Bowers M S
Appl Opt. 1992 Mar 20;31(9):1185-98. doi: 10.1364/AO.31.001185.
It is shown numerically that the diffractive transverse (Fox-Li) eigenmodes supported by an unstable cavity with tilted end mirrors can be computed by expanding these modes in terms of the fully aligned (aberration-free) eigenmodes of the same cavity. Circular mirror resonators are considered in which the aligned cavity eigenmodes can be decomposed into different azimuthal components. The biorthogonality property of the aligned cavity eigenmodes is used to obtain the coefficients in the modal expansion of the misaligned modes. Results are given for two different resonators: a conventional hard-edge unstable cavity with a small tilt of the output coupler and one that uses a graded reflectivity output mirror with a small tilt of the primary mirror. It is shown that the series expansion of the misaligned modes in terms of the aligned modes converges, and the converged eigenvalues are virtually identical to those computed by using the Prony method. Symmetry considerations and other new insights into the effects of a mirror tilt on the modes of a resonator are also discussed.
数值结果表明，对于由具有倾斜端镜的不稳定腔所支持的衍射横向（福克斯 - 李）本征模，可以通过将这些模式按照同一腔的完全对准（无像差）本征模展开来进行计算。考虑了圆形镜谐振腔，其中对准的腔本征模可分解为不同的方位角分量。利用对准腔本征模的双正交性来获得未对准模式的模态展开系数。给出了两种不同谐振腔的结果：一种是输出耦合器有小倾斜的传统硬边不稳定腔，另一种是主镜有小倾斜的渐变反射率输出镜的谐振腔。结果表明，未对准模式按照对准模式的级数展开是收敛的，并且收敛后的本征值与使用 Prony 方法计算得到的本征值几乎相同。还讨论了对称性考虑以及关于镜倾斜对谐振腔模式影响的其他新见解。
