Abstract

We examine the wave equation for an open resonator with flat mirrors in the case in which it is driven by a nonlinear gain term and formulate an integral equation from first principles. The eigenvalues and eigenfunctions of such a resonator equation may be obtained in the limit in which the nonlinear susceptibility is small or has a weak transverse dependence. In particular, we find that for the loaded cavity, the losses and eigenfunctions (modes) may be obtained by solving a linear Fresnel–Kirchhoff integral equation with gain-renormalized eigenvalue and Fresnel number. Relations are presented that may be used to predict for which conditions the effects of gain significantly change the modes from those of an empty resonator.

© 1980 Optical Society of America

Analytic variational method for determining the modes of marginally stable resonators

J. Nagel and D. Rogovin
J. Opt. Soc. Am. 70(12) 1525-1538 (1980)

Asymptotic approaches to marginally stable resonators

J. Nagel, D. Rogovin, P. Avizonis, and R. Butts
Opt. Lett. 4(9) 300-302 (1979)

Resonator studies with the Gardner–Fresnel–Kirchhoff propagator

W. P. Latham and T. C. Salvi
Opt. Lett. 5(6) 219-221 (1980)

Gaussian modes of resonators containing saturable gain medium

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Synthesis of the vector resonator modes from scalar results

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