Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Experimental and Theoretical Physics Letters

Nonreciprocal Propagation of Solitons in a Chiral Medium

Alexander A. Zabolotskii

Published Sep 1, 2019• 2 citations
Publisher

Abstract

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.

DOI
10.1134/s0021364019170144

Related papers

Solitons in a Chiral Medium

Alexander A. Zabolotskii

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.

Journal of Experimental and Theoretical Physics•Mar 1, 2021•0 citations

Nonlinear electromagnetic pulse isolator

Alexander A. Zabolotskii

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.

Physical Review A•May 18, 2020•1 citation

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

Alexander A. Zabolotskii

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.

Journal of Experimental and Theoretical Physics•Nov 1, 2019•1 citation

Evolution of the unidirectional electromagnetic pulses in an anisotropic two-level medium

Alexander A. Zabolotskii

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.

Physical Review E•Mar 5, 2008•8 citations

Amplification of extremely short pulses in optical media

Alexander A. Zabolotskii

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.

Journal of Experimental and Theoretical Physics•May 1, 2002•8 citations

Analysis of the soliton solutions of a 3-level Maxwell-Bloch system with rotational symmetry

Richard James Waterton

The dynamics of soliton pulses for use in nonlinear optical devices is mathematically modelled by Maxwell-Bloch systems of equations for the interaction of light with a uniform distribution of quantum-mechanical atoms. We study the Reduced Maxwell-Bloch (RMB) equations occurring when an ensemble of rotationally symmetric 3-level atoms is assumed. The model applies for on and off-resonance conditions and is completely integrable using Inverse Scattering theory, since it arises as the compatibility condition of a 3 x 3 AKNS-system. Furthermore this integrability remains valid for all timescales of the optical field because only the “one-way wave approximation” is required during the derivation. Solutions are constructed in two ways: 1. Darboux-Bäcklund transforms are applied, generating single soliton pulses of ultrashort (< 1ps) duration, and families of elliptically polarised 2-solitons not possible in lower dimensional problems. 2. A general Inverse Scattering scheme is developed and tested. The Direct Scattering Problem is dealt with first to obtain a complete set of scattering data. Subsequently the Inverse Problem is solved both formally and then in explicit closed form for the special case that the reflection coefficients vanish for real values of the spectral parameter. In this case the main result is a determined system of n linear algebraic equations which yield the n-soliton of our RMB-system. It is confirmed that the 1-solitons found by means of Darboux transform are precisely the same as those given by the full mechanism of Inverse Scattering. Finally we calculate the invariants of the motion for the RMB-equations, and derive an evolution equation giving the variation with propagation distance of the invariant functionals when the original RMB-system is modified by an arbitrary perturbing term. As an application dissipative effects on 1-solitons are considered.

•Jan 1, 2004•1 citation
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 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.
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 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 dynamics of soliton pulses for use in nonlinear optical devices is mathematically modelled by Maxwell-Bloch systems of equations for the interaction of light with a uniform distribution of quantum-mechanical atoms. We study the Reduced Maxwell-Bloch (RMB) equations occurring when an ensemble of rotationally symmetric 3-level atoms is assumed. The model applies for on and off-resonance conditions and is completely integrable using Inverse Scattering theory, since it arises as the compatibility condition of a 3 x 3 AKNS-system. Furthermore this integrability remains valid for all timescales of the optical field because only the “one-way wave approximation” is required during the derivation. Solutions are constructed in two ways: 1. Darboux-Bäcklund transforms are applied, generating single soliton pulses of ultrashort (< 1ps) duration, and families of elliptically polarised 2-solitons not possible in lower dimensional problems. 2. A general Inverse Scattering scheme is developed and tested. The Direct Scattering Problem is dealt with first to obtain a complete set of scattering data. Subsequently the Inverse Problem is solved both formally and then in explicit closed form for the special case that the reflection coefficients vanish for real values of the spectral parameter. In this case the main result is a determined system of n linear algebraic equations which yield the n-soliton of our RMB-system. It is confirmed that the 1-solitons found by means of Darboux transform are precisely the same as those given by the full mechanism of Inverse Scattering. Finally we calculate the invariants of the motion for the RMB-equations, and derive an evolution equation giving the variation with propagation distance of the invariant functionals when the original RMB-system is modified by an arbitrary perturbing term. As an application dissipative effects on 1-solitons are considered.