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arXiv:physics/0605194 · Physical Review Letters

Slow-Light Optical Bullets in Arrays of Nonlinear Bragg-Grating Waveguides

Andrey A. Sukhorukov, Yuri S. Kivshar

Published Dec 4, 2006• 39 citations
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Abstract

We demonstrate that propagation direction and velocity of optical pulses can be controlled independently in the structures with multiscale modulation of the refractive index in transverse and longitudinal directions. We reveal that, in arrays of waveguides with phase-shifted Bragg gratings, the refraction angle does not depend on the speed of light, allowing for efficient spatial steering of slow light. In this system, both spatial diffraction and temporal dispersion can be designed independently, and we identify the possibility for self-collimation of slow light when spatial diffraction is suppressed for certain propagation directions. We also show that broadening of pulses in space and time can be eliminated in nonlinear media, supporting the formation of slow-light optical bullets that remain localized irrespective of propagation direction.

DOI
10.1103/physrevlett.97.233901

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We demonstrate that propagation direction and velocity of optical pulses can be controlled independently in the structures with multiscale modulation of the refractive index in transverse and longitudinal directions. We reveal that, in arrays of waveguides with phase-shifted Bragg gratings, the refraction angle does not depend on the speed of light, allowing for efficient spatial steering of slow light. In this system, both spatial diffraction and temporal dispersion can be designed independently, and we identify the possibility for self-collimation of slow light when spatial diffraction is suppressed for certain propagation directions. We also show that broadening of pulses in space and time can be eliminated in nonlinear media, supporting the formation of slow-light optical bullets that remain localized irrespective of propagation direction.
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Time and space are dual variables which bring a lot of analogies during theoretical study. In this paper, we extend the concept of a spatial optical waveguide to the temporal domain. Here we show that it is possible to confine the optical pulse within a time interval by introducing the temporal index boundaries. The confined pulse will propagate at a speed of the index change in the waveguide, and it will be behind the original optical pulse which propagates without the temporal index variations. In this way, we may offer an approach to broaden the bandwidth of the slow light and to tune the light speed based on the existing slow light devices. The temporal waveguide has modes, which are the temporal waveforms maintaining their shapes during the propagation. In a single-mode temporal waveguide, the pulse retains its shape as the only mode of the waveguide just like an optical soliton. In a multimode temporal waveguide, multimode interference effect exists, which can duplicate a single pulse into multiple copies and be potentially implemented for all-optical signal processing.
A standing-wave control field applied to a three-level atomic medium in a planar hollow-core photonic crystal waveguide creates periodic variations of linear and nonlinear refractive indexes of the medium. This property can be used for efficient steering of light. In this work, we study, both analytically and numerically, the dynamics of probe optical beams in such structures. By properly designing the spatial dependence of the nonlinearity, it is possible to induce long-living Bloch oscillations of spatial gap solitons, thus providing desirable change in the direction of the beam propagation without inducing appreciable diffraction. Due to the significant enhancement of the nonlinearity, such self-focusing of the probe beam can be reached at extremely weak light intensities.
A Bragg waveguide is analyzed from the viewpoint of obtaining slow light. It is shown that, for this system, a complete mathematical analysis of the pulse propagation with allowance for leakage is possible. Calculations are presented that show that, in a TiO 2 /SiO 2 -based Bragg waveguide, one can obtain a group index of ∼1000 with a spatial decay length of ∼3 mm for a nanosecond-scale pulse. Distortion of the pulse due to the group index dispersion proves to be acceptable, in this case, for the pulse propagation length of about 3 mm, which corresponds to the fractional pulse delay ∼10. We also analyze the propagation of the light pulse in the Bragg waveguide with a quantum well inside and show possibility of obtaining a group index of ∼10000.