We have modeled the response of a nonlinear periodic structure by means of the Abele´s 2×2 matrix method. Our structure differs from the usual rejection‐band filter designs, in that we have chosen the filter elements to be index matched in the absence of radiation, providing a rejection band that both grows and shifts as a function of incident intensity. The intensity output function of the model not only directly demonstrates optical bistability, but also limiting, switching, self‐pulsing, and chaos.