Nonlinear effects in one-dimensional photonic lattices

Abstract

Optical waves propagating in photonic periodic structures are known to exhibit a fundamentally different behavior when compared to their homogeneous counterparts in bulk materials. In such systems the spatially periodic refractive index experienced by light waves is analogous to the situation in crystalline solids, where electrons travel in a periodic Coulomb potential [1]. Consequently, the propagating extended (Floquet Bloch) modes of a linear periodic optical system form a spectrum that is divided into allowed bands, separated by forbidden gaps, too, and the two different physical systems share most of their mathematical description. Photonic band-gap materials, which may be artificially fabricated to be periodic in three, two, or only one dimension, hold strong promise for future photonic applications like miniaturized all-optical switches, filters, or memories [2]. Here novel opportunities are offered when nonlinear material response to light intensity is taken into account. When studying such nonlinear photonic crystals it turns out that light propagation is governed by two competing processes: linear coupling among different lattice sites and energy localization due to nonlinearity. For an exact balance of these counteracting effects self-localized states can be obtained, which are called lattice solitons [3-6]. © 2009 Springer-Verlag Berlin Heidelberg.