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Photonics 2014, 1(4), 390-403; doi:10.3390/photonics1040390

Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers

1
Department of Mathematics and Statistics, Amherst College, Amherst, MA 01002, USA
2
Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA
3
Faculty of Electrical Engineering, Helmut Schmidt University, Hamburg 22043, Germany
*
Author to whom correspondence should be addressed.
Received: 2 October 2014 / Revised: 20 October 2014 / Accepted: 20 October 2014 / Published: 27 October 2014
(This article belongs to the Special Issue Nonlinear Fiber Optics)
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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. View Full-Text
Keywords: saturable nonlinearity; asymmetry; discrete Schrödinger saturable nonlinearity; asymmetry; discrete Schrödinger
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Law, D.; D'Ambroise, J.; Kevrekidis, P.G.; Kip, D. Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers. Photonics 2014, 1, 390-403.

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