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

Physical Review A

Influence of finite bandwidth on the propagation of information in fast- and slow-light media

Heisuke Amano, Makoto Tomita

Published Jun 28, 2016• 5 citations
Publisher

Abstract

We examined the propagation of information encoded as nonanalytical points on temporally Gaussian-shaped optical pulses in fast- and slow-light systems. The bandwidth of the input pulses determined the sharpness of the nonanalytical points. A sharp bending nonanalytical point propagated with luminal velocity in both fast- and slow-light systems, in good agreement with relativistic causality. As the bandwidth was reduced, the bending point became broad and propagated with the relevant group velocities. This transition was, however, qualitatively different in the fast- and slow-light systems. We also examined the predictability of the future pulse shape beyond the practical nonanalytical point on the basis of the expansion. When the bandwidth was reduced below a critical value, the expansion well predicted the future pulse shape.

DOI
10.1103/physreva.93.063854

Related papers

Causal propagation of nonanalytical points in fast- and slow-light media

Ryuta X. SUZUKI, Makoto Tomita

We examined the propagation of bending nonanalytical points encoded on temporally smooth Gaussian-shaped optical pulses in fast- and slow-light media, using an optical ring resonator. For bending nonanalytical points, the pulse function is continuous, but the first-order derivative is discontinuous, in contrast to traditional nonanalytical points in which the pulse function itself is discontinuous. The nonanalytical points were neither advanced nor delayed, but appeared at the same instance as they entered the ring resonator, in good accordance with the fact that the information velocity was equal to the light velocity in vacuum or the background medium. The differences between the traditional discontinuous and the present bending nonanalytical points were investigated.

Physical Review A•Nov 15, 2013•8 citations

Luminal pulse velocity in a superluminal medium

Heisuke Amano, Makoto Tomita

To investigate the physical meaning of pulse peak in fast and slow light media, we investigated propagation of differently shaped pulses experimentally, controlling the sharpness of the pulse peak. Symmetric behavior with respect to fast and slow light was observed in traditional Gaussian pulses; that is, propagated pulses were advanced or delayed, respectively, whereas the pulse shape remained unchanged. This symmetry broke down when the pulse peak was sharpened; in the fast light medium, the sharp pulse peak propagated with luminal velocity, and the transmitted pulse deformed into a characteristic asymmetric profile. In contrast, in the slow light medium, a time-delayed smooth peak appeared with a bending point at $t=0$. This symmetry breaking with respect to fast and slow light is a universal characteristic of pulse propagation in causal dispersive systems. The sharp pulse peak can be recognized as a bending nonanalytical point and may be capable of transferring information.

Physical Review A•Dec 23, 2015•2 citations

Propagation of phase nonanalytical points in fast- and slow-light media

Yuma Morita, Makoto Tomita

We performed a series of experiments to examine the arrival of phase nonanalytical points in fast- and slow-light media, using a Gaussian-shaped temporal pulse and encoding phase nonanalytical points at various positions within the pulse envelope. For the phase nonanalytical points, the amplitude of the slowly varying pulse envelope, as well as any order of the derivatives, is continuous, but the phase of the carrier wave is discontinuous. The phase nonanalytical points were neither advanced nor delayed, but appeared at the same instance as they entered the fast- and slow-light media, in good accordance with the idea that the information velocity was equal to the velocity of light in a vacuum, $c$, or in the background medium.

Physical Review A•Aug 7, 2017•2 citations

Causal information velocity in fast and slow pulse propagation in an optical ring resonator

Makoto Tomita, 弘之 上杉, Parvin Sultana +1 more

We examined the propagation of nonanalytical points encoded on temporally Gaussian-shaped optical pulses in fast and slow light in an optical ring resonator at $\ensuremath{\lambda}$ = 1.5 \ensuremath{\mu}m. The temporal peak of the Gaussian pulse was either advanced or delayed, reflecting anomalous or normal dispersions in the ring resonator, relevant to under- or overcoupling conditions, respectively. The nonanalytical points were neither advanced nor delayed but appeared as they entered the ring resonator. The nonanalytical points could be interpreted as information; therefore, the experimental results suggested that information velocity is equal to the light velocity in vacuum or the background medium, independent of the group velocity. The transient behaviors at the leading and trailing edges of the nonanalytical points are discussed in terms of optical precursors.

Physical Review A•Oct 24, 2011•26 citations

Nonanalytic pulse discontinuities as carriers of information

Ahmed H. Dorrah, Mo Mojahedi

In this paper, we consider optical pulses encoded with two nonanalytic points, and we evaluate the detectable information of these pulses in media supporting slow- and fast-light propagation. It is shown that, in some configurations of slow- (subluminal) light propagation, the signal is not readily detectable, albeit the arrival of the encoded nonanalytic points at the receiver. It is thus argued that, from a practical point of view, information should not be entirely associated with the pulse discontinuities. On the other hand, it is confirmed that for propagation in vacuum or a fast-light medium, detectable information is bounded by the nonanalytic points, which create a space-time window within which detectable information cannot escape. As such, the distinction between the nonanalytic points of a signal, its energy transport, and detectable information is demonstrated.

Physical Review A•Jan 14, 2016•3 citations

Causality and information transfer in simultaneously slow- and fast-light media

Jon D. Swaim, Ryan T. Glasser

We demonstrate the simultaneous propagation of slow- and fast-light optical pulses in a four-wave mixing scheme using warm potassium vapor. We show that when the system is tuned such that the input probe pulses exhibit slow-light group velocities and the generated pulses propagate with negative group velocities, the information velocity in the medium is nonetheless constrained to propagate at, or less than, c. These results demonstrate that the transfer and copying of information on optical pulses to those with negative group velocities obeys information causality, in a manner that is reminiscent of a classical version of the no-cloning theorem. Additionally, these results support the fundamental concept that points of non-analyticity on optical pulses correspond to carriers of new information.

arXiv:1709.09244•Optics Express•Sep 26, 2017•7 citations
We examined the propagation of information encoded as nonanalytical points on temporally Gaussian-shaped optical pulses in fast- and slow-light systems. The bandwidth of the input pulses determined the sharpness of the nonanalytical points. A sharp bending nonanalytical point propagated with luminal velocity in both fast- and slow-light systems, in good agreement with relativistic causality. As the bandwidth was reduced, the bending point became broad and propagated with the relevant group velocities. This transition was, however, qualitatively different in the fast- and slow-light systems. We also examined the predictability of the future pulse shape beyond the practical nonanalytical point on the basis of the expansion. When the bandwidth was reduced below a critical value, the expansion well predicted the future pulse shape.
We examined the propagation of bending nonanalytical points encoded on temporally smooth Gaussian-shaped optical pulses in fast- and slow-light media, using an optical ring resonator. For bending nonanalytical points, the pulse function is continuous, but the first-order derivative is discontinuous, in contrast to traditional nonanalytical points in which the pulse function itself is discontinuous. The nonanalytical points were neither advanced nor delayed, but appeared at the same instance as they entered the ring resonator, in good accordance with the fact that the information velocity was equal to the light velocity in vacuum or the background medium. The differences between the traditional discontinuous and the present bending nonanalytical points were investigated.
To investigate the physical meaning of pulse peak in fast and slow light media, we investigated propagation of differently shaped pulses experimentally, controlling the sharpness of the pulse peak. Symmetric behavior with respect to fast and slow light was observed in traditional Gaussian pulses; that is, propagated pulses were advanced or delayed, respectively, whereas the pulse shape remained unchanged. This symmetry broke down when the pulse peak was sharpened; in the fast light medium, the sharp pulse peak propagated with luminal velocity, and the transmitted pulse deformed into a characteristic asymmetric profile. In contrast, in the slow light medium, a time-delayed smooth peak appeared with a bending point at t=0t=0t=0. This symmetry breaking with respect to fast and slow light is a universal characteristic of pulse propagation in causal dispersive systems. The sharp pulse peak can be recognized as a bending nonanalytical point and may be capable of transferring information.
We performed a series of experiments to examine the arrival of phase nonanalytical points in fast- and slow-light media, using a Gaussian-shaped temporal pulse and encoding phase nonanalytical points at various positions within the pulse envelope. For the phase nonanalytical points, the amplitude of the slowly varying pulse envelope, as well as any order of the derivatives, is continuous, but the phase of the carrier wave is discontinuous. The phase nonanalytical points were neither advanced nor delayed, but appeared at the same instance as they entered the fast- and slow-light media, in good accordance with the idea that the information velocity was equal to the velocity of light in a vacuum, ccc, or in the background medium.
We examined the propagation of nonanalytical points encoded on temporally Gaussian-shaped optical pulses in fast and slow light in an optical ring resonator at $\ensuremath{\lambda}$ = 1.5 \ensuremath{\mu}m. The temporal peak of the Gaussian pulse was either advanced or delayed, reflecting anomalous or normal dispersions in the ring resonator, relevant to under- or overcoupling conditions, respectively. The nonanalytical points were neither advanced nor delayed but appeared as they entered the ring resonator. The nonanalytical points could be interpreted as information; therefore, the experimental results suggested that information velocity is equal to the light velocity in vacuum or the background medium, independent of the group velocity. The transient behaviors at the leading and trailing edges of the nonanalytical points are discussed in terms of optical precursors.
In this paper, we consider optical pulses encoded with two nonanalytic points, and we evaluate the detectable information of these pulses in media supporting slow- and fast-light propagation. It is shown that, in some configurations of slow- (subluminal) light propagation, the signal is not readily detectable, albeit the arrival of the encoded nonanalytic points at the receiver. It is thus argued that, from a practical point of view, information should not be entirely associated with the pulse discontinuities. On the other hand, it is confirmed that for propagation in vacuum or a fast-light medium, detectable information is bounded by the nonanalytic points, which create a space-time window within which detectable information cannot escape. As such, the distinction between the nonanalytic points of a signal, its energy transport, and detectable information is demonstrated.
We demonstrate the simultaneous propagation of slow- and fast-light optical pulses in a four-wave mixing scheme using warm potassium vapor. We show that when the system is tuned such that the input probe pulses exhibit slow-light group velocities and the generated pulses propagate with negative group velocities, the information velocity in the medium is nonetheless constrained to propagate at, or less than, c. These results demonstrate that the transfer and copying of information on optical pulses to those with negative group velocities obeys information causality, in a manner that is reminiscent of a classical version of the no-cloning theorem. Additionally, these results support the fundamental concept that points of non-analyticity on optical pulses correspond to carriers of new information.