Analysis of Transient Optical Bistability and Stability in a Nonlinear Fiber Fabry-Perot Resonator Based on an Iterative Method

Abstract

We perform a transient analysis, steady-state analysis, and linear stability analysis of a nonlinear Fabry-Perot resonator in order to examine the possibility of a fiber bistable device. We here develop two iterative methods for calculating the dynamics of the Fabry-Perot resonator containing a nonlinear medium with an instantaneous response time. The treatment of the counter-propagating field within the cavity is very important in estimating the nonlinear phase shift due to propagation. A trapezoid rule and midpoint rule are used here for the numerical integration. The iterative method using the trapezoid rule gives excellent agreement with the multiple-beam method developed by Bischofberger and Shen (Phys. Rev. A 19 (1979) 1169), which is more complicated than the proposed procedure. Unfortunately it is found that the midpoint approximation is numerically unstable. Assuming a conventional optical fiber, the switching power for optical bistability is less than 1 kW for a resonator length of 1-2 cm. On the basis of the iterative method, we perform a linear stability analysis to examine whether Ikeda instability affects bistable device application or not. The stability analysis shows that the instability threshold is two orders of magnitude larger than the switching power for optical bistability.