Third harmonic generation in layered media in presence of optical bistability of the fundamental

We study third harmonic generation in layered configuration when the fundamental exhibits bistable response. We consider two geometries, namely, a Fabry-Perot cavity with reflection coatings and a distributed feedback structure with alternate nonlinear layers. In both the cases for suitable choice of frequency, the power response at the fundamental frequency is bistable. We show that bistability of the fundamental leads to a multivalued character of the generated third harmonic in both the forward and backward directions. Moreover, we study frequency response in the case of the Fabry-Perot cavity and show that additional structures arise in the generated third harmonic due to frequency bistability of the fundamental. Our calculations suggest the possibility of an all optical switch at third harmonic frequency controlled by the parameters (like intensity, frequency) of the fundamental.