In this paper, mode patterns and losses are determined for unstable laser resonators with finite, rectangular reflectors of spherical curvature. An analysis of the uniform intensity mode, based upon the Cornu spiral is given. For more general calculations, gaussian quadrature integration is used to convert the integral equation for the modes into a matrix equation. The latter is solved using ALLMAT on a digital computer, thereby simultaneously determining many modes. The mode competition effect reported by Siegman and Arrathoon is shown to occur because the unstable modes do not generally retain their ordering, according to relative loss, as the reflector size changes. We also discuss a perturbation calculation in which the infinite mirror solutions of Bergstein are used as expansion functions.
© 1969 Optical Society of America
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