Dispersive optical bistability in unidirectional ring cavity

The mathematical models of dispersive optical bistability in unidirectional ring cavity yield the transmitted intensity I-t as a function of the input intensity I-in with additional parameters (mirror reflectivity R and phase shift beta). There are two feedback elements in this description: the energy (and, hence, also causal) feedback quantified by R and the purely causal feedback given by dependence of the phase shift on the transmitted power, beta = beta(0) + beta(2)I(1). The apparatus of causal diagrams method is used to represent and analyze phenomena in the ring cavity. The region of physically unstable states is marked by the condition t(loop) > 1, where t(loop) is the transmission function of the feedback loop I(t)beta IinIt present in the diagram. Besides the critical points defined by t(loop) = 1 (which are linked to the existence of bistability), there are two conditions marked by t(loop) = beta in which the cavity state is insensitive to the values of R.