoustic wave in a film whose acoustic velocity is lower than the substrate's, without suspension.", "sources": [ { "citation": "F. M. Mayor et al., \"Gigahertz Phononic Integrated Circuits on Thin-Film Lithium Niobate on Sapphire\", Physical Review Applied 15 014039 (2021)", "doi": "10.1103/PhysRevApplied.15.014039", "ref": "03-sound/p09" } ], "term": "phononic index guiding" }, { "aliases": [ "sigma_ph" ], "category": "quirks", "chapters": [ "04-quirks" ], "id": "photoconductivity", "long": "In LN it short-circuits the photovoltaic current: MgO doping at or above 4.5 at.% raises photoconductivity about 100x (Bryan et al. 1984), which collapses the space-charge field and the photorefractive index change. The ratio sigma_ph / sigma_d also governs how fast holograms are written and erased.", "origin": "canonical", "related": [ "mgo-doping", "photorefraction", "dark-conductivity", "bulk-photovoltaic-effect" ], "short": "Photoconductivity sigma_ph is the light-induced increase of electrical conductivity, proportional to intensity in the simplest one-center model.", "sources": [ { "locator": "abstract", "source_id": "bryan1984" }, { "source_id": "volk2008" }, { "citation": "Judith R. M.-L. Schwesyg, \"Interaction of light with impurities in lithium niobate crystals\", Dr. rer. nat. dissertation, Universität Bonn (2011)", "ref": "04-quirks/schwesyg2011" } ], "symbol": "sigma_ph", "term": "photoconductivity" }, { "aliases": [ "strain-optic effect", "elasto-optic effect" ], "category": "acoustics", "chapters": [ "03-sound" ], "id": "photoelastic-effect", "long": "For 3m, p_IJ has eight independent components and is not symmetric (p14 differs from p41). Sets at 633 nm disagree in magnitude and in the signs of p14 and p41: the Avakyants 1976 set (p13 = 0.133, p31 = 0.179, p41 = -0.151) appears in Weis & Gaylord 1985 and Zhu et al. 2021, while Andrushchak et al. 2009 gives p13 = 0.172 and p41 = -0.109. Combining p14 and p41 from one paper with c14 and e22 from another requires checking that the frames match.", "notes": "Measured p13 and p33 include an indirect piezoelectric-electro-optic part (weis1985 p. 201).", "origin": "canonical", "related": [ "acousto-optic-effect", "voigt-notation", "elastic-stiffness", "piezo-optomechanics" ], "short": "The photoelastic effect is the linear change of optical impermeability with strain, Delta B_I = p_IJ S_J, described in LiNbO3 by the photoelastic tensor p_IJ.", "sources": [ { "locator": "Table 7, p. 201", "source_id": "weis1985" }, { "source_id": "andrushchak2009" }, { "source_id": "mytsyk2021" }, { "source_id": "weis1985" } ], "symbol": "p_IJ", "term": "photoelastic effect" }, { "chapters": [ "06-devices" ], "id": "photon-lifetime", "long": "tau = Q_L / omega_0, the decay time of energy stored in a resonator; it sets the scale of a resonant modulator's bandwidth.", "origin": "chapter", "short": "tau = Q_L / omega_0, the decay time of energy stored in a resonator; it sets the scale of a resonant modulator's bandwidth.", "sources": [], "term": "photon lifetime" }, { "chapters": [ "02-light" ], "id": "photonic-molecule", "long": "Coupled optical resonators whose normal modes (symmetric, antisymmetric) are split by twice the coupling rate.", "origin": "chapter", "short": "Two coupled resonators with split supermodes.", "sources": [], "term": "photonic molecule" }, { "chapters": [ "05-making" ], "id": "photonic-wire-bonding", "long": "Connecting chips with 3D-printed polymer waveguides written in place. Used to join amplifiers to TFLN circuits [Franken et al. 2025; P(abs)].", "origin": "chapter", "short": "Connecting chips with 3D-printed polymer waveguides written in place.", "sources": [ { "citation": "Franken, Cheng, Powell, Kyriazidis, Rosborough, Musolf et al., \"High-power and narrow-linewidth laser on thin-film lithium niobate enabled by photonic wire bonding\", APL Photonics 10 026107 (2025)", "doi": "10.1063/5.0231827", "ref": "05-making/franken2025" } ], "term": "Photonic wire bonding" }, { "aliases": [ "photorefractive effect", "optical damage", "PRE" ], "category": "quirks", "chapters": [ "04-quirks", "07-history" ], "id": "photorefraction", "long": "First reported as 'optical damage' (Ashkin et al. 1966), it was explained by charge drift (Chen 1969) and the bulk photovoltaic effect (Glass et al. 1974). Traps are Fe2+/Fe3+ impurities and, in undoped LN, Nb_Li polarons; MgO above threshold suppresses it by raising photoconductivity (Bryan et al. 1984). In TFLN microresonators it responds fast and shifts resonances opposite to the thermal shift (Jiang et al. 2017).", "origin": "canonical", "related": [ "space-charge-field", "bulk-photovoltaic-effect", "photoconductivity", "mgo-doping", "fe-doping", "hologram-fixing" ], "short": "Photorefraction is the light-induced refractive-index change in LiNbO3 caused by photoexcited charge redistribution, whose space-charge field alters the index through the Pockels effect.", "sources": [ { "source_id": "ashkin1966" }, { "source_id": "chen1969" }, { "source_id": "glass1974" }, { "source_id": "volk2008" }, { "source_id": "jiang2017" } ], "term": "photorefraction" }, { "aliases": [ "PRD" ], "chapters": [ "04-quirks" ], "id": "photorefractive-damage", "long": "Photorefraction when it is unwanted: beam distortion and scattering by the beam's own index change.", "origin": "chapter", "short": "Photorefraction when it is unwanted: beam distortion and scattering by the beam's own index change.", "sources": [ { "citation": "Judith R. M.-L. Schwesyg, \"Interaction of light with impurities in lithium niobate crystals\", Dr. rer. nat. dissertation, Universität Bonn (2011)", "ref": "04-quirks/schwesyg2011" } ], "term": "photorefractive damage" }, { "aliases": [ "beta_ijk" ], "chapters": [ "04-quirks" ], "id": "photovoltaic-tensor", "long": "Third-rank tensor in j_i = beta_ijk e_j e_k I; for point group 3m its symmetric part has the same nonzero pattern as the piezoelectric d tensor.", "origin": "chapter", "short": "Third-rank tensor in j_i = beta_ijk e_j e_k I; for point group 3m its symmetric part has the same nonzero pattern as the piezoelectric d tensor.", "sources": [ { "source_id": "volk2008" } ], "term": "photovoltaic tensor" }, { "aliases": [ "photonic integrated circuit" ], "chapters": [ "07-history" ], "id": "pic", "long": "Multiple optical components fabricated on one chip.", "origin": "chapter", "short": "Multiple optical components fabricated on one chip.", "sources": [], "term": "PIC" }, { "aliases": [ "piezo-optomechanical transduction", "optomechanical crystal" ], "category": "acoustics", "chapters": [ "03-sound", "06-devices" ], "id": "piezo-optomechanics", "long": "LN is both piezoelectric and photoelastic, so one suspended structure can host both interactions. LN optomechanical crystals co-localize GHz phonons and telecom photons in a patterned nanobeam (Jiang et al. 2019); with an integrated piezoelectric drive they act as bidirectional microwave-optical transducers (Jiang et al. 2020).", "origin": "canonical", "related": [ "microwave-to-optical-transduction", "photoelastic-effect", "piezoelectric-effect", "acousto-optic-effect" ], "short": "Piezo-optomechanics couples microwave signals to optical modes through a mechanical mode that is driven piezoelectrically and modulates an optical cavity photoelastically and by boundary motion.", "sources": [ { "source_id": "jiang2019" }, { "source_id": "jiang2020" }, { "citation": "W. Jiang et al., \"Optically heralded microwave photon addition\", Nature Physics 19 1423-1428 (2023)", "doi": "10.1038/s41567-023-02129-w", "ref": "03-sound/p17" } ], "term": "piezo-optomechanics" }, { "aliases": [ "piezoelectric stress constants", "piezoelectric strain constants" ], "category": "acoustics", "chapters": [ "03-sound" ], "id": "piezoelectric-coefficients", "long": "Kushibiki et al. 1999 gives e15 = 3.655, e22 = 2.407, e31 = 0.328 and e33 = 1.894 C/m² for congruent LN, and Ogi et al. 2002 agrees within its stated uncertainties. Piezoelectric d33 is the least certain constant (6-16 pC/N across compilations); the measured hydrostatic coefficient d_h = 2 d31 + d33 = 6.31 pC/N favours about 8-9 pC/N. For 3m, d16 = -2 d22 and d24 = d15.", "origin": "canonical", "related": [ "piezoelectric-effect", "elastic-stiffness", "voigt-notation", "ieee-176" ], "short": "The piezoelectric stress constants e_iJ (C/m²) and strain constants d_iJ (pC/N) of LiNbO3 relate polarization to strain and to stress respectively, with d = e s^E.", "sources": [ { "source_id": "kushibiki1999" }, { "source_id": "ogi2002" }, { "locator": "Table 3, p. 198; Eq. (8)", "source_id": "weis1985" } ], "symbol": "e_iJ, d_iJ", "term": "piezoelectric coefficients e_ij and d_ij" }, { "aliases": [ "piezoelectricity" ], "category": "acoustics", "chapters": [ "03-sound" ], "id": "piezoelectric-effect", "long": "In stress-charge form, T = c^E S - e^t E and D = e S + eps^S E. LN's strong coupling (e15 = 3.655 C/m², Kushibiki et al. 1999) underlies SAW and bulk acoustic devices, piezo-optomechanics, and the gap between clamped and unclamped EO and dielectric constants. The sign rule (compression makes the +z face negative) fixes the signs of all odd-rank tensors.", "origin": "canonical", "related": [ "piezoelectric-coefficients", "elastic-stiffness", "saw", "clamped", "plus-z-face" ], "short": "The piezoelectric effect is the linear coupling between mechanical strain or stress and electric polarization, allowed in LiNbO3 because it lacks an inversion center.", "sources": [ { "source_id": "kushibiki1999" }, { "locator": "Table 3, p. 198", "source_id": "weis1985" }, { "locator": "p. 22", "source_id": "ieee176" }, { "source_id": "ieee176" } ], "term": "piezoelectric effect" }, { "chapters": [ "03-sound" ], "id": "piezoelectric-stiffening", "long": "Added term (e_mij n_m n_i)(e_nkl n_n n_l)/(eps^S_rs n_r n_s) (IEEE 176 Eq. 47). LN Z-longitudinal: 7328.6 m/s stiffened vs 7102.1 m/s unstiffened (status derived; measured 7328.20, Kushibiki et al. 1999, P).", "origin": "chapter", "short": "Increase of the effective elastic constant because the wave's own electric field resists deformation.", "sources": [ { "source_id": "ieee176" }, { "source_id": "kushibiki1999" } ], "term": "piezoelectric stiffening" }, { "chapters": [ "05-making" ], "id": "place", "long": "Photolithography-assisted chemo-mechanical etching, in which a patterned Cr mask protects LN while CMP removes the exposed film. Cr 600 nm, fs-laser patterned; anneal 450 C 2 h; Q_i 4.04 x 10^7 [Li et al. 2023; P].", "origin": "chapter", "short": "Photolithography-assisted chemo-mechanical etching, in which a patterned Cr mask protects LN while CMP removes the exposed film.", "sources": [ { "citation": "Li, Guan, Lin, Gao, Wang, Qiao et al., \"Ultra-high Q lithium niobate microring monolithically fabricated by photolithography assisted chemo-mechanical etching\", Optics Express 31 31556 (2023)", "doi": "10.1364/oe.498086", "ref": "05-making/li2023oe" } ], "term": "PLACE" }, { "chapters": [ "05-making" ], "id": "plasma-activated-direct-bonding", "long": "Joining two polished wafers without adhesive after a plasma treatment makes their surfaces bond at room temperature. RCA clean, N2 plasma, room-temperature bond, 150 C 2 h anneal [You et al. 2019; P].", "origin": "chapter", "short": "Joining two polished wafers without adhesive after a plasma treatment makes their surfaces bond at room temperature.", "sources": [ { "citation": "You, Huang, Zhao, Yi, Chen, Ren et al., \"Engineering of self-rectifying filamentary resistive switching in LiNbO3 single crystalline thin film via strain doping\", Scientific Reports 9 19134 (2019)", "doi": "10.1038/s41598-019-55628-3", "ref": "05-making/you2019" } ], "term": "Plasma-activated direct bonding" }, { "aliases": [ "linear electro-optic effect", "EO effect", "Pockels effect (linear electro-optic effect)" ], "category": "electro-optics", "chapters": [ "02-light", "06-devices" ], "id": "pockels-effect", "long": "It is written Delta(1/n²)_I = r_Ij E_j with the r tensor in Voigt notation; for E along z, Delta n_e = -(1/2) n_e³ r33 E_z. Electronic and ionic contributions are always present, and below the acoustic resonances a piezoelectric-photoelastic contribution adds to them, so the coefficient depends on the clamping condition.", "origin": "canonical", "related": [ "eo-tensor", "r33", "clamped", "unclamped", "index-ellipsoid" ], "short": "The Pockels effect is a change of refractive index linear in an applied electric field, allowed only in crystals without inversion symmetry, such as LiNbO3.", "sources": [ { "locator": "Table 4 and Eq. (13), p. 199", "source_id": "weis1985" }, { "source_id": "turner1966" } ], "term": "Pockels effect" }, { "aliases": [ "piezoelectric-on-insulator", "piezoelectric on insulator" ], "chapters": [ "03-sound", "06-devices", "07-history", "08-industry" ], "id": "poi", "long": "Soitec Connect POI: LT6, LT8, LN6 products made by Smart Cut.", "origin": "chapter", "short": "Piezoelectric-on-insulator: a thin LT or LN layer bonded on oxide on silicon for SAW filters.", "sources": [ { "citation": "Soitec SA, \"Connect POI\"", "ref": "03-sound/soitec-poi", "url": "https://www.soitec.com/en/products/poi" }, { "source_id": "eenews-2020-soitec" } ], "term": "POI" }, { "aliases": [ "c axis", "crystal-physics z axis" ], "category": "crystal", "chapters": [ "01-crystal" ], "id": "polar-axis", "long": "Because +c and -c differ, the signs of odd-rank tensor components depend on which end is called +z; the IRE 1949 and IEEE 176-1987 rules give the same +z for LN. Ferroelectric switching reverses the polar direction locally, the basis of domain engineering. The c axis is also the optic axis.", "origin": "canonical", "related": [ "plus-z-face", "spontaneous-polarization", "optic-axis", "ferroelectric-domain" ], "short": "The c axis (crystal-physics z axis) of LiNbO3 is polar: its two ends are inequivalent, and the spontaneous polarization points along it.", "sources": [ { "locator": "pp. 192-193", "source_id": "weis1985" }, { "locator": "Table 5 (p. 18)", "source_id": "ieee176" } ], "term": "polar c-axis" }, { "aliases": [ "domain inversion", "electric-field poling" ], "category": "ferroelectric", "chapters": [ "01-crystal", "05-making", "07-history" ], "id": "poling", "long": "Patterned electric-field poling through a periodic electrode (Yamada et al. 1993) is the standard route to PPLN. In thin films, X-cut coplanar electrodes give a depth-nonuniform field, so incomplete depth, domain merging at sub-micrometre periods and back-switching are controlled with shaped pulses and in-situ monitoring (Chakkoria et al. 2025).", "origin": "canonical", "related": [ "ppln", "coercive-field", "ferroelectric-domain", "qpm", "x-cut" ], "short": "Poling is the reversal of ferroelectric domains in LiNbO3 by a field above the coercive field, either over a whole crystal (single-domain) or in a pattern.", "sources": [ { "source_id": "yamada1993" }, { "source_id": "chakkoria2025" }, { "source_id": "volk2008" } ], "term": "poling" }, { "chapters": [ "08-industry" ], "id": "postdeadline-paper", "long": "A late-submitted conference paper accepted for results judged exceptional; OFC 2026 had 24.", "origin": "chapter", "short": "A late-submitted conference paper accepted for results judged exceptional; OFC 2026 had 24.", "sources": [], "term": "postdeadline paper" }, { "chapters": [ "05-making" ], "id": "preston-equation", "long": "Empirical CMP law that removal rate is proportional to applied pressure times relative velocity, dz/dt = Kp P v. Attributed to Preston 1927 [F. W. Preston 1927; U bibliographic]; no Kp for LN sourced.", "origin": "chapter", "short": "Empirical CMP law that removal rate is proportional to applied pressure times relative velocity, dz/dt = Kp P v.", "sources": [ { "citation": "F. W. Preston, \"The theory and design of plate glass polishing machines\", Journal of the Society of Glass Technology 11, 214 (1927)", "ref": "05-making/preston1927" } ], "term": "Preston equation" }, { "aliases": [ "Rp" ], "chapters": [ "05-making" ], "id": "projected-range", "long": "Mean depth at which implanted ions come to rest, set mainly by ion species and energy. He+ at 195 keV peaks at 0.68 µm in LN [Andrea Guarino et al. 2007; P]; full range curves need SRIM [Ziegler et al. 2010] (open-questions Q6).", "origin": "chapter", "short": "Mean depth at which implanted ions come to rest, set mainly by ion species and energy.", "sources": [ { "source_id": "guarino2007" }, { "citation": "Ziegler, Ziegler, Biersack, \"SRIM – The stopping and range of ions in matter (2010)\", Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 268 1818-1823", "doi": "10.1016/j.nimb.2010.02.091", "ref": "05-making/ziegler2010" } ], "term": "Projected range" }, { "category": "optics", "chapters": [ "02-light", "05-making", "06-devices" ], "id": "propagation-loss", "long": "Etched TFLN reached 2.7 dB/m in a 2017 microring (Zhang et al. 2017), and bulk whispering-gallery resonators indicate a material loss below 0.4 dB/m (as cited in Zhu et al. 2021). Sidewall roughness, residual implantation damage and impurity or OH absorption set the floor in thin films. Intrinsic Q and loss are related by Q_i = 2 pi n_g / (lambda alpha), with alpha the power attenuation coefficient.", "origin": "canonical", "related": [ "q-factor", "microring", "transparency-window", "ar-milling" ], "short": "Propagation loss is the power attenuation per unit length of a guided mode from absorption and scattering, usually given in dB/m or dB/cm.", "sources": [ { "source_id": "zhang2017" }, { "source_id": "zhu2021" } ], "symbol": "alpha", "term": "propagation loss" }, { "aliases": [ "PE", "annealed proton exchange", "APE", "proton exchange (PE), APE", "proton exchange; annealed proton exchange" ], "category": "fabrication", "chapters": [ "05-making", "07-history" ], "id": "proton-exchange", "long": "Jackel et al. 1982 introduced it as a low-temperature route to high-index waveguides. Annealing after exchange (APE) recovers nonlinear and EO response, and APE waveguides became the basis of PPLN waveguide devices; exchanged layers are also resistant to optical damage.", "origin": "canonical", "related": [ "ti-indiffusion", "ppln", "photorefraction" ], "short": "Proton exchange replaces Li+ by H+ near the LiNbO3 surface in an acid melt such as benzoic acid, raising n_e and lowering n_o to form waveguides that guide only the extraordinary polarization.", "sources": [ { "source_id": "jackel1982" }, { "citation": "Carsten Langrock, \"Classical and low-light-level detection and pulse characterization using optical-frequency mixers\", PhD dissertation, Department of Electrical Engineering, Stanford University (advisor M. M. Fejer) (2007)", "ref": "05-making/langrock2007" } ], "term": "proton exchange" }, { "aliases": [ "push-pull" ], "category": "electro-optics", "chapters": [ "06-devices", "02-light" ], "id": "push-pull", "long": "In X-cut LN with a ground-signal-ground electrode, the fields across the two waveguides point in opposite directions relative to c, giving push-pull from one signal line. Push-pull V_pi is half the single-arm value at equal length, which must be stated when quoting V_pi*L.", "origin": "canonical", "related": [ "mzm", "vpi", "vpil", "x-cut" ], "short": "Push-pull drive applies opposite phase shifts to the two arms of an MZM, doubling the differential phase per volt and cancelling the common-mode phase (chirp).", "sources": [ { "source_id": "zhang2021" }, { "source_id": "alferness1982" } ], "term": "push-pull drive" }, { "chapters": [ "08-industry" ], "id": "pyrochlore", "long": "The niobium ore mineral mined in Brazil and Canada; the main primary source of niobium.", "origin": "chapter", "short": "The niobium ore mineral mined in Brazil and Canada; the main primary source of niobium.", "sources": [], "term": "pyrochlore" }, { "aliases": [ "p3" ], "chapters": [ "04-quirks" ], "id": "pyroelectric-coefficient", "long": "Rate of change of spontaneous polarization with temperature, dPs/dT; negative in LiNbO3.", "origin": "chapter", "short": "Rate of change of spontaneous polarization with temperature, dPs/dT; negative in LiNbO3.", "sources": [ { "source_id": "savage1966" } ], "term": "pyroelectric coefficient" }, { "category": "ferroelectric", "chapters": [ "01-crystal", "04-quirks" ], "id": "pyroelectric-effect", "long": "p3 = dP_s/dT is negative in the IEEE/IRE frame, so on cooling the +c face becomes more positive (Weis & Gaylord 1985; Volk & Wöhlecke 2009). Room-temperature magnitudes span about 4e-5 to 9.5e-5 C/(m² K) across sources (Weis & Gaylord 1985 Eq. (2) gives -4e-5, citing Savage 1966). Unscreened charge produces fields that shift n_e through r33, a concern for Z-cut devices and cryogenic cooldown.", "origin": "canonical", "related": [ "spontaneous-polarization", "plus-z-face", "z-cut", "dc-bias-drift" ], "short": "The pyroelectric effect is the change of spontaneous polarization with temperature, which leaves bound charge on the c faces of LiNbO3 after a temperature change.", "sources": [ { "locator": "Eq. (2), p. 196", "source_id": "weis1985" }, { "source_id": "savage1966" }, { "locator": "p. 2", "source_id": "volk2008" } ], "symbol": "p3", "term": "pyroelectric effect" }, { "aliases": [ "E_pyro" ], "chapters": [ "04-quirks" ], "id": "pyroelectric-field", "long": "Field from uncompensated bound charge after a temperature change; decays as free charge screens it.", "origin": "chapter", "short": "Field from uncompensated bound charge after a temperature change; decays as free charge screens it.", "sources": [ { "citation": "Judith R. M.-L. Schwesyg, \"Interaction of light with impurities in lithium niobate crystals\", Dr. rer. nat. dissertation, Universität Bonn (2011)", "ref": "04-quirks/schwesyg2011" } ], "term": "pyroelectric field" }, { "aliases": [ "quality factor", "intrinsic Q", "loaded Q", "Q_L", "Q (quality factor)" ], "category": "optics", "chapters": [ "02-light", "06-devices", "07-history" ], "id": "q-factor", "long": "The loaded Q combines intrinsic loss and coupling, 1/Q_L = 1/Q_i + 1/Q_c. Intrinsic Q of TFLN rings serves as a loss metric through Q_i = 2 pi n_g / (lambda alpha). Higher Q lowers OPO thresholds and comb pump powers and raises resonant EO efficiency.", "origin": "canonical", "related": [ "microring", "propagation-loss", "group-index", "opo" ], "short": "The quality factor Q = omega0 tau = lambda0 / delta_lambda (FWHM, for a Lorentzian resonance) measures stored energy relative to the energy lost per optical cycle.", "sources": [ { "source_id": "zhang2017" }, { "source_id": "zhu2021" } ], "symbol": "Q", "term": "Q factor" }, { "aliases": [ "quantum frequency conversion" ], "chapters": [ "06-devices" ], "id": "qfc", "long": "Changing the frequency of single photons by SFG or DFG while preserving their quantum state.", "origin": "chapter", "short": "Changing the frequency of single photons by SFG or DFG while preserving their quantum state.", "sources": [], "term": "QFC" }, { "chapters": [ "04-quirks" ], "id": "quadrature", "long": "Bias point at half transmission of an MZM, where the transfer slope is largest.", "origin": "chapter", "short": "Bias point at half transmission of an MZM, where the transfer slope is largest.", "sources": [], "term": "quadrature" }, { "aliases": [ "QPM", "quasi-phase matching" ], "category": "nonlinear-optics", "chapters": [ "02-light", "05-making", "07-history", "01-crystal", "06-devices" ], "id": "qpm", "long": "Proposed by Armstrong et al. 1962 and analysed for tuning and tolerances by Fejer et al. 1992, it lets all waves be e-polarized to use d33, avoids walk-off, and reaches any process in the transparency window by choice of period. In LN the sign reversal is ferroelectric domain inversion: first by growth striations (Feng et al. 1980), then by electric-field poling (Yamada et al. 1993).", "origin": "canonical", "related": [ "ppln", "coherence-length", "d-eff", "poling", "phase-matching" ], "short": "Quasi-phase matching (QPM) compensates phase mismatch by periodically reversing the sign of the nonlinear coefficient, adding a grating wave vector K = 2 pi m / Lambda to the momentum balance.", "sources": [ { "source_id": "armstrong1962" }, { "source_id": "fejer1992" }, { "source_id": "feng1980" }, { "source_id": "yamada1993" } ], "term": "quasi-phase matching (QPM)" }, { "chapters": [ "01-crystal" ], "id": "r-3c", "long": "The centrosymmetric space group (No. 167) of the paraelectric phase above the Curie temperature.", "origin": "chapter", "short": "The centrosymmetric space group (No. 167) of the paraelectric phase above the Curie temperature.", "sources": [ { "source_id": "boysen1994" } ], "term": "R-3c" }, { "chapters": [ "01-crystal" ], "id": "r1-r2", "long": "Composition ratios [Li]/[Nb] and [Li]/([Li] + [Nb]); R2 times 100 equals the Li2O content in mol%.", "origin": "chapter", "short": "Composition ratios [Li]/[Nb] and [Li]/([Li] + [Nb]); R2 times 100 equals the Li2O content in mol%.", "sources": [ { "source_id": "volk2008" } ], "term": "R1, R2" }, { "category": "electro-optics", "chapters": [ "02-light" ], "id": "r13", "long": "Weis & Gaylord 1985 lists r13^T = +10.0 pm/V and r13^S = +7.7 pm/V (Kaminow et al. 1980) or 8.6 pm/V (Turner 1966) at 633 nm, with the sign stated as positive. Because r13 is about a third of r33, a z field changes n_e and n_o by different amounts and so changes the birefringence.", "origin": "canonical", "related": [ "r33", "eo-tensor", "ordinary-index", "birefringence" ], "short": "r13 (= r23) is the electro-optic coefficient that changes n_o for a field along c.", "sources": [ { "locator": "Table 4, p. 199", "source_id": "weis1985" }, { "source_id": "kaminow1980" }, { "source_id": "turner1966" } ], "symbol": "r13", "term": "r13" }, { "category": "electro-optics", "chapters": [ "02-light" ], "id": "r22", "long": "Weis & Gaylord 1985 lists r22^T of 6.7-6.8 pm/V and r22^S = 3.4 pm/V at 633 nm, so clamping roughly halves it. Unclamped r22 depends on composition: values of 1.5-9.9 pm/V are reported (Abdi et al. 1998, known here only through a secondary source), with a minimum near 48.9 mol% Li2O (Volk & Wöhlecke 2009 p. 150).", "origin": "canonical", "related": [ "eo-tensor", "clamped", "unclamped", "congruent" ], "short": "r22 is the electro-optic coefficient through which a field perpendicular to c changes and rotates the ordinary-index axes (r12 = r61 = -r22).", "sources": [ { "locator": "Table 4, p. 199", "source_id": "weis1985" }, { "locator": "p. 150", "source_id": "volk2008" } ], "symbol": "r22", "term": "r22" }, { "category": "electro-optics", "chapters": [ "02-light", "06-devices" ], "id": "r33", "long": "Weis & Gaylord 1985 Table 4 lists r33^T = +32.2 pm/V (Zook et al. 1967) and r33^S = +28.8 pm/V (Kaminow et al. 1980) or 30.8 pm/V (Turner 1966), all at 633 nm; TFLN papers usually take about 31 pm/V. No 1550 nm value appears in the sources checked. Clamping changes r33 only slightly.", "origin": "canonical", "related": [ "pockels-effect", "eo-tensor", "vpi", "clamped", "x-cut" ], "short": "r33 is the electro-optic coefficient that changes n_e for a field along c, the largest Pockels coefficient of LiNbO3 and the one most modulators use.", "sources": [ { "locator": "Table 4, p. 199", "source_id": "weis1985" }, { "source_id": "kaminow1980" }, { "source_id": "turner1966" } ], "symbol": "r33", "term": "r33" }, { "chapters": [ "01-crystal" ], "id": "r3c", "long": "The space group (No. 161) of ferroelectric LiNbO3: a rhombohedral lattice with a threefold axis and c-glide planes, no inversion centre.", "origin": "chapter", "short": "The space group (No. 161) of ferroelectric LiNbO3: a rhombohedral lattice with a threefold axis and c-glide planes, no inversion centre.", "sources": [ { "source_id": "weis1985" } ], "term": "R3c" }, { "category": "crystal", "chapters": [ "01-crystal" ], "id": "space-group-r3c", "long": "Oxygen ions form distorted octahedra stacked along c, filled by Li, Nb and a vacancy in turn. Above the Curie temperature the structure becomes centrosymmetric R-3c (No. 167), per high-temperature CIFs in the Crystallography Open Database; Volk & Wöhlecke 2009 p. 2 prints R3m instead, without a reference.", "origin": "canonical", "related": [ "point-group-3m", "hexagonal-cell", "curie-temperature" ], "short": "R3c (No. 161) is the space group of LiNbO3 below the Curie temperature: a rhombohedral lattice with glide planes containing the threefold axis.", "sources": [ { "locator": "p. 192, Sec. 2.1", "source_id": "weis1985" }, { "locator": "p. 2", "source_id": "volk2008" }, { "source_id": "cod" } ], "symbol": "R3c", "term": "R3c space group" }, { "category": "electro-optics", "chapters": [ "02-light" ], "id": "r51", "long": "Weis & Gaylord 1985 lists r51^T = 32 pm/V and r51^S = +18.2 pm/V (Kaminow et al. 1980, judged probably the most accurate) or 28 pm/V (Turner 1966) at 633 nm. The 28 pm/V value used in many tables is about 35% above the 1980 clamped value. The large T-S gap reflects a large piezoelectric-photoelastic contribution.", "origin": "canonical", "related": [ "eo-tensor", "clamped", "unclamped", "index-ellipsoid" ], "short": "r51 (= r42) is the electro-optic coefficient through which a field perpendicular to c creates xz or yz impermeability components, tilting the principal axes out of the basal plane.", "sources": [ { "locator": "Table 4, p. 199", "source_id": "weis1985" }, { "source_id": "kaminow1980" }, { "source_id": "turner1966" } ], "symbol": "r51", "term": "r51" }, { "chapters": [ "05-making" ], "id": "redeposition", "long": "Etched material that lands back on the sidewalls or mask during physical etching. Removed with SC-1 (NH4OH:H2O2:H2O = 1:1:5) [Li et al. 2023; P] or avoided by tuning bias and pressure [Kaufmann et al. 2023; P].", "origin": "chapter", "short": "Etched material that lands back on the sidewalls or mask during physical etching.", "sources": [ { "citation": "Li, Wang, Lihachev, Zhang, Tan, Churaev et al., \"High density lithium niobate photonic integrated circuits\", Nature Communications 14 4856 (2023)", "doi": "10.1038/s41467-023-40502-8", "ref": "05-making/li2023nc" }, { "citation": "Kaufmann, Finco, Maeder, Grange, \"Redeposition‐free inductively‐coupled plasma etching of lithium niobate for integrated photonics\", Nanophotonics 12 1601-1611 (2023)", "doi": "10.1515/nanoph-2022-0676", "ref": "05-making/kaufmann2023" } ], "term": "Redeposition" }, { "chapters": [ "02-light" ], "id": "retardation", "long": "Gamma = (2 pi d / lambda)(n_1 cos theta_1 - n_2 cos theta_2) for eigenwaves 1 and 2 through a plate of thickness d. Unit: rad.", "origin": "chapter", "short": "Phase lag between the two polarizations after a plate.", "sources": [], "symbol": "Gamma", "term": "retardation" }, { "chapters": [ "06-devices" ], "id": "rf-loss", "long": "Attenuation of the microwave on the electrode, in dB/cm at a stated frequency (atlas `rf_loss_db_per_cm` at `rf_loss_freq_ghz`); conductor loss scales about as sqrt(f).", "origin": "chapter", "short": "Attenuation of the microwave on the electrode, in dB/cm at a stated frequency (atlas `rf_loss_db_per_cm` at `rf_loss_freq_ghz`); conductor loss scales about as sqrt(f).", "sources": [], "term": "RF loss" }, { "chapters": [ "01-crystal" ], "id": "rhombohedral-setting", "long": "Description of the same lattice by its primitive cell with edge a_R = 5.494 A, angle 55.87 deg and two formula units (10 atoms).", "origin": "chapter", "short": "Description of the same lattice by its primitive cell with edge a_R = 5.494 A, angle 55.87 deg and two formula units (10 atoms).", "sources": [ { "source_id": "weis1985" } ], "term": "rhombohedral setting" }, { "chapters": [ "02-light" ], "id": "rib-waveguide", "long": "Waveguide with film thickness t, etch depth e (slab t - e), top width w and sidewall angle; the slab carries part of the mode and of the electro-optic effect.", "origin": "chapter", "short": "Partially etched film forming a ridge on a thin slab.", "sources": [], "term": "rib waveguide" }, { "chapters": [ "06-devices" ], "id": "ring-modulator", "long": "A ring resonator whose resonance wavelength is shifted by the Pockels effect; efficient and compact, but its speed is limited by the photon lifetime.", "origin": "chapter", "short": "A ring resonator whose resonance wavelength is shifted by the Pockels effect; efficient and compact, but its speed is limited by the photon lifetime.", "sources": [], "term": "ring modulator" }, { "chapters": [ "03-sound" ], "id": "rotational-photoelastic-contribution", "long": "Nelson and Lax; in LN it gives p44 an antisymmetric part not resolved by available data.", "origin": "chapter", "short": "Index change from local rotation (antisymmetric displacement gradient) in birefringent crystals.", "sources": [ { "citation": "D. F. Nelson & M. Lax, \"New Symmetry for Acousto-Optic Scattering\", Physical Review Letters 24 379-380 (1970)", "doi": "10.1103/PhysRevLett.24.379", "ref": "03-sound/nelsonlax1970" }, { "citation": "D. F. Nelson & M. Lax, \"Theory of the Photoelastic Interaction\", Physical Review B 3 2778-2794 (1971)", "doi": "10.1103/PhysRevB.3.2778", "ref": "03-sound/nelsonlax1971" }, { "source_id": "weis1985" } ], "term": "rotational photoelastic contribution" }, { "chapters": [ "03-sound" ], "id": "sagittal-plane", "long": "The plane containing the propagation direction and the surface normal.", "origin": "chapter", "short": "The plane containing the propagation direction and the surface normal.", "sources": [], "term": "sagittal plane" }, { "chapters": [ "08-industry" ], "id": "saw-grade-optical-grade", "long": "Wafer specifications for acoustic filters (rotated-Y cuts, e.g. 128-degree Y LN) versus optics (x- or z-cut, optical quality).", "origin": "chapter", "short": "Wafer specifications for acoustic filters (rotated-Y cuts, e.g. 128-degree Y LN) versus optics (x- or z-cut, optical quality).", "sources": [], "term": "SAW grade / optical grade" }, { "aliases": [ "SHG", "frequency doubling", "second-harmonic generation" ], "category": "nonlinear-optics", "chapters": [ "02-light", "07-history" ], "id": "shg", "long": "Efficient SHG requires phase matching, Delta k = k(2 omega) - 2 k(omega) = 0, or quasi-phase matching. LiNbO3 was identified as an efficient, phase-matchable SHG crystal in 1964 (Boyd et al. 1964). In waveguides the low-power efficiency eta = P_2omega / (P_omega² L²) is quoted in %/W/cm².", "origin": "canonical", "related": [ "phase-matching", "qpm", "ppln", "d-eff", "griira" ], "short": "Second-harmonic generation (SHG) is the chi(2) process in which two photons at frequency omega combine into one at 2 omega.", "sources": [ { "source_id": "boyd1964" }, { "source_id": "fejer1992" } ], "term": "second-harmonic generation (SHG)" }, { "aliases": [ "chi(2)", "d tensor", "nonlinear coefficient", "second-order susceptibility" ], "category": "nonlinear-optics", "chapters": [ "02-light" ], "id": "second-order-susceptibility", "long": "For 3m with Kleinman symmetry the independent components are d33, d31 (= d15) and d22. Absolute values depend on the measurement scale: compilations list d33, d31, d22 = 34, 6, 3 pm/V at 1.06 µm for congruent LN (Volk & Wöhlecke 2009 Table 1.2, legacy scale), and Shoji et al. 1997 found many accepted standard values overestimated. The signs of the d components reverse with the +z convention and inside inverted domains.", "origin": "canonical", "related": [ "d33", "d-eff", "kleinman-symmetry", "shg", "millers-rule" ], "short": "The second-order susceptibility chi(2), usually given as the d tensor (d = chi(2)/2), describes the polarization quadratic in the optical field that drives SHG, SFG, DFG and parametric processes in LiNbO3.", "sources": [ { "locator": "Table 1.2, p. 4", "source_id": "volk2008" }, { "locator": "abstract", "source_id": "shoji1997" }, { "source_id": "armstrong1962" } ], "symbol": "chi(2), d_ij", "term": "second-order susceptibility chi(2)" }, { "chapters": [ "06-devices" ], "id": "self-injection-locking", "long": "Narrowing a laser's linewidth by feeding back light from a high-Q resonator.", "origin": "chapter", "short": "Narrowing a laser's linewidth by feeding back light from a high-Q resonator.", "sources": [], "term": "self-injection locking" }, { "aliases": [ "dispersion formula" ], "category": "optics", "chapters": [ "02-light" ], "id": "sellmeier-equation", "long": "Zelmon et al. 1997 fits congruent and 5 mol% MgO LN at 21 C over 0.4-5 µm; its MgO o/e headings were swapped, as noted by Gayer et al. 2008 and corrected in a 2026 erratum. Temperature-dependent forms (Jundt 1997 for congruent n_e; Gayer et al. 2008 for MgO:LN) add terms in f = (T - 24.5)(T + 570.82), and generalized forms add Li content and dopants (Schlarb & Betzler 1993). dn/dT computed from the Gayer et al. 2008 coefficients disagrees strongly with Jundt 1997, so they should not be used for absolute dn/dT.", "origin": "canonical", "related": [ "ordinary-index", "extraordinary-index", "thermo-optic-coefficient", "qpm", "negative-uniaxial" ], "short": "A Sellmeier equation is an empirical fit of refractive index versus wavelength, n² = 1 + sum_i B_i lambda² / (lambda² - C_i), with separate coefficients for n_o and n_e of LiNbO3.", "sources": [ { "source_id": "zelmon1997" }, { "source_id": "jundt1997" }, { "locator": "Table 1, p. 345; p. 348", "source_id": "gayer2008" }, { "source_id": "schlarb1993" }, { "source_id": "rii" } ], "term": "Sellmeier equation" }, { "chapters": [ "03-sound" ], "id": "sh0-mode", "long": "Used for collinear acousto-optic modulation in suspended X-cut TFLN (440 MHz, status reported).", "origin": "chapter", "short": "Fundamental shear-horizontal plate mode; in-plane displacement normal to propagation.", "sources": [ { "citation": "C. J. Sarabalis et al., \"Acousto-optic modulation of a wavelength-scale waveguide\", Optica 8 477 (2021)", "doi": "10.1364/OPTICA.413401", "ref": "03-sound/p10" } ], "term": "SH0 mode" }, { "aliases": [ "second-harmonic / sum-frequency / difference-frequency generation" ], "chapters": [ "06-devices" ], "id": "shg-sfg-dfg", "long": "chi(2) processes that produce light at 2 omega, omega1 + omega2, or omega1 - omega2.", "origin": "chapter", "short": "chi(2) processes that produce light at 2 omega, omega1 + omega2, or omega1 - omega2.", "sources": [], "term": "SHG / SFG / DFG" }, { "chapters": [ "05-making" ], "id": "sidewall-angle", "long": "Angle between an etched waveguide wall and the substrate plane; 90 deg is vertical. About 60 deg typical for SiO2-masked ridges, 75 deg with Cr, 80 deg with DLC (manuscript 5.7).", "origin": "chapter", "short": "Angle between an etched waveguide wall and the substrate plane; 90 deg is vertical.", "sources": [], "term": "Sidewall angle" }, { "chapters": [ "03-sound" ], "id": "sign-frame", "long": "A 180 deg rotation about Z flips c14, e22, d22, p14, p41, r22 together; requiring d22 > 0 removes the freedom, giving c14 > 0 for LN. Flipping +Z flips all odd-rank tensors.", "origin": "chapter", "short": "The choice of +X, +Y, +Z that fixes the signs of odd-rank and some even-rank tensor components.", "sources": [ { "source_id": "ieee176" }, { "source_id": "weis1985" } ], "term": "sign frame" }, { "chapters": [ "07-history" ], "id": "single-domain-poled-crystal", "long": "Crystal whose spontaneous polarization points one way throughout, prepared by applying a field near the Curie temperature (K. Nassau et al. 1966).", "origin": "chapter", "short": "Crystal whose spontaneous polarization points one way throughout, prepared by applying a field near the Curie temperature (K. Nassau et al. 1966).", "sources": [ { "source_id": "nassau1966b" } ], "term": "single-domain (poled) crystal" }, { "chapters": [ "05-making" ], "id": "single-domain-poling-boule", "long": "Making the spontaneous polarization point the same way throughout a grown crystal. Reported by Nassau et al. 1966 [K. Nassau et al. 1966; P(title)]; procedure values unverified here (open-questions Q3).", "origin": "chapter", "short": "Making the spontaneous polarization point the same way throughout a grown crystal.", "sources": [ { "source_id": "nassau1966b" } ], "term": "Single-domain poling (boule)" }, { "chapters": [ "01-crystal" ], "id": "sln-nsln", "long": "Stoichiometric or near-stoichiometric lithium niobate, with Li2O content close to 50 mol%.", "origin": "chapter", "short": "Stoichiometric or near-stoichiometric lithium niobate, with Li2O content close to 50 mol%.", "sources": [ { "source_id": "volk2008" } ], "term": "SLN, NSLN" }, { "chapters": [ "06-devices" ], "id": "slow-light", "long": "Propagation with a large optical group index in a structured waveguide; it raises the phase shift per unit index change and per unit length.", "origin": "chapter", "short": "Propagation with a large optical group index in a structured waveguide; it raises the phase shift per unit index change and per unit length.", "sources": [], "term": "slow light" }, { "chapters": [ "06-devices" ], "id": "slow-wave-electrode", "long": "A periodically loaded electrode that lowers the microwave phase velocity (raises n_RF) to match a high optical group index.", "origin": "chapter", "short": "A periodically loaded electrode that lowers the microwave phase velocity (raises n_RF) to match a high optical group index.", "sources": [], "term": "slow-wave electrode" }, { "chapters": [ "03-sound" ], "id": "slowness-surface", "long": "Group velocity is normal to the slowness surface; the power-flow angle is the angle between group and phase velocity.", "origin": "chapter", "short": "Plot of 1/v versus propagation direction; one sheet per bulk mode.", "sources": [ { "citation": "J. W. Jaeken & S. Cottenier, \"Solving the Christoffel equation: Phase and group velocities\", Computer Physics Communications 207 445-451 (2016)", "doi": "10.1016/j.cpc.2016.06.014", "ref": "03-sound/jaeken2016" } ], "term": "slowness surface" }, { "aliases": [ "bipolaron", "bound polaron", "free polaron", "bound polaron (Nb_Li^4+)", "free polaron (Nb_Nb^4+)" ], "category": "defects", "chapters": [ "01-crystal", "04-quirks" ], "id": "polaron", "long": "Electron species are the bound polaron Nb_Li^4+, the free polaron Nb_Nb^4+ and the bipolaron Nb_Li^4±Nb_Nb^4+; holes self-trap as O^- polarons near Li vacancies. Their broad absorption bands produce GRIIRA and BLIIRA, and light-induced polarons take part in photorefractive charge transport in undoped LN.", "origin": "canonical", "related": [ "antisite-nb-li", "griira", "bliira", "photorefraction" ], "short": "A small polaron in LiNbO3 is an electron or hole self-trapped on a single ion by the lattice distortion it creates.", "sources": [ { "source_id": "schirmer2009" }, { "source_id": "imlau2015" }, { "source_id": "volk2008" }, { "citation": "Judith R. M.-L. Schwesyg, \"Interaction of light with impurities in lithium niobate crystals\", Dr. rer. nat. dissertation, Universität Bonn (2011)", "ref": "04-quirks/schwesyg2011" } ], "term": "small polaron" }, { "chapters": [ "04-quirks" ], "id": "snspd", "long": "Superconducting nanowire single-photon detector.", "origin": "chapter", "short": "Superconducting nanowire single-photon detector.", "sources": [], "term": "SNSPD" }, { "chapters": [ "02-light" ], "id": "soliton-step", "long": "Discrete step in transmitted or intracavity power during a red-detuning scan, one per change in soliton number.", "origin": "chapter", "short": "Plateau in intracavity power as solitons form during a laser scan.", "sources": [ { "citation": "T. Herr et al., \"Temporal solitons in optical microresonators\", Nature Photonics 8 145-152 (2013)", "doi": "10.1038/nphoton.2013.343", "ref": "02-light/herr2014" } ], "term": "soliton step" }, { "aliases": [ "E_sc" ], "category": "quirks", "chapters": [ "04-quirks" ], "id": "space-charge-field", "long": "In LN it changes the index through the Pockels effect, Delta n_e = -(1/2) n_e³ r33 E_sc. Its steady state is set by the balance of photovoltaic, drift and diffusion currents (about j_pv / (sigma_d + sigma_ph) in the photovoltaic limit), and its dark lifetime by the dielectric relaxation time eps eps0 / sigma_d. Periodic illumination writes a periodic E_sc, i.e. a volume hologram.", "origin": "canonical", "related": [ "photorefraction", "bulk-photovoltaic-effect", "dark-conductivity", "hologram-fixing", "r33" ], "short": "The space-charge field E_sc is the electrostatic field of charges separated by photoexcitation, transport and retrapping in a photorefractive crystal.", "sources": [ { "source_id": "chen1969" }, { "source_id": "glass1974" }, { "source_id": "volk2008" } ], "symbol": "E_sc", "term": "space-charge field" }, { "chapters": [ "05-making" ], "id": "splitting-anneal", "long": "The heating step that makes implanted gas coalesce in a buried plane until the film separates from the donor. About 230 C after a below-200 C strengthening anneal [er_smartcut2022; P (arXiv)].", "origin": "chapter", "short": "The heating step that makes implanted gas coalesce in a buried plane until the film separates from the donor.", "sources": [ { "citation": "Sihao Wang, Likai Yang, Mohan Shen, Wei Fu, Yuntao Xu, et al. (H. X. Tang group, Yale), \"SmartCut Er:LiNbO3 with high optical coherence enabling optical thickness control\", arXiv preprint (2022)", "ref": "05-making/er_smartcut2022", "url": "https://arxiv.org/abs/2206.12645v1" } ], "term": "Splitting anneal" }, { "aliases": [ "spontaneous polarization (Ps)", "Ps" ], "category": "ferroelectric", "chapters": [ "01-crystal", "04-quirks" ], "id": "spontaneous-polarization", "long": "Reported room-temperature magnitudes disagree: Gopalan et al. 1998 gives 80 ± 5 µC/cm² for both congruent and near-stoichiometric crystals, while Volk & Wöhlecke 2009 Table 1.1 lists 71 µC/cm² for congruent LN (its near-stoichiometric entry cites a LiTaO3 paper and has no LN source). P_s decreases with rising temperature, the origin of the negative pyroelectric coefficient. Inverting P_s in a domain reverses the sign of all odd-rank tensors there.", "origin": "canonical", "related": [ "ferroelectric", "pyroelectric-effect", "ferroelectric-domain", "polar-axis" ], "short": "The spontaneous polarization P_s of LiNbO3 is the electric dipole moment per unit volume along c present without an applied field below T_c.", "sources": [ { "locator": "abstract", "source_id": "gopalan1998" }, { "locator": "Table 1.1", "source_id": "volk2008" }, { "source_id": "savage1966" }, { "source_id": "gopalan1998" } ], "symbol": "P_s", "term": "spontaneous polarization" }, { "chapters": [ "06-devices" ], "id": "squeezed-light", "long": "Light whose noise in one quadrature is below the vacuum (shot-noise) level; quoted in dB, measured or loss-corrected (inferred).", "origin": "chapter", "short": "Light whose noise in one quadrature is below the vacuum (shot-noise) level; quoted in dB, measured or loss-corrected (inferred).", "sources": [], "term": "squeezed light" }, { "chapters": [ "02-light" ], "id": "stimulated-raman-scattering", "long": "Inelastic scattering with gain at the phonon frequency offset; strong in LN and a competitor to soliton formation in TFLN rings.", "origin": "chapter", "short": "Light scattering from lattice vibrations that can steal comb power.", "sources": [ { "citation": "Zheng Gong et al., \"Near-octave lithium niobate soliton microcomb\", Optica 7 1275 (2020)", "doi": "10.1364/OPTICA.400994", "ref": "02-light/gong2020" } ], "term": "stimulated Raman scattering" }, { "aliases": [ "SLN", "near-stoichiometric LN" ], "category": "defects", "chapters": [ "01-crystal", "05-making" ], "id": "stoichiometric", "long": "Because it does not grow congruently, it is made by double-crucible Czochralski growth with continuous powder supply (Kitamura et al. 1992) or by vapor transport equilibration of congruent wafers (Bordui et al. 1992). Relative to congruent LN it has a lower coercive field, a near-zero internal field, a higher Curie temperature (1206 C in Volk & Wöhlecke 2009 Table 1.1) and a UV edge at shorter wavelength.", "origin": "canonical", "related": [ "congruent", "vte", "coercive-field", "internal-field", "uv-absorption-edge" ], "short": "Stoichiometric (in practice near-stoichiometric, about 49.8-50 mol% Li2O) LiNbO3 has [Li]/[Nb] close to 1 and far fewer intrinsic defects than congruent LN.", "sources": [ { "locator": "Table 1.1, p. 3", "source_id": "volk2008" }, { "locator": "abstract", "source_id": "gopalan1998" }, { "source_id": "kitamura1992" }, { "source_id": "bordui1992" } ], "term": "stoichiometric lithium niobate (SLN)" }, { "aliases": [ "SFG", "up-conversion", "sum-frequency generation" ], "category": "nonlinear-optics", "chapters": [ "02-light" ], "id": "sfg", "long": "Energy conservation omega3 = omega1 + omega2 and momentum matching k3 = k1 + k2 (plus a grating vector 2 pi m / Lambda for QPM) set the interaction. In PPLN it is used for up-conversion detection and quantum frequency conversion.", "origin": "canonical", "related": [ "dfg", "shg", "phase-matching", "qpm" ], "short": "Sum-frequency generation (SFG) is the chi(2) process omega1 + omega2 -> omega3 that combines two input photons into one at the sum frequency.", "sources": [ { "source_id": "armstrong1962" } ], "term": "sum-frequency generation (SFG)" }, { "aliases": [ "SAW", "Rayleigh wave", "surface acoustic wave" ], "category": "acoustics", "chapters": [ "03-sound", "07-history", "06-devices" ], "id": "saw", "long": "On piezoelectric LN a SAW carries an electric potential, so interdigital transducers can launch and detect it (White & Voltmer 1965). Velocity and coupling depend on cut and propagation direction, hence specific orientations such as the 128 deg Y-X cut for filters (Shibayama et al. 1976). In TFLN photonics, SAWs drive acousto-optic modulators (Sarabalis & et al. 2020).", "origin": "canonical", "related": [ "idt", "128-y-x-cut", "electromechanical-coupling", "acousto-optic-effect" ], "short": "A surface acoustic wave (SAW) is an elastic wave bound to the surface of a solid, decaying within about one wavelength into the bulk.", "sources": [ { "source_id": "white1965" }, { "source_id": "shibayama1976" }, { "source_id": "sarabalis2020" }, { "citation": "Lord Rayleigh, \"On Waves Propagated along the Plane Surface of an Elastic Solid\", Proceedings of the London Mathematical Society s1-17 4-11 (1885)", "doi": "10.1112/plms/s1-17.1.4", "ref": "03-sound/rayleigh1885" }, { "citation": "J. J. Campbell & W. R. Jones, \"A method for estimating optimal crystal cuts and propagation directions for excitation of piezoelectric surface waves\", IEEE Transactions on Sonics and Ultrasonics 15 209-217 (1968)", "doi": "10.1109/T-SU.1968.29477", "ref": "03-sound/campbell1968" }, { "source_id": "kushibiki1999" } ], "term": "surface acoustic wave (SAW)" }, { "chapters": [ "02-light" ], "id": "te-tm-quasi-modes", "long": "Quasi-TE: dominant electric field parallel to the film; quasi-TM: dominant field normal to it. In high-contrast anisotropic guides both carry all three field components.", "origin": "chapter", "short": "Modes polarized mainly in the plane or normal to the film.", "sources": [], "term": "TE, TM (quasi-)modes" }, { "chapters": [ "03-sound" ], "id": "temperature-coefficient-of-frequency", "long": "Vendor values for LN cuts: -95 (Y-Z), -72 (128 deg Y-X), -70 (41 and 64 deg Y-X) ppm/K (status V).", "origin": "chapter", "short": "TCF: relative change of a resonator's or filter's frequency per kelvin, in ppm/K.", "sources": [ { "citation": "OJSC Fomos-Materials, \"Lithium niobate (knowledge base)\"", "ref": "03-sound/fomos-ln", "url": "https://en.newpiezo.com/knowledge_base/1/lithium-niobate/" } ], "term": "temperature coefficient of frequency" }, { "aliases": [ "thin-film lithium niobate; thin-film lithium tantalate" ], "chapters": [ "07-history" ], "id": "tfln-tflt", "long": "Photonic platforms on LNOI or LTOI wafers; TFLT PICs for volume manufacturing reported in 2024 (Wang et al. 2024).", "origin": "chapter", "short": "Photonic platforms on LNOI or LTOI wafers; TFLT PICs for volume manufacturing reported in 2024 (Wang et al. 2024).", "sources": [ { "source_id": "wang2024" } ], "term": "TFLN, TFLT" }, { "chapters": [ "04-quirks" ], "id": "thermal-lens", "long": "Lens formed by the temperature profile of an absorbing beam through dn/dT.", "origin": "chapter", "short": "Lens formed by the temperature profile of an absorbing beam through dn/dT.", "sources": [ { "citation": "Judith R. M.-L. Schwesyg, \"Interaction of light with impurities in lithium niobate crystals\", Dr. rer. nat. dissertation, Universität Bonn (2011)", "ref": "04-quirks/schwesyg2011" } ], "term": "thermal lens" }, { "chapters": [ "04-quirks" ], "id": "thermal-triangle", "long": "Triangular resonance shape in a self-heated resonator when the laser is swept toward longer wavelength; a form of thermal bistability.", "origin": "chapter", "short": "Triangular resonance shape in a self-heated resonator when the laser is swept toward longer wavelength; a form of thermal bistability.", "sources": [ { "citation": "T. Carmon et al., \"Dynamical thermal behavior and thermal self-stability of microcavities\", Optics Express 12 4742 (2004)", "doi": "10.1364/OPEX.12.004742", "ref": "04-quirks/carmon2004" } ], "term": "thermal triangle" }, { "aliases": [ "dn/dT" ], "category": "optics", "chapters": [ "02-light", "04-quirks" ], "id": "thermo-optic-coefficient", "long": "Near 1.5 µm, dn_e/dT of congruent LN is about 3.3e-5 to 3.8e-5 /K (Moretti et al. 2005 as quoted in Zhu et al. 2021; computed from Jundt 1997), while dn_o/dT is several times smaller. In resonators the thermal red shift competes with the photorefractive blue shift (Jiang et al. 2017).", "origin": "canonical", "related": [ "extraordinary-index", "sellmeier-equation", "photorefraction", "microring" ], "short": "The thermo-optic coefficient dn/dT is the change of refractive index with temperature; in LiNbO3 it is much larger for n_e than for n_o.", "sources": [ { "source_id": "jundt1997" }, { "source_id": "zhu2021" }, { "locator": "Eqs. (2.26)-(2.27)", "source_id": "schwesyg2011" }, { "source_id": "jiang2017" }, { "source_id": "moretti2005" } ], "symbol": "dn/dT", "term": "thermo-optic coefficient" }, { "aliases": [ "TFLN", "thin-film LN", "Thin-film lithium niobate", "thin-film lithium niobate" ], "category": "devices", "chapters": [ "05-making", "06-devices", "07-history" ], "id": "tfln", "long": "Tight confinement shortens bends, places electrodes close to the mode and lowers V_pi*L, while keeping the EO, chi(2) and piezoelectric response of LN (Zhu et al. 2021; Boes et al. 2023). Low-loss etched rings (Zhang et al. 2017) and CMOS-voltage modulators (Wang et al. 2018) marked its 2017-2018 revival. In 1973, 'thin-film LN' meant an out-diffused surface guide in bulk LN (Kaminow et al. 1973).", "origin": "canonical", "related": [ "lnoi", "tflt", "ion-slicing", "mzm", "vpil" ], "short": "TFLN (thin-film lithium niobate) is integrated photonics in sub-micrometre LiNbO3 films, typically LNOI, patterned into high-confinement waveguides.", "sources": [ { "source_id": "zhu2021" }, { "source_id": "boes2023" }, { "source_id": "wang2018" }, { "source_id": "kaminow1973" } ], "term": "thin-film lithium niobate (TFLN)" }, { "aliases": [ "TFLT", "LTOI", "thin-film lithium tantalate" ], "category": "devices", "chapters": [ "06-devices", "08-industry", "07-history", "04-quirks" ], "id": "tflt", "long": "Wang et al. 2024 introduced LT photonic integrated circuits for volume manufacturing, citing much lower birefringence than LN and the existing LT wafer supply for RF SAW filters. LiTaO3 is the tantalum analogue of LiNbO3; ferroelectricity in both was reported together in 1949 (Matthias & Remeika 1949).", "origin": "canonical", "related": [ "tfln", "lnoi", "dc-bias-drift" ], "short": "TFLT (thin-film lithium tantalate) is the LiTaO3 counterpart of TFLN: integrated photonics in thin LiTaO3 films on insulator.", "sources": [ { "source_id": "wang2024" }, { "source_id": "matthias1949" }, { "citation": "K. Powell et al., \"DC-stable electro-optic modulators using thin-film lithium tantalate\", Optics Express 32 44115 (2024)", "doi": "10.1364/OE.538870", "ref": "04-quirks/powell2024" } ], "term": "thin-film lithium tantalate (TFLT)" }, { "chapters": [ "01-crystal", "04-quirks" ], "id": "threshold-concentration", "long": "The dopant level above which photorefraction drops by orders of magnitude and many properties change abruptly, about 5 mol% MgO in congruent LiNbO3.", "origin": "chapter", "short": "The dopant level above which photorefraction drops by orders of magnitude and many properties change abruptly, about 5 mol% MgO in congruent LiNbO3.", "sources": [ { "source_id": "volk2008" } ], "term": "threshold concentration" }, { "aliases": [ "Ti:LN waveguide", "titanium indiffusion", "Titanium indiffusion", "Ti:LN", "titanium-indiffused lithium niobate waveguide" ], "category": "fabrication", "chapters": [ "05-making", "07-history", "04-quirks" ], "id": "ti-indiffusion", "long": "Introduced by Schmidt & Kaminow 1974, Ti:LN waveguides guide both polarizations and were the basis of commercial LN modulators for decades (Wooten et al. 2000). The index contrast is small, so modes are large and electrodes sit far from the guide, giving a larger V_pi*L than TFLN.", "origin": "canonical", "related": [ "proton-exchange", "mzm", "vpil", "li-out-diffusion" ], "short": "Ti indiffusion forms optical waveguides in bulk LiNbO3 by depositing titanium stripes and diffusing them in at high temperature, raising both n_o and n_e locally.", "sources": [ { "source_id": "schmidt1974" }, { "source_id": "wooten2000" }, { "citation": "Luo, Brauner, Eigner, Sharapova, Ricken, Meier et al., \"Nonlinear integrated quantum electro-optic circuits\", Science Advances 5 eaat1451 (2019)", "doi": "10.1126/sciadv.aat1451", "ref": "05-making/luo2019sciadv" } ], "term": "Ti indiffusion" }, { "chapters": [ "01-crystal" ], "id": "top-seeded-solution-growth-tssg", "long": "Growth of near-stoichiometric LiNbO3 from a K2O-containing high-temperature solution.", "origin": "chapter", "short": "Growth of near-stoichiometric LiNbO3 from a K2O-containing high-temperature solution.", "sources": [ { "citation": "K. Polgar, A. Peter, L. Kovacs, G. Corradi, Zs. Szaller, \"Growth of stoichiometric LiNbO3 single crystals by top seeded solution growth method\", J. Cryst. Growth 177, 211-216 (1997)", "doi": "10.1016/S0022-0248(96)01098-6", "ref": "01-crystal/polgar1997" } ], "term": "top-seeded solution growth (TSSG)" }, { "aliases": [ "transmitter optical sub-assembly" ], "chapters": [ "08-industry" ], "id": "tosa", "long": "The packaged laser, modulator, and optics on the transmit side of a pluggable module.", "origin": "chapter", "short": "The packaged laser, modulator, and optics on the transmit side of a pluggable module.", "sources": [], "term": "TOSA" }, { "category": "optics", "chapters": [ "02-light" ], "id": "transparency-window", "long": "Volk & Wöhlecke 2009 Table 1.2 lists 0.32-5 µm for congruent and 0.3-5 µm for near-stoichiometric LN, without stating the criterion; the limits depend on thickness and absorption threshold. Inside the window, an OH stretch band at 2.87 µm (2.83 µm in MgO-doped crystals; Bryan et al. 1984) and impurity absorption set the residual loss.", "origin": "canonical", "related": [ "uv-absorption-edge", "bandgap", "propagation-loss", "fe-doping" ], "short": "The transparency window of LiNbO3 spans roughly 0.32 to 5 µm, bounded by electronic absorption in the UV and lattice absorption in the mid-IR.", "sources": [ { "locator": "Table 1.2, p. 4", "source_id": "volk2008" }, { "locator": "abstract", "source_id": "bryan1984" }, { "source_id": "schwesyg2011" } ], "term": "transparency window" }, { "aliases": [ "traveling-wave modulator", "TW electrode", "TWE" ], "category": "rf", "chapters": [ "06-devices" ], "id": "traveling-wave-electrode", "long": "Bandwidth is then set by the mismatch between microwave index and optical group index, by RF loss, and by impedance matching to the source and termination. Coplanar ground-signal-ground lines on X-cut LN are typical. Micro-structured (segmented) electrodes reduce RF loss and allow long, low-V_pi devices with high bandwidth (Kharel et al. 2021).", "origin": "canonical", "related": [ "velocity-matching", "characteristic-impedance", "eo-bandwidth", "mzm", "group-index" ], "short": "A traveling-wave electrode is a transmission line running along the optical waveguide so that the modulating microwave co-propagates with the light, removing the RC limit of a lumped electrode.", "sources": [ { "source_id": "alferness1982" }, { "source_id": "zhang2021" }, { "source_id": "kharel2021" } ], "term": "traveling-wave electrode" }, { "chapters": [ "04-quirks" ], "id": "two-center-model", "long": "Charge-transport scheme in LiNbO3 with a deep trap (for example Fe) and the Nb antisite as a shallow electron trap.", "origin": "chapter", "short": "Charge-transport scheme in LiNbO3 with a deep trap (for example Fe) and the Nb antisite as a shallow electron trap.", "sources": [ { "source_id": "volk2008" } ], "term": "two-center model" }, { "aliases": [ "free", "constant stress", "low-frequency value", "superscript T" ], "category": "electro-optics", "chapters": [ "02-light", "03-sound" ], "id": "unclamped", "long": "It includes the piezoelectric strain contribution, so the 633 nm unclamped EO coefficients in Weis & Gaylord 1985 exceed their clamped values, by about a factor 2 for r22. DC and kHz measurements of a modulator therefore probe T values, and in TFLN are further altered by charge relaxation (Holzgrafe et al. 2024).", "notes": "volk2008 p. 150 labels Yonekura et al. (2007) r22 values 'constant stress (clamped)', a contradiction; constant stress means unclamped.", "origin": "canonical", "related": [ "clamped", "eo-tensor", "dielectric-permittivity", "dc-bias-drift" ], "short": "An unclamped (free) coefficient (superscript T) is defined at constant stress, the condition reached at frequencies below the mechanical resonances, where the crystal deforms freely under the field.", "sources": [ { "locator": "Table 4 and Eq. (13), p. 199", "source_id": "weis1985" }, { "source_id": "holzgrafe2024" } ], "term": "unclamped (constant stress, T)" }, { "chapters": [ "02-light" ], "id": "uniaxial-crystal", "long": "Crystal whose dielectric tensor has two equal principal values (n_o, n_o, n_e). Negative uniaxial: n_e < n_o (LN).", "origin": "chapter", "related": [ "optic-axis", "index-ellipsoid" ], "short": "A crystal with one optic axis; LN is uniaxial along c.", "sources": [], "term": "uniaxial crystal" }, { "chapters": [ "01-crystal" ], "id": "unipolarity", "long": "The asymmetry of the ferroelectric hysteresis loop caused by the internal field.", "origin": "chapter", "short": "The asymmetry of the ferroelectric hysteresis loop caused by the internal field.", "sources": [ { "source_id": "volk2008" } ], "term": "unipolarity" }, { "category": "optics", "chapters": [ "02-light", "01-crystal" ], "id": "uv-absorption-edge", "long": "The calibration attributed to Kovács et al. 1997, as given in Volk & Wöhlecke 2009, is lambda20 = 320.4 - 1.829 x - 5.485 x² nm (absorption 20 cm⁻¹, E parallel to c, 22 C) with x = mol% Li2O - 48.38. It gives 320.4 nm at 48.38 mol% and 303.0 nm at 50.0 mol%.", "origin": "canonical", "related": [ "congruent", "stoichiometric", "bandgap", "transparency-window" ], "short": "The UV absorption edge of LiNbO3 moves to shorter wavelength as the Li content rises, and its position is used to measure composition.", "sources": [ { "source_id": "kovacs1997" }, { "locator": "Eqs. (6.5)-(6.6), p. 142", "source_id": "volk2008" } ], "term": "UV absorption edge" }, { "aliases": [ "half-wave voltage-length product" ], "chapters": [ "02-light", "06-devices" ], "id": "v-pi-l", "long": "Product of V_pi and active length; comparable between devices only with the same convention (push-pull vs single arm, DC vs RF, wavelength). Unit: V cm.", "origin": "chapter", "short": "Half-wave voltage times electrode length; a modulator's efficiency figure.", "sources": [], "term": "V_pi L" }, { "aliases": [ "VpiL", "voltage-length product" ], "category": "electro-optics", "chapters": [ "06-devices" ], "id": "vpil", "long": "From V_pi*L = lambda g / (n_e³ r33 Gamma), it scales with electrode gap divided by overlap, so the tight confinement of TFLN lowers it relative to bulk Ti:LN. Definitions differ (single arm or push-pull, DC or RF, wavelength), so published values are not strictly comparable. Narrower gaps lower V_pi*L but raise optical loss from the metal.", "origin": "canonical", "related": [ "vpi", "overlap-factor", "tfln", "ti-indiffusion" ], "short": "V_pi*L is the product of half-wave voltage and electrode length, a length-independent figure of merit for electro-optic modulation efficiency, usually in V cm.", "sources": [ { "source_id": "zhang2021" }, { "source_id": "rao2018" } ], "symbol": "Vpi*L", "term": "V_pi*L" }, { "aliases": [ "half-wave voltage; voltage-length product" ], "chapters": [ "07-history" ], "id": "v-pi-v-pi-l", "long": "Voltage for a pi phase difference; V_pi L normalizes by electrode length (units V cm).", "origin": "chapter", "short": "Voltage for a pi phase difference; V_pi L normalizes by electrode length (units V cm).", "sources": [], "term": "V_pi, V_pi L" }, { "chapters": [ "03-sound" ], "id": "vacuum-optomechanical-coupling-rate", "long": "LN piezo-optomechanical crystal: g0/2pi approx 120 kHz (p03); transducer of p05: 70 kHz measured, 84 kHz deduced (status reported).", "origin": "chapter", "short": "g0: optical frequency shift produced by the zero-point motion of the mechanical mode.", "sources": [ { "source_id": "jiang2019" }, { "source_id": "jiang2020" } ], "term": "vacuum optomechanical coupling rate" }, { "aliases": [ "VTE", "vapor transport equilibration", "Vapour transport equilibration" ], "category": "fabrication", "chapters": [ "05-making", "01-crystal", "04-quirks" ], "id": "vte", "long": "Bordui et al. 1992 prepared off-congruent crystals this way and fitted T_c = 39.064 c - 746.73 against composition. Because it is diffusion-limited, it suits wafers rather than thick crystals. Near-stoichiometric LN with 2% Mg made by VTE showed a coercive field of 1.8 ± 0.2 kV/mm (Volk & Wöhlecke 2009 Table 7.1).", "origin": "canonical", "related": [ "stoichiometric", "curie-temperature", "coercive-field" ], "short": "Vapor transport equilibration (VTE) raises the Li content of LiNbO3 wafers toward stoichiometry by annealing them next to Li-rich powder so that Li2O diffuses in through the vapor phase.", "sources": [ { "source_id": "bordui1992" }, { "locator": "Eqs. (6.2)-(6.3), p. 140; Table 7.1, p. 185", "source_id": "volk2008" } ], "term": "vapor transport equilibration (VTE)" }, { "aliases": [ "microwave index matching" ], "category": "rf", "chapters": [ "06-devices" ], "id": "velocity-matching", "long": "For a lossless traveling-wave modulator with mismatch Delta n = n_m - n_g, the response follows |sin(x)/x| with x = pi f L Delta n / c, which bounds the product f L. In bulk LN the microwave index far exceeds the optical group index, while TFLN on low-permittivity substrates can bring the two close.", "origin": "canonical", "related": [ "traveling-wave-electrode", "group-index", "dielectric-permittivity", "eo-bandwidth" ], "short": "Velocity matching equalizes the microwave phase velocity on the electrode (index n_m) with the optical group velocity (index n_g), so the light sees the same modulating phase along the whole device.", "sources": [ { "source_id": "zhang2021" }, { "source_id": "rao2018" } ], "term": "velocity matching" }, { "aliases": [ "contracted index notation", "matrix notation" ], "category": "general", "chapters": [ "01-crystal", "03-sound" ], "id": "voigt-notation", "long": "Factors of 2 enter through engineering shear strain (S4 = 2 S23): for 3m, s66 = 2(s11 - s12) and s56 = 2 s14, while c66 = (c11 - c12)/2 and c56 = c14; for piezoelectric strain constants d16 = -2 d22. Each data set must state its convention, and full-rank tensors avoid manual factor errors. The photoelastic matrix p_IJ is not symmetric (p14 differs from p41).", "origin": "canonical", "related": [ "elastic-stiffness", "piezoelectric-coefficients", "photoelastic-effect", "eo-tensor" ], "short": "Voigt notation contracts symmetric index pairs (xx, yy, zz, yz, xz, xy) to 1-6, so rank-3 and rank-4 property tensors of LiNbO3 become 3x6 and 6x6 matrices.", "sources": [ { "locator": "Eqs. (16)-(17), pp. 199-200; Eq. (8)", "source_id": "weis1985" }, { "source_id": "ogi2002" }, { "source_id": "weis1985" }, { "source_id": "ieee176" } ], "term": "Voigt notation" }, { "chapters": [ "06-devices" ], "id": "vpi-convention", "long": "The definition behind a quoted V_pi (per-arm phase shifter, push-pull MZM, differential V+ minus V-, single arm); conventions differ by factors of 2 and are never converted on this site.", "origin": "chapter", "short": "The definition behind a quoted V_pi (per-arm phase shifter, push-pull MZM, differential V+ minus V-, single arm); conventions differ by factors of 2 and are never converted on this site.", "sources": [], "term": "Vpi convention" }, { "aliases": [ "direct bonding" ], "category": "fabrication", "chapters": [ "05-making" ], "id": "wafer-bonding", "long": "Rabiei & Gunter 2004 combined crystal ion slicing with wafer bonding to make submicrometre LN slab waveguides with EO function, a route to LNOI. LN's anisotropic thermal expansion (alpha_a = 14.1e-6 /K, alpha_c = 4.1e-6 /K for congruent LN at 300 K, Volk & Wöhlecke 2009) produces stress against Si or other handles during post-bond anneals.", "origin": "canonical", "related": [ "ion-slicing", "lnoi", "tfln" ], "short": "Wafer bonding joins two polished wafers, for example an implanted LiNbO3 donor and an oxidized Si or LN handle, by direct or adhesive bonding.", "sources": [ { "source_id": "rabiei2004" }, { "source_id": "poberaj2012" }, { "locator": "Table 1.1", "source_id": "volk2008" } ], "term": "wafer bonding" }, { "chapters": [ "05-making" ], "id": "wafer-flat", "long": "A straight edge ground on a wafer whose position encodes the crystal orientation. Flat lengths and orientations are vendor-specific; not sourced here (open-questions Q4).", "origin": "chapter", "short": "A straight edge ground on a wafer whose position encodes the crystal orientation.", "sources": [], "term": "Wafer flat" }, { "aliases": [ "Poynting vector walk-off", "spatial walk-off" ], "category": "nonlinear-optics", "chapters": [ "02-light" ], "id": "walk-off", "long": "For propagation at angle theta to the optic axis, tan(rho) = (n(theta)² / 2) |1/n_e² - 1/n_o²| sin(2 theta), which vanishes at theta = 0 and 90 deg. This is why noncritical (90 deg) phase matching in LN avoids walk-off (Miller et al. 1965), as does QPM along a principal axis.", "origin": "canonical", "related": [ "birefringent-phase-matching", "birefringence", "qpm" ], "short": "Walk-off is the angle rho between the Poynting vector and the wave vector of an extraordinary wave in a birefringent crystal, which separates beams and limits the useful interaction length.", "sources": [ { "source_id": "miller1965" } ], "symbol": "rho", "term": "walk-off" }, { "category": "fabrication", "chapters": [ "05-making", "06-devices", "02-light" ], "id": "x-cut", "long": "In X-cut TFLN, coplanar electrodes on both sides of a waveguide apply an in-plane field along z, and a TE mode polarized along z uses n_e and r33; this is the common TFLN modulator geometry. Periodic poling of X-cut films also uses coplanar electrodes, which give a field that is nonuniform in depth.", "origin": "canonical", "related": [ "z-cut", "y-cut", "r33", "poling", "mzm" ], "short": "An X-cut LiNbO3 wafer or film has its surface normal along the crystal x axis, so the c axis lies in the plane.", "sources": [ { "source_id": "zhu2021" }, { "source_id": "zhang2021" } ], "term": "X-cut" }, { "chapters": [ "05-making" ], "id": "x-cut-y-cut-z-cut", "long": "Wafer named after the crystal axis normal to its surface. x-cut TFLN puts Z in plane so TE modes use r33 [Wang et al. 2018; P].", "origin": "chapter", "short": "Wafer named after the crystal axis normal to its surface.", "sources": [ { "source_id": "wang2018a" } ], "term": "x-cut, y-cut, z-cut" }, { "aliases": [ "XBAR", "laterally excited bulk-wave resonator", "laterally excited bulk acoustic resonator" ], "category": "acoustics", "chapters": [ "03-sound", "06-devices", "07-history" ], "id": "xbar", "long": "The resonance is set mainly by plate thickness rather than electrode pitch, which allows GHz operation with relaxed lithography; Plessky et al. 2019 reported 5 GHz XBARs on thin LN platelets. Thin-film LN resonators of this class are being extended to mm-wave filters (Lu 2025).", "origin": "canonical", "related": [ "baw", "electromechanical-coupling", "idt" ], "short": "An XBAR is a suspended thin LiNbO3 plate with interdigital electrodes on its surface whose lateral field excites a thickness-shear bulk mode.", "sources": [ { "source_id": "plessky2019" }, { "source_id": "lu2025" }, { "source_id": "murata-2022" } ], "term": "XBAR (laterally excited bulk acoustic resonator)" }, { "aliases": [ "rotated Y-cut", "rotated Y cut" ], "category": "fabrication", "chapters": [ "03-sound", "05-making" ], "id": "y-cut", "long": "The rotation angle selects the velocity, coupling and spurious responses of acoustic waves on the plate. Shibayama et al. 1976 identified a rotated Y-cut near 128 deg with X propagation as optimum for surface-acoustic-wave filter substrates.", "origin": "canonical", "related": [ "x-cut", "z-cut", "128-y-x-cut", "saw" ], "short": "A Y-cut LiNbO3 wafer has its surface normal along the crystal y axis, which lies in a mirror plane; a rotated Y-cut tilts that normal about x by a stated angle.", "sources": [ { "source_id": "shibayama1976" }, { "source_id": "ieee176" } ], "term": "Y-cut" }, { "chapters": [ "01-crystal" ], "id": "y-wall", "long": "A domain wall parallel to a (11-20) plane, i.e. parallel to the yz plane, the low-energy wall that bounds hexagonal domains in LiNbO3.", "origin": "chapter", "short": "A domain wall parallel to a (11-20) plane, i.e. parallel to the yz plane, the low-energy wall that bounds hexagonal domains in LiNbO3.", "sources": [ { "citation": "D. Lee, H. Xu, V. Dierolf, V. Gopalan, S. R. Phillpot, \"Shape of ferroelectric domains in LiNbO3 and LiTaO3 from defect/domain-wall interactions\", Appl. Phys. Lett. 98, 092903 (2011)", "doi": "10.1063/1.3560343", "ref": "01-crystal/lee2011" } ], "term": "Y-wall" }, { "category": "fabrication", "chapters": [ "05-making", "06-devices", "04-quirks", "02-light" ], "id": "z-cut", "long": "In Z-cut TFLN a vertical field couples to TM-like modes through r33, while TE modes see n_o and smaller coefficients. Poling is done with a field through the film or by poling a bulk wafer before bonding. A temperature change leaves pyroelectric charge on the faces, producing a vertical field that overlaps strongly with the mode.", "origin": "canonical", "related": [ "x-cut", "y-cut", "plus-z-face", "pyroelectric-effect", "poling" ], "short": "A Z-cut LiNbO3 wafer or film has its surface normal along the polar c axis, so its two faces are the +z and -z faces.", "sources": [ { "source_id": "zhu2021" } ], "term": "Z-cut" }, { "aliases": [ "characteristic impedance" ], "chapters": [ "06-devices" ], "id": "z0", "long": "The ratio of voltage to current of a wave on the line, sqrt(L'/C') for a quasi-TEM line; mismatch to the 50 ohm source and load reduces and ripples the response.", "origin": "chapter", "short": "The ratio of voltage to current of a wave on the line, sqrt(L'/C') for a quasi-TEM line; mismatch to the 50 ohm source and load reduces and ripples the response.", "sources": [], "term": "Z0" } ] }