Production and propagation of cylindrically polarized Laguerre–Gaussian laser beams

The x-polarized and y-polarized beam modes of simple confining circularly symmetric spherical-mirror laser resonators may be represented with Laguerre–Gaussian functions. The corresponding r- and ϕ-polarized beam-mode profiles are found to be represented by a different Laguerre–Gaussian mode set. Though similar in name, these cylindrically polarized modes are fundamentally different from their rectangularly polarized counterparts. For example, the fundamental x-polarized mode is Gaussian, which has a maximum at the center of the beam, while the fundamental ϕ-polarized mode has a null at the beam center. The complete propagation characteristics of several types of azimuthally polarized Laguerre–Gaussian beams through optical systems representable by complex ABCD matrices are obtained. Cylindrically polarized Laguerre–Gaussian beams may be produced by inserting the appropriate Brewster window into a simple confining circularly symmetric laser resonator.