Pulsed light beams in vacuum with superluminal and negative group velocities

Porras, Miguel A.; Gonzalo, Isabel; Mondello, Alessia

doi:10.1103/physreve.67.066604

Cited by 22 publications

(19 citation statements)

References 11 publications

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“…Ever since Brittingham proposed in 1983 a pulsed optical beam that is transported rigidly in free space at a group velocity equal to the speed of light c [1], there has been significant interest in the study of propagationinvariant wave packets [2][3][4][5][6][7][8][9][10]. A variety of examples have been identified [11][12][13] whose group velocity in free space -intriguingly -take on arbitrary values.…”

Section: Introductionmentioning

confidence: 99%

What is the maximum differential group delay achievable by a space-time wave packet in free space?

Yessenov¹,

Mach²,

Bhaduri³

et al. 2019

Opt. Express

101

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The group velocity of 'space-time' wave packets -propagation-invariant pulsed beams endowed with tight spatio-temporal spectral correlations -can take on arbitrary values in free space. Here we investigate theoretically and experimentally the maximum achievable group delay that realistic finite-energy space-time wave packets can achieve with respect to a reference pulse traveling at the speed of light. We find that this delay is determined solely by the spectral uncertainty in the association between the spatial frequencies and wavelengths underlying the wave packet spatiotemporal spectrum -and not by the beam size, bandwidth, or pulse width. We show experimentally that the propagation of space-time wave packets is delimited by a spectral-uncertainty-induced 'pilot envelope' that travels at a group velocity equal to the speed of light in vacuum. Temporal walkoff between the space-time wave packet and the pilot envelope limits the maximum achievable differential group delay to the width of the pilot envelope. Within this pilot envelope the spacetime wave packet can locally travel at an arbitrary group velocity and yet not violate relativistic causality because the leading or trailing edge of superluminal and subluminal space-time wave packets, respectively, are suppressed once they reach the envelope edge. Using pulses of width ∼ 4 ps and a spectral uncertainty of ∼ 20 pm, we measure maximum differential group delays of approximately ±150 ps, which exceed previously reported measurements by at least three orders of magnitude.

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Section: Introductionmentioning

confidence: 99%

What is the maximum differential group delay achievable by a space-time wave packet in free space?

Yessenov¹,

Mach²,

Bhaduri³

et al. 2019

Opt. Express

101

View full text Add to dashboard Cite

show abstract

“…While the notation is different in the works referred, it is easy to see that Equation (29) of [78] is the same as (3.7) with g v = 1 and γ v = 0. Equation (35) of [169] is more general than the previous one, and contains the possible variation of beams size with wavelength, but the wave-front is assumed to be frequency independent, so substituting γ v = 0 into (3.7) gives the same result. The (3.7) formula of this work can be considered as a generalized expression of the cases published before.…”

Section: On-axis Phase and Group Velocity In Aberration-free Focusingmentioning

confidence: 65%

“…The group velocity of short pulses got considerable attention when it was shown that a superluminal value of the group velocity (v g > c) is possible in amplifying media [167]. Later it was shown that the wave packet can travel with a group velocity faster than the speed of light even in vacuum [168,169]. This, however, does not contradict special relativity either, as in the presence of dispersion -even if it is caused by diffraction -the group velocity is not necessarily equal to the speed of energy propagation, so it does not give how fast the information travels (which never travels faster than c) [170,171].…”

Section: Phase and Group Velocitymentioning

confidence: 99%

“…Details of the calculation can be found in Appendix C.2. Some special cases of (3.7) had been formulated before [78,169]. While the notation is different in the works referred, it is easy to see that Equation (29) of [78] is the same as (3.7) with g v = 1 and γ v = 0.…”

Section: On-axis Phase and Group Velocity In Aberration-free Focusingmentioning

confidence: 99%

“…In the previous works referred, only cases were considered when the pulsed Gaussian beam was focused at its waist, and the plane of the waist was the same for all wavelengths [78,169]. In this simple situation, g v simply refers to the wavelength variation of source beam's waist size.…”

Section: On-axis Phase and Group Velocity In Aberration-free Focusingmentioning

confidence: 99%

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Phase and polarization changes of pulsed Gaussian beams during focusing and propagation

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Ultrasonic Imaging with Limited‐Diffraction Beams

2007

Localized Waves

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Limited-diffraction beams are a class of waves that may be localized in space and time. Theoretically, these beams are propagation invariant and can propagate to an infinite distance without spreading. In practice, when these beams are produced with wave sources of a finite aperture and energy, they have a very large depth of field, meaning that they can keep a small beam width over a large distance. Because of this property, limited-diffraction beams may have applications in various areas such as medical imaging and tissue characterization. In this paper, fundamentals of limiteddiffraction beams are reviewed and the studies of these beams are put into a unified theoretical framework. Theory of limited-diffraction beams is further developed. New limited-diffraction solutions to Klein-Gordon Equation and Schrodinger Equation, as well as limited-diffraction solutions to these equations in confined spaces are obtained. The relationship between the transformation that converts any solutions to an ( -1)-dimensional wave equation to limited-diffraction solutions of an -dimensional equation and the Lorentz transformation is clarified and extended. The transformation is also applied to the Klein-Gordon Equation. In addition, applications of limited-diffraction beams are summarized. N N

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Pulsed light beams in vacuum with superluminal and negative group velocities

Cited by 22 publications

References 11 publications

What is the maximum differential group delay achievable by a space-time wave packet in free space?

What is the maximum differential group delay achievable by a space-time wave packet in free space?

Phase and polarization changes of pulsed Gaussian beams during focusing and propagation

Ultrasonic Imaging with Limited‐Diffraction Beams

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