The Kerr phenomenon in 1D multilayers: a comparison between an approximated and a quasi-analytic method

Introduction: In this article, we present a study of the Kerr effect in one-dimensional multilayers using simple methods that take less than 5 min to compute on a 2.4 GHz processor. Materials and methods: The behavior of structures using a nonlinear Fabry–Perot cavity is modelled by 1D numerical models and a method for accelerating convergence is applied. Two methods are proposed. The first one is quasi-analytic electromagnetic-based and the second is a mean-field approximated one. The appeal of these two methods lies in their simplicity. Results: We present the effect of nonlinearity on the transmission peak of the Fabry–Perot mode and we discuss the results concerning the cavity mode shift and the resulting bistability. We then reveal that the phenomenon of bistability with a hysteresis loop can be obtained in this simple 1D periodic structure. These models could be of great interest to research on agile switching applications. Conclusions: The effect of the nonlinear Kerr effect on the cavity mode of a one-dimensional periodic structure containing a defect can be studied using the two methods presented here without any convergence issues. In fact, convergence can be accelerated, and the computation time is very short. The hysteresis loop of the bistability is evident for both methods, with an overestimation of the intensity threshold for the approximate method. These results demonstrate that a very simple method can be used to model such a nonlinear effect, characterized by a variation in the refractive index linked to an increase in the intensity of the incident wave.