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 θrad, satisfying no(λfundamental) = ne,eff(λSH, θ)。
3. Calculate the group index ng(λ) = n(λ) - λ (dn/dλ)， for the effective index use finite differences.
4. Optimal thickness L = c·τ / |ng,o - ng,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.

Notes:

  1. This is only a simplified estimate: it ignores chirp, group-velocity dispersion (GVD), nonlinear coupling, and other more complex effects.
  2. 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.