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Nonlinear Optics Calculator

Calculate phase-matching angles and SHG conversion efficiency for nonlinear optical crystals.

Second-harmonic generation (SHG) requires both phase matching — equalizing the phase velocities of the fundamental and harmonic beams — and sufficient nonlinear coupling to achieve useful conversion efficiency. Phase matching determines the crystal cut angle at which the ordinary and extraordinary refractive indices satisfy the momentum-conservation condition; walk-off angle and effective nonlinearity d_eff follow from that angle. The tool supports two modes: phase-matching angle calculation for BBO, KDP, KTP, and LBO using material Sellmeier coefficients, and SHG conversion efficiency estimation using the undepleted-pump approximation, including PPLN. Inputs include fundamental wavelength, phase-matching type (Type I or II), crystal length, and peak intensity. Biaxial crystals display principal indices only and flag that full optimization requires a dedicated solver.

Parameters
SHG: λ₂ = λ₁ = 1064.0 nm
λ₃ = λ₁/2 = 532.00 nm
Phase-Matching Results
Phase-matching angle θ
22.80°
Walk-off angle ρ
55.60mrad
Effective nonlinearity d_eff
2.000pm/V
SHG wavelength λ₃
532.0nm
n_o(ω)
Ordinary index at fundamental
1.6544
n_o(2ω)
Ordinary index at harmonic
1.6741
n_e(2ω)
Extraordinary index at harmonic
1.5547
Abridged Optics — Nonlinear Optics Calculator v1.0Phase matching uses Sellmeier equations for uniaxial crystals. Biaxial crystals show principal refractive indices only. SHG efficiency uses the undepleted-pump approximation.

All information, equations, and calculations have been compiled and verified to the best of our ability. For mission-critical applications, we recommend independent verification of all values. If you find an error, please let us know.