Abstract
In the present paper we consider nonlinear dimers and trimers (more generally, oligomers) embedded within a linear Schrödinger lattice where the nonlinear sites are of saturable type. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties also persists in the case of such wavepackets.
Highlights
In the last two decades, the subject of nonlinear dynamical lattices has gained considerable attraction and interest due to its emergence and relevance to a wide range of diverse applications
In comparing our results with those of [19], we find that the asymmetry associated with the saturable nonlinearity is less pronounced than that of a system with a cubic nonlinearity and a linear potential term
We considered a lattice setting where embedded in a linear Schrödinger chain was a nonlinear “segment” of the saturable type
Summary
In the last two decades, the subject of nonlinear dynamical lattices has gained considerable attraction and interest due to its emergence and relevance to a wide range of diverse applications. A specific phenomenon that has been intensely explored in a wide variety of recent studies is that of potentially asymmetric (i.e., non-reciprocal) wave propagation This has been examined e.g., in asymmetric phonon transmission through a nonlinear interface layer between two very dissimilar crystals [9]. In this way, we identify the asymmetry between left and right transmittivities, due to the nonlinear propagation through the asymmetric dimer, trimer or more generally oligomer (i.e., few site) configuration.
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