The numerical technique of Fox and Li for computing laser resonator modes is applied to the case of three-dimensional laser resonators without circular or rectangular symmetries. The computation techniques are explained, and results are presented for several specific resonators, both stable and unstable. The effect of laser medium shock waves on the refractive index of the optical cavity is approximated by a thin sheet near one resonator mirror. The near-field burn pattern of the laser output beam exactly follows the phase pattern of the shock fronts, in good qualitative agreement with experimental results reported for gas dynamic lasers. The far-field output beam demonstrates pronounced astigmatism, being considerably broadened at right angles to the flow direction, and it suggests a breakup of the far-field pattern into several separate intensity spots. The optical phase of the resonator mode is quite smooth, even in the worst cases studied, suggesting the possibility of phase compensation by suitable optics.
Arthur N. Chester, "Three-Dimensional Diffraction Calculations of Laser Resonator Modes," Appl. Opt. 12, 2353-2366 (1973)