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

arXiv:1212.6474 · Physical Review A

Propagation of subcycle pulses in a two-level medium: Area-theorem breakdown and pulse shape

Denis V. Novitsky

Published Dec 27, 2012• 40 citations
arXivHTMLPDF

Abstract

We solve the problem of ultrashort pulse propagation in a two-level medium beyond the rotating-wave (RWA) and slowly varying-envelope approximations. The method of solution is based on the Maxwell-Bloch equations represented in the form that allows one to switch between RWA and general (non-RWA) cases in the framework of a single numerical algorithm. Using this method, the effect of a subcycle pulse (containing less than a single period of field oscillations) on the two-level medium was analyzed. It is shown that for such short pulses, the clear breakdown of the area theorem occurs for the pulses of large enough area. Moreover, deviations from the area theorem appear to be strongly dependent on the pulse shape that cannot be observed for longer few-cycle pulses.

DOI
10.1103/physreva.86.063835

Related papers

Area evolution of a few-cycle pulse laser in a two-level-atom medium

Jian Xiao, Zhongyang Wang, Zhizhan Xu

By solving the Maxwell-Bloch equations, we study the area evolution of a few-cycle pulse laser propagating in a resonant two-level-atom medium. We find that in short propagation distance, the pulse envelope, obtained within the slowly varying envelope approximation and the rotating-wave approximation, agrees nicely with the carrier field. In this case, the area theorem can still predict the profile of the area evolution of a few-cycle optical pulse. However, contrary to the long-pulse case, the variation of the few-cycle pulse area is caused by the pulse splitting but not by the pulse broadening or the pulse compression. Furthermore, the negative area occurs when the pulse area decreases. As a result, a pulse with area less than $\ensuremath{\pi}$ is not absorbed rapidly according to the usual Beer's law of absorption but evolves to nonvanishing zero $\ensuremath{\pi}$ pulse.

Physical Review A•Feb 5, 2002•62 citations

Propagation of ultrashort pulses in a two-level medium beyond the slowly varying envelope approximation

Daqing Wen, Longzhao Lu, Xiangyang Yu

The semiclassical Maxwell–Bloch equations beyond the slowly varying envelope approximation (SVEA) are derived in order to study the propagation of the ultrashort pulse in a two-level medium. The evolutions of the pulse shape, the group velocity and the pulse peak of 2[Formula: see text] ultrashort pulse are investigated as well as the pulse splitting of 4[Formula: see text] ultrashort pulse. By comparing the numerical results with those obtained using the SVEA, the error introduced by the approximation is quantitatively evaluated with respect to the pulse width and the applicable condition of the SVEA is discussed consequently. The envelope solutions presented by us allow clear observation on the evolution of the envelope.

International Journal of Modern Physics B•Apr 26, 2018•0 citations

Shaping of few-cycle laser pulses via a subwavelength structure

Liang Guo, Xiao-Tao Xie, Zhiming Zhan

We theoretically investigate the propagation of few-cycle laser pulses in resonant two-level dense media with a subwavelength structure, which is described by the full Maxwell—Bloch equations without the frame of slowly varying envelope and rotating wave approximations. The input pulses can be shaped into shorter ones with a single or less than one optical cycle. The effect of the parameters of the subwavelength structure and laser pulses is studied. Our study shows that the media with a subwavelength structure can significantly shape the few-cycle pulses into a subcycle pulse, even for the case of chirp pulses as input fields. This suggests that such subwavelength structures have potential application in the shaping of few-cycle laser pulses.

Chinese Physics B•Sep 1, 2013•3 citations

Interaction of ultrashort pulse with two-level medium beyond the slowly varying envelope approximation

Xiangyang Yu, Daqing Wen, Longzhao Lu

By solving the Maxwell-Bloch equations beyond the slowly varying envelope approximation (SVEA), we investigate the interaction of ultrashort pulse with two-level medium. When the pulse width decreases to the order of the optical period, the evolutions of the 2π, 4π and 6π ultrashort pulses deviate from the results obtained using the SVEA and present some new features, such as the frequency shift occurring on the trailing edge of the pulse. Moreover, a factor is defined to quantify the envelope deviation between the cases of the SVEA and the non-SVEA in order to quantitatively evaluate the error caused by the SVEA, then we discuss the applicable condition of the approximation.

•Oct 24, 2017•0 citations

Spatiotemporal evolution and multiple self-focusing of ultrashort pulses in a resonant two-level medium

Yueping Niu, Keyu Xia, Ni Cui +2 more

The spatiotemporal evolutions of ultrashort pulses in two dimensions are investigated numerically by solving the coupled Maxwell-Bloch equations without invoking the slowly varying envelope approximation and rotating-wave approximation. For an on-axis $2n\ensuremath{\pi}$ sech pulse, local delay makes the temporal split $2\ensuremath{\pi}$ sech pulses crescent-shaped in the transverse distribution. Due to the transverse effect, the temporal split $2\ensuremath{\pi}$ sech pulses become unstable and experience reshaping during the propagation process. Then, interference occurs between the successive crescent-shaped pulses and multiple self-focusing can form.

Physical Review A•Dec 30, 2008•14 citations

Propagation of Few-Cycle Pulse Laser in Two-Level Atom Medium

Xiao Jian, Zhongyang Wang, Zhizhan Xu

By comparing the numerical solutions of Maxwell-Bloch equations beyond and within the slowly-varying envelope approximation and the rotating-wave approximation for the propagation of a few-cycle pulse laser in a resonant two-level atom medium, we found that both the Rabi flopping and the refractive index, and subsequently the carrier and the propagation velocity of the few-cycle pulse, are closely connected with the time-derivative behaviour of the electric field. This is because the Rabi flopping is such that the soliton pulse splits during propagation and that a shorter pulse propagates faster than a broader one.

Chinese Physics Letters•Jul 1, 2001•3 citations
We solve the problem of ultrashort pulse propagation in a two-level medium beyond the rotating-wave (RWA) and slowly varying-envelope approximations. The method of solution is based on the Maxwell-Bloch equations represented in the form that allows one to switch between RWA and general (non-RWA) cases in the framework of a single numerical algorithm. Using this method, the effect of a subcycle pulse (containing less than a single period of field oscillations) on the two-level medium was analyzed. It is shown that for such short pulses, the clear breakdown of the area theorem occurs for the pulses of large enough area. Moreover, deviations from the area theorem appear to be strongly dependent on the pulse shape that cannot be observed for longer few-cycle pulses.
By solving the Maxwell-Bloch equations, we study the area evolution of a few-cycle pulse laser propagating in a resonant two-level-atom medium. We find that in short propagation distance, the pulse envelope, obtained within the slowly varying envelope approximation and the rotating-wave approximation, agrees nicely with the carrier field. In this case, the area theorem can still predict the profile of the area evolution of a few-cycle optical pulse. However, contrary to the long-pulse case, the variation of the few-cycle pulse area is caused by the pulse splitting but not by the pulse broadening or the pulse compression. Furthermore, the negative area occurs when the pulse area decreases. As a result, a pulse with area less than $\ensuremath{\pi}$ is not absorbed rapidly according to the usual Beer's law of absorption but evolves to nonvanishing zero $\ensuremath{\pi}$ pulse.
The semiclassical Maxwell–Bloch equations beyond the slowly varying envelope approximation (SVEA) are derived in order to study the propagation of the ultrashort pulse in a two-level medium. The evolutions of the pulse shape, the group velocity and the pulse peak of 2[Formula: see text] ultrashort pulse are investigated as well as the pulse splitting of 4[Formula: see text] ultrashort pulse. By comparing the numerical results with those obtained using the SVEA, the error introduced by the approximation is quantitatively evaluated with respect to the pulse width and the applicable condition of the SVEA is discussed consequently. The envelope solutions presented by us allow clear observation on the evolution of the envelope.
We theoretically investigate the propagation of few-cycle laser pulses in resonant two-level dense media with a subwavelength structure, which is described by the full Maxwell—Bloch equations without the frame of slowly varying envelope and rotating wave approximations. The input pulses can be shaped into shorter ones with a single or less than one optical cycle. The effect of the parameters of the subwavelength structure and laser pulses is studied. Our study shows that the media with a subwavelength structure can significantly shape the few-cycle pulses into a subcycle pulse, even for the case of chirp pulses as input fields. This suggests that such subwavelength structures have potential application in the shaping of few-cycle laser pulses.
By solving the Maxwell-Bloch equations beyond the slowly varying envelope approximation (SVEA), we investigate the interaction of ultrashort pulse with two-level medium. When the pulse width decreases to the order of the optical period, the evolutions of the 2π, 4π and 6π ultrashort pulses deviate from the results obtained using the SVEA and present some new features, such as the frequency shift occurring on the trailing edge of the pulse. Moreover, a factor is defined to quantify the envelope deviation between the cases of the SVEA and the non-SVEA in order to quantitatively evaluate the error caused by the SVEA, then we discuss the applicable condition of the approximation.
The spatiotemporal evolutions of ultrashort pulses in two dimensions are investigated numerically by solving the coupled Maxwell-Bloch equations without invoking the slowly varying envelope approximation and rotating-wave approximation. For an on-axis $2n\ensuremath{\pi}$ sech pulse, local delay makes the temporal split $2\ensuremath{\pi}$ sech pulses crescent-shaped in the transverse distribution. Due to the transverse effect, the temporal split $2\ensuremath{\pi}$ sech pulses become unstable and experience reshaping during the propagation process. Then, interference occurs between the successive crescent-shaped pulses and multiple self-focusing can form.
By comparing the numerical solutions of Maxwell-Bloch equations beyond and within the slowly-varying envelope approximation and the rotating-wave approximation for the propagation of a few-cycle pulse laser in a resonant two-level atom medium, we found that both the Rabi flopping and the refractive index, and subsequently the carrier and the propagation velocity of the few-cycle pulse, are closely connected with the time-derivative behaviour of the electric field. This is because the Rabi flopping is such that the soliton pulse splits during propagation and that a shorter pulse propagates faster than a broader one.