We present analytical solutions valid for large Fresnel number of the Fresnel–Kirchhoff integral equation for marginally stable resonators, for the specific case of flat circular mirrors. The asymptotic approaches used for curved mirrors have been extended to the waveguide region given by
. The resonator modes are expressed in terms of a slowly varying core term similar in form to the electromagnetic fields of a closed resonator and a small, rapidly oscillating term arising from diffraction around the mirror edge.
© 1979 Optical Society of America
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