Fabry-Perot resonators in uniaxially anisotropic media

This paper investigates the resonant modes of Fabry-Perot interferometers with end reflectors embedded in linear, homogeneous, uniaxially anisotropic media. It is shown that for almost all practical cases the resonant modes consist of transverse electric (TE) modes and transverse magnetic (TM) modes relative to the direction of the optic axis in the medium. Two distinct integral equations are derived which together with Maxwell's equations are sufficient to perform a detailed analysis of these modes. However, since the results of the analysis of Fabry-Perot resonators in isotropic regions are available and well understood, the approach of the paper is to reduce a given "anisotropic resonator" to two corresponding equivalent "isotropic resonators": one for determining the TE modes and the other for determining the TM modes. The equivalent isotropic resonator for the TE modes has the same geometry as the actual resonator in the anisotropic medium. The geometry of the equivalent isotropic resonator for the TM modes is derivable in a very simple manner from the geometry of the actual resonator in the anisotropic medium and from the specified orientation of the direction of the optic axis in the medium. The well-known results for resonators embedded in isotropic media may henceforth be applied to determine the resonant modes of the anisotropic resonator.