Abstract

We solve the wave equation for stimulated Raman and Brillouin scattering from Gaussian pump beams by a transformation to a system of coexpanding and contracting coordinates in which the pump beam has constant radius. The resulting equation has a quadratic potential term and is equivalent to the Schrödinger equation for a harmonic oscillator in two dimensions. If the typical gain length is small compared to the Rayleigh range of the pump, the decrease of pump intensity away from the center will lead to strong narrowing of the amplified Stokes beam. The pump intensity distribution can then be expanded to second order in the radius about the center. In this approximation the wave equation can be solved exactly by Gaussians for arbitrary Gaussian initial Stokes fields. A lowest-order mode is found whose radius is narrower than the pump radius by about the inverse fourth root of the gain. For almost all initial Gaussian fields the amplified Stokes beam develops into this stationary mode. By transforming back to laboratory coordinates simple closed-form expressions for Stokes beam divergence and apparent location of the waist are found. Results agree very well with numerical calculations and recent experimental observations.

© 1985 Optical Society of America