H-polarized plane-wave scattering by a PEC strip grating on top of a dielectric substrate: analytical regularization based on the Riemann-Hilbert Problem solution

ABSTRACT

We consider the H-polarized plane wave scattering from an infinite flat grating of perfectly electrically conducting strips, placed on the interface of a dielectric slab. We reduce this problem to a dual series equation for the complex amplitudes of the Floquet spatial harmonics. Then, we perform analytical regularization of this equation, based on the inversion of the static part of the problem 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. Numerical results obtained demonstrate how the rate of convergence depends on the geometrical parameters and then concentrate on the resonance effects in the reflection and transmission. We reveal and discuss ultra-high-Q resonances on the lattice modes of such a composite grating, overlooked in earlier studies.

KEYWORDS:

• Strip grating
• scattering
• regularization

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).

Alexander I. Nosich

Alexander I. Nosich was born in 1953 in Kharkiv, Ukraine. He received the M.S., Ph.D., and D.Sc. degrees in radio physics from the V. N. Karazin Kharkiv National University, Ukraine, in 1975, 1979, and 1990, respectively. Since 1979, he has been with IRE NASU, Kharkiv, where he is currently Professor, Principal Scientist and Head, Laboratory of Micro and Nano Optics. Since 1992, he held many guest fellowships and professorships in the EU, the UK, Japan, Singapore, and Turkey. His research interests include the method of analytical regularization, propagation and scattering of waves, open waveguides, antennas and lasers, and the history of microwaves. Prof. Nosich was initiator and technical committee chairman of the international conference series on Mathematical Methods in Electromagnetic Theory (MMET), held in Ukraine since 1990. In 1995, he organized the IEEE AP-S East Ukraine Chapter, the first one in the former USSR. Currently he represents Ukraine in the European Association on Antennas and Propagation. He was awarded the honorary title of Doctor Honoris Causa of the University of Rennes 1, France in 2015 and the Galileo Galilei Medal of the International Commission for Optics in 2017, and elected Fellow of IEEE in 2003 and Fellow of the Optical Society (OSA) in 2019. He was also co-recipient the 2017 National Prize of Ukraine in Science and Technology for the works entitled, “Photonics of semiconductor and dielectric nanostructures” and the 2018 Solomon I. Pekar Award of NASU in the solid state physics theory.