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

Effects of the near-dipole–dipole interaction on gap solitons in resonantly absorbing gratings

Jing Cheng, Jianying Zhou

Published Sep 18, 2002• 12 citations
Publisher

Abstract

Gap solitons can exist in a periodic refractive-index grating modified by periodic layers of near-resonant two-level systems. In this work, we include the effect of the density-dependent near-dipole-dipole (NDD) interaction in order to generalize this model. For certain values of the grating parameters, we find that the NDD interaction significantly modifies the frequency bands in which gap solitons can exist. The difference between the model with and without the NDD interaction is discussed. The stability of gap solitons is studied numerically.

DOI
10.1103/physreve.66.036606

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Gap solitons can exist in a periodic refractive-index grating modified by periodic layers of near-resonant two-level systems. In this work, we include the effect of the density-dependent near-dipole-dipole (NDD) interaction in order to generalize this model. For certain values of the grating parameters, we find that the NDD interaction significantly modifies the frequency bands in which gap solitons can exist. The difference between the model with and without the NDD interaction is discussed. The stability of gap solitons is studied numerically.
We consider an optical medium consisting of a periodic refractive-index grating and a periodic set of thin layers of two-level systems resonantly interacting with the electromagnetic field. Recently, it has been shown that such a system gives rise to a vast variety of stable bright solitons. In this work, we demonstrate that the system has another very unusual property: stable bright solitons can coexist with stable continuous-wave (cw) states and stable dark solitons (DS's). Depending on the parameters' values, a DS frequency band coexists (without overlap) with one or two bright-soliton bands. Quiescent (standing) DS's are found in an analytical form, and moving ones are obtained numerically. Simulations show that a considerable part of the DS solutions are completely stable against arbitrary small perturbations. The fact that this system supports both stable bright and dark solitons for the same parameters values may find interesting applications in photonics.
We present hitherto unknown forms of soliton dynamics in the forbidden frequency gap of a Bragg reflector, modified by periodic layers of near-resonant two-level systems (TLS). Remarkably, even extremely low TLS densities create an allowed band within the forbidden gap. This spectrum gives rise, for any Bragg reflectivity, to a vast family of stable gap solitons, both standing and moving, having a unique analytic form, an arbitrary pulse area, and inelastic collision properties. These findings suggest new possibilities of transmission control, noise filtering, or ``dynamical cavities'' (self-traps) for both weak and strong signal pulses.
In condensed matter of densities such that there are many atoms within a cubic atomic resonance wavelength, induced near dipole-dipole interactions (NDD) effects can cause dynamic frequency chirp in near resonant electromagnetic field-matter interactions.1 Using semiclassical theory for two-level atomic systems and a Green's function solution to the wave equation, we derive a self-consistent set of renormalized Bloch–Maxwell equations, useful for discussion of nonlinear optical processes in condensed matter systems, and discuss some of their implications. The strength of the induced near dipole-dipole coupling is found to be ε = (4π/3) u2n, and it causes inversion-dependent frequency chirp in the system. Here, u is the matrix element of the transition dipole moment and n is the density of atoms.
Summary form only given. In recent years, there has been considerable interest in nonlinear and quantum optics of photonic bandgap structures. Some of this attention has centered on the properties of gap solitary waves, which are light pulses tuned at a Bragg frequency within a forbidden bandgap of the periodic structure. These solitary waves may occur in a periodically modulated medium with a Kerr-like nonlinearity, and in the resonance grating as a two-wave soliton of self-induced transparency. In the later case, the coupled-mode Maxwell-Bloch equations which describe the on-resonance coherent interaction of the intense field with a periodic structure of thin layers of two-level atoms in the ground state, lead to an integrable sine-Gordon equation. In our study, we concentrate on the nonintegrable case, that is, amplification in a resonant Bragg structure by means of a comprehensive analysis that includes and numerical modelling of Dicke superradiance and coherent amplification.