Constrained focusing of vector fields intensity in near zone and/or complex scenarios as a low-dimensional global optimization

Abstract

A hybrid effective approach is proposed to focus the intensity of a vector field generated by an arbitrary fixed-geometry array antenna into a target point and keep it bounded elsewhere. To overcome the complexity of the underlying non-convex problem involving a possibly large number of unknowns, we show how the space of possible polarizations can be regarded as a 5-sphere and introduce a nested procedure which jointly relies on an (external) global optimization of the field polarization on the target point plus an (internal) convex optimization of the array excitations. The approach can deal with both the cases of near-field (NF) and far-field (FF) focusing as well as with complex inhomogeneous 3-D media. The high-performance results achieved through full-wave simulations of realistic scenarios confirm the actual feasibility of tackling the problem as a low-dimensional global optimization, so that the best possible focusing can be hopefully realized.

KEYWORDS:

• Array synthesis
• convex programming
• electromagnetic focusing
• hybrid optimization

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 As continuous aperture sources can be properly discretized [3], the presented approach is of interest also for that case.

2 Although written for the FF case, which is the reason while it has been overlooked in the NF literature, [1] explicitly notes the applicability to the cases of NF constraints and NF focusing.

3 For instance, in case of oncological hyperthermia treatments, the upper bounds will be enforced in such a way to guarantee a safe field value on the healthy tissues surrounding the tumor [9].

4 The ga algorithm is a stochastic, population-based algorithm that searches randomly by mutation and crossover among population members. Its parameters configuration has been performed as follows (see [30] for more details concerning the different variables): population size=50; elite count: 0.05*Population Size; number of variables=5; number of generations=100*number of variables; constraint tolerance: 1e-3; function tolerance: 1e-6; crossover fraction: 0.8.

On the other side, the fmincon algorithm setup has been performed as follows (see [31] for more details concerning the different variables): Algorithm: 'active-set'; Constraint tolerance: 1e-6; Max function evaluations: 3000; Max iterations: 1000; Optimality tolerance: 1e-6; Step tolerance: 1e-10.

Additional information

Funding

This work was supported by the Italian Ministry of Education, Universities, and Research, under the Project of National Interest (PRIN) no 2015KJE87K.

Notes on contributors

G. M. Battaglia

G. M. Battaglia was born in Melito Di Porto Salvo, Italy, in 1993. She received the M.S. Laurea degree (summa cum laude) in electronic engineering from the University Mediterranea of Reggio Calabria, Reggio Calabria, Italy, in 2017. She is currently working toward the Ph.D. degree in information engineering (applied electromagnetics) at the University Mediterranea of Reggio Calabria, Reggio Calabria, Italy. Her current research interests include array antennas, optimal synthesis, and biomedical applications. She is a member of the Italian Electromagnetics Society.

A. F. Morabito

A. F. Morabito received the Laurea degree (summa cum laude) in telecommunications engineering and the Ph.D. degree in computer, biomedical, and telecommunications engineering from the University Mediterranea of Reggio Calabria, Reggio Calabria, Italy. He has been an Assistant Professor in electromagnetic fields with the University Mediterranea of Reggio Calabria since 2010, where he is currently a member of the LEMMA Research Group. He has also been a Visiting Researcher with the Eledia Research Center, University of Trento, Trento, Italy. He has authored more than 80 papers published in peer-reviewed scientific journals or international conference proceedings. His current research interests include models and effective strategies for electromagnetic forward and inverse scattering problems, antenna theory, design, optimal synthesis, and therapeutic applications, with applications ranging from biomedical imaging to radar and satellite telecommunications. Dr. Morabito is a member of the Italian Electromagnetics Society and the European Association on Antennas and Propagation. He received the Barzilai and Latmiral Prizes from the Italian Electromagnetics Society.

R. Palmeri

R. Palmeri was born in Catania, Italy, in 1989. She received the M.S. Laurea degree (summa cum laude) in telecommunication engineering from the University of Catania (Catania, Italy) in 2014 and the Ph.D degree in information engineering from Università Mediterranea of Reggio Calabria (Reggio Calabria, Italy) in 2018. From December 2017 to November 2019 she was a Post Doc Researcher of the LEMMA Research Group at Università Mediterranea, where she is currently an Assistant Professor. Her scientific activities are concerned with inverse problems in electromagnetics. In particular, she is presently focused on the development of new strategies based on inverse scattering for the synthesis of innovative devices. Dr. Palmeri was the recipient of the Best Italian Remote Sensing Thesis Prize from the IEEE Geoscience and Remote Sensing South Italy Chapter in 2014, the IEEE Antennas and Propagation Society (Central and South Italy Chapter) prize in 2017 and the Young Scientist Award at the 2nd URSI Atlantic Radio Science Meeting in 2018.

T. Isernia

T. Isernia (SM’15) received the Laurea (summa cum laude) and Ph.D. degrees from the University of Naples Federico II, Naples, Italy.He is currently a Full Professor in electromagnetic fields with the University Mediterranea of Reggio Calabria, Reggio Calabria, Italy, where he currently serves as the Supervisor of the LEMMA Research Group and the Director of the Information Engineering Department. He is also with the Consorzio Nazionale Interuniversitario per le Telecomunicazioni, Parma, Italy, where he serves as a member of the Board of Administrators. His current research interests include field synthesis problems for biomedical imaging and therapeutic applications, inverse problems in electromagnetics, with particular emphasis on phase retrieval, inverse scattering, and antenna synthesis problems.Dr. Isernia was a recipient of the G. Barzilai Award from the Italian Electromagnetics Society in 1994.