Laser mode analysis

A new integral equation for optical resonators was derived from the boundary value problem. This equation, called the Source Integral Equation (SIE) was solved approximately and mode shapes compared with those from the widely used Fox-Li Integral Equation (FLIE). A double resonance condition was obtained from a self-consistency condition. Approximations to the resonance condition was 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 the 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 and the FLIE.