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
(190.3270) Nonlinear optics : Kerr effect
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(230.4320) Optical devices : Nonlinear optical devices
(260.5950) Physical optics : Self-focusing
Björn Maes, Peter Bienstman, and Roel Baets, "Bloch modes and self-localized waveguides in nonlinear photonic crystals," J. Opt. Soc. Am. B 22, 613-619 (2005)