Laser Resonator Studies.

The goal of the study was to find a hole-coupled resonator with good azimuthal mode discrimination for potential uses in high power laser applications. Two computer programs were developed to aid in the Analysis of hole-coupled resonators. The first program calculates the scalar eigenmodes, of circular cylindrical resonators with exp or - jl times phi where l is an integer azimuthal variaton and arbitrary radical mirror figure. Graphs of the radial mode eigenvalues versus Fresnel number for the four lowest order azimuthal modes revealed that typically, the larger the hole becomes in a hole-coupled resonator, the higher the azimuthal index of the dominant lowest loss mode media gain saturation not included. The lowest order azimuthal mode losses were almost identical in one negative branch toroidal hole-coupled resonator and in a positive branch resonator where both mirrors had on-axis holes. The second computer program calculates the radial mirror profiles by a non-linear multiple regression technique such that the eigenmode mangitude andor phase profiles are best, least squares, fits to use specified radial mode profiles. Tests showed, for example, that a field, uniform magnitude and phase, could be achieved in the hole for l 0 of a hole-coupled resonator. In most instances however the l 0 mode was not the dominant arbitrary azimuthal field variation so that best fits to desired azimuthal is designed for the lowest loss mode. Author