Spatial effects in intrinsic optical bistability

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Abstract
Using the nonlinear oscillator model as a prototype medium exhibiting intrinsic optical bistability, we investigate the inhomogeneous absorption of the electromagnetic field. The forward- and backward-field amplitudes and diffraction effects are retained in the mathematical description. Analytic results are given in the limit of plane-wave propagation under steady-state conditions. The transmitted and reflected intensity exhibit a structure that is determined by the spatial inhomogeneity of the absorption in the longitudinal direction. The transmitted intensity has a structure that is dependent on the length of the medium. The reflected intensity has an interference structure from light reflected at the front surface and the internal boundary separating a high-polarization from a low-polarization branch. A degenerate-four-wave-mixing experiment is predicted to be a very sensitive probe of the internal boundary and the interference between the forward and backward field. The phase-conjugate signal develops large oscillations as the input field is varied. Numerical results for diffraction effects are also given, and we find that the plane-wave results for the center of the beam remain reliable down to Fresnel numbers of order unity and in media that are smaller than the linear absorption length.