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Abstract
We consider a plane E-polarized wave scattering from an infinite flat grating of slots cut in a perfect electrically conducting plane, backed with a dielectric slab. At first, we reduce this problem to a dual series equation for the complex amplitudes of the Floquet spatial harmonics. Then we perform its analytical regularization, based on the inversion of the main part with the aid of the Riemann-Hilbert Problem. This yields a Fredholm second-kind infinite matrix equation, numerical solution of which has a guaranteed convergence. We perform numerical experiments demonstrating how the rate of convergence depends on the thickness and dielectric permittivity of the slab. Our computations demonstrate the Fano-shape resonances on the so-called lattice modes, responsible for the phased array blindness. Their frequencies lay near to the Rayleigh anomalies and, if the slots or strips are narrow and the slab is thin, may have ultrahigh Q-factors.
Acknowledgement
This work was supported, in part, by the National Research Foundation of Ukraine, project no. 2020.02.0150.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Notes on contributors
Fedir O. Yevtushenko
Fedir O. Yevtushenko was born in 1995 in Kharkiv, Ukraine. He received the B.S. and M.S. degrees in photonics and optoinformatics from the National University of Radio Electronics, Kharkiv, Ukraine, in 2017 and 2019, respectively. Currently he is Ph.D. student and part-time Junior Scientist at the Laboratory of Micro and Nano Optics (LMNO), Institute of Radio-Physics and Electronics of the National Academy of Sciences of Ukraine (IRE NASU), Kharkiv. His research interests are in the wave scattering from gratings, made of perfect and imperfect flat strips and the method of analytical regularization. He was recipient of Young Scientist Prize of the European Microwave Association at the IEEE Ukraine Conference on Electrical and Computer Engineering (UKRCON-2019), Lviv, 2019 and Young Scientist Special Grant of the International Conference on Microwaves, Communications, Antennas, and Electronic Systems (COMCAS-2019), Tel Aviv, 2019.
Sergii V. Dukhopelnykov
Sergii V. Dukhopelnykov was born in Kharkiv, Ukraine in 1982. He received the B.S., M.S. and Ph.D. degrees in mathematical modeling and numerical methods from the V. N. Karazin Kharkiv National University in 2003, 2004 and 2010, respectively. From 2007 to 2018, he was a Lecturer, Senior Lecturer and Assistant Professor at the Department of Mathematics, National Technical University “Kharkiv Polytechnic Institute” in Kharkiv, Ukraine. Since 2018, he is Senior Scientist at LMNO, IRE NASU, Kharkiv and part-time Assistant Professor at the School of Mathematics of the V. N. Karazin Kharkiv National University. His research interests are in singular integral equations, Nystrom methods, and patterned graphene scattering. He was recipient of the Ph.D. scholarship award of the N. I. Akhiyezer Foundation, Kharkiv (2010) and the Young Scientist Prize of the International Conference on Mathematical Methods in Electromagnetic Theory (2018).
Tatiana L. Zinenko
Tatiana L. Zinenko was born in Alchevsk, Ukraine. She earned her combined B.S. and M.S. degree in radio physics from the V.N. Karazin Kharkiv National University, Kharkiv, Ukraine in 1982. Then she joined IRE NASU, where she is currently a senior scientist in the Department of Quasi-Optics and also part-time senior scientist in the Laboratory of Micro and Nano Optics. From 1996 to 2000 she was with the Department of Computer and Electrical Engineering, Kumamoto University, Kumamoto, Japan, as a research student. She earned the Doctor of Engineering degree in system science from the Kumamoto University in 2000 and also a Ph.D. degree in radio physics from IRE NASU in 2004. Her research interests are in integral equation methods and electromagnetic wave scattering from imperfect scatterers and periodic gratings. She was a recipient of Graduate Student Fellowship in Advanced Electromagnetics from the SUMMA Foundation, USA (1999) and Researcher Mobility Grant from the "Newfocus" Research and Training Network of the European Science Foundation (2013).