Last updated: May 2026. All SNLO examples verified against version 2023.1.
OPA / OPO threshold and gain
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Crystal nonlinear optics studies how electromagnetic waves interact in nonlinear crystalline media to produce new frequencies, mix signals, or alter beam properties. Nonlinear effects arise when the material polarization P responds nonlinearly to the electric field E:
Example (BBO SHG, ( w_0 = 100 ) μm, ( \rho = 3.5^\circ ) ≈ 61 mrad): [ L_a \approx \frac1.77 \times 0.01 \text cm0.061 \approx 0.29 \text cm ] So longer crystals yield little gain beyond ~3 mm. SNLO plots this explicitly.
The induced polarization is expanded as: [ P(t) = \varepsilon_0 \left( \chi^(1) E(t) + \chi^(2) E^2(t) + \chi^(3) E^3(t) + \dots \right) ] For second-order (( \chi^(2) )) processes—relevant to most frequency conversion crystals—the material must lack inversion symmetry. Common crystals include .
(originally written by Arlee Smith at Sandia National Laboratories, now maintained by AS-Photonics) is a freeware Windows application that performs numerical analysis of nonlinear optical interactions. It includes:
