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 the Optical Society of America B

Steady-state pulse propagation in inhomogeneously broadened absorbers in the presence of a Kerr nonlinearity

Ljubomir Matulic, J. J. Sánchez-Mondragón, G. E. Torres-Cisneros, Christopher Palmer

Published Aug 1, 1988• 4 citations
Publisher

Abstract

We consider the effect of a background dielectric on the steady-state propagation of a laser pulse through inhomogeneously broadened two-level atoms embedded in the dielectric. Because this problem apparently does not admit of analytic solutions, we have solved it numerically. A comparison of our results with the known analytic solutions for the homogeneously broadened atomic line shows that the two are similar. It seems that the new numerical solutions, unlike those for the homogeneous line, are not factorable, a fact to which we ascribe the difficulty in finding analytic solutions. We have found that as the atomic line broadens, the pulse widens and its height decreases, maintaining its area virtually constant.

DOI
10.1364/josab.5.001673

Related papers

Coherent pulse propagation in a resonant absorber with Kerr-type nonlinearity

Ljubomir Matulic, G. E. Torres-Cisneros, Javier J. Sanchez-Mondragon

We present a numerical study of the non-steady-state pulse propagation in a resonant inhomogeneously broadened absorber embedded in a dielectric medium with a Kerr-type nonlinearity. We find that the individual atomic dipoles are dephased and that their evolution depends on their detunings. We think that this is the reason for small energy losses that prevent the pulse from attaining a truly steady-state nature. We discuss the implications of this result in relation to previous studies. Our results point to the existence of near-steady-state Kerr pulses, similar to the ideal solitons.

Journal of the Optical Society of America B•Jun 1, 1991•6 citations

Coherent resonant pulse propagation in a Kerr absorber

Ljubomir Matulic, G. F. Torres-Cisneros, J. J. Sánchez-Mondragón

We present a numerical study of the nonsteady state pulse propagation in a resonant inhomogeneously broadened absorber embedded in a dielectric medium with a Kerr-type nonlinearity. We abandon the a priori assumption for the existence of steady state solutions and examine the problem from a more physical point of view, i.e., we study the way in which the pulse actually propagates in the resonant Kerr medium and whether it eventually evolves toward a steady state. We find that the individual atomic dipoles are dephased and that their evolution depends on detunings. We believe that this is the reason for small energy losses which deny the attainment of a truly steady state pulse.

Annual Meeting Optical Society of America•Jan 1, 1989•0 citations

Self-induced transparency in the presence of the Kerr nonlinearity

R. Michalska-Trautman

The self-induced transparency solution of the Bloch-Maxwell equations is found in the case of inhomogeneously broadened resonant atomic lines and a host medium with a Kerr-type nonlinearity in the index of refraction. The characteristic feature of the solution is that the atomic functions are not factorized. The time dependence of the pulse phase is different from that in the case of a sharp atomic line. In addition to the known term quadratic in the pulse envelope, it contains a term increasing in time, attaining a maximum at the trailing edge of the pulse, and rapidly decreasing afterwards. The average carrier frequency is proportional to the square of the spectral width of the atomic line divided by the squared width of the pulse. A satisfactory solution is found by modulation of the center of the Lorentz distribution function of the purely resonant solutions. It is shown that in the presence of the inhomogeneous broadening the problem cannot be solved by a linear perturbation expansion with respect to the Kerr constant. This method leads to divergencies near the trailing edge of the pulse.

Physical Review A•May 1, 1978•6 citations

Self-induced transparency in a dispersive and nonlinear Kerr host medium

Tsun-Yee Wang, Sien Chi

A steady-state solution that describes pulse propagation in inhomogeneously broadening two-level atoms embedded in a dispersive and nonlinear Kerr lossless host medium has been found. The solution is of an unchirped hyperbolic-secant form with a linear spatial phase delay. The features of the solution are (i) the group velocity, the amplitude, and the width of the pulse are uniquely determined for given parameters of the medium and the carrier frequency; (ii) the group velocity is independent of the density of the resonant atoms; and (iii) the solution can exist in the positive dispersion region.

Optics Letters•Oct 15, 1991•10 citations

Self-induced transparency solitons in a nonlinear Kerr host

Tsun-Yee Wang, Sien Chi

We have found a steady-state solution for a pulse propagating in imhogeneously broadened resonant two-level atoms embedded in a dispersive and nonlinear Kerr lossless host medium. The pulse is of an unchirped hyperbolic-secant form with a linear spatial phase delay. There are several salient features in this solution which are different from the results obtained previously. First, for the given parameters of the medium and carrier frequency, the group velocity, the amplitude, and the pulse width are uniquely determined. Second, the group velocity is independent of the density of the resonant atoms. Third, the solution exists in the positive dispersion region, which is different from solitons in fibers.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations

Coherent absorption in a homogeneously broadened medium

Lee E. Estes, D. Eteson, Lorenzo M. Narducci

An investigation of the propagation properties of a short pulse in a resonant absorber with a homogeneously broadened transition is presented with two main questions in mind: 1) the influence of the input pulse area on the transitory regime and on the steady-state propagation; 2) the effects of atomic coherence on the pulse shaping and the time delay of the leading edge of the pulse. The transitory regime of a propagating pulse is investigated and the stability of some asymptotic wave form confirmed. As expected, the transversal relaxation mechanism affects critically the major features of the coherent interaction. A detailed analysis of this problem is also presented.

IEEE Journal of Quantum Electronics•Sep 1, 1970•8 citations
We consider the effect of a background dielectric on the steady-state propagation of a laser pulse through inhomogeneously broadened two-level atoms embedded in the dielectric. Because this problem apparently does not admit of analytic solutions, we have solved it numerically. A comparison of our results with the known analytic solutions for the homogeneously broadened atomic line shows that the two are similar. It seems that the new numerical solutions, unlike those for the homogeneous line, are not factorable, a fact to which we ascribe the difficulty in finding analytic solutions. We have found that as the atomic line broadens, the pulse widens and its height decreases, maintaining its area virtually constant.
We present a numerical study of the non-steady-state pulse propagation in a resonant inhomogeneously broadened absorber embedded in a dielectric medium with a Kerr-type nonlinearity. We find that the individual atomic dipoles are dephased and that their evolution depends on their detunings. We think that this is the reason for small energy losses that prevent the pulse from attaining a truly steady-state nature. We discuss the implications of this result in relation to previous studies. Our results point to the existence of near-steady-state Kerr pulses, similar to the ideal solitons.
We present a numerical study of the nonsteady state pulse propagation in a resonant inhomogeneously broadened absorber embedded in a dielectric medium with a Kerr-type nonlinearity. We abandon the a priori assumption for the existence of steady state solutions and examine the problem from a more physical point of view, i.e., we study the way in which the pulse actually propagates in the resonant Kerr medium and whether it eventually evolves toward a steady state. We find that the individual atomic dipoles are dephased and that their evolution depends on detunings. We believe that this is the reason for small energy losses which deny the attainment of a truly steady state pulse.
The self-induced transparency solution of the Bloch-Maxwell equations is found in the case of inhomogeneously broadened resonant atomic lines and a host medium with a Kerr-type nonlinearity in the index of refraction. The characteristic feature of the solution is that the atomic functions are not factorized. The time dependence of the pulse phase is different from that in the case of a sharp atomic line. In addition to the known term quadratic in the pulse envelope, it contains a term increasing in time, attaining a maximum at the trailing edge of the pulse, and rapidly decreasing afterwards. The average carrier frequency is proportional to the square of the spectral width of the atomic line divided by the squared width of the pulse. A satisfactory solution is found by modulation of the center of the Lorentz distribution function of the purely resonant solutions. It is shown that in the presence of the inhomogeneous broadening the problem cannot be solved by a linear perturbation expansion with respect to the Kerr constant. This method leads to divergencies near the trailing edge of the pulse.
A steady-state solution that describes pulse propagation in inhomogeneously broadening two-level atoms embedded in a dispersive and nonlinear Kerr lossless host medium has been found. The solution is of an unchirped hyperbolic-secant form with a linear spatial phase delay. The features of the solution are (i) the group velocity, the amplitude, and the width of the pulse are uniquely determined for given parameters of the medium and the carrier frequency; (ii) the group velocity is independent of the density of the resonant atoms; and (iii) the solution can exist in the positive dispersion region.
We have found a steady-state solution for a pulse propagating in imhogeneously broadened resonant two-level atoms embedded in a dispersive and nonlinear Kerr lossless host medium. The pulse is of an unchirped hyperbolic-secant form with a linear spatial phase delay. There are several salient features in this solution which are different from the results obtained previously. First, for the given parameters of the medium and carrier frequency, the group velocity, the amplitude, and the pulse width are uniquely determined. Second, the group velocity is independent of the density of the resonant atoms. Third, the solution exists in the positive dispersion region, which is different from solitons in fibers.
An investigation of the propagation properties of a short pulse in a resonant absorber with a homogeneously broadened transition is presented with two main questions in mind: 1) the influence of the input pulse area on the transitory regime and on the steady-state propagation; 2) the effects of atomic coherence on the pulse shaping and the time delay of the leading edge of the pulse. The transitory regime of a propagating pulse is investigated and the stability of some asymptotic wave form confirmed. As expected, the transversal relaxation mechanism affects critically the major features of the coherent interaction. A detailed analysis of this problem is also presented.