Focused X-shaped pulses

Zamboni‐Rached, Michel; Shaarawi, Amr M.; Recami, Erasmo

doi:10.1364/josaa.21.001564

Cited by 34 publications

(30 citation statements)

References 39 publications

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“…X waves decay very slowly with increasing distance [240]. X waves can propagate not only with a subluminal [241,242], but also with a superluminal, velocity [238][239][240][241]243]; in the latter case, they can propagate through a waveguide [244]. As was shown in [241,245], superlu minal X waves cannot carry energy and information, since their superluminal velocity is the phase velocity.…”

Section: Shaped Wavesmentioning

confidence: 99%

Superluminal motion (review)

Malykin

Romanets

2012

Opt. Spectrosc.

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Prior to the development of Special Relativity, no restrictions were imposed on the velocity of the motion of particles and material bodies, as well as on energy transfer and signal propagation. At the end of the 19th century and the beginning of the 20th century, it was shown that a charge that moves at a velocity faster than the speed of light in an optical medium, in particular, in vacuum, gives rise to impact radiation, which later was termed the Vavilov-Cherenkov radiation. Shortly after the development of Special Relativity, some researchers considered the possibility of superluminal motion. In 1923, the Soviet physicist L.Ya. Strum sug gested the existence of tachyons, which, however, have not been discovered yet. Superluminal motions can occur only for images, e.g., for so called "light spots," which were considered in 1972 by V.L. Ginzburg and B.M. Bolotovskii. These spots can move with a superluminal phase velocity but are incapable of transferring energy and information. Nevertheless, these light spots may induce quite real generation of microwave radi ation in closed waveguides and create the Vavilov-Cherenkov radiation in vacuum. In this work, we consider various paradoxes, illusions, and artifacts associated with superluminal motion.

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Section: Shaped Wavesmentioning

confidence: 99%

Superluminal motion (review)

Malykin

Romanets

2012

Opt. Spectrosc.

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“…In relation (7) Such INPs possess an infinite energy, and so, for real applications, they must be spatially truncated (i.e., generated by finite apertures) [11][12][13][14], resulting in finite energy solutions, with a finite depth of field.…”

Section: The Heuristic Approachmentioning

confidence: 99%

“…When such truncation is made, the resulting pulse in general cannot be obtained in an analytically form, but has to be numerically calculated from the diffraction theory, by using, for example, the Rayleigh-Sommerfeld formula [10][11][12][13][14]. That is, once we have a known INP solution Ψ IN P , its truncated version Ψ T N P , generated by a finite aperture of radius R on the plane z = 0, results given by…”

Section: The Heuristic Approachmentioning

confidence: 99%

Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures

Zamboni‐Rached

2006

J. Opt. Soc. Am. A

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In this paper, starting from some general and plausible assumptions based on geometrical optics and on a common feature of the truncated Bessel beams, a heuristic derivation is presented of very simple analytical expressions, capable of describing the longitudinal (on-axis) evolution of axially-symmetric nondiffracting pulses when truncated by finite apertures. We apply our analytical formulation to several situations involving subluminal, luminal or superluminal localized pulses, and compare the results with those obtained by numerical simulations of the Rayleigh-Sommerfeld diffraction integrals. The results are in excellent agreement. The present approach can be rather useful, because it yields, in general, closed-form expressions, avoiding the need of time-consuming numerical simulations; and also because such expressions provide a powerful tool for exploring several important properties of the truncated localized pulses, as their depth of fields, the longitudinal pulse behavior, the decaying rates, and so on.

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“…Many contributions were devoted to this topic, both from a theoretical and experimental point of view [1,2,3,4,5,6].…”

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confidence: 99%

Superluminal propagation: Light cone and Minkowski spacetime

Mugnai

2007

Physics Letters A

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Bessel X-waves, or Bessel beams, have been extensively studied in last years, especially with regard to the topic of superluminality in the propagation of a signal. However, in spite of many efforts devoted to this subject, no definite answer has been found, mainly for lack of an exact definition of signal velocity. The purpose of the present work is to investigate the field of existence of Bessel beams in order to overcome the specific question related to the definition of signal velocity. Quite surprisingly, this field of existence can be represented in the Minkowski space-time by a Super-Light Cone which wraps itself around the well-known Light Cone.The propagation of Bessel X-waves has been extensively analyzed in last years, especially with regard to the topic of superluminality in connection to the signal propagation. Many contributions were devoted to this topic, both from a theoretical and experimental point of view [1,2,3,4,5,6].Bessel X-waves, which are also known as Bessel beams, belong to the class of localized waves. The peculiarity of this type of waves is that they are well localized in space, unlike a "usual" wave which occupies the entire space. As is well known, a u B Bessel beam is the result of superimposing an infinite number of plane waves, each of them with a direction of propagation tilted by the same angle θ 0 with respect to a given axis, say z. In cylindrical coordinates (ρ, z, ψ), the beam is given bywhere k 0 = ω/c is the wavenumber in the vacuum, and ω is the frequency of the beam. Function J 0 denotes the zero-order Bessel function of first kind, which, apart from inessential factors, can be written as [7]The characteristic features of a Bessel beam are that it supplies well-localized energy, that propagates along the z-axis with no deformation in its amplitude [8,9], and that both phase and group velocities are greater than the light velocity c [2,3]. A U B Bessel pulse limited in time, which is the theoretical definition of signal, can be obtained by superimposing an infinite number of frequencies. After integration of Eq. (1) over dω, and by substituting the Bessel function J 0 with its integral form, we obtainwhich is different from zero only ifwhere 0 ≤ θ 0 < θ max , θ max ≪ π/2 depends on the experimental set-up. Thus, the time interval in which the beam is different from zero is t min (θ 0 = θ max ) ≤ t < t max (θ 0 = 0). (5) *

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Focused X-shaped pulses

Cited by 34 publications

References 39 publications

Superluminal motion (review)

Superluminal motion (review)

Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures

Superluminal propagation: Light cone and Minkowski spacetime

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