2.7 Waveguides in TFLN

Thin-film LN on insulator (LNOI, TFLN) is a crystalline film, 300 to 900 nm thick in one supplier's range V, bonded on a silica layer. Partial etching leaves a rib on a thinner slab: Li et al. 2026 use a 300 nm film, 120 nm slab and 3.5 µm rib reported. The mode fills a cross-section of order λ², the index contrast to the silica cladding allows tight bends, and electrodes sit micrometres from the guide (6 µm gap in Li et al. 2026 reported).

Propagation loss: 0.27 dB/cm on 4- and 6-inch wafers patterned by deep-UV lithography reported; 1.3 dB/m in dry-etched rings (intrinsic Q 29 million) reported; Q above 1e8 in chemo-mechanically polished rings reported. The material limit of annealed ion-sliced film is estimated at 0.2 dB/m (Q 1.6e8) reported.

Geometry. Film thickness t, etch depth e (slab t − e), top width w, sidewall angle; cladding air or oxide. Li et al. 2026: t = 300 nm, e = 180 nm, slab 120 nm, w = 3.5 µm, sidewall 60° (reference direction not stated), 2 µm PECVD SiO₂ cladding reported; engine n_eff = 1.7696, n_g = 2.135 at 1550 nm engine.

x-cut vs z-cut

Indices: Zelmon Sellmeier, congruent LN, 21 °C. Coefficient mapping: 2.2 (r tensor) and 2.3 (d tensor).

Anisotropy around a ring (x-cut, bulk approximation). For TE propagating at angle φ from crystal z within the film plane, the in-plane polarization sees

varying between n_e (propagation along y) and n_o (propagation along z): 2.1376 to 2.2111 at 1550 nm derived, mode confinement ignored. The local phase velocity, the QPM condition and the r₃₃ projection all vary twice per round trip.

Mode hybridization. Where a TE and a TM mode of the same waveguide would cross in n_eff, any broken symmetry (slanted sidewalls, a slab on one side, an off-axis crystal orientation) couples them into hybrid modes with an anticrossing (hybridization). In TFLN ridges this affects even the fundamental modes (Pan et al. 2019). In x-cut strip waveguides the hybrid regions depend on dimensions, sidewall angle and wavelength, and tapers through them convert TM0 to higher-order TE (99.5%, numerical) reported. In x-cut microrings the rotating birefringence converts TE to TM and creates avoided mode crossings that suppress one four-wave-mixing sideband reported. Arrayed-waveguide gratings need anisotropy-aware layouts (Wang 2024).

Loss and Q.

At 1550 nm with n_g = 2.3 template: Q_i = 1e7 → 4.05 dB/m; 2.9e7 → 1.40 dB/m; 1.6e8 → 0.25 dB/m derived. Published conversions use each device's own n_g (e.g. 1.3 dB/m for Q_i 29 million reported).

Loss and Q records

1e−4 /cm = 0.043 dB/m. Q-only rows are plotted as upper bounds on loss at n_g = 2.3, 1550 nm.

Loss mechanisms

• Sidewall and top-surface roughness scattering, set by lithography and Ar⁺ milling (redeposition: chapter 05).
• Material absorption: transition-metal impurities give up to 0.04 /cm in as-grown crystals, H-related bands about 0.001 /cm at 2300 to 2800 nm; annealing lowers absorption up to 10× P. Ion-slicing damage: post-fabrication annealing raises the material-limited Q (Shams-Ansari et al. 2022).
• Cladding absorption in the mid-IR: silica absorbs beyond 2.5 µm, which motivates LN on sapphire reported.
• Bend radiation and substrate leakage (slab modes, thin buried oxide).
• Metal absorption where electrodes approach the mode; Li et al. 2026 attribute their 2.8 dB on-chip loss to splitters, propagation and electrode absorption reported.
• Photorefractive and charge effects at high power (chapter 04); removing the dielectric cladding mitigates photorefraction in rings reported.

Computing modes

Full-vector finite-element method (FEM) with the anisotropic permittivity rotated into the lab frame (x lateral, y vertical, z propagation; x-cut with propagation along crystal y puts crystal z along lab x) (eo-modulator-atlas engine). A scalar or effective-index solver is wrong for high-contrast anisotropic ribs. The n_eff 1.7696 and n_g 2.135 engine of the Li et al. 2026 rib come from this solver.

Measuring loss

Ring transmission fits give loaded Q and, with the coupling regime identified (under- vs overcoupled), intrinsic Q; conversion to dB/m needs n_g from the measured FSR:

Cut-back measurements separate propagation from facet loss but need many lengths for sub-dB/cm accuracy.

Errors

Bulk Zelmon indices at 21 °C stand in for film indices; ion-sliced and annealed films may differ (composition, residual strain, Li out-diffusion: chapters 01, 05). Film-thickness nonuniformity across a wafer moves n_eff and therefore the QPM wavelength (2.3) and ring resonances. Real x-cut ring modes need an azimuthal treatment of the confined mode; the ring index above is the bulk indicatrix projection.