Abstract: We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or $\chi^{(2)}$) nonlinear interfaces embedded in a linear layered structure-a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete $\chi^{(2)}$ equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media.

Keywords: band-gap materials; 2nd-harmonic generation; wave-propagation; crystal; solitons; lattices; systems

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