On the filamentary nature of laser action

Abstract

Many solid-state lasers show features which have not been predicted by the prevalent laser theories. The laser action in a ruby crystal usually produces a spotty pattern on the end faces, and the output exhibits relaxation oscillations in a random manner. These properties are closely connected with one another through the filamentary nature of the laser action. The theory for a Fabry-Perot interferometer with rectangular mirrors and a large Fresnel number is outlined. It is demonstrated that the observable single mode patterns are in the form of parabolic cylinder functions (Gaussian distribution of intensity for lowest-order eigenmode) and not of cosine and sine functions as is widely believed. This theoretical result predicts the filamentary nature of the laser action between plane parallel end faces and suggests that the irregular spiking behavior of a solid-state laser may be considered a superposition of outputs from several filaments. If the laser is operated only slightly above threshold the relaxation oscillations die away faster than predicted by the linearized Statz and deMars equations.