Long-range interaction and nonlinear localized modes in photonic crystal waveguides

Abstract

We develop the theory of nonlinear localised modes (intrinsic localised modes or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We consider different geometries of the waveguides created by an array of nonlinear dielectric rods in an otherwise perfect linear 2D photonic crystal, and demonstrate that the effective interaction in such waveguides is nonlocal, being described by a new type of nonlinear lattice models with long-range coupling and nonlocal nonlinearity. We reveal the existence of different types of nonlinear guided modes which are also localised in the waveguide direction, and describe their unique properties including bistability. 42.70.Qs, 42.79.Gn, 42.65.Wi, 42.65.Tg

Pulse trapping inside a one-dimensional photonic crystal with relaxing cubic nonlinearity

“…Photonic crystals (including two-and three-dimensional) allow to control dispersion and diffraction properties of light [4,5], obtain pulse reshaping [6], pulsed high-harmonic generation [7], etc. The processes of light self-action in such systems result in localization effects such as gap solitons formation, discrete mode existence or light energy localization (see, for example, [8][9][10][11]). …”

Instabilities and bifurcations of nonlinear impurity modes

“…Spatially localized modes of the discrete nonlinear Schrödinger (DNLS) equation, known as discrete solitons, have appeared in many diverse areas of physics, such as biophysics, nonlinear optics, solid state physics [6] and, more recently, in the studies of the Bose-Einstein condensates in optical lattices [2] and photonic-crystal waveguides and circuits [3].…”

Kink propagation and trapping in a two-dimensional curved Josephson junction

“…Nonlinear localized modes in twodimensional photonic crystal waveguides were investigated in Ref. 12. A curved chain of nonlinear oscillators was considered in Ref.…”