Defect modes and solitons supported by optically induced lattices in highly saturable nonlinear media with quadratic electro-optic effect

We theoretically investigate the defect modes and defect solitons supported by optically induced lattices in highly saturable nonlinear media with quadratic electro-optic effect. It is shown that positive and negative defect modes bifurcate from the right and left edge of each band into the bandgaps, respectively, and the distances between the eigenvalues of defect mode and band edge increase with the defect strength. Defect solitons bifurcate from every infinitesimal linear defect mode. When the defect is attractive, lower power defect soliton can propagate stably, but the soliton with high intensity are unable. In repulsive defects, defect soliton are stable in entire regions of their existence in lower bandgaps but only the higher power solitons are stable in higher bandgaps. Especially, when the repulsive defect is strong, both the defect mode and soliton power diagram branches terminate on the right edge of this gap and then appear in higher band gaps, and these solitons can propagate stably in whole soliton existing regime.