Instabilities for absorptive optical bistabilities in a nonideal Fabry-Perot cavity

Abstract: Instabilities are predicted for absorptive optical bistability in a nonideal Fabry-Perot cavity on the basis of Maxwell-Bloch theory. The authors show that the stability problem of the Maxwell-Bloch equations can be formulated in terms of a Riccati differential equation with boundary conditions. They have integrated this equation numerically. The results crucially depend on the value of the transmission coefficient of the mirrors. For finite values of this quantity they find that the nearest side mode is responsible for two disconnected instability domains in the plane spanned by the output intensity and the medium response time. One of these domains can generate instabilities in the upper and the lower branch of the steady-state curve if the cooperation parameter is sufficiently large. Higher side modes can give rise to positive-slope instabilities as well. From these findings it can be understood why a recent experimental search for instabilities in absorptive optical bistability has led to a negative result. The authors finally demonstrate that the instability spectra of a Fabry-Perot cavity and a so-called equivalent ring cavity differ considerably