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5 October 2005 Nonlinear lattice model for self-localized waveguides in nonlinear photonic crystals
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The combination of photonic crystals and nonlinearities is the subject of intense research. Because of the strong dispersion and localization effects in band gap structures, even weak nonlinearities can be exploited. The inclusion of the Kerr effect gives rise to nonlinear energy localization. In combination with the discrete nature of the photonic crystals this may lead to nonlinear modes, such as gap solitons or discrete breathers. We examine a novel kind of solitary wave. The used geometry is a photonic crystal formed by a square lattice of rods containing a Kerr type material: in the linear case a wave with frequency within the band gap is exponentially dampened. However, in the nonlinear regime, the wave creates its own waveguide channel, by changing the indices of the center rods. In the transversal direction with respect to the propagation, the mode is still confined. By applying a Green's function method limited to a photonic crystal strip perpendicular to the propagation direction, we have been able to describe these Bloch modes. To that end, we review a nonlinear lattice model that includes the long-range rod-to-rod interaction between the scattered fields and the non-local nonlinear response of the photonic crystal. The advantages of this semi- analytical approach are discussed and a comparison with a rigorous numerical analysis is given.
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Guy Van der Sande, Björn Maes, Peter Bienstman, Jan Danckaert, Roel Baets, and Irina Veretennicoff "Nonlinear lattice model for self-localized waveguides in nonlinear photonic crystals", Proc. SPIE 5949, Nonlinear Optics Applications, 59490M (5 October 2005);

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