Stable all-optical limiting in nonlinear periodic structures. I. Analysis

We consider propagation of coherent light through a nonlinear periodic optical structure consisting of two alternating layers with different linear and nonlinear refractive indices. A coupled-mode system is derived from the Maxwell equations and analyzed for the stationary-transmission regimes and linear time-dependent dynamics. We find the domain for existence of true all-optical limiting when the input–output transmission characteristic is monotonic and clamped below a limiting value for output intensity. True all-optical limiting can be managed by compensating the Kerr nonlinearities in the alternating layers, when the net-average nonlinearity is much smaller than the nonlinearity variance. The periodic optical structures can be used as uniform switches between lower-transmissive and higher-transmissive states if the structures are sufficiently long and out-of-phase, i.e., when the linear grating compensates the nonlinearity variations at each optical layer. We prove analytically that true all-optical limiting for zero net-average nonlinearity is asymptotically stable in time-dependent dynamics. We also show that weakly unbalanced out-of-phase gratings with small net-average nonlinearity exhibit local multistability, whereas strongly unbalanced gratings with large net-average nonlinearity display global multistability.