Universal character of the discrete nonlinear Schrödinger equation

Fratalocchi, Andrea; Assanto, Gaetano

doi:10.1103/physreva.76.042108

Cited by 5 publications

(3 citation statements)

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“…Lattice solitons are continuous counterparts of discrete solitons existing in waveguide arrays (for a recent reviews on discrete solitons see Aubry [1997]; Flach and Willis [1998]; ; Christodoulides, Lederer, and Silberberg [2003]; Aubry [2006]). The discrete NLSE that is used to describe the evolution of nonlinear excitations in such systems has a rather universal character and can be used to describe light propagation even in tensorial systems and in the presence of nonparaxial and vectorial effects (Fratalocchi, Assanto [2007c]). As mentioned above, mathematically, the equations describing propagation of laser radiation in periodic media are analogous to that describing evolution of Bose-Einstein condensates in optical lattices, hence, many soliton phenomena predicted in nonlinear optics were encountered in BECs and vice versa (Dalfovo, Giorgini, Pitaevskii, and Stringari [1999]; Pitaevskii and Stringari [2003]; Abdullaev, Gammal, Kamchatnov, and Tomio [2005]; Morsch and Oberthaler [2006]).…”

Section: §5 One-dimensional Lattice Solitonsmentioning

confidence: 99%

Soliton Shape and Mobility Control in Optical Lattices

2009

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We present a progress overview focused on the recent theoretical and experimental advances in the area of soliton manipulation in optical lattices. Optical lattices offer the possibility to engineer and to control the diffraction of light beams in media with periodicallymodulated optical properties, to manage the corresponding reflection and transmission bands, and to form specially designed defects. Consequently, they afford the existence of a rich variety of new families of nonlinear stationary waves and solitons, lead to new rich dynamical phenomena, and offer novel conceptual opportunities for all-optical shaping, switching and routing of optical signals encoded in soliton formats. In this overview, we consider reconfigurable optically-induced lattices as well as waveguide arrays made in suitable nonlinear materials. We address both, one-dimensional and multi-dimensional geometries.We specially target the new possibilities made possible by optical lattices induced by a variety of existing non-diffracting light patterns, we address nonlinear lattices and soliton arrays, and we briefly explore the unique features exhibited by light propagation in defect modes and in random lattices, an area of current topical interest and of potential crossdisciplinary impact.

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Section: §5 One-dimensional Lattice Solitonsmentioning

confidence: 99%

Soliton Shape and Mobility Control in Optical Lattices

2009

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“…From a fundamental point of view, these archetypal discrete systems enable exploration of universal discrete-like dynamics [5] and discrete non-linear behavior [6] via the study of the field evolution in each individual waveguide. They have been exploited both in the linear [7,8] and non linear [2,9,10] regimes to demonstrate Bloch oscillations [7,8], discrete diffraction engineering [11] and discrete optical solitons [4,12,13].…”

Section: Introductionmentioning

confidence: 99%

Confining light flow in weakly coupled waveguide arrays by structuring the coupling constant: towards discrete diffractive optics

Belabas¹,

Bouchoule²,

Sagnes³

et al. 2009

Opt. Express

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Structuring the coupling constant in coupled waveguide arrays opens up a new route towards molding and controlling the flow of light in discrete structures. We show coupled mode theory is a reliable yet very simple and practical tool to design and explore new structures of patterned coupling constant. We validate our simulation and technological choices by successful fabrication of appropriate III-V semiconductor patterned waveguide arrays. We demonstrate confinement of light in designated areas of one-dimensional semi-conductor waveguide arrays.

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“…Let us first consider an infinitely extended one-dimensional (1D) array of weakly coupled single mode channel waveguides. The coupled mode equations for the amplitudes Q n of the eigensolutions in the periodic channels can be cast in a nondimensional form [23,24], which in the local regime reduce to the discrete nonlinear Schrödinger (DNLS) equation…”

mentioning

confidence: 99%