Gap solitons in a two-channel microresonator structure.

We show that, when two channel waveguides are coupled by a sequence of periodically spaced microresonators, the group-velocity dispersion is low in the vicinity of the gap associated with the resonant frequency of the resonators. This low dispersion permits the excitation of a gap soliton with much lower energy than in a gap of similar width caused by Bragg reflection.

Field profiles and spectral properties of chirped Bragg grating Fabry-Perot interferometers.

We analyze, theoretically, a Fabry-Perot interferometer constructed from superimposed, chirped fiber Bragg gratings. Interference effects between the superimposed gratings play a large role in determining the exact positions of the FP resonances. We give formulae to determine the spatial position of the resonances of the system, and, in certain cases, the profile of their field intensity.

Direct laser writing of three-dimensional photonic-crystal templates for telecommunications.

The past decade has witnessed intensive research efforts related to the design and fabrication of photonic crystals. These periodically structured dielectric materials can represent the optical analogue of semiconductor crystals, and provide a novel platform for the realization of integrated photonics. Despite intensive efforts, inexpensive fabrication techniques for large-scale three-dimensional photonic crystals of high enough quality, with photonic bandgaps at near-infrared frequencies, and built-in functional elements for telecommunication applications, have been elusive.

Effective field theory for the nonlinear optical properties of photonic crystals.

We introduce an effective field theory for the nonlinear optics of photonic crystals of arbitrary dimensionality. Based on a canonical Hamiltonian formulation of Maxwell's equations, canonical effective fields are introduced to describe the electromagnetic field. Conserved quantities are easily constructed and their physical significance identified; the formalism can be easily quantized.

Depositing light in a photonic stop gap by use of Kerr nonlinear microresonators.

We show theoretically that it is possible to trap light in a microresonator structure by use of four-wave mixing. The efficiency of the parametric process is substantially increased by the high group delay of light inside the structure. The energy that is trapped has a half-life of approximately 500 ps in the presence of both linear and nonlinear loss in the channel waveguides and resonators.

All-optical AND gate by use of a Kerr nonlinear microresonator structure.

We numerically demonstrate the feasibility of constructing an all-optical AND gate by using a microresonator structure with Kerr nonlinearity. The gate is much smaller than similar AND gates based on Bragg gratings and has lower power requirements.

Hamiltonian formulation of the nonlinear coupled mode equations.

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.

Canonical Hamiltonian formulation of the nonlinear Schrödinger equation in a one-dimensional, periodic Kerr medium.

A canonical Hamiltonian formulation of the nonlinear Schrödinger equation has been derived in this paper. This formulation governs the dynamics of pulse propagation in a one-dimensional, periodic Kerr medium when the frequency content of the pulse is sufficiently narrow relative to a carrier frequency, and sufficiently far removed from a photonic band gap of the medium. Our Hamiltonian is numerically equal to the energy, and our fields obey canonical commutation relations, so the theory can easily be quantized.