Matrix formalism for dispersive laser cavities

A matrix formalism for dispersive optical elements is applied to the study of laser cavities with dispersive elements such as gratings or prisms. The formalism consists of 3×3 matrices describing each element with complex coefficients to account for loss or gain. It is shown how to determine the frequency dependence of the beam center, propagation angle, gain, and transit time delay. In this manner, the linewidth selectivity, cavity group velocity dispersion, output spectral angular dispersion, and transverse walkoff of any arbitrary design can be determined