Stability properties of a rotating astigmatic optical cavity

We study the effects of rotation on the stability properties of an astigmatic two-mirror cavity. We show that rotation can both stabilize and destabilize a cavity and investigate the effects of such a rotationally-induced transition on the spatial structure and the orbital angular momentum of the cavity modes. Our method relies on the connection between ray and wave optics and is exact within the time-dependent paraxial approximation.