K. Z. Nobrega

Localized superluminal solutions to the wave equation in (vacuum or) dispersive media, for arbitrary frequencies and with adjustable bandwidth☆

In this paper we set forth new exact analytical superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple and its results can be expressed in terms of the ordinary, so-called “X-shaped waves”. Moreover, by the present formalism we obtain the first analytical localized superluminal approximate solutions which represent pulses propagating in dispersive media. Our solutions may find application in different fields, like optics, microwaves, radio waves, and so on.

Analytic description of Airy-type beams when truncated by finite apertures

In this paper, we have developed an analytic method for describing Airy-type beams truncated by finite apertures. This new approach is based on suitable superposition of exponentially decaying Airy beams. Regarding both theoretical and numerical aspects, the results here shown are interesting because they have been quickly evaluated through a simple analytic solution, whose propagation characteristics agree with those already published in literature through the use of numerical methods. To demonstrate the methods potentiality three different truncated beams have been analyzed: ideal Airy, Airy-Gauss and Airy-Exponential.