Diffraction Resistant Scalar Beams Generated by a Parabolic Reflector and a Source of Spherical Waves

In this work, we propose the generation of diffraction resistant beams by using a parabolic reflector and a source of spherical waves positioned at a point slightly displaced from its focus (away from the reflector). In our analysis, considering the reflector dimensions much greater than the wavelength, we describe the main characteristics of the resulting beams, showing their properties of resistance to the diffraction effects. Due to its simplicity, this method may be an interesting alternative for the generation of long range diffraction resistant waves.Comment: 22 pages, 9 figures, Applied Optics, 201

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]Comment: LaTeX paper of 37 pages, with 20 Figures in jpg [to be processed by PDFlatex

Unidirectional decomposition method for obtaining exact localized waves solutions totally free of backward components

In this paper we use a unidirectional decomposition capable of furnishing localized wave pulses, with luminal and superluminal peak velocities, in exact form and totally free of backward components, which have been a chronic problem for such wave solutions. This decomposition is powerful enough for yielding not only ideal nondiffracting pulses but also their finite energy versions still in exact analytical closed form. Another advantage of the present approach is that, since the backward spectral components are absent, the frequency spectra of the pulses do not need to possess ultra-widebands, as it is required by the usual localized waves (LWs) solutions obtained by other methods. Finally, the present results bring the LW theory nearer to the real experimental possibilities of usual laboratories.Comment: 28 pages, 6 figure