MAXWELL EQUATIONS IN A NONLINEAR KERR MEDIUM

In this paper we present an exact calculation of the transfer function associated with the nonlinear Fabry-Perot resonator. While our exact result cannot be evaluated in terms of elementary functions, it does p ermit us to obtain a number of simple approximate expressions of vario us orders of accuracy. In addition, our derivation yields criteria of validity for the approximate formulae. Our approach is to be compared with others in which approximations are introduced in the model itself , either through the equations or through the boundary conditions. Our lowest order approximate formula turns out to be identical, interesti ngly, with the result obtained from the slowly varying envelope approx imation (SVEA). Thus, our validity criteria apply to the SVEA result, and predict well its domain of validity and its breakdown for short wa velengths and for very high intensities and nonlinearities. The simple higher order formulae we present provide improved estimations in such regimes.