Vector modes of lasers with radially birefringent elements

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.