Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures

In this paper, starting from some general and plausible assumptions based on geometrical optics and on a common feature of the truncated Bessel beams, a heuristic derivation is presented of very simple analytical expressions, capable of describing the longitudinal (on-axis) evolution of axially-symmetric nondiffracting pulses when truncated by finite apertures. We apply our analytical formulation to several situations involving subluminal, luminal or superluminal localized pulses and compare the results with those obtained by numerical simulations of the Rayleigh-Sommerfeld diffraction integrals. The results are in excellent agreement. The present approach can be very useful, because it can yield, in general, closed analytical expressions, avoiding the need of time-consuming numerical simulations, and also because such expressions provide a powerful tool for exploring several important properties of the truncated localized pulses, as their depth of fields, the longitudinal pulse behavior, the decaying rates, and so on.Comment: 27 pages, 7 figure

Diffraction-Attenuation Resistant Beams in Absorbing Media

In this work, in terms of suitable superpositions of equal-frequency Bessel beams, we develop a theoretical method to obtain nondiffractive beams in absorbing media (weakly conductive) capable to resist the loss effects for long distances.Comment: 12 pages, 3 figure

Chirped optical X-shaped pulses in material media

In this paper we analyze the properties of chirped optical X-shaped pulses propagating in material media without boundaries. We show that such ("superluminal") pulses may recover their transverse and longitudinal shape after some propagation distance, while the ordinary chirped gaussian-pulses can recover their longitudinal shape only (since gaussian pulses suffer a progressive spreading during their propagation). We therefore propose the use of chirped optical X-type pulses to overcome the problems of both dispersion and diffraction during the pulse propagation.Comment: Replaced with a much larger and deepened version (the number of pages going on from 4 to 24; plus 4 Figures added

Modeling Of Space-time Focusing Of Localized Nondiffracting Pulses

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)In this paper we develop amethod capable of modeling the space-time focusing of nondiffracting pulses. These pulses can possess arbitrary peak velocities and, in addition to being resistant to diffraction, can have their peak intensities and focusing positions chosen a priori. More specifically, we can choose multiple locations (spatial ranges) of space and time focalization; also, the pulse intensities can be chosen in advance. The pulsed wave solutions presented here can have very interesting applications in many different fields, such as free-space optical communications, remote sensing, medical apparatus, etc.944Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [2015/26444-8]Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) [312376/2013-8]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq