Stability analysis for absorptive optical bistability in a Fabry-Perot cavity

Abstract: A stability analysis is performed for absorptive optical bistability in a medium of arbitrary absorption coefficient, which is contained in a Fabry-Perot cavity with nonideal mirrors. In order to describe this system the authors use a hierarchical set of equations which is obtained from Maxwell-Bloch theory by expanding the polarization and population inversion in slowly varying harmonics. They reduce the stability problem to two pairs of coupled differential equations for the amplitudes and the phases of the space-dependent deviations of the forward and the backward electric field envelopes. The coefficients of these equations depend on the stationary inversion fields for which a representation in terms of Chebyshev polynomials depending on the electric field envelopes is given. The influence of a truncation of the Bloch hierarchy on the instabilities is studied numerically in the uniform-field limit.