Optical-axis perturbation singularity in an out-of-plane ring resonator

I use a matrix approach to determine the optical-axis perturbation sensitivity of an out-of-plane stable ring resonator. It is found to have a singularity for certain design parameters. On one side of the singularity the cavity behaves abnormally: the longer the mirror radius, the larger the mode volume and, surprisingly, the less the perturbation sensitivity. This is opposite the behavior of conventional stable resonators, a finding that is important to the cavity designs of out-of-plane ring lasers.