[ n_e(\theta) = \left( \frac\cos^2\thetan_o^2 + \frac\sin^2\thetan_e^2 \right)^-1/2 ]
The phase matching condition ( n_e(\omega_3, \theta) = n_o(\omega_1) ) for Type I SHG determines the angle ( \theta_pm ). crystal nonlinear optics with snlo examples pdf
Biaxial crystals (e.g., KTP) require more complex principal plane calculations, but SNLO handles these automatically. | Crystal | Transparency (μm) | ( d_eff ) (pm/V) | Damage Threshold (GW/cm²) | Typical Use | |---------|------------------|----------------------|---------------------------|--------------| | BBO (β-BaB₂O₄) | 0.19–3.5 | ~2.0 (Type I SHG 1064→532) | ~10 (ns pulses) | UV generation, OPO | | LiNbO₃ (congruent) | 0.4–5.0 | ~4.5 (Type I) | ~0.1 (CW), ~10 (pulsed) | Telecom OPO, SHG | | KTP (KTiOPO₄) | 0.35–4.5 | ~3.6 (Type II 1064→532) | ~0.5 (ns) | High-power green lasers | ~10 (pulsed) | Telecom OPO
[ \eta = \frac2\omega^2 d_eff^2 L^2 In^3 \epsilon_0 c^3 \textsinc^2(\Delta k L / 2) ] crystal nonlinear optics with snlo examples pdf