Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures

We consider the general problem of electromagnetic wave propagation through a one-dimensional system consisting of a nonlinear medium sandwiched between two linear structures. Special emphasis is given to systems where the latter comprise Bragg reflectors. We obtain an exact expression for the nonlinear response of such dielectric superlattices when the nonlinear impurity is very thin, or in the δ-function limit. We find that both the switching-up and switching-down intensities of the bistable response can be made very low, when the frequency of the incident wave matches that of the impurity mode of the structure. Numerical results for a nonlinear layer of finite width display qualitatively similar behavior, thus confirming the usefulness of the simpler δ-function model. In addition, an analytical solution for the resonance states of an infinitely extended finite-width superlattice with a finite-width nonlinear impurity is presented.