Non-diffracting solutions to the wave equations: contribution to theory, experimental generation, and applications

• Grant number: 13/12025-8
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: July 01, 2013
• End date: June 30, 2014
• Field of knowledge: Engineering - Electrical Engineering
• Principal Investigator: Michel Zamboni Rached
• Grantee: Michel Zamboni Rached
• Visiting researcher: Erasmo Recami
• Visiting researcher institution: Università degli studi di Bergamo (Unibg), Italy
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Localized Waves (LW), or Non-Diffracting Waves (NDW), are beams and pulses resisting diffraction for long distances: initially in vacuum, and, subsequently, in dispersive and attenuating media. Today, we know how to get solutions resisting diffraction, dispersion, and attenuation. Such solutions to the wave equations (e.g., to Maxwell equations) were theoretically constructed (as suitable superpositions of Bessel beams), and soon after experimentally. Actually, it has been recently discovered that Localized Beams and Pulses exist, which propagate in one direction practically without deforming, in the sectors of Electromagnetism (optics, microwaves,...) and of Acoustics: That is, that "soliton-like" solutions exist also for linear equations like the wave equations. They self-reconstruct themselves after obstacles with size smaller of the antenna's. The most important objectives and activities of the present Project are: 1) Theoretical and experimental generation of moving "Frozen Waves" (FW), where the FWs are Non-Diffracting beams modeled in space (and with a static envelope). Regular FWs in Optics have been experimentally produced in 2012, for the first time in the world, in Brazil, confirming the theory of the Docent, Prof. Michel, and the proposed Visitant, Prof. Recami; and getting their remarkable applications nearer, in areas like (new types of) optical or acoustical tweezers, optical atom guiding, remote sensing, optical communications in free space, micro-lithography, etc., and especially medicine [indeed, FWs' intensity pattern can be modeled as one desires, over a very tiny space-interval: For instance, as an intense peak that falls rapidly down by a factor even of one million: so that an (acoustic) FW can heat, and destroy, tumor cells, without affecting the surrounding tissues]. The first aim of this Project consists in investigating "dynamical" Frozen Waves by: (a) generalization of our original FW method for the case when the envelope is no longer static, but moves; (b) experimental generation of such dynamical FWs in Optics, via numerical holography (and a Spatial Modulator of Light). 2) Analitic description for any desired truncated beam. In past recent work, the docent Michel and the proposed visitant Recami have developed a method (based on appropriate superpositions of Bessel-Gauss beams), which in the Fresnel regime describes in analytic form the 3D evolution of a few important waves, even in the realistic case of finite energies. [One of the byproducts of such a mathematical method of ours is that one gets in few seconds, or minutes, high-precision results which normally require quite long times of numerical simulation]. Our second aim is generalizing our method for any known beams whatsoever, even when spatially truncated. 3) Obtaining super-resolution by evanescent beams. A "last" aim is studying how to superpose Bessel beams, this time evanescent, so as to obtain striking sub-wavelength localizations. In this case, micro- and nano-technological applications are expected (more than biophysical). In the sector of evanescent waves the Visitant has a quite long experience, initiated in 1990.Further (also didactic) activities. This collaboration will go on with Michel, and with Professor Hugo E. Hernandez Figueroa. It will include also participation by the Visitant in many didactic and educational activities. Additional aims are: a Second Volume on NDWs c/o J. Wiley (Berlin); and a Review invited by Phys. Reports (impact factor 13). Obs: the present Project is bound to the current, Regular "Projeto de Auxilio à Pesquisa" of Prof.Dr.Michel (process no. 2011-51200-4), and to the two thematic Projects FOTONICOM (process 2008-57875-2) and CePOF (process 2005-51689-2). (AU)

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

PREGO-BORGES, JOSE L.; ZAMBONI-RACHED, MICHEL; RECAMI, ERASMO; COSTA, EDUARDO TAVARES. Producing acoustic `Frozen Waves': Simulated experiments with diffraction/attenuation resistant beams in lossy media. ULTRASONICS, v. 54, n. 6, p. 1620-1630, AUG 2014. (13/12025-8)

RECAMI, ERASMO. Ettore Majorana: The scientist and the man. INTERNATIONAL JOURNAL OF MODERN PHYSICS D, v. 23, n. 14, SI, DEC 2014. (13/12025-8)

PREGO-BORGES, JOSE L.; ZAMBONI-RACHED, MICHEL; RECAMI, ERASMO; HERNANDEZ-FIGUEROA, HUGO E.. Producing Acoustic Frozen Waves: Simulated Experiments. IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL, v. 60, n. 11, p. 2414-2425, NOV 2013. (13/12025-8)

RECAMI, ERASMO. Ettore Majorana: The scientist and the man. INTERNATIONAL JOURNAL OF MODERN PHYSICS D, v. 23, n. 14, p. 17-pg., 2014-12-01. (13/12025-8)

PREGO-BORGES, JOSE L.; ZAMBONI-RACHED, MICHEL; RECAMI, ERASMO; COSTA, EDUARDO TAVARES. Producing acoustic 'Frozen Waves': Simulated experiments with diffraction/attenuation resistant beams in lossy media. ULTRASONICS, v. 54, n. 6, p. 11-pg., 2014-08-01. (13/12025-8)