Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark

Abstract: Employing the technique based on Green's function, we develop a consistent theory of nonlinearity-induced self-trapping effects in 2D photonic bandgap (PBG) crystals with a Kerr nonlinearity. Specifically, we consider nonlinear localised modes in PBG crystals of reduced symmetry and in PBG crystal waveguides. We show that such modes can be described by the nonlinear Schrödinger equation with long-range dispersion in both, linear and nonlinear, terms. We demonstrate that the long-range character of the dispersion is responsible for new qualitative effects such as stabilisation of low-amplitude 2D nonlinear localised modes in reduced symmetry PBG crystals or multistability of nonlinear localised modes in the waveguides.