Unstable resonator with aspherical mirrors

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Abstract
The geometric analysis of unstable optical resonators is extended to include mirrors with aspherical surfaces. This leads to a functional equation for the wave front of the geometric mode in terms of the mirror surface figures. In an example case, a solution is obtained for the aspherical feedback mirror required to produce a desired asphericaloutput wave front, and the equivalent Fresnel number is calculated as a function of mirror aperture. Various possible uses of aspherical mirrors in unstable resonators are suggested.

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