Properties of defect modes in one-dimensional optically induced photonic lattices

In this article, localized defect modes in one-dimensional optically induced photonic lattices are studied comprehensively. First, the origin of these defect modes is investigated analytically in the weak-defect limit by perturbation methods. It is shown that in an attractive defect where the lattice light intensity at the defect site is higher than that of nearby sites, a defect mode bifurcates from the left edge of every Bloch band; while in a repulsive defect, a defect mode bifurcates from the right edge of every Bloch band. When the defect is not weak, defect modes are examined by numerical methods. It is shown that in a repulsive defect, the strongest confinement of defect modes arises when the lattice light intensity at the defect site is nonzero rather than zero. In addition, as the potential strength increases, defect modes disappear from lower bandgaps and appear in higher bandgaps. In an attractive defect, however, defect modes persist in every bandgap as the potential strength increases. Using a piecewise-constant potential model, defect modes are calculated analytically for a general defect. The analytical results qualitatively explain the main features in numerical results.