Dispersive optical bistability in a nonideal Fabry-Perot cavity II. Numerical results on side-mode instabilities

Instabilities in the nearest side-modes are predicted for dispersive optical bistability in a nonideal Fabry-Perot cavity. The results are based on a linear stability analysis of the Maxwell-Bloch equations. This analysis leads to a boundary value problem for a four-dimensional set of linear differential equations, which the authors have solved numerically. The findings show that the instability spectrum strongly depends on the detuning parameters and on the transmission coefficient of the cavity mirrors. If the atomic detuning gradually increases, instability domains are found to merge. If moreover the cavity detuning grows, instabilities spread along the upper branch of the bistability curve, even for high values of the medium response time. The authors have made a comparison between our results and recent experimental data, the outcome of which is satisfactory from a qualitative point of view. Finally, they show that the side-mode instabilities for dispersive optical bistability in a Fabry-Perot cavity are incorrectly predicted, if a so-called equivalent ring cavity is adopted as a model.