title: Hamiltonian formulation of the nonlinear coupled mode equations.
abstract: We derive a canonical Hamiltonian formulation of the nonlinear coupled mode equations (CME) that govern the dynamics of pulse propagation in a one-dimensional, periodic Kerr medium when the frequency content of the pulse is in the vicinity of a photonic band gap, and sufficiently narrow relative to a carrier frequency. The Hamiltonian is equal to the energy in the electromagnetic field. We show that even for large photonic band gaps (25% of the Bragg frequency), the CME give an excellent approximation to the dispersion relation of the linear, periodic medium. This suggests that two- and three-dimensional photonic band-gap materials, which necessarily have large index contrasts, might be effectively described by a set of generalized CME.
authors.affiliation: Department of Physics, University of Toronto, Toronto, M5S 1A7, Canada.
authors.forename: Suresh
authors.initials: S
authors.lastname: Pereira
authors.forename: J E
authors.initials: JE
authors.lastname: Sipe