title: Nonlinear lattice model for spatially guided solitons in nonlinear photonic crystals.
abstract: Numerical simulations have shown the existence of transversely localized guided modes in nonlinear two-dimensional photonic crystals. These soliton-like Bloch waves induce their own waveguide in a photonic crystal without the presence of a linear defect. By applying a Green's function method which is limited to within a strip perpendicular to the propagation direction, we are able to describe these Bloch modes by a nonlinear lattice model that includes the long-range site-to-site interaction between the scattered fields and the non-local nonlinear response of the photonic crystal. The advantages of this semi-analytical approach are discussed and a comparison with a rigorous numerical analysis is given in different configurations. Both monoatomic and diatomic nonlinear photonic crystals are considered.
authors.forename: Guy
authors.initials: G
authors.lastname: Van der Sande
authors.forename: Björn
authors.initials: B
authors.lastname: Maes
authors.forename: Peter
authors.initials: P
authors.lastname: Bienstman
authors.forename: Jan
authors.initials: J
authors.lastname: Danckaert
authors.forename: Roel
authors.initials: R
authors.lastname: Baets
authors.forename: Irina
authors.initials: I
authors.lastname: Veretennicoff