Nonlinear pulse propagation in birefringent fiber Bragg gratings

Hybrid nanowires for phase-matching of third-harmonic generation in hyperbolic metamaterial

We propose a phase-matching technique for third-harmonic generation, called hyperbolic phase matching, that possibly can be achieved by optimal designing and engineering dispersion of hybrid-nanowire hyperbolic metamaterial. We demonstrate phase-matched conditions for two different third-harmonic interacting configurations, which can be created at two optimal incident angles of the pump field. Moreover, each composed hybrid nanowire can enhance third-harmonic generation by using strong field confinement along the metal/dielectric interface due to plasmonic resonance. Finally, conversion efficiencies of transmitted and reflected third-harmonic pulses as a function of incident angle and input pulse intensity are examined by numerical integration of nonlinear birefringent coupled-mode equations. The numerical results validate the idea that, using a combination of phase-matched conditions and pump field confinement, we can achieve a dramatic enhancement of conversion efficiencies of third-harmonic generation.

Optical AND gate based on soliton interaction in a fiber Bragg grating

Using computer simulations, we demonstrate an optical cascadable AND gate based on soliton interaction in a fiber Bragg grating. A single soliton that is launched into the device is backreflected. When two solitons are launched, one of the solitons is transmitted while the other is backreflected. The time delay between the solitons may be few times longer than the duration of the solitons. We show that the interaction causes an increase in the frequency of one of the solitons that enables its transmission through the grating bandgap.

Light propagation through birefringent, nonlinear media with deep gratings

We present a theory that includes birefringence in the description of one-dimensional photonic band-gap materials with a Kerr nonlinearity. The Bloch functions in the absence of nonlinearity completely characterize the linear problem, for deep as well as shallow gratings, and the method of multiple scales is used to include the effects of nonlinearity and finite optical pulse length. We derive two sets of equations appropriate in different frequency regimes, a set of coupled mode equations and a set of coupled nonlinear Schrodinger equations; we investigate the connections between these equations and where their regimes of validity overlap. Finally, we use our results to describe energy exchange between polarization modes in a birefringent medium.

Bragg-grating-enhanced polarization instabilities

Experiments demonstrate a dramatic decrease in polarization-instability threshold as an optical pulse is tuned near the short-wavelength edge of the photonic bandgap formed by a fiber Bragg grating. These enhanced nonlinear interactions and birefringent effects are modeled with coupled-mode numerical simulations. Nonlinearities are shown to increase much more rapidly than the effective birefringence as the pulse wavelength approaches the bandgap edge.

Corrections to coupled mode theory for deep gratings

We generalize the standard coupled mode equations describing interactions between forward and backward propagating waves in a nonlinear optical Bragg grating. Including the lowest order corrections of the grating depth, we obtain a Hamiltonian system that can be regarded as an extension of the usual coupled mode equations for shallow gratings. The results are consistent with existing results based on a Bloch wave expansion. We also obtain exact traveling solitary wave solutions, that can be regarded as a generalized gap soliton, modified by the grating's depth.