Nonlinear localized modes in 2D photonic crystals

Summary form only given. A low-intensity light cannot propagate through a photonic bandgap (PBG) crystal if its frequency falls into a band gap. However, it has been recently suggested, in the framework of the couple-mode theory, that in the case of a two-dimensional (2D) periodic medium with a Kerr-type nonlinear high-intensity light with the frequency inside the gap can propagate in the form of finite energy solitary waves as 2D gap solitons, which are localized in both directions. Employing the technique based on Greens function, we develop a consistent theory of nonlinearity-induced self-trapping effects in 2D photonic crystals with a Kerr nonlinearity. As an example, we consider 2D reduced-symmetry photonic crystals which have recently attracted considerable interest because of their ability to possess larger absolute band gaps.