C.M. de Sterke

Multipole method for microstructured optical fibers. I. Formulation

We describe a multipole method for calculating the modes of microstructured optical fibers. The method uses a multipole expansion centered on each hole to enforce boundary conditions accurately and matches expansions with different origins by use of addition theorems. We also validate the method and give representative results.

Confinement losses in microstructured optical fibers

We describe a multipole formulation that can be used for high-accuracy calculations of the full complex propagation constant of a microstructured optical fiber with a finite number of holes. We show how the imaginary part of the microstructure, which describes confinement losses not associated with absorption, varies with hole size, the number of rings of holes, and wavelength, and give the minimum number of rings of holes required for a specific loss for given parameters.

High-intensity pulse propagation in uniform gratings and grating superstructures

We briefly review our recent nonlinear propagation experiments in optical fiber Bragg gratings (FBGs). These experiments demonstrate nonlinear pulse compression, and pulse shaping, and also show how a train of pulses may be generated from a single input pulse. Our results also demonstrate the existence of Bragg grating solitons, solitons which exist by balancing of the nonlinearity of the glass and the dispersion of the grating.

Dynamical localization and AC Bloch oscillations in periodic optical waveguide arrays

We show in detail that an array of optical waveguides whose curvature periodically changes can give rise to AC optical Bloch oscillations. The equivalent of the AC driving field is generated by the periodic curvature change of the waveguide array. For certain ratios of the Bloch oscillation frequency and the drive frequency our numerical simulations show dynamical localization where the optical spatial wavepacket periodically returns to its initial shape and lateral position in the array. We also discuss the experimental implications of this finding.

Two-dimensional Green tensor and local density of states in finite-sized two-dimensional photonic crystals

Abstract The two-dimensional Green tensor for two-dimensional photonic crystals, consisting of clusters of circular cylinders of infinite length, is constructed using the exact theory of multipole expansions. On the basis of this Green tensor, the local density of states for both polarizations is calculated, showing how the density of states depends on the position inside the crystal. We include results for clusters with a waveguide, obtained by removing a line of cylinders, and a cavity, obtained by forming a localized defect.

Efficient slow light coupling into photonic crystals

We study light coupling between two photonic crystal wave-guides, one of which supports slow light. We show theoretically that a short photonic crystal waveguide between the two that need to be coupled, can lead to a vanishingly small reflectivity. The design relies on the analogy with a lambda/4 anti-reflection layer in thin-film optics.We find that some of the usual relationships between the Fresnel coefficients at an interface no longer hold.

Interaction of Bragg solitons in fiber gratings

We investigate numerically the interaction between two copropagating Bragg solitons in a fiber grating. We find that, in the low-intensity limit, the interaction is reminiscent of the nonlinear Schrodinger solitons in that Bragg solitons attract or repel each other, depending on their relative phases. However, the relative phase between two Bragg solitons is found to depend on their initial separation. We discuss the implications of the numerical results for laboratory experiments.

Add-drop multiplexing by dispersion inverted interference coupling

We demonstrate experimentally a previously proposed add-drop multiplexer in a two-moded structure with a symmetric Bragg grating. The strong dispersion in the forward direction outside the reflective region of the grating is used to create a phase change for frequencies between the bandgaps of the supermodes of a twin core fiber. The phase change in transmission inverts the interference pattern at the end of the device. Signals within a narrow wavelength range couple out to one core; all other wavelengths couple out to the opposite core. Preliminary experimental results show a crosstalk ratio of 15 dB.

Soliton dynamics in nonuniform fiber Bragg gratings

The dynamics of optical pulses in nonuniform fiber gratings is studied analytically and numerically. Our approach is based on the inhomogeneous nonlinear Schrodinger equation, derived from the nonlinear coupled-mode equations. The problem is analyzed in the context of an adiabatic soliton compressor. The dependences of the soliton amplitude and width on the propagation distance are found. We also show the presence of the phase modulation during propagation. The possibility of optimizing the fiber-grating compressor by choice of a proper length to minimize the phase modulation is suggested. Comparison of analytical results with numerical simulations shows qualitatively good agreement.

Nonlinear pulse reflections from chirped fiber gratings.

We study the nonlinear evolution of optical pulses reflected from a chirped fiber grating experimentally and with numerical simulations. Over a broad range of grating parameters the nonlinearly reflected pulse splits into a pair of pulses in the range of incident pulse intensities where the transmitted pulse is a single narrowed pulse evolving into a fundamental soliton.