Influence of cavity properties on the interpretation of experimental results in bistability

Abstract

The analysis of experiments on bistability and instability in nonlinear optical resonators depends critically on an understanding of the properties of the corresponding empty (linear) resonators, Both real and ideal cavities exhibit behavior which can lead to a misinterpretation of experimental results, and in both cases this behavior becomes more pronounced with increasing finesse. As an example of the first case, consider a real cavity which is nonideal in that different methods of measurement of the cavity loss give different values for it and hence for the cooperativity C. A simple but realistic model for such a cavity leads to the derivation of a state equation for bistability which differs in functional form from the usual state equation derived assuming an ideal cavity. In such a nonideal cavity, one might find its loss by measuring the decay time of the transmitted light after rapidly cutting off the incident light or by scanning the length of the cavity to measure the finesse. If these two different values of loss differ by a factor of two, as they have in certain of our experiments, then making either one or the other measurement and applying the usual state equation would cause one to overestimate or underestimate the value of C necessary for the critical onset of bistability by as much as 40%. Exemplifying the second case, the transient regime of even an ideal cavity can exhibit behavior which mimics period doubling, quasiperiodicity, and optical chaos. These appear in the transmission of a cavity excited off-resonance by a pulse with rise or fall times comparable to or shorter than the cavity response time, obscuring the investigation of optical nonlinear dynamics in the transient regime.