Kahn W K
Polytechnic Institute of Brooklyn, Brooklyn, New York, USA.
Appl Opt. 1966 Mar 1;5(3):407-13. doi: 10.1364/AO.5.000407.
A technique, firmly based on a development from ray optics, is presented for calculating the loss due to the finite sizes of curved mirrors when these form an unstable optical resonator. If paraxial rays launched within such a resonator are confined near the resonator axis, the resonator is termed stable; otherwise it is termed unstable, and is known to have high losses. Siegman has recently presented a geometrical method, brilliantly constructed ad hoc, for calculating these losses in unstable resonators, and indicated where these might be advantageous in laser application. The ray optical theory presented here, which employs the concept of ray modes in an equivalent beam waveguide, is shown to yield results equivalent to those of Siegman for all cases considered by him. However, being derived from conventional ray optics, the validity of the formulas is independently established, and these formulas are immediately applicable to re-entrant resonators and resonators containing inhomogeneous media. The fractional loss per resonator pass is equal to 1-|lambda(2)|, where |lambda(2)| < this 1 is an eigenvalue of the transfer matrix T, representing the corresponding ray transformation.
本文提出了一种基于光线光学发展而来的技术，用于计算当曲面镜构成不稳定光学谐振腔时，由于其有限尺寸所导致的损耗。如果在这样一个谐振腔内发射的傍轴光线被限制在谐振腔轴附近，那么该谐振腔被称为稳定的；否则它被称为不稳定的，并且已知具有高损耗。西格曼最近提出了一种专门巧妙构建的几何方法，用于计算不稳定谐振腔中的这些损耗，并指出了它们在激光应用中可能具有优势的地方。这里提出的光线光学理论，在等效光束波导中采用了光线模式的概念，结果表明，对于西格曼所考虑的所有情况，该理论得出的结果与他的结果等效。然而，由于该理论是从传统光线光学推导而来，其公式的有效性是独立确立的，并且这些公式可立即应用于重入式谐振腔和包含非均匀介质的谐振腔。每个谐振腔单程的分数损耗等于1 - |λ(2)|，其中|λ(2)| < 1是表示相应光线变换的传输矩阵T的一个本征值。
