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 thc delta-function limit. We find that both the switching-up and switching-down intensities of the bistable response can be made very lour, when the frequency of the incident wave matches that of the impurity mode of the structure, Numerical results for it nonlinear layer of finite width display qualitatively similar behavior, thus confirming the usefulness of the simpler delta-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 delta-function model in describing the electromagnetic wave propagation in periodic structures consistent of thin layers of materials with an intensity-dependent dielectric constant. Copyright (C) 1998 Elsevier Science B.V.