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Proceedings Paper

Nonlinear lattice model for self-localized waveguides in nonlinear photonic crystals
Author(s): Guy Van der Sande; Björn Maes; Peter Bienstman; Jan Danckaert; Roel Baets; Irina Veretennicoff
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Paper Abstract

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.

Paper Details

Date Published: 5 October 2005
PDF: 8 pages
Proc. SPIE 5949, Nonlinear Optics Applications, 59490M (5 October 2005);
Show Author Affiliations
Guy Van der Sande, Vrije Univ. Brussel (Belgium)
Björn Maes, Ghent Univ. (Belgium)
Peter Bienstman, Ghent Univ. (Belgium)
Jan Danckaert, Vrije Univ. Brussel (Belgium)
Roel Baets, Ghent Univ. (Belgium)
Irina Veretennicoff, Vrije Univ. Brussel (Belgium)

Published in SPIE Proceedings Vol. 5949:
Nonlinear Optics Applications
Miroslaw A. Karpierz; Allan Dawson Boardman; George I. Stegeman, Editor(s)

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