Second-Harmonic Generation & Phase Matching

Second-harmonic generation (SHG) is the textbook example of nonlinear optics: an intense beam passing through a crystal with second-order susceptibility χ² partly converts into light at exactly twice its frequency — the mechanism behind every green laser pointer, which doubles a 1064 nm infrared Nd:YAG beam into 532 nm green. This simulator renders a real 3D beam propagating through a nonlinear crystal and numerically tracks the coupled-wave conversion efficiency along its length, using the exact tanh² saturation solution at perfect phase matching and the sinc² interference pattern that appears the moment the fundamental and second-harmonic wavevectors fall out of step. Sliders for pump strength, crystal length and phase mismatch let you watch the beam color shift from red toward green, observe conversion saturate or oscillate, and read off the coherence length that sets how precisely a real crystal must be angle- or temperature-tuned.