Generalized Sagnac Effect in Rotating Optical Cavities

We study the effect of rotation on resonances of an optical cavity in an accelerated frame of reference. We show that, even when the resonant modes of an optical cavity are wave-chaotic, degenerate resonant frequency of those modes split into different frequencies due to the rotation of the cavity. The frequency difference is proportional to the rotation rate, although the splitting resonant modes are still wave-chaotic, which do not have any corresponding counter-propagating waves as well as ray-dynamical counterparts.