Integral Equations and Functional Methods for Laser Mode Profiles.

摘要

A new integral equation for optical resonators has been derived from the boundary value problem. This equation, called the Source Integral Equation (SIE), has been solved approximately and mode shapes compared with those from the widely used Fox-Li Integral Equation (FLIE). A double resonance condition (constraints on both mirror separation and transverse dimension) has been obtained from a self-consistency condition. Approximations to the resonance condition have been devised for the limiting case of flat mirrors. The results obtained from a Functional Equation Method (FEM) are compared with traditional computer solutions. The locations of the peaks and valleys agree well and the overall mode shapes are similar. This verifies the utility of the FEM for spherical mirrors of circular aperture. The FLIE and SIE results from the FEM, are compared to confirm the validity of the FEM approach for the SIE. The SIE results are compared to the traditional computer results to find effects of the corrections of the SIE to the FLIE. (Author)