Theory of a lossless nonlinear Fabry-Perot interferometer

A Fabry-Perot interferometer filled with a medium whose refractive index depends upon intensity has a multiple-valued transmission-vs-intensity characteristic. When the incident light is circularly polarized, and the nonlinearity is only cubic in the fields, Maxwell's equations may be solved exactly for the plane-parallel resonator field in terms of elliptic functions. An accurate approximate analysis is given for more general cases, including resonators with spherical mirrors and finite beams, where self-focusing is important. The theory is developed to yield design information for operation as an optical switch, "transistor," and power limiter.