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Hamiltonian formulation of the nonlinear coupled mode equations
Phys. Rev. E 66, 026606 – Published 28 August, 2002
DOI: https://doi.org/10.1103/PhysRevE.66.026606
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.
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