Abstract

We present a modeling technique that uses eigenmode expansion to simulate infinite periodic structures with Kerr nonlinearity. Using a unit cell with Bloch boundary conditions, our iterative algorithm efficiently calculates self-consistent two-dimensional Bloch modes. We show how it can be used to study the band structure of nonlinear photonic crystals and to gain rapid insight in the operation of devices. Furthermore, we present nonlinear transversely localized guided modes, which are kinds of gap solitons or intrinsic localized modes, that induce their own waveguide through a photonic crystal without linear defects.

© 2005 Optical Society of America

Nonlinear lattice model for spatially guided solitons in nonlinear photonic crystals

Guy Van der Sande, Björn Maes, Peter Bienstman, Jan Danckaert, Roel Baets, and Irina Veretennicoff
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Local probing of Bloch mode dispersion in a photonic crystal waveguide

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J. Opt. Soc. Am. B 30(7) 1786-1793 (2013)