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

Self-induced transparency of circularly polarized femtosecond pulses

Alexander A. Zabolotskii

Published May 1, 2003• 17 citations
Publisher

Abstract

The phenomenon of self-induced transparency in a two-level medium is studied using a new integrable set of evolution equations for the optical pulses with a duration on the order of the energy-transition oscillation period. A mathematical apparatus is developed for the inverse scattering problem and used to obtain solitonic solutions to the model. The characteristics of linearly and circularly polarized pulses are compared with each other.

DOI
10.1134/1.1591970

Related papers

Unidirectional optical solitons in a two-level medium

Alexander A. Zabolotskii

Self-induced transparency is analyzed for optical pulses interacting with a two-level system by solving an integrable system of evolution equations without using the slowly varying envelope approximation. A suitable modification of the inverse scattering method is developed to find soliton solutions. The characteristics of linearly and circularly polarized optical solitons (including those created in a laser) are compared. To assess the scope of the two-level model, the effects due to additional levels are analyzed in the adiabatic approximation. It is shown that these effects violate the integrability of the model and lead to loss of self-induced transparency for pulses with duration comparable to oscillation period. However, self-induced transparency is recovered in the quasi-monochromatic limit. Applications of the results are discussed.

Journal of Experimental and Theoretical Physics•Jun 1, 2004•3 citations

New exactly integrable models of self-induced transparency

Ashat M. Basharov

A new physical and mathematical formulation of the pulse evolution problem is proposed based on the inverse scattering transform method and a new spectral problem. The polarization of ultrashort pulse and level degeneracy of atoms are taken into account. The Gel'fand-Levitan-Marchenko equations and soliton solutions are obtained. The change in polarization of colliding solitons is demonstrated.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 31, 2006•0 citations

Self-induced transparency in a dispersive medium

Alexander A. Zabolotskii

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.

Journal of Experimental and Theoretical Physics•Jul 1, 2012•0 citations

Propagation of a self-induced transparency pulse in a spatially dispersive medium

Yu. G. Gladush, A. M. Kamchatnov

Propagation of a self-induced transparency pulse in spatially dispersive media is analyzed. A generalized model of two-level systems allowing for excitonic energy transfer is proposed. Periodic and soliton solutions to the governing equations are found. Estimates show that the spatial dispersion of a pulse propagating in a slow-light medium can be substantially enhanced and become important in the case of resonant transition and sufficiently long pulse duration.

Journal of Experimental and Theoretical Physics•Apr 1, 2006•0 citations

Dynamical model of coherent circularly polarized optical pulse interactions with two-level quantum systems

Gabriela M. Slavcheva, Ortwin G. Hess

We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference $(\ensuremath{\Delta}{J}_{z}=\ifmmode\pm\else\textpm\fi{}1)$ excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms.

Physical Review A•Nov 3, 2005•19 citations

Solitons of the reduced Maxwell–Bloch equations for circularly polarized light

Heinz Steudel, Alexander A. Zabolotskii

It is shown that the reduced Maxwell–Bloch equations for circularly polarized light are integrable by the inverse scattering transform method. A Bäcklund transformation is given and used to construct a hierarchy of N -soliton solutions. The breather solution corresponding to the 2π-pulse of self-induced transparency is discussed in some detail.

Journal of Physics A Mathematical and General•Apr 21, 2004•13 citations
The phenomenon of self-induced transparency in a two-level medium is studied using a new integrable set of evolution equations for the optical pulses with a duration on the order of the energy-transition oscillation period. A mathematical apparatus is developed for the inverse scattering problem and used to obtain solitonic solutions to the model. The characteristics of linearly and circularly polarized pulses are compared with each other.
Self-induced transparency is analyzed for optical pulses interacting with a two-level system by solving an integrable system of evolution equations without using the slowly varying envelope approximation. A suitable modification of the inverse scattering method is developed to find soliton solutions. The characteristics of linearly and circularly polarized optical solitons (including those created in a laser) are compared. To assess the scope of the two-level model, the effects due to additional levels are analyzed in the adiabatic approximation. It is shown that these effects violate the integrability of the model and lead to loss of self-induced transparency for pulses with duration comparable to oscillation period. However, self-induced transparency is recovered in the quasi-monochromatic limit. Applications of the results are discussed.
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.
We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference $(\ensuremath{\Delta}{J}_{z}=\ifmmode\pm\else\textpm\fi{}1)$ excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms.