Much experimental evidence of superluminal phenomena has been available by electromagnetic wave propagation experiments, with the results showing that the phase time do describe the barrier traversal time. Based on the extrapolated phase time approach and numerical methods, we show that, in contrary to the ordinary Bessel waves of real argument, the group velocities of modified Bessel waves are superluminal, and obtain the following results: 1) the group velocities increase with the increase of propagation distance, which is similar to the evanescent plane-wave cases; 2) for large wave numbers, the group velocities fall off as the wave numbers increase, which is similar to the evanescent plane-wave cases; 3) for small wave numbers, the group velocities increase with the increase of wave numbers, this is different from the evanescent plane-wave cases.
We report on an interferometry-based measurement of the phase and group velocities of optical Bessel beams, providing confirmation of their superluminal character in the non-diffractive region. The measurements were performed in free space with a continuous wave laser and femtosecond pulses for phase and group velocities respectively. The Bessel beams were produced using a conical mirror.
Superluminal behavior has been extensively studied in recent years, especially with regard to the topic of superluminality in the propagation of a signal. Particular interest has been devoted to Bessel-X waves propagation, since some experimental results showed that these waves have both phase and group velocities greater that light velocity c. However, because of the lack of an exact definition of signal velocity, no definite answer about the signal propagation (or velocity of information) has been found. The present paper is a short note that deals in a general way with this vexed question. …
We experimentally analyze a Bessel beam produced with a conical mirror, paying particular attention to its superluminal and diffraction-free properties. We spatially characterized the beam in the radial and on-axis dimensions, and verified that the central peak does not spread over a propagation distance of 73 cm. In addition, we measured the superluminal phase and group velocities of the beam in free space. Both spatial and temporal measurements show good agreement with the theoretical predictions.
The motion of an electromagnetic wave, through a classically-forbidden region, has recently attracted renewed interest because of its implication with regard to the theoretical and experimental problems of superluminality. From an experimental point of view, many papers provide an evidence of superluminality in different physical systems. Theoretically, the problem of a passage through a forbidden gap has been treated by considering plane waves at oblique incidence into a plane parallel layer of a medium with a refractive index smaller than the index of the surrounding medium, and also confine…
The relativistic aberration of a wavevector and the corresponding Doppler shift are examined in connection with superluminal and subluminal spatiotemporally localized pulsed optical waves. The requirement of a null Doppler shift is shown to give rise to a speed associated with the relativistic velocity composition law of a double (two-step) Lorentz transformation. The effects of such a transformation are examined both in terms of four-coordinates and in the spectral domain. It is established that a subluminal pulse reverses its direction. In addition to a change in direction, the propagation t…
In this paper we extend for the case of Maxwell equations the "X-shaped" solutions previously found in the case of scalar (e.g., acoustic) wave equations. Such solutions are localized in theory, i.e., diffraction-free and particle-like (wavelets), in that they maintain their shape as they propagate. In the electromagnetic case they are particularly interesting, since they are expected to be Superluminal. We address also the problem of their practical, approximate production by finite (dynamic) radiators. Finally, we discuss the appearance of the X-shaped solutions from the purely geometric poi…
A unified description of the free-space cylindrical vector beams is presented, which is an integral transformation solution to the vector Helmholtz equation and the transversality condition. The amplitude 2-form of the angular spectrum involved in this solution can be arbitrarily chosen. When one of the two elements is zero, we arrive at either transverse-electric or transverse-magnetic beam mode. In the paraxial condition, this solution not only includes the known $J_1$ Bessel-Gaussian vector beam and the axisymmetric Laguerre-Gaussian vector beam that were obtained by solving the paraxial wa…
We report, in theory and experiment, on a novel class of controlled light capsules with nearly perfect darkness, directly employing intrinsic properties of modified Bessel-Gauss beams. These beams are able to naturally create three-dimensional bottle-shaped region during propagation as long as the parameters are properly chosen. Remarkably, the optical bottle can be controlled to demonstrate various geometries through tuning the beam parameters, thereby leading to an adjustable light capsule. We provide a detailed insight into the theoretical origin and characteristics of the light capsule der…
In a previous paper of ours [Phys. Rev. E64 (2001) 066603, e-print physics/0001039] we have shown localized (non-evanescent) solutions to Maxwell equations to exist, which propagate without distortion with Superluminal speed along normal-sized waveguides, and consist in trains of "X-shaped" beams. Those solutions possessed therefore infinite energy. In this note we show how to obtain, by contrast, finite-energy solutions, with the same localization and Superluminality properties. [PACS nos.: 41.20.Jb; 03.50.De; 03.30.+p; 84.40.Az; 42.82.Et. Keywords: Wave-guides; Localized solutions to Maxwell…
We investigate the dynamics of spatiotemporal optical waves with one transverse dimension that are obtained as the intersections of the dispersion cone with a plane. We show that, by appropriate spectral excitations, the three different types of conic sections (elliptic, parabolic, and hyperbolic) can lead to optical waves of the Bessel, Airy, and modified Bessel type, respectively. We find closed form solutions that accurately describe the wave dynamics and unveil their fundamental properties.
The space-time focusing of a (continuous) succession of localized X-shaped pulses is obtained by suitably integrating over their speed, i.e., over their axicon angle, thus generalizing a previous (discrete) approach. First, new Superluminal wave pulses are constructed, and then tailored in such a wave to get them temporally focused at a chosen spatial point, where the wavefield can reach for a short time very high intensities. Results of this kind may find applications in many fields, besides electromagnetism and optics, including acoustics, gravitation, and elementary particle physics. PACS n…
In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in terms of the ordinary, so-called "X-shaped waves". Moeover, by the present formalism we obtain the first analytical localized Superluminal approximate solutions which represent beams propagating in dispersive media. Our solutions may find application in different fields, like optics, microwaves, radio waves, and so on. [PACS nos.: 03.50.De ; 41.20.Jb ; 83.50.…
In a previous paper [Phys. Rev. E64 (2001) 066603; e-print physics/0001039], we showed that localized Superluminal solutions to the Maxwell equations exist, which propagate down (non-evanescence) regions of a metallic cylindrical waveguide. In this paper we construct analogous non-dispersive waves propagating along coaxial cables. Such new solutions, in general, consist in trains of (undistorted) Superluminal "X-shaped" pulses. Particular attention is paid to the construction of finite total energy solutions. Any results of this kind may find application in the other fields in which an essenti…
Recently, a series of theoretical and experimental papers on free-space propagation of pulsed Laguerre-Gaussian and Bessel beams was published, which reached contradictory and controversial results about group velocities of such pulses. Depending on themeasurement scheme, the group velocity can be defined differently.We analyze how different versions of group velocity are related to the measurable travel time (time of flight) of the pulse between input (source) and output (detecting) planes. The analysis is tested on a theoretical model---the Bessel-Gauss pulse whose propagation path exhibits …
The feasibility of a 220 - 330 GHz zero order axicon generated Bessel beam for corneal water content was explored. Simulation and experimental data from the 25-degree cone angle hyperbolic-axicon lens illuminating metallic spherical targets demonstrate a monotonically decreasing, band integrated, backscatter intensity for increasing radius of curvature from 7 - 11 mm, when lens reflector and optical axis are aligned. Further, for radii >= 9.5 mm, maximum signal was obtained with a 1 mm transverse displacement between lens and reflector optical axes arising from spatial correlation between main…
In the first part of this article the various experimental sectors of physics in which Superluminal motions seem to appear are briefly mentioned, after a sketchy theoretical introduction. In particular, a panoramic view is presented of the experiments with evanescent waves (and/or tunneling photons), and with the "Localized superluminal Solutions" (SLS) to the wave equation, like the so-called X-shaped waves. In the second part of this paper we present a series of new SLSs to the Maxwell equations, suitable for arbitrary frequencies and arbitrary bandwidths: some of them being endowed with fin…
In the first part of this paper (mainly a review) we present general and formal (simple) introductions to the ordinary gaussian waves and to the Bessel waves, by explicitly separating the cases of the beams from the cases of the pulses; and, finally, an analogous introduction is presented for the Localized Waves (LW), pulses or beams. Always we stress the very different characteristics of the gaussian with respect to the Bessel waves and to the LWs, showing the numerous and important properties of the latter w.r.t. the former ones: Properties that may find application in all fields in which an…
In the FIRST PART we present simple introductions to gaussian and Bessel waves, and to the Localized Waves (LW), pulses or beams, showing the important properties of the latter, and their applications whenever a role is played by a wave-equation (electromagnetism, optics, acoustics, seismology, geophysics, gravitation, elementary particle physics,...). The First Part ends with a historical APPENDIX, recalling how the geometrical methods of Special Relativity (SR) had predicted the most interesting LWs, i.e., the X-shaped pulses; and presenting a bird's-eye view of the experiments performed wit…
