Effects of finite apertures on transverse eigenmodes of optical resonators

We examine the properties of the transverse eigenmodes of optical resonator s containing a hard aperture. We show that for orthogonal optics and arbitr ary aperture shape, the trace of the ray matrix and the scaled aperture siz e determine the major properties of interest: loss, frequency, and distorti on that is due to diffraction. We discuss three different methods of reduci ng the Huygen-Fresnel integral equation to a matrix equation whose eigenval ues and eigenvectors can be easily found. The dependence of loss, frequency , distortion, and required matrix order on cavity parameters is presented f or cylindrically symmetrical resonators. We show that undiffracted modes in adequately approximate the actual modes in nearly unstable cavities. (C) 19 99 Optical Society of America [S0740-3232(99)02311-X].