Spatial-temporal engineering of light using Frozen Waves and Airy pulses

In this paper we combine two important theoretical methodologies, one related to the Frozen Wave beams (also referred to as Longitudinally Structured Light), which are non -diffracting beams whose longitudinal intensity pattern can be chosen a priori in a medium (absorbing or not), and the other related to the Airy -Type pulses, which are pulses resistant to dispersion effects in dispersive materials. As a result, a new method emerges capable of providing pulsed -beams resistant to three concomitant effects, i.e.: diffraction, dispersion, and attenuation; while concurrently the spatial variation of the wave along its axis of propagation can be engineered "at will". The new approach can be seen as a generalization of the Localized Waves Theory in the paraxial regime and the new pulses can have potential applications in different fields such as optical communications, nonlinear optics, optical micromanipulations, optical microfabrication, and so on.