Nonlinear optics describes the interaction of intense light with matter, where the polarization response becomes nonlinear, leading to phenomena such as second-harmonic generation (SHG), sum-frequency mixing, and optical parametric oscillation (OPO). Practical implementation of these effects requires precise phase matching in birefringent crystals. This essay explores the fundamental theory of nonlinear frequency conversion, details the critical parameters of common nonlinear crystals (β-BaB₂O₄, LiNbO₃, KTiOPO₄), and provides step-by-step examples using —a free software package from Sandia National Laboratories—to model realistic conversion efficiencies and tolerances.
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