An effective field perspective on the nonlinear optical properties of artificially structured materials

J.E. Sipe

Department of Physics
University of Toronto, and
Photonics Research Ontario

In recent years there have been a number of breakthroughs in the fabrication of artificially structured materials with optical properties are of interest. These include not only photonic crystals, but coupled cavity and coupled microresonator structures as well. Because these structures are periodic or nearly so in at least one dimension, their linear optical properties are characterized by dispersion relations that can exhibit regions of high and low group velocity, and high and low dispersion. Their nonlinear properties will therefore be characterized by soliton and solitary-wave like effects, should be of interest from the fundamental perspective of nonlinear dynamics, and may be of use in switching operations for telecommunication applications.

Despite the fact that the index contrast of the constituent materials in these structures can be quite large, and varies on the order of the wavelength of light, realistic effective field theories for these materials can be developed for the propagation of pulses of light whose length is many times the lattice period. We describe one approach to constructing such theories, based on a canonical description of the electromagnetic field, that allows for an easy construction of conserved quantities and their relation to the symmetries of the system.

Illustrations are given using structures of both fundamental and practical interest.