Optical response of nonlinear multilayer structures: Bilayers and superlattices

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Abstract
We discuss the normal-incidence reflectivity and transmissivity of a multilayer structure which contains N films, each of which has a dielectric constant dependent on light intensity, through a term proportional to the local intensity. We show the method introduced in a previous paper for the isolated film [Wei Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987)] may be generalized to the present case, retaining the feature that a numerical solution may be achieved by means of a search for a single real number bounded between zero and unity. Explicit calculations for a bilayer show that such a structure exhibits bistability with nonreciprocal character: The threshold for the onset of bistability with light incident from the left may differ substantially from that with light incident from the right. We also apply the theory to finite superlattices. For frequencies close to the edge of a stop gap of the structure, for rather low power, we find the system may switch from a state where the transmissivity is unity to a state where it is exponentially small. Solitons play a key role as mediators of the switching in extended superlattices.