On Localized "X-shaped" Superluminal Solutions to Maxwell Equations

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 point of view of the Special Relativity theory. [PACS nos.: 03.50.De; 1.20.Jb; 03.30.+p; 03.40.Kf; 14.80.-j. Keywords: X-shaped waves; localized solutions to Maxwell equations; Superluminal waves; Bessel beams; Limited-dispersion beams; electromagnetic wavelets; Special Relativity; Extended Relativity].Comment: Replaced in order to add the missing Figures. Paper of 33 pages with 6 Figures, originally submitted for pub. on March 1, 1996 (nineteen ninety-six), and appeared in print two years later

The Tolman "Antitelephone" Paradox: Its Solution by Tachyon Mechanics

Some recent experiments led to the claim that something can travel faster than light in vacuum. However, such results do not seem to place relativistic causality in jeopardy. Actually, it is possible to solve also the known causal paradoxes, devised for "faster than $c$" motion: even if this is not widely recognized. Here we want to show, in detail and rigorously, how to solve the oldest causal paradox, originally proposed by Tolman, which is the kernel of so many further tachyon paradoxes. The key to the solution is a careful application of {\em tachyon mechanics}, that can be unambiguously derived from special relativity

A simple and effective method for the analytic description of important optical beams, when truncated by finite apertures

In this paper we present a simple and effective method, based on appropriate superpositions of Bessel-Gauss beams, which in the Fresnel regime is able to describe in analytic form the 3D evolution of important waves as Bessel beams, plane waves, gaussian beams, Bessel-Gauss beams, when truncated by finite apertures. One of the byproducts of our mathematical method is that one can get in few seconds, or minutes, high-precision results which normally require quite long times of numerical simulation. The method works in Electromagnetism (Optics, Microwaves,...), as well as in Acoustics. OCIS codes: (999.9999) Non-diffracting waves; (260.1960) Diffraction theory; (070.7545) Wave propagation; (070.0070) Fourier optics and signal processing; (200.0200) Optics in computing; (050.1120) Apertures; (070.1060) Acousto-optical signal processing; (280.0280) Remote sensing and sensors; (050.1755) Computational electromagnetic methods.Comment: Paper of 21 pages with 13 Figures. Source file in LaTe

On the Phenomenology of Tachyon Radiation

We present a brief overview of the different kinds of electromagnetic radiations expected to come from (or to be induced by) space-like sources (tachyons). New domains of radiation are here considered; and the possibility of experimental observation of tachyons via electromagnetic radiation is discussed

Droplet-shaped waves: Causal finite-support analogs of X-shaped waves

A model of steady-state X-shaped wave generation by a superluminal (supersonic) pointlike source infinitely moving along a straight line is extended to a more realistic causal scenario of a source pulse launched at time zero and propagating rectilinearly at constant superluminal speed. In the case of infinitely short (delta) pulse, the new model yields an analytical solution, corresponding to the propagation-invariant X-shaped wave clipped by a droplet-shaped support, which perpetually expands along the propagation and transversal directions, thus tending the droplet-shaped wave to the X-shaped one.Comment: 14 pages, 6 figure