By a generalized bidirectional decomposition method, we obtain new Superluminal localized solutions to the wave equation (for the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; several 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. Results of this kind may find application in the other fields in which an essential role is played by a wave-equation (like acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.).

-In this paper it is shown how one can use Bessel beams to obtain a stationary localized wavefield with high transverse localization, and whose longitudinal intensity pattern can assume any desired shape within a chosen interval 0 ≤ z ≤ L of the propagation axis. This intensity envelope remains static, i.e., with velocity v = 0; and because of this we call "Frozen Waves" such news solutions to the wave equations (and, in particular, to the Maxwell equations). These solutions can be used in many different and interesting applications, as optical tweezers, atom guides, optical or acoustic bistouries, various important medical purposes, etc.

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

-In this work, starting by suitable superpositions of equal-frequency Bessel beams, we develop a theoretical and experimental methodology to obtain localized stationary wave fields, with high transverse localization, whose longitudinal intensity pattern can approximately assume any desired shape within a chosen interval 0 ≤ z ≤ L of the propagation axis z. Their intensity envelope remains static, i.e. with velocity v = 0; so that we have named "Frozen Waves" (FW) these new solutions to the wave equations (and, in particular, to the Maxwell equations). Inside the envelope of a FW only the carrier wave does propagate: And the longitudinal shape, within the interval 0 ≤ z ≤ L, can be chosen in such a way that no nonnegligible field exists outside the pre-determined region (consisting, e.g., in one or more high intensity peaks). Our solutions are noticeable also for the different and interesting applications they can have, especially in electromagnetism and acoustics, such as optical tweezers, atom guides, optical or acoustic bistouries, ( †) Work partially supported by MIUR and INFN (Italy), and by FAPESP (Brazil).

Frozen waves (FWs) are very interesting particular cases of nondiffracting beams whose envelopes are static and whose longitudinal intensity patterns can be chosen a priori. We present here for the first time (that we know of) the experimental generation of FWs. The experimental realization of these FWs was obtained using a holographic setup for the optical reconstruction of computer generated holograms (CGH), based on a 4-f Fourier filtering system and a nematic liquid crystal spatial light modulator (LC-SLM), where FW CGHs were first computationally implemented, and later electronically implemented, on the LC-SLM for optical reconstruction. The experimental results are in agreement with the corresponding theoretical analytical solutions and hold excellent prospects for implementation in scientific and technological applications.