BBO (Type I) SHG Reference Thickness Estimation

Brief physical logic:
1. Use the Sellmeier equations to calculate the refractive index of BBO at different wavelengths (o-ray & e-ray).
2. Use the bisection method to solve the phase-matching angle θ_rad, satisfying n_o(λ_fundamental) = n_e,eff(λ_SH, θ)。
3. Calculate the group index n_g(λ) = n(λ) - λ (dn/dλ)， for the effective index use finite differences.
4. Optimal thickness L = c·τ / |n_g,o - n_g,e,eff|， considering only group-velocity mismatch. c ~ 3×10⁸ m/s, τ is pulse duration (s).
5. The final phase-matching angle shown on this page is 90° - θ, for more intuitive comparison with practical crystal cut angles.

Fundamental wavelength (nm): Pulse width (fs):

Notes:

This is only a simplified estimate: it ignores chirp, group-velocity dispersion (GVD), nonlinear coupling, and other more complex effects.
If higher accuracy is required, use more accurate Sellmeier coefficients, include temperature and pulse-bandwidth effects, and validate with experiments or more advanced simulation tools.

BBO (Type I) SHG Reference Thickness Estimation

Results

Reference Thickness Estimation of BBO (Type I) for SHG