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

IEEE Journal of Quantum Electronics

Some effects of group-velocity dispersion on parametric interactions

John A. Armstrong, Sudhanshu Shekhar Jha, N. S. Shiren

Published Feb 1, 1970• 83 citations
Publisher

Abstract

Three-wave parametric interactions are studied in media exhibiting group-velocity dispersion. Under certain conditions these interactions may be described by the same equations that govern pulse propagation in a two-level resonant system. This analogy suggests the existence of steady-state pulse solutions in the three-wave parametric system. Such solutions are found, and are analogues of pi and two-pi pulses. The variety of solutions in the parametric system is greater than in the resonant case.

DOI
10.1109/jqe.1970.1076386

Related papers

Π-pulse propagation in the presence of host dispersion

John A. Armstrong, E. Courtens

A steady-state solution describing\Pi-pulse propagation in a homogeneously broadened laser amplifier embedded in a dispersive lossy host is found. For a given model of dispersion, the solution satisfies exactly the second-order wave equation together with the equations of motion for the density matrix of the two-level resonant system. The salient feature of the solution is that a small amount of dispersion in the host group velocity causes a large monotonic frequency sweep during the pulse. The effects of this chirp on the pulse properties are described in detail, and the relation of the theory to experiments is discussed.

IEEE Journal of Quantum Electronics•May 1, 1969•50 citations

Theory of shape-preserving short pulses in inhomogeneously broadened three-level media

Ashiqur Rahman, Joseph H. Eberly

We introduce an ansatz that permits a treatment of the effects of Doppler broadening in the theory of intense steady-state pulse pairs propagating in three-level (\ensuremath{\Lambda} or V) media. We have derived analytic solutions for pulse amplitudes, for group and phase velocities, and for the probability amplitudes of the atoms in the transmission medium. The solutions are different for the \ensuremath{\Lambda} and V cases.

Physical Review A•Aug 1, 1998•44 citations

Theory of propagation of ultrashort light pulses in a threelevel medium

Maria V. Bogdanova, Tamara M. Il'inova

The results are given of a theoretical investigation of the interaction between two ultrashort pulses J1 and J2 of frequencies ω31 and ω21 with a three-level amplifying medium. It is assumed that the signal J1 of frequency ω31 is a steady-state π pulse and the signal J2 is weak so that its influence on the level populations can be ignored. The case when the signal J2 has a steady-state amplitude profile and an exponential gain is considered. The analysis is made ignoring the group delay effects and also allowing for the mismatch of the group velocities of the signals. The results obtained can be used in studies of the amplification of ultrashort pulses in molecular media such as organic dyes or CO2 molecules.

Soviet Journal of Quantum Electronics•Oct 31, 1975•0 citations

Phase modulation and parametric broadening of the spectrum of a pulse in a two-level resonant medium

Grigorii G Grigoryan, A. O. Melikyan

An analytic solution is obtained for the self-consistent equations describing propagation of an ultrashort pulse in a resonant two-level medium. The first approximation in respect of the dispersion is used to allow for phase modulation and for the dependence of the group velocity on the intensity and on the running value of the frequency. The conditions for the formation of a shock wave are established. It is shown that asymmetric broadening of the spectrum of a pulse results in coherent absorption, as a result of which the propagation of this pulse in such a medium leaves behind a polarization at the atomic transition frequency responsible for the radiation represented by the pulse.

Soviet Journal of Quantum Electronics•Dec 31, 1986•0 citations

Soliton interaction in a nonlinear waveguide in the presence of resonances

Joao F. L. de Freitas, E. J. S. Fonseca, Solange Bessa Cavalcanti +1 more

Using the coherent dynamics of a three-level system together with nonlinear and dispersive pulse propagation we show, through breakup and parametric amplification, the interaction between two solitary waves.

Nonlinear Guided Waves and Their Applications•Jan 1, 2001•0 citations

Self-induced transparency in self-chirped media

Carlos R. Stroud, C. M. Bowden, L. Allen

Resonant absorbing media having many atoms within a cubic resonance wavelength can exhibit large frequency chirps in pulse propagation due to dipole-dipole interactions among the atoms. Analytic solutions are obtained for invariant pulse propagation in such a medium consisting of interacting two-level atoms. Departures from the McCall-Hahn results include nonhyperbolic secant pulse shapes and different than 2π-area pulses. In addition, the excitation of the medium is comparatively suppressed for the same group velocity. The results are interpreted to suggest new experiments.

Optics Communications•Aug 1, 1988•51 citations
Three-wave parametric interactions are studied in media exhibiting group-velocity dispersion. Under certain conditions these interactions may be described by the same equations that govern pulse propagation in a two-level resonant system. This analogy suggests the existence of steady-state pulse solutions in the three-wave parametric system. Such solutions are found, and are analogues of pi and two-pi pulses. The variety of solutions in the parametric system is greater than in the resonant case.
A steady-state solution describing\Pi-pulse propagation in a homogeneously broadened laser amplifier embedded in a dispersive lossy host is found. For a given model of dispersion, the solution satisfies exactly the second-order wave equation together with the equations of motion for the density matrix of the two-level resonant system. The salient feature of the solution is that a small amount of dispersion in the host group velocity causes a large monotonic frequency sweep during the pulse. The effects of this chirp on the pulse properties are described in detail, and the relation of the theory to experiments is discussed.
The results are given of a theoretical investigation of the interaction between two ultrashort pulses J1 and J2 of frequencies ω31 and ω21 with a three-level amplifying medium. It is assumed that the signal J1 of frequency ω31 is a steady-state π pulse and the signal J2 is weak so that its influence on the level populations can be ignored. The case when the signal J2 has a steady-state amplitude profile and an exponential gain is considered. The analysis is made ignoring the group delay effects and also allowing for the mismatch of the group velocities of the signals. The results obtained can be used in studies of the amplification of ultrashort pulses in molecular media such as organic dyes or CO2 molecules.
An analytic solution is obtained for the self-consistent equations describing propagation of an ultrashort pulse in a resonant two-level medium. The first approximation in respect of the dispersion is used to allow for phase modulation and for the dependence of the group velocity on the intensity and on the running value of the frequency. The conditions for the formation of a shock wave are established. It is shown that asymmetric broadening of the spectrum of a pulse results in coherent absorption, as a result of which the propagation of this pulse in such a medium leaves behind a polarization at the atomic transition frequency responsible for the radiation represented by the pulse.
Resonant absorbing media having many atoms within a cubic resonance wavelength can exhibit large frequency chirps in pulse propagation due to dipole-dipole interactions among the atoms. Analytic solutions are obtained for invariant pulse propagation in such a medium consisting of interacting two-level atoms. Departures from the McCall-Hahn results include nonhyperbolic secant pulse shapes and different than 2π-area pulses. In addition, the excitation of the medium is comparatively suppressed for the same group velocity. The results are interpreted to suggest new experiments.