Whispering-gallery laser resonators. I. Diffraction of whispering-gallery modes

Whispering-gallery optics for use at soft X-ray and extreme ultraviolet wavelengths are examined for their potential applications in laser resonators. An examination is made of beam divergence at the exit of a whispering gallery resonator. The properties of whispering-gallery eigenmodes are reviewed, and the features of their Fourier transforms discussed. The Fraunhofer approximation is then used to describe the farfield pattern resulting from the diffraction of a whispering-gallery eigenmode. Explicit formulas are given for the farfield beamwidth and the Rayleigh distance. For modes of high order the results can be understood in terms of geometrical optics.<
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