Faraday Effect in High-$Q$ Whispering-Gallery Mode Optical Cavities

The general theory of Faraday rotation in high-
Q
whispering-gallery (WG) mode optical cavities is investigated. We have derived a matrix equation for the transmitted optical field through a WG mode optical cavity in a time-independent magnetic field. Using the corresponding mathematical framework, we have studied the behavior of the output power spectrum as a function of the magnetic field strength for a typical WG mode optical cavity. The effects of input polarization, optical quality factor, and cavity diameter on the magnetic response are studied.