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Journal of Experimental and Theoretical Physics

Envelope-Free Solitons in a Two-Level Medium Implanted into an Anisotropic Matrix

Alexander A. Zabolotskii

Published Nov 1, 2019• 1 citation
Publisher

Abstract

Abstract A model of evolution of field pulses in a medium of two-level atoms implanted into an anisotropic matrix is considered. It is shown that the system of reduced Maxwell–Bloch equations in the approximation of unidirectional propagation can be completely integrable. For a particular case of the model, soliton solutions describing the field pulse evolution are obtained. It is shown that by changing the anisotropy parameters of the external medium, pulse parameters can be controlled.

DOI
10.1134/s1063776119090140

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Abstract A model of evolution of field pulses in a medium of two-level atoms implanted into an anisotropic matrix is considered. It is shown that the system of reduced Maxwell–Bloch equations in the approximation of unidirectional propagation can be completely integrable. For a particular case of the model, soliton solutions describing the field pulse evolution are obtained. It is shown that by changing the anisotropy parameters of the external medium, pulse parameters can be controlled.
We find a general integrable system of reduced Maxwell-Bloch equations describing the interaction of a two-component electromagnetic field with the dipole transition of a two-level medium. The anisotropy of the anisotropic dipole momentum of the transition as a permanent dipole momentum is taken into account. A solution of the model is found for a particular case by using the inverse scattering transform. The method is based on a solution of the Riemann-Hilbert problem taking into account the symmetry properties of the corresponding fundamental solutions.
The evolution of the electromagnetic field in a two-level medium occurring in a matrix with finite response time has been studied. An integrable variant of the Maxwell-Bloch equations with allowance for nonlinear dispersion is derived and solved using the inverse scattering problem. It is shown that the nonlinear dispersion caused by the finite response time of the matrix yields a new possibility of controlling soliton parameters. A particular case of the constructed model can be used to describe field pulses in the parameter domain that occurs between the regions of applicability of the quasi-monochromatic approximation and the approximation of unidirectional propagation of pulses with durations on the order of the oscillation period.
Abstract The dynamics of a field in a thin waveguide surrounded by helically arranged two-level atoms is studied. The interaction of the induced polarizations of atoms with the field propagating inside the waveguide is described by a system of reduced Maxwell–Bloch equations (RMBEs) in the approximation of unidirectional propagation of the field. Nonlocal dipole–dipole interaction (DDI) of the polarizations of atoms in the helix is described in the approximation of the interaction of nearest neighbors in a curvilinear medium. Soliton solutions of an integrable reduction of the system of equations describing the asymmetric propagation of field pulses in the waveguide in the forward and backward directions are found by the method of Riemann problem with zeros. It is shown that, depending on the chirality sign or the propagation direction, a field pulse in the waveguide can have either the shape of a sharp peak or a nearly rectangular shape. Solutions describing the evolution of field pulses on a nonzero pedestal show that the shape and amplitude of the field pulses can be controlled by the external pumping parameters.
A nonlinear medium with nonreciprocal propagation of electromagnetic field pulses is proposed and studied. The medium consists of a long waveguide surrounded by two-level media implanted in a straight spiral. Respective Maxwell-Bloch system describing evolution of the pulses in the waveguide with nonlinear feedback is derived. The influence of the neighbors' dipole fields taken into account in the tight bounding approximation manifests itself in the appearance of the nonlinear differential terms. Under the condition of unidirectional propagation of field pulses, the Maxwell-Bloch system of equations is reduced to an integrable system. Analysis of obtained exact solutions have shown that these differential terms are responsible for the nonreciprocity of the propagation of field pulses in the waveguide. Using the soliton solution as an example, it is shown that the spiral arrangement of atoms yields critical dependence of the evolution of field pulses on the direction of their propagation or on the chirality of the medium.
The evolution of polarization of a light pulse in a system consisting of two-level atoms located on symmetric helices twisted into a bundle has been considered. The interaction of induced dipoles is taken into account by additional third order differential terms in Maxwell’s equations in the nearest neighbor approximation. An integrable generalization of the reduced Maxwell-Bloch equations has been derived under the conditions of almost unidirectional propagation. The analysis of the solutions obtained has shown that the evolution of field pulses critically depends on the direction of their propagation or on the chirality of the medium.
Abstract An integrable model is proposed for a two-level medium with a constant dipole moment, which describes the evolution of electromagnetic field pulses without an envelope with account for the dipole–dipole interaction. In the nearest neighbor approximation, this interaction is taken into account in the form of quadratic dispersion. It is found that such a generalization of the reduced Maxwell–Bloch equations preserves the complete integrability. It is shown using the obtained exact soliton solutions as examples that the joint effect of quadratic dispersion and the constant dipole moment has a number of unique features and provides new opportunities for controlling the shape of field pulses. In particular, it is found that the shape and amplitude of a field pulse depend on the signs of the dipole–dipole interaction as well as on the sign of the constant dipole moment.