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Journal of Experimental and Theoretical Physics

Solitons in a Chiral Medium

Alexander A. Zabolotskii

Published Mar 1, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776121030213

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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.
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.
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 formation and dynamics of excitations in an atomic or molecular nano chain of a helical shape are studied. The dipole-dipole interaction between the circular polarizations of the optical transitions of neighboring molecules is taken into account. The derived Bloch equations are solved in a continuum approximation using the Frenet–Serret coordinate system. Solutions are obtained that describe the formation of stable localized structures (solitons) due to the curvature of the chain, which can have a critical influence on the luminescent properties of the chiral medium.
The dynamics of pulses with durations comparable to the inverse transition frequency that propagate in an optical medium is studied in terms of two integrable systems of Maxwell-Bloch equations. The first model describes the field interaction with a nondegenerate medium with a permanent dipole moment and permanent external pumping. A general formula is derived for the N -soliton solution. Particular solutions are used as examples to investigate the effect of permanent dipole moment and pumping on the soliton dynamics. The second model describes the interaction between two-component electric-field pulses and a two-level degenerate medium with permanent upper-level pumping. For different initial magnetic-sublevel populations, soliton solutions are used as examples to show that pumping causes a change in polarization dynamics. A two-soliton solution is used to analyze the interaction of solitons in a two-level medium with external pumping.
The evolution equations of two-frequency stimulated Raman scattering in a molecular quasithree- level medium with static dipole moments have been derived in the approximations of the nondepletion of the pump field and the unidirectional propagation of the Stokes field. Completely integrable particular cases of the resulting system of equations have been found. New mechanisms of controlling the parameters of microwave pulses generated in such a system have been studied within this model. The numerical analysis and particular exact solutions demonstrate the possibility of switch between the regimes of generation of narrow Stokes field pulses and nearly rectangular pulses.