Closed-form solutions for the propagation of Gaussian beams in multiple-element optics. Optical elements include lenses, lens arrays, prisms, prism arrays, reflection gratings, transmission gratings, mirrors, and optical slabs, or a combinations of these elements. Analyses can be made in either single-pass or multiple-pass configurations. Price depends on complexity of the optical array and on the required beam pass configuration.

Note: this is a typical multiple-element intracavity optics array for which propagation matrices can be derived as explained in F. J. Duarte, Tunable Laser Optics, 2nd Edition (CRC, New York, 2015) (see Chapter 6). In this particular case the elements considered in the matrix calculations are the grating, the multiple-prism array, the gain medium, the output coupler, and the spaces between the elements. This particular narrow-linewidth oscillator was disclosed in F. J. Duarte et al., Long pulse narrow-linewidth dispersive solid-state dye-laser oscillator, Appl. Opt. 37, 3987-3989 (1998).