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 permit us to obtain a number of simple approximate expressions of various 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, interestingly, with the result obtained from the slowly varying envelope approximation (SVEA). Thus, our validity criteria apply to the SVEA result, and predict well its domain of validity and its breakdown for short wavelengths and for very high intensities and nonlinearities. The simple higher order formulae we present provide improved estimations in such regimes.
© 1994 The Royal Society. Received August 16, 1993; Accepted April 12, 1994. O.B. gratefully acknowledges support from NSF through grant no. DMS-9200002. This work was partly supported by the Army Research Office and the National Science Foundation through the Center for Nonlinear Analysis.