lithium niobate / Lab / Phase matching

Phase matching

Calculator

type 0, e + e → e; first-order and odd-order QPM

Inputsmodel P-db

Process

Model

λ fund.1.550 µm

λ2 (n/a)1.550 µm

OPO period Λ30.00 µm

Temperature21.0 °C

Length L10.0 mm

QPM order m

Duty cycle D0.50

λ sliders span 0.4 to 5 µm on a log scale; values outside the chosen model's window print a dash.

Readoutsmodel derived

λ fundamental	1.5500	µm
λ fundamental	1.5500	µm
λ second harmonic	0.7750	µm
n_e at 1, 2, 3	2.13756 2.13756 2.17837
Δk material	0.33088	rad/µm
Λ_QPM, m = 1	18.989	µm
coherence length π/\|Δk\|	9.495	µm
d_eff / d₃₃	0.637
FWHM λ_fund, L = 10.0 mm	1.176	nm
FWHM T	n/a	K
type I o+o→e angle	49.55	deg

FWHM T: model has no temperature dependence

Tuning curve, period fixedsinc²(Δk L/2)

Period curveOPO: signal and idler vs Λ

Poling period Λ: 18.99µm
Generated wavelength: 775.0nm
Coherence length: 9.49µm
Acceptance FWHM: 1.176nm

Process

Dispersion model

Status of the coefficients: P-db

Wavelengths

λ fund.1.550 µm

λ2 (n/a)1.550 µm

OPO period Λ30.00 µm

Crystal

Temperature21.0 °C

Length L10.0 mm

Duty cycle D0.50

Tuning curve at fixed period, sinc²(Δk L/2)

Period against wavelength; OPO: signal and idler against period

Wavelength sliders span 0.4 to 5 µm on a log scale; a value outside the chosen model's window prints a dash.

λ fundamental	1.5500	µm
λ fundamental	1.5500	µm
λ second harmonic	0.7750	µm
n_e at 1, 2, 3	2.13756 2.13756 2.17837
Δk material	0.33088	rad/µm
Λ_QPM, m = 1	18.989	µm
coherence length π/\|Δk\|	9.495	µm
d_eff / d₃₃	0.637
FWHM λ_fund, L = 10.0 mm	1.176	nm
FWHM T	n/a	K
type I o+o→e angle	49.55	deg

FWHM T: model has no temperature dependence

Model and sources

bulk, plane waves, no depletion

Waves 1 and 2 mix to wave 3 with 1/λ₃ = 1/λ₁ + 1/λ₂; for DFG and OPO, wave 3 is the pump. All three waves are extraordinary (polarized along z), so d₃₃ couples them; a period Λ of reversed domains adds the grating vector 2πm/Λ.

Δ k = 2 π (\frac{n_{3}}{λ_{3}} - \frac{n_{1}}{λ_{1}} - \frac{n_{2}}{λ_{2}}) - \frac{2 π m}{Λ}, d_{eff} = \frac{2}{m π} \sin (m π D) d_{33}

(1)

Output scales as sinc²(Δk L/2), which falls to one half at Δk L/2 = 1.3916. The full width in a parameter x (wavelength or temperature) follows from the local slope:

{FWHM}_{x} = \frac{2 \times 2.7831}{L | \partial Δ k / \partial x |}

(2)

The period is held fixed when temperature changes (thermal expansion of Λ not included). dn/dT from the Gayer 2008 coefficients is anomalous in magnitude or sign (MgO5: 2.65×10⁻⁴ and 1.11×10⁻⁴ /K, MgO:SLN: −7.1×10⁻⁵ /K at 1550 nm), so the temperature acceptance is not computed from them.

Dispersion models

Model	Axes	Window	Notes	Status
Zelmon 1997, congruent	o, e	0.4 to 5 µm, 21 °C	21 °C only; 0.4 to 5.0 µm	P-db
Zelmon 1997, 5 mol% MgO	o, e	0.4 to 5 µm, 21 °C	21 °C only; o and e rows of Table 2 swapped back per the 2026 erratum	P-db
Gayer 2008, 5 mol% MgO:CLN	o, e	0.5 to 4 µm, 20 to 200 °C	n_e 0.5 to 4.0 µm, 20 to 200 °C; n_o to 1.62 µm, 20 to 100 °C; dn/dT from these coefficients is anomalous	P
Gayer 2008, 1 mol% MgO:SLN	e	0.5 to 4 µm, 20 to 200 °C	n_e only; 0.5 to 4.0 µm, 20 to 200 °C; dn/dT from these coefficients is anomalous	P
Jundt 1997, congruent (n_e)	e	0.4 to 5 µm, 20 to 250 °C	n_e only; 0.4 to 5.0 µm, 20 to 250 °C; coefficients via a secondary transcription	S

Coefficients and windows: dispersion models; JSON at /api/v1/dispersion.json. Check values: Zelmon CLN, 21 °C, SHG 1064 → 532 nm needs Λ = 6.82 µm and 1550 → 775 nm needs 18.99 µm.