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

Optics and Spectroscopy

On the propagation of a light pulse in the “transparency window” of a medium with population inversion

Nikolai S. Bukhman

Published Nov 1, 2017• 2 citations
Publisher

Abstract

The propagation of a light pulse through a layer of a substance with population inversion and, correspondingly, with an anomalous dispersion in the transparency range is considered. It is shown that, when the wave packet approaches the layer of the substance with a strong anomalous dispersion, two additional wave packets arise at the rear boundary of the layer. One of these packets has a negative energy and moves in the layer from its rear to the front boundary, while the other packet moves away from the rear boundary of the layer into a vacuum. As the initial wave packet comes into contact with the front boundary of the layer of the substance, it meets the packet of the negative energy. As a result, the two packets annihilate one another, after which only one packet remains, which moves away from the layer.

DOI
10.1134/s0030400x17110030

Related papers

On the distortion of a wave packet propagating in an amplifying medium

Nikolai S. Bukhman

The propagation of a narrow-band signal (wave packet) in a medium with population inversion is considered. It is shown that in an optically thick medium layer the signal decomposes into the initial and amplified signals propagating at different velocities and having different durations. The initial signal propagates without distortions at the velocity c / n 0 ( n 0 is the refractive index of the medium away from the resonance frequency) and plays the role of a precursor of the amplified signal. The amplified signal moves at a lower velocity. It lags behind the initial signal during propagation and acquires a universal Gaussian shape (irrespective of the shape of the initial signal and the spectral line profile). The appearance of the amplified signal, which substantially differs from the initial signal in all the parameters, as well as the interference between the amplified and initial signals looks like a 'extra-distortion' of the initial signal.

Quantum Electronics•Apr 30, 2004•9 citations

Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity

Arthur Dogariu, A. Kuzmich, L. J. Wang

Anomalous dispersion cannot occur in a transparent passive medium where electromagnetic radiation is being absorbed at all frequencies, as pointed out by Landau and Lifshitz. Here we show, both theoretically and experimentally, that transparent linear anomalous dispersion can occur when a gain doublet is present. Therefore, a superluminal light-pulse propagation can be observed even at a negative 7group velocity through a transparent medium with almost no pulse distortion. Consequently, a negative transit time is experimentally observed resulting in the peak of the incident light pulse to exit the medium even before entering it. This counterintuitive effect is a direct result of the rephasing process owing to the wave nature of light and is not at odds with either causality or Einstein's theory of special relativity.

arXiv:physics/0012060•Physical Review A•Apr 12, 2001•328 citations

Superluminal light pulse propagation via rephasing in a transparent anomalously dispersive medium

Arthur Dogariu, A. Kuzmich, Hongzhuang Cao +1 more

We study the propagation of light pulses through a transparent anomalous dispersion medium where the group velocity of the pulse exceeds c and can even become negative. Because the medium is transparent, we can apply the Kelvin's method of stationary phase to obtain the general properties of the pulse propagation process for interesting conditions when the group velocity: U < c, U = +/- , and even becomes negative: U < 0. A numerical simulation illustrating pulse propagation at a negative group velocity is also presented. We show how rephasing can produce these unusual pulse propagation phenomena.

Optics Express•Mar 12, 2001•72 citations

Propagation of a Gaussian wave packet in an absorbing medium

Masayoshi Tanaka, Masami Fujiwara, Hideo Ikegami

Propagation of a Gaussian wave packet in an absorbing medium is examined in order to shed light on the physical basis of group velocity which exhibits a singular behavior. It is found that the velocity of the wave packet, defined as the traveling distance of the peak amplitude divided by its flight time, decreases in the absorption range of frequency, although the group velocity becomes infinite in the same range. Fast pulse propagation, which was observed by Chu and Wong and is characterized by a packet velocity faster than the light velocity, turns out to be a characteristic in the early stage of the flight and is understood in terms of packet distortion due to damping of Fourier-component waves in an anomalous dispersion region. It also turns out that slow pulse propagation characterized by a packet velocity less than the light velocity appears for long traveling distance. The results provided a unified picture of wave-packet propagation in an absorbing medium.

Physical Review A•Dec 1, 1986•50 citations

Superluminal (but causal) propagation of wave packets in transparent media with inverted atomic populations

R. Y. Chiao

The propagation of limited-bandwidth signals, such as Gaussian wave packets, tuned to a transparent spectral region far below the resonance of an inverted two-level atomic medium, can be superluminal, i.e., with phase, group, and energy velocities all exceeding the vacuum speed of light c. Causality is not violated, however. Little distortion and gain can accompany this propagation.

Physical Review A•Jul 1, 1993•249 citations

Negative group velocity and distortion of a pulse in an anomalous dispersion medium

Chao-Guang Huang, Yuan‐Zhong Zhang

Analysis of an infinitely long train of sine-squared pulses—as a toy model—propagating in a medium exhibiting anomalous dispersion shows that although the shape of the light pulses seems to be almost preserved on a small scale, the pulses are severely distorted on a large scale. The frequency of the sine-squared pulses is doubled before they propagate a tenth of the width (FWHM) of a pulse in the medium. The analysis and a numerical calculation show that the front of a wave with a step-function envelope propagates at the speed of light, c , through a medium with two gain lines. Finally, the propagation of a Gaussian pulse—a more realistic pulse—in a medium exhibiting anomalous dispersion is studied. The distortion of the pulse in a Wang–Kuzmich–Dogariu (WKD) experiment (Wang L J, Kuzmich A and Dogariu A 2000 Nature 406 277) should be observable at a precision of ±1 ns. If a Gaussian pulse travels in the medium for 1/50 of a width (FWHM), it will collapse. 'Snapshots' of a Gaussian pulse show that the shape of the pulse in space will have more than one peak at certain times. A possible picture of light propagation in WKD-like experiments is proposed on the basis on these findings.

Journal of Optics A Pure and Applied Optics•Mar 14, 2002•7 citations
The propagation of a light pulse through a layer of a substance with population inversion and, correspondingly, with an anomalous dispersion in the transparency range is considered. It is shown that, when the wave packet approaches the layer of the substance with a strong anomalous dispersion, two additional wave packets arise at the rear boundary of the layer. One of these packets has a negative energy and moves in the layer from its rear to the front boundary, while the other packet moves away from the rear boundary of the layer into a vacuum. As the initial wave packet comes into contact with the front boundary of the layer of the substance, it meets the packet of the negative energy. As a result, the two packets annihilate one another, after which only one packet remains, which moves away from the layer.
The propagation of a narrow-band signal (wave packet) in a medium with population inversion is considered. It is shown that in an optically thick medium layer the signal decomposes into the initial and amplified signals propagating at different velocities and having different durations. The initial signal propagates without distortions at the velocity c / n 0 ( n 0 is the refractive index of the medium away from the resonance frequency) and plays the role of a precursor of the amplified signal. The amplified signal moves at a lower velocity. It lags behind the initial signal during propagation and acquires a universal Gaussian shape (irrespective of the shape of the initial signal and the spectral line profile). The appearance of the amplified signal, which substantially differs from the initial signal in all the parameters, as well as the interference between the amplified and initial signals looks like a 'extra-distortion' of the initial signal.
Anomalous dispersion cannot occur in a transparent passive medium where electromagnetic radiation is being absorbed at all frequencies, as pointed out by Landau and Lifshitz. Here we show, both theoretically and experimentally, that transparent linear anomalous dispersion can occur when a gain doublet is present. Therefore, a superluminal light-pulse propagation can be observed even at a negative 7group velocity through a transparent medium with almost no pulse distortion. Consequently, a negative transit time is experimentally observed resulting in the peak of the incident light pulse to exit the medium even before entering it. This counterintuitive effect is a direct result of the rephasing process owing to the wave nature of light and is not at odds with either causality or Einstein's theory of special relativity.
We study the propagation of light pulses through a transparent anomalous dispersion medium where the group velocity of the pulse exceeds c and can even become negative. Because the medium is transparent, we can apply the Kelvin's method of stationary phase to obtain the general properties of the pulse propagation process for interesting conditions when the group velocity: U < c, U = +/- , and even becomes negative: U < 0. A numerical simulation illustrating pulse propagation at a negative group velocity is also presented. We show how rephasing can produce these unusual pulse propagation phenomena.
Propagation of a Gaussian wave packet in an absorbing medium is examined in order to shed light on the physical basis of group velocity which exhibits a singular behavior. It is found that the velocity of the wave packet, defined as the traveling distance of the peak amplitude divided by its flight time, decreases in the absorption range of frequency, although the group velocity becomes infinite in the same range. Fast pulse propagation, which was observed by Chu and Wong and is characterized by a packet velocity faster than the light velocity, turns out to be a characteristic in the early stage of the flight and is understood in terms of packet distortion due to damping of Fourier-component waves in an anomalous dispersion region. It also turns out that slow pulse propagation characterized by a packet velocity less than the light velocity appears for long traveling distance. The results provided a unified picture of wave-packet propagation in an absorbing medium.
Analysis of an infinitely long train of sine-squared pulses—as a toy model—propagating in a medium exhibiting anomalous dispersion shows that although the shape of the light pulses seems to be almost preserved on a small scale, the pulses are severely distorted on a large scale. The frequency of the sine-squared pulses is doubled before they propagate a tenth of the width (FWHM) of a pulse in the medium. The analysis and a numerical calculation show that the front of a wave with a step-function envelope propagates at the speed of light, c , through a medium with two gain lines. Finally, the propagation of a Gaussian pulse—a more realistic pulse—in a medium exhibiting anomalous dispersion is studied. The distortion of the pulse in a Wang–Kuzmich–Dogariu (WKD) experiment (Wang L J, Kuzmich A and Dogariu A 2000 Nature 406 277) should be observable at a precision of ±1 ns. If a Gaussian pulse travels in the medium for 1/50 of a width (FWHM), it will collapse. 'Snapshots' of a Gaussian pulse show that the shape of the pulse in space will have more than one peak at certain times. A possible picture of light propagation in WKD-like experiments is proposed on the basis on these findings.