Production and propagation of Hermite–sinusoidal-Gaussian laser beams

Abstract

Hermite–sinusoidal-Gaussian solutions to the wave equation have recently been obtained. In the limit of large Hermite–Gaussian beam size, the sinusoidal factors are dominant and reduce to the conventional modes of a rectangular waveguide. In the opposite limit the beams reduce to the familiar Hermite–Gaussian form. The propagation of these beams is examined in detail, and resonators are designed that will produce them. As an example, a special resonator is designed to produce hyperbolic-sine-Gaussian beams. This ring resonator contains a hyperbolic-cosine-Gaussian apodized aperture. The beam mode has finite energy and is perturbation stable.