Chester A N
Appl Opt. 1972 Nov 1;11(11):2584-90. doi: 10.1364/AO.11.002584.
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.
众所周知，使用大输出耦合和大菲涅耳数操作可以实现不稳定激光谐振器的单横模操作。然而，尚未认识到可用菲涅耳数存在上限，该上限由诸如镜面对准稳定性等效应决定。我们使用祖克获得的模式解分析了可变反射率不稳定谐振器。如果要实现单模操作，最低阶模式之间的差分损耗会导致菲涅耳数和输出耦合的条件。通过微扰分析扩展了祖克解，以研究镜面未对准引起的模式畸变。激光输出远场中的轴上强度显示为镜面未对准的敏感函数，并且允许的镜面对准公差与菲涅耳数成反比。在实际中，这对可用菲涅耳数设置了上限。该理论结果与使用不稳定谐振器的激光实验一致。
