Mode selectivity and mirror misalignment effects in unstable laser resonators

It is known that single transverse mode operation of an unstable laser resonator can be achieved using large output coupling and large Fresnel number operation. However, it has not been recognized that there is an upper limit on usable Fresnel number, determined by such effects as mirror alignment stability. We have analyzed a variable-reflectivity unstable resonator using mode solutions obtained by Zucker. The differential loss between the lowest order modes leads to conditions on the Fresnel number and the output coupling if single mode operation is to be realized. The Zucker solution is extended by a perturbation analysis to examine mode distortion caused by mirror misalignment. The on-axis intensity in the far field of the laser output is shown to be a sensitive function of mirror misalignment, and the mirror alignment tolerance permitted varies inversely as the Fresnel number. In practice, this places an upper limit on the usable Fresnel number. The results of this theory are shown to be consistent with laser experiments using unstable resonators.