Solitons in one-dimensional photonic crystals

We report on results of a systematic analysis of spatial solitons in the model of one-dimensional photonic crystals, built as a periodic lattice of waveguiding channels, of width D, separated by empty channels of width L -D. The system is characterized by its structural "duty cycle," DC ≡ D/L. In the case of the self-defocusing (SDF) intrinsic nonlinearity in the channels, one can predict new effects caused by competition between the linear trapping potential and the effective nonlinear repulsive one. Several species of solitons are found in the first two finite bandgaps of the SDF model, as well as a family of fundamental solitons in the semi-infinite gap of the system with the self-focusing nonlinearity. At moderate values of DC (such as 0.50), both fundamental and higher-order solitons populating the second bandgap of the SDF model suffer destabilization with an increase of the total power. Passing the destabilization point, the solitons assume a flat-top shape, while the shape of unstable solitons gets inverted with local maxima appearing in empty layers. In the model with narrow channels (around DC = 0.25), fundamental and higher-order solitons exist only in the first finite bandgap, where they are stable, despite the fact that they also feature the inverted shape.