Effect of Gaussian Beam Spread on Phase Velocity Matching in cw Optical Second-Harmonic Generation

This paper reports the results of an experimental and theoretical study of the angular variation of optical second-harmonic generation in ammonium dihydrogen phosphate using a Gaussian single-transverse-mode cw gas-laser beam. The observed angular dependence of the second-harmonic output near the phase matching angle is significantly different from the ${\left[\frac{\left(sin\psi \right)}{\psi }\right]}^2$ angular dependence predicted by plane-wave theory. The difference can be quantitatively explained by an extended analysis which takes into account the Gaussian amplitude distribution and spherical wavefront of the cw laser beam. The theory predicts small but significant corrections to the results of measurements of the nonlinear coefficients of materials. These corrections can also account, at least approximately, for the effects of small crystal defects and imperfectly Gaussian beam patterns.