Abstract

Discreteness provides unique opportunities for controlling the flow of light. As in solidstate physics, optical discrete or lattice configurations are known to exhibit a succession of allowed Floquet-Bloch bands and forbidden bandgaps. In weakly coupled systems, the Floquet-Bloch states can be accurately described by local modes, and thus the tight-binding approximation or coupled-mode theory is applicable. As a result, the field dynamics become effectively discretized. In optics, arrays of evanescently coupled waveguides, photonic crystal fibers, chains of coupled microresonators, and photonic crystals are prime examples of such structures where discrete wave dynamics can be experimentally investigated. Perhaps the most exciting outcome of the interplay between discreteness and optica nonlinearity is the existence of self-localized entities better known as discrete solitons. This class of optical solitons were first suggested in the late 1980s and successfully observed in AlGaAs waveguide arrays a decade later. Since then, discrete optical solitons have been observed in many other material systems such as in optically induced lattices, in quadratic waveguide arrays, and in liquid-crystal cells. This experimental work has not only resulted in a deeper understanding of nonlinear processes in periodic environments, but it has also helped to assess the potential of these self-trapped states toward future applications. Nowadays, the field of discrete optical dynamics in nonlinear lattices is at an exciting stage of development. Even though some of the basic concepts in this area have been around for a while, much remains to be explored and discovered.

© 2005 Optical Society of America

Introduction

Discreteness provides unique opportunities for controlling the flow of light. As in solid-state physics, optical discrete or lattice configurations are known to exhibit a succession of allowed Floquet-Bloch bands and forbidden bandgaps. In weakly coupled systems, the Floquet-Bloch states can be accurately described by local modes, and thus the tight-binding approximation or coupled-mode theory is applicable. As a result, the field dynamics become effectively discretized. In optics, arrays of evanescently coupled waveguides, photonic crystal fibers, chains of coupled microresonators, and photonic crystals are prime examples of such structures where discrete wave dynamics can be experimentally investigated. Perhaps the most exciting outcome of the interplay between discreteness and optical nonlinearity is the existence of self-localized entities better known as discrete solitons. This class of optical solitons were first suggested in the late 1980s and successfully observed in AlGaAs waveguide arrays a decade later. Since then, discrete optical solitons have been observed in many other material systems such as in optically induced lattices, in quadratic waveguide arrays, and in liquid-crystal cells. This experimental work has not only resulted in a deeper understanding of nonlinear processes in periodic environments, but it has also helped to assess the potential of these self-trapped states toward future applications. Nowadays, the field of discrete optical dynamics in nonlinear lattices is at an exciting stage of development. Even though some of the basic concepts in this area have been around for a while, much remains to be explored and discovered.

In putting together this Focus Issue, an attempt was made to present a balanced view of this area with respect to theory and experiment. In the first article of this issue, Lahini et al. discuss band structure anomalies arising from the polarization properties of nonlinear waveguide arrays. In the second paper, reconfigurable discrete soliton networks using Bessel beams are suggested by Xu et al., while in the third article Fleischer et al. provide a review of recent developments in the newly emerging field of two-dimensional lattice solitons. In two other interesting articles, Meier and collaborators present nonlinear interactions in Kerr arrays and Fratalocchi et al. demonstrate discrete soliton propagation in liquid-crystal cells. Chen et al. address the formation of discrete solitons in light-induced photonic lattices, and finally, Droulias et al. examine the possibility of nonlinear X waves in normally dispersive waveguide arrays.

It has been a great pleasure hosting this Focus Issue in Optics Express.

Demetrios Christodoulides

College of Optics/CREOL

University of Central Florida

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