Ray method for unstable resonators

The previously developed ray-optical method for unstable, symmetric, bare resonators with sharp-edged stop and circular mirrors is reviewed here. A deductive stepwise procedure is presented, with emphasis on the physical implications. It is shown how the method can accommodate other edge configurations such as those produced by rounding, and also more complicated nonaxial structures such as the half-symmetric resonator with internal axicon. For the latter, the ray approach categorizes those rays that must be eliminated from the equivalent aligned unfolded symmetric resonator, and it identifies the canonical diffraction problems that must be addressed to account for shadowing and scattering due to the axicon tip. Effects due to shielding or truncation of the axicon tip are also considered. Approximate calculations of the eigenvalues for the lowest-loss modes illustrate the effects due to various tip shielding lengths and spacings of the axicon from the output mirror.