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Non-Diffracting Waves and Frozen Waves

Abstract

Localized Waves (LW), or Non-Diffrating Waves (NDW), are beams or pulses resisting diffraction for long distances: either in vacuum, or in dispersive (and lossy) media. We know today [and I am referring to the research Group formed by Professors Hugo E. Hernández Figueroa (o "Docente Responsavel") e Michel Zamboni Rached, e pelo Visitante proposto Prof. Recami; and collaborators] how to obtain solutions resisting diffraction, dispersion, and attenuation. Such solutions to the wave equations (e.g., to Maxwell equations) were constructed by us theoretically (by suitable superpositions of Bessel beams), and soon later experimentally. There exist, indeed, Localized Beams and Pulses propagating in a single direction, almost without deforming, in the sectors of Electromagnetism (optics, micro-waves,...) and of Acoustics: That is, "soliton-type" solutions exist also for linear equations like the wave equations. They are moreover able to self-reconstruct themselves after obstacles with sizes smaller than those of their ANTENNA. In recent years we devoted ourselves to the theoretical and experimental generation of the "Frozen Waves" (FW), which are non-diffracting beams that can be modeled in space (and possess a static envelope). Optical FWs were produced experimentally, for the first time in the world, in Brazil, in 2012: confirming our theory. One of our present desires is to continue exploring the application of FWs for constructing microwave antennas [a Patent already was requested], as well as (new types of) optical or acoustic tweezers; without forgetting Medicine [a Patent was already granted to us by USA in 2013]. The experimental generation of FWs in Optics was got by holography (and a Light Space Modulator). An important fact is that the FWs allow constructing "Pieces of Light at rest", and connecting varios of them together, so as to obtain --both in theory and in practice-- "LEGO-type beams" with many applications [Phys. Rev. Applied, 2018]. The first objective of this Project is as follows -- Professors Hugo and Michel, together with Recami, edited two Books, of about 500 pages each: "Localized Waves", 2008, J.Wiley (ed. by Hugo, Michel, Recami), and "Non-Diffracting Waves", J. Wiley, 2014 (ed. by Hugo, Recami, Michel); which are the unique existing collections of papers on our topic, in which however we only could insert (long) introductory chapters. But in 2018 we obtained the acceptation, by another international publisher (Taylor & Francis), of a whole Book written by ourselves on Non-Diffracting Waves and Frozen Waves, and Applications. Our main objective is the preparation of such a common Book: something that needs a side-by-side (and not by far)collaboration. Information about this Book stays in a specific Document. Another objective is investigating how to superpose Bessel beams (this time evanescent), so to get localizations surprisely smaller than a wavelength. In this case, micro- and nano-technology applications are expected (rather than biophysical). In the evanescent-wave sector the expected "PVE" has a long experience, which dates back e.g. to a paper published in 1990 together with the "Docente Responsavel" Prof. Hugo. Further objectives aim to continue: d) constructing "LEGO-type beams", for example by "dynamical FWs"; e) investigating the transmission of FWs through stratified materials; f) controlling the orbital angular momentum of non-diffracting beams during propagation; g) studying "soliton-like" solutions to Shroedinger's (and Einstein's) equations; h) and more Applications, in general. Further activities (also didactic): To continue with the partecipation of the "PVE" in several didactic and educational activities, and in co-supervisions. Obs: the present Project is associated with the Thematic Project by Prof. Hugo, FAPESP number 2015/24517-8 [Main Project], and two further Projects by the Master students T. Viana Souza and Jéssica Nobre P. (AU)