PHYSICA D Wave propagation in linear and nonlinear 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 S-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 b-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. Finally, we investigate the adequacy of the Kronig-Penney S-function model in describing the electromagnetic wave propagation in periodic structures consistent of thin layers of materials with an intensity-dependent dielectric constant. Copyright 0 1998 Elsevier Science B.V. 1