Second Harmonic Generation Efficiency Guide
Second harmonic generation turns two photons at a fundamental frequency into one photon at twice that frequency. The process needs a nonlinear crystal, strong optical intensity, and good phase matching. This calculator combines measured data with a plane wave estimate, so it supports laboratory checks and early design work.
Why Efficiency Matters
Efficiency tells how much input power becomes the new color. A small change in waist, length, or mismatch can change output strongly. The result helps compare crystals, coatings, focusing plans, and alignment quality. It also flags unrealistic expectations before hardware is built.
Main Inputs
The fundamental power drives the nonlinear interaction. Crystal length sets the interaction distance. The effective nonlinear coefficient represents material strength and polarization choice. Refractive indices describe propagation at both wavelengths. Beam waist estimates optical area. Phase mismatch controls coherent buildup. Loss values reduce the useful interaction length.
Interpreting Results
Measured efficiency is the ratio of generated harmonic power to fundamental power. The theoretical estimate uses a simplified undepleted pump model. It assumes low conversion, stable beam overlap, and constant material properties. Pulsed mode converts average power into approximate peak power. This can reveal why short pulses produce high harmonic output.
Phase Matching
The sinc squared term shows the cost of phase error. When mismatch is zero, waves add coherently through the crystal. When mismatch grows, generated fields cancel partly. The coherence length shows the distance over which phase slips by pi radians. It is useful for choosing crystal temperature, angle, or poling period.
Practical Notes
Real systems may differ from the estimate. Walk off, absorption, thermal lensing, pump depletion, spectral bandwidth, coating loss, and imperfect focusing all matter. Treat the theoretical value as a guide, not a guarantee. Compare it with measured efficiency to understand alignment and crystal quality.
Best Use
Start with manufacturer values for the nonlinear coefficient and indices. Enter measured power after accounting for filters and detector calibration. Test several beam waists and lengths. Keep the overlap factor below one when mode quality is poor. Use the exported data to document each design iteration. Repeat calculations after every alignment change. Record temperature, wavelength, and polarization. These notes make future comparisons easier and prevent confusing setup drift with material limits during testing.