Laser resonators containing self-focusing elements

Laser resonators containing self-focusing elements are described using the matrix formalism appropriate for Gaussian beams. The laser rods are not approximated by traditional optical elements but treated as thick materials showing a radial quadratic dependence of their refractive index. Cavities incorporating an arbitrary number of lenses, mirrors, and crystals (including rods with spherical endfaces) are described with no restriction on the value of the pump power. Stability domains and beam size in the resonator and inside the rods are calculated. A few experimental tests with Nd:YAP lasers are presented.