Impurity Modes and Wave Scattering in Discrete Chains with Nonlinear Defect States

We study the properties of localized impurity modes and the transmission of plane waves across a general nonlinear impurity embedded in an infinite one-dimensional linear chain. Using the formalism of the lattice Green function, we obtain nonlinear equations for the bound state energy and the transmission coefficient, for a wide class of nonlinear impurities. We specialize to a saturable nonlinear impurity, obtaining closed form expressions for the bound state energy and transmission coefficient