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].