Coupled-mode theory of diffraction-induced transverse effects in nonlinear optical resonators

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Abstract
We develop a one-dimensional theory of diffraction-induced transverse effects in nonlinear Fabry-Pérot resonators addressed by finite-width incident beams. This is achieved in the framework of the coupled-mode analysis, which takes full advantage of the fact that nonlinear Fabry-Pérot devices are resonant. As compared with a recently published theory dealing with the same subject [M. Haelterman, Opt. Commun. 75, 165 (1990); M. Haelterman, G. Vitrant, and R. Reinisch, J. Opt. Soc. Am. B 7, 1309 (1990); and G. Vitrant, M. Haelterman, and R. Reinisch, ibid. 7, 1319 (1990)], where the nonlinearity is introduced in an approximate way, the formalism developed here takes the nonlinearity associated with the optical Kerr effect rigorously into account. This feature has an important consequence: It leads to a theory that can be generalized to the TM case and also to anisotropic nonlinear media. The theory presented here is valid for any value of the angle of incidence. Under normal (or quasinormal) incidence, two counterpropagating modes, having the same absolute value of the wave-vector component parallel to the plane of the mirrors, are resonantly (or nearly resonantly) excited, whereas under oblique incidence, only one of these modes is excited.