Optical pulse propagation in nonlinear photonic crystals - art. no. 056604

We present a formalism for optical pulse propagation in nonlinear photonic crystals of arbitrary dimensionality. Using a multiple-scale analysis, we d erive the dynamical nonlinear Schrodinger equation obeyed by the envelope f unction modulating an underlying Bloch function. Effective coefficients app ear in that equation characterizing the effects of Kerr nonlinearity, linea r gain or loss, and material dispersion. They depend on how the underlying Bloch function "samples" these effects in the photonic crystal, and require for their calculation a specification of these effects throughout the phot onic crystal, and the calculated bandstructure of the photonic crystals in the linear, nondispersive limit. We show that wave packets from different b ands can experience significantly modified effective material properties.