Second Harmonic Generation
χ⁽²⁾ · phase matching · frequency doubling
Physics: SHG: P^(2ω) = ε₀χ⁽²⁾E²; intensity I_2ω ∝ χ⁽²⁾²·I_ω²·L²·sinc²(ΔkL/2). Perfect phase matching (Δk=0) gives quadratic growth I_2ω ∝ L²; phase mismatch causes oscillations with period L_c = π/Δk. Birefringent phase matching (Type I: oo→e) or quasi-phase matching (QPM) via periodic domain reversal in PPLN (period Λ = 2π/Δk) corrects phase. χ⁽²⁾: LiNbO₃ ≈ 30 pm/V, BBO ≈ 2 pm/V. Green laser pointers: 1064 nm Nd:YAG doubled to 532 nm via KTP or PPLN; efficiency can exceed 50%.