Coupled Mode Theory in Low-Contrast Nonlinear Photonic Crystals

Nonlinear photonic crystals may enable all-optical signal processing. Developed herein is an analytical method by which the propagation of light in low-contrast nonlinear photonic crystals can be understood. In solving Maxwell’s equations in nonlinear photonic crystals, their constituent pe-riodicity and nonlinearity are treated as perturbations to an underlying homogeneous medium. The method of multiple scales is then used to obtain coupled mode equations governing the evolution of resonantly coupled normal modes in the perturbed medium, thus providing an approximation to the electric field therein. The method developed here applies to photonic crystals of any dimensionality and reproduces as a special case the one-dimensional theory of which it is a generalization. Being explicitly intended for low-contrast photonic crystals, this method provides a more direct means for their analysis than studying methods intended for high-contrast media in the limit of low-contrast. It is also more general than previous instances of multi-dimensional nonlinear coupled mode theory