The normal modes of infinite aperture ring lasers are Gauss Laguerre functions. The effects of finite apertures on these normal modes are not well understood. Finite mirror size distorts the eigenvectors and eigenvalues. The Huygen-Fresnel integral relates the electric field profiles before and after propagation around the cavity.
Different bases generate differing matrix representations but provide the same normal modes.
Certain bases, however, will be more convenient in certain regions of study. This project compares two bases, determined by the zeros of the Laguerre and Legendre polynomials. In order to study the distortion of the infinite aperture modes, one must somehow relate the finite aperture modes to the infinite aperture modes. One method of relating the distorted and undistorted modes will be presented.