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

Superluminal Localized Solutions to Maxwell Equations propagating along a waveguide: The finite-energy case

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 equations; Superluminal waves; Bessel beams; Limited-dispersion beams; Finite-energy waves; Electromagnetic wavelets; X-shaped waves; Evanescent waves; Electromagnetism; Microwaves; Optics; Special relativity; Localized acoustic waves; Seismic waves; Mechanical waves; Elastic waves; Guided gravitational waves.]Comment: plain LaTeX file (12 pages), plus 10 figure

Superluminal X-shaped beams propagating without distortion along a coaxial guide

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 essential role is played by a wave-equation (like acoustics, geophysics, etc.). [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; Coaxial cables; Bidirectional decomposition; Bessel beams; X-shaped waves; Maxwell equations; Microwaves; Optics; Special relativity; Coaxial metallic waveguides; Acoustics; Seismology; Mechanical waves; Elastic waves; Guided gravitational waves.]Comment: plain LaTeX file (22 pages), plus 15 figures; in press in Phys. Rev.

Architecting new diffraction-resistant light structures and their possible applications in atom guidance

CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOIn this work we extend the so called frozen wave method in order to obtain new diffraction resistant light structures that can be shaped on demand, with possible applications in atom guidance. The resulting beams and the corresponding optical dipole potentials exhibit a strong resistance to diffraction effects and their longitudinal and transverse intensity patterns can be chosen a priori. Besides the theoretical development, we also present the experimental confirmation of our approach; specifically, by generating three different beam profiles using a spatial light modulator that is addressed by a computer-generated hologram. In addition to its many potential applications in atom guiding, the method developed here can also lead to many new developments in optics and photonics in general. (C) 2016 Optical Society of AmericaIn this work we extend the so called frozen wave method in order to obtain new diffraction resistant light structures that can be shaped on demand, with possible applications in atom guidance. The resulting beams and the corresponding optical dipole potentials exhibit a strong resistance to diffraction effects and their longitudinal and transverse intensity patterns can be chosen a priori. Besides the theoretical development, we also present the experimental confirmation of our approach, specifically, by generating three different beam profiles using a spatial light modulator that is addressed by a computer-generated hologram. In addition to its many potential applications in atom guiding, the method developed here can also lead to many new developments in optics and photonics in general.24222540325408CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO141977/2013-2, 312376/2013-82015/26444-

An Improved Hazard Rate Twisting Approach for the Statistic of the Sum of Subexponential Variates

In this letter, we present an improved hazard rate twisting technique for the estimation of the probability that a sum of independent but not necessarily identically distributed subexponential Random Variables (RVs) exceeds a given threshold. Instead of twisting all the components in the summation, we propose to twist only the RVs which have the biggest impact on the right-tail of the sum distribution and keep the other RVs unchanged. A minmax approach is performed to determine the optimal twisting parameter which leads to an asymptotic optimality criterion. Moreover, we show through some selected simulation results that our proposed approach results in a variance reduction compared to the technique where all the components are twisted