The nonlinear Fabry-Perot resonator: direct numerical integration

A numerical integration method is presented for the classical anharmonic-oscillator model describing the nonlinear response of a medium to an applied optical field within the single-frequency approximation for self-action effects. The formalism is applied to an analysis of the multistability of a Fabry-Perot resonator. The optical polarization P, rather than the optical E field, is retained as the dynamical variable. We develop an algorithm for integration of the nonlinear wave equation in P and with addition of the nonlinear boundary conditions at the resonator surfaces we are able to find the transmission as a function of intensity and frequency. The formalism applies specifically to materials such as ferroelectrics with strong resonances in the far-infrared spectral region. Illustrative graphs of transmission versus incident intensity throughout the resonance region are presented. (C) 2001 Elsevier Science B.V. All rights reserved.