Huygens' principle in inhomogeneous, isotropic media and a general integral equation applicable to optical resonators

Huygens' principle is derived for short wavelengths in inhomogeneous, isotropic media from considerations of Green's second theorem and the solution to the time-independent wave-equation for a point-source in an inhomogeneous, isotropic medium. This principle leads to an integral equation for the field distribution on optical resonator mirrors, whose parameters depend only upon the geometrical-optics ABCD-matrices. The resonator parametersF, G1,G2, the resonance and stability conditions as well as the spot size of the fundamental mode at the mirrors are given as functions of A, B, C, D, for the special case of a rotationally symmetric optical system between square mirrors. The resonator parameters,F, G1,G2, are calculated by this new method for a case familiar from the literature.