Abstract
An investigation of rectangular resonators with a view to the compensation of astigmatism has been performed. In order to have beam waists placed at the same positions in the tangential and sagittal planes, pairs of equal mirrors were considered. It was found that at least two concave mirrors are necessary to obtain compensation. Four-concave-mirror systems are most stable close to the quadratic geometry, although the symmetric quadratic resonator itself cannot be compensated for astigmatism. Using four equal concave mirrors, compensation of astigmatism can be obtained in two arms at the same time. Usually several stability ranges are found for four-mirror resonators with pair-wise equal mirrors, and it is possible with these systems to obtain small compensated beam waist radii suitable for frequency conversion. Relevant formulae are given and several relevant examples are shown using simulation software.
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