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Michel Zamboni-Rached

Publications and source records attributed to Michel Zamboni-Rached.

44 records · Page 3Linked to original sources
arXiv2007

On the Localized superluminal Solutions to the Maxwell Equations

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 finite total energy. Among the others, we set forth an infinite family of generalizations of the classic X-shaped wave; and show how to deal with the case of a dispersive medium. Results of this kind may find application in other fields in which an essential role is played by a wave-equation (like acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.). This e-print, in large part a review, was prepared for the special issue on "Nontraditional Forms of Light" of the IEEE JSTQE (2003); and a preliminary version of it appeared as Report NSF-ITP-02-93 (KITP, UCSB; 2002). Further material can be found in the recent e-prints arXiv:0708.1655v2 [physics.gen-ph] and arXiv:0708.1209v1 [physics.gen-ph]. The case of the very interesting (and more orthodox, in a sense) subluminal Localized Waves, solutions to the wave equations, will be dealt with in a coming paper. [Keywords: Wave equation; Wave propagation; Localized solutions to Maxwell equations; Superluminal waves; Bessel beams; Limited-dispersion beams; Electromagnetic wavelets; X-shaped waves; Finite-energy beams; Optics; Electromagnetism; Microwaves; Special relativity]

physics.class-ph↗
arXiv2007

Localized Waves: A scientific and historical introduction

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 essential role is played by a wave-equation (like electromagnetism, optics, acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.). In the second part of this paper (namely, in its Appendix), we recall at first how, in the seventies and eighties, the geometrical methods of Special Relativity (SR) had predicted --in the sense below specified-- the existence of the most interesting LWs, i.e., of the X-shaped pulses. At last, in connection with the circumstance that the X-shaped waves are endowed with Superluminal group-velocities (as carefully discussed in the first part of this article), we briefly mention the various experimental sectors of physics in which Superluminal motions seem to appear: In particular, a bird's-eye view is presented of the experiments till now performed with evanescent waves (and/or tunneling photons), and with the "localized Superluminal solutions" to the wave equations.

physics.gen-ph↗
arXiv2007

Structure of the Nondiffracting (Localized) Waves, and some interesting applications

Since the early works[1-4] on the so-called nondiffracting waves (called also Localized Waves), a great deal of results has been published on this important subject, from both the theoretical and the experimental point of view. Initially, the theory was developed taking into account only free space; however, in recent years, it has been extended for more complex media exhibiting effects such as dispersion[5-7], nonlinearity[8], anisotropy[9] and losses[10]. Such extensions have been carried out along with the development of efficient methods for obtaining nondiffracting beams and pulses in the subluminal, luminal and superluminal regimes[11-18]. This paper (partly a review) addresses some theoretical methods related to nondiffracting solutions of the linear wave equation in unbounded homogeneous media, as well as to some interesting applications of such waves. In section II we analyze the general structure of the Localized Waves, develop the so called Generalized Bidirectional Decomposition, and use it to obtain several luminal and superluminal (especially X-shaped) nondiffracting solutions of the wave equation. In section III we develop a space-time focusing method by a continuous superposition of X-Shaped pulses of different velocities. Section IV addresses the properties of chirped optical X-Shaped pulses propagating in material media without boundaries. Finally, in Section V, we show how a suitable superposition of Bessel beams can be used to obtain stationary localized wave fields, with a static envelope and a high transverse localization, and whose longitudinal intensity pattern can assume any desired shape within a chosen interval of the propagation axis.

physics.gen-ph↗
arXiv2006

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

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 very useful, because it can yield, in general, closed analytical 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.

physics.optics↗
arXiv2005

Diffraction-Attenuation Resistant Beams in Absorbing Media

In this work, in terms of suitable superpositions of equal-frequency Bessel beams, we develop a theoretical method to obtain nondiffractive beams in absorbing media (weakly conductive) capable to resist the loss effects for long distances.

physics.optics↗
arXiv2004

Chirped optical X-shaped pulses in material media

In this paper we analyze the properties of chirped optical X-shaped pulses propagating in material media without boundaries. We show that such ("superluminal") pulses may recover their transverse and longitudinal shape after some propagation distance, while the ordinary chirped gaussian-pulses can recover their longitudinal shape only (since gaussian pulses suffer a progressive spreading during their propagation). We therefore propose the use of chirped optical X-type pulses to overcome the problems of both dispersion and diffraction during the pulse propagation.

physics.optics↗
arXiv2002

New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies

By a generalized bidirectional decomposition method, we obtain many new Superluminal localized solutions to the wave equation (for the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; various of them being endowed with finite total energy. We construct, among the others, an infinite family of generalizations of the so-called "X-shaped" waves. [PACS nos.: 03.50.De; 41.20;Jb; 83.50.Vr; 62.30.+d; 43.60.+d; 91.30.Fn; 04.30.Nk; 42.25.Bs; 46.40.Cd; 52.35.Lv. Keywords: Wave equations; Wave propagation; Localized beams; Superluminal waves; Bidirectional decomposition; Bessel beams; X-shaped waves; Microwaves; Optics; Special relativity; Acoustics; Seismology; Mechanical waves; Elastic waves; Gravitational waves; Elementary particle physics].

physics.gen-ph↗