On the dynamics of Airy beams in nonlinear media with nonlinear losses.

We investigate on the nonlinear dynamics of Airy beams in a regime where nonlinear losses due to multi-photon absorption are significant. We identify the nonlinear Airy beam (NAB) that preserves the amplitude of the inward Hänkel component as an attractor of the dynamics. This attractor governs also the dynamics of finite-power (apodized) Airy beams, irrespective of the location of the entrance plane in the medium with respect to the Airy waist plane. A soft (linear) input long before the waist, however, strongly speeds up NAB formation and its persistence as a quasi-stationary beam in comparison to an abrupt input at the Airy waist plane, and promotes the formation of a new type of highly dissipative, fully nonlinear Airy beam not described so far.

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 method's potentiality three different truncated beams have been analyzed: ideal Airy, Airy-Gauss and Airy-Exponential.

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

In a previous paper we showed that localized superluminal solutions to the Maxwell equations exist, which propagate down (nonevanescence) regions of a metallic cylindrical waveguide. In this paper we construct analogous nondispersive 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.).