Mode Analysis in a Misaligned Unstable Resonator

摘要

The integral equation that describes mode structure of an unstable resonator with rectangular apertures is developed from scalar diffraction theory. This equation, modified to account for misalignments, is solved by applying the asymptotic methods developed by Horowitz. A second order approximation of the method of stationary phase is then employed to calculate phase and intensity values for all points in the output plane. The phase front is also curve fitted to a straight line over the geometrical region for the lowest loss mode. From the slope of the straight line, a direction of propagation can be attributed to the wave. This is a diffracted beam steering angle and is additional to the geometric steering angle (i.e., the beam steering angle due to the geometric misalignment of either or both mirrors). Plots of intensity and phase for various degrees of misalignments are presented as results of a computer program that utilizes the derived expressions. Also included are graphs of the phase slope versus mirror misalignment. (Author)