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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide

John E. Heebner, Robert W. Boyd, Q‐Han Park

Published Mar 6, 2002• 150 citations
Publisher

Abstract

We describe an optical transmission line that consists of an array of wavelength-scale optical disk resonators coupled to an optical waveguide. Such a structure leads to exotic optical characteristics, including ultraslow group velocities of propagation, enhanced optical nonlinearities, and large dispersion with a controllable magnitude and sign. This device supports soliton propagation, which can be described by a generalized nonlinear Schrodinger equation.

DOI
10.1103/physreve.65.036619

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We describe an optical transmission line that consists of an array of wavelength-scale optical disk resonators coupled to an optical waveguide. Such a structure leads to exotic optical characteristics, including ultraslow group velocities of propagation, enhanced optical nonlinearities, and large dispersion with a controllable magnitude and sign. This device supports soliton propagation, which can be described by a generalized nonlinear Schrodinger equation.
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An optical fiber consists of a transparent core surrounded by a transparent cladding material with a lower refractive index. Fibers which can be used for many propagation paths or transverse modes are called Multi-Mode Fibers whereas those which can only support a single mode are called Single Mode Fiber. Optical solitons are localized as electromagnetic waves that propagate in nonlinear media resulting from a balance between nonlinearity and linear broadening due to dispersion and/or diffraction. Ring resonators are employed to generate signals used for optical communication applications, where they can be integrated in a single system. A PANDA ring resonator can be used to generate chaotic signals. Slow light refers to the control of the light velocity in a particular medium. Slow light techniques can be used for future optical communication systems, including optical buffering, data synchronization and optical memories.
We investigate the formation and propagation of optical solitons in an asymmetric double quantum-well structure. Using a standard method of multiple scales we derive a nonlinear Schr\"odinger (NLS) equation with some high-order correction terms that describe effects of linear and differential absorption, nonlinear dispersion, delay response of nonlinear refractive index, and third-order dispersion of a probe field. We show that in order to make slowly varying envelope approximation be valid an excitation scheme of interband transition should be adopted. We also show that for realistic quantum-well parameters the probe field with time length of picosecond or shorter must be used to make dispersion and nonlinear lengths of the system be smaller than absorption length, only by which a shape-preserving propagation of optical solitons is available. In addition, we clarify validity domains for the perturbed NLS equation as well as the high-order NLS equation and provide various optical soliton solutions in different regimes both analytically and numerically. We demonstrate that the solitons obtained have ultraslow propagating velocity and can be generated under very low input light intensity.
We investigate the simultaneous formation and propagation of coupled ultraslow optical soliton pairs in a cold, lifetime-broadened three-state double-Lambda atomic system. Starting from the equations of motion of atomic response and two-mode probe-control electromagnetic fields, we derive coupled nonlinear Schrödinger equations that govern the nonlinear evolution of the envelopes of the probe fields in this four-wave mixing scheme by means of the standard method of multiple scales. We demonstrate that for weak probe fields and with suitable operation conditions, a pair of coupled optical solitons moving with remarkably slow propagating velocity can be established in such a highly resonant atomic medium. The key elements to such a shape preserving, well matched yet interacting soliton pair is the balance between dispersion effect and self- and cross-phase modulation effects of the system.