Resonant Waves in a Fabry-Perot Interferometer

Abstract

The resonant waves in a Fabry-Perot Interferometer are investigated on the basis of a standing-wave type formulation. This formulation leads to a homogeneous Fredholm integral equation whose kernel is real and symmetric when cartesian coordinates are used but it cannot be represented as a product of two uni-dependent functions. Therefore the auxiliary problem of a system of two plane parallel strip mirrors of infinite length is considered. The corresponding integral equation depends only upon one coordinate variable, but otherwise its characteristic features are identical with those ones of the equation which describes the Fabry-Perot Interferometer. The lowest-order eigenfunctions are computed by a numerical method. A model to construct the mode pattern as it is observed in a laser experiment if several eigenmodes are excited simultaneously, is suggested. A phenomenon is discussed which predicts a “doughnut”-shaped pattern. It is believed that Siegman has already observed this anomalous mode pattern in experiments with a ruby laser. An internal aperture which limits the laser action in a Fabry-Perot Interferometer does not appreciably discriminate against higher-order eigenmodes.