Multimode Resonators with a Small Fresnel Number (Lowest-Order Eigenmodes)

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Abstract
The Fabry-Pèrot Interferometer, the confocal and the spherical resonator systems are investigated. The lowest-order traveling-wave type eigenmodes are calculated. Numerical values for the diffraction losses are given. The smallest diffraction losses are obtained for the general-type eigenmode of a confocal resonator system. The eigenfunctions of an open-walled resonator show a point of inflection as their characteristic feature. They are complex if the Fresnel Number is finite. When calculate over appropriate surfaces, their imaginary part, in the region close to the axis, decreases as F increases. In that region the waves resonate between the reflectors. Towards the rim of the system the imaginary part increases rapidly as do the diffracted waves associated with the imaginary part.

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