Second Harmonic Generation

Second harmonic generation: in non-centrosymmetric crystals (KTP, BBO, LiNbO₃), the χ² polarization P = ε₀χ²E² creates new frequency 2ω from ω.

Phase matching (Δk = 0) is critical — SHG builds coherently only when the pump and harmonic travel in phase. Off-resonance, conversion oscillates with crystal length (sinc² dependence).

Coupled wave equations:
dA₁/dz = -iγA₁*A₂e^{-iΔkz}
dA₂/dz = -iγA₁²e^{+iΔkz}