Mode behavior in laser resonators with zones of different indices of refraction

Laser resonators naturally contain zones of different indices of refraction. By investigating the propagation of Gaussian beams through plane stratified slabs, the transverse- and longitudinal-mode equations for laser resonators can be derived. Equivalent lengths, equivalent radii of curvature, and the equivalent g parameters are defined. The results are markedly different from those given by using the optical equivalent length, i.e., the sum of the product of the individual slab thicknesses and their respective indices of refraction. The effective cavity length associated with transverse-mode phenomena is shorter than the vacuum length.