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

Abstract

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.]