Wave propagation in periodic nonlinear dielectric superlattices

Novel phenomena such as photo& band gaps and possible light localization occur when electromagnetic (EM) waves propagate in dielectric superlattices.1-6 In an approximation where only the scalar nature of the EM wave is taken into account, wave propagation in a periodic or disordered medium resembles the dynamics of an electron in a crystal lattice. As a result, photonic bands and gaps arise in the periodic lattice case whereas EM wave localization is theoretically possible in the disordered case. In the latter case and when the dielectric medium is one dimensional, Andersontype optical localization has been predicted.r3* In an ordered dielectric superlattice, on the other hand, photon band gaps have been demonstrated for various realistic configurations.5 One issue that has not been widely addressed yet is the possibility of using superlattices with nonlinear dielectric properties and, in particular, thenonlinear Kerr effect, to construct optical devices with desired transmission characteristics.277 This is the problem we are addressing in the present letter. We consider the propagation of plane EM waves in the scalar approximation in a one-dimensional continuous linear dielectric medium. In the medium we embed periodically small dielectric regions that have non-negligible third order nonlinear susceptibility xC3’ (Fig. 1). We will assume for simplicity that the width of the nonlinear dielectric regions is much smaller than the distance between two adjacent ones. We are thus led to a model for a periodic nonlinear superlattice and the propagation of a plane wave injected on one side of the structure can be described through the following nonlinear Kronig-Penney equation: