Ferguson T R
Appl Opt. 1995 Jul 20;34(21):4210-6. doi: 10.1364/AO.34.004210.
A general theory of steady-state diffractive vector modes for lasers with polarizing optical elements is reviewed. The problems inherent in including radially birefringent media such as solid-state rods are emphasized. A trade-off between ease of implementation, ease of interpretation, and cost of computation arises from the choices of representations of the field. In the scalar theory for axisymmetric resonators, the polar representation with expansion of the field in azimuthal Fourier series yields separation into an integral equation for each azimuthal index. A theoretical investigation of this approach for the vector case is presented. For a simple resonator composed of two mirrors and a bifocal lens, separation into coupled pairs of integral equations is obtained. Numerical solutions that use fast Hankel transforms from scalar theory are straightforward. Complications arise when other optical elements are introduced into the resonator. Methods for handling the general case are discussed.
回顾了具有偏振光学元件的激光器的稳态衍射矢量模式的一般理论。强调了包含诸如固态棒之类的径向双折射介质所固有的问题。场表示的选择导致了在易于实现、易于解释和计算成本之间的权衡。在轴对称谐振器的标量理论中，用场在方位角傅里叶级数中的展开的极坐标表示会分离为每个方位角指数的积分方程。给出了针对矢量情况的这种方法的理论研究。对于由两个反射镜和一个双焦透镜组成的简单谐振器，可得到分离为耦合的积分方程对。使用标量理论中的快速汉克尔变换的数值解很直接。当将其他光学元件引入谐振器时会出现复杂情况。讨论了处理一般情况的方法。
