Laser cavities bounded by crossed cylindrical mirrors

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Abstract
A four-parameter family of anisotropic Gaussian beams is presented as exact solutions to the paraxial wave equation. These beams are shown to be the fundamental resonant modes of laser cavities bounded by crossed cylindrical mirrors. Explicit expressions for the beam parameters are given in terms of the resonator parameters. Propagation characteristics of these beams are analyzed; it is shown that there are two transverse planes where the intensity distribution is rotationally invariant about the beam axis and two planes where the phase front is spherical. As a consequence we show that the symmetric confocal resonator bounded by spherical mirrors has a two-parameter family of degenerate anisotropic Gaussian beams, rather than a unique Gaussian beam, as its fundamental resonant modes. The connection of this result with the results of Boyd and Gordon [Bell Syst. Tech. J. 40, 489 (1961)] is established.

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