G. Guattari

Bio: G. Guattari is an academic researcher from Sapienza University of Rome. The author has contributed to research in topics: Coherence theory & Beam (structure). The author has an hindex of 15, co-authored 42 publications receiving 1635 citations. Previous affiliations of G. Guattari include Centre national de la recherche scientifique.

Cylindrical vector beams: from mathematical concepts to applications

Abstract: An overview of the recent developments in the field of cylindrical vector beams is provided. As one class of spatially variant polarization, cylindrical vector beams are the axially symmetric beam solution to the full vector electromagnetic wave equation. These beams can be generated via different active and passive methods. Techniques for manipulating these beams while maintaining the polarization symmetry have also been developed. Their special polarization symmetry gives rise to unique high-numerical-aperture focusing properties that find important applications in nanoscale optical imaging and manipulation. The prospects for cylindrical vector beams and their applications in other fields are also briefly discussed.

The Shannon sampling theorem—Its various extensions and applications: A tutorial review

Abstract: It has been almost thirty years since Shannon introduced the sampling theorem to communications theory. In this review paper we will attempt to present the various contributions made for the sampling theorems with the necessary mathematical details to make it self-contained. We will begin by a clear statement of Shannon's sampling theorem followed by its applied interpretation for time-invariant systems. Then we will review its origin as Whittaker's interpolation series. The extensions will include sampling for functions of more than one variable, random processes, nonuniform sampling, nonband-limited functions, implicit sampling, generalized functions (distributions), sampling with the function and its derivatives as suggested by Shannon in his original paper, and sampling for general integral transforms. Also the conditions on the functions to be sampled will be summarized. The error analysis of the various sampling expansions, including specific error bounds for the truncation, aliasing, jitter and parts of various other errors will be discussed and summarized. This paper will be concluded by searching the different recent applications of the sampling theorems in other fields, besides communications theory. These include optics, crystallography, time-varying systems, boundary value problems, spline approximation, special functions, and the Fourier and other discrete transforms.

Accelerating finite energy Airy beams

Abstract: We investigate the acceleration dynamics of quasi-diffraction-free Airy beams in both one- and two-dimensional configurations. We show that this class of finite energy waves can retain their intensity features over several diffraction lengths. The possibility of other physical realizations involving spatiotemporal Airy wave packets is also considered.

Realization of general nondiffracting beams with computer-generated holograms

Abstract: A new class of solutions to the scalar wave equation was introduced recently that represents transversely localized but totally nondiffracting fields. We show by the method of stationary phase that any of these wave fields can be realized approximately with a laser and a single computer-generated hologram. We briefly discuss various techniques for coding and fabrication of the required hologram and the associated diffraction efficiencies. Using both binary-amplitude and four-level phase holograms, we demonstrate experimentally the formation of arbitrary-order Bessel beams and rotationally nonsymmetric beams.