Guest Editorial: Method of analytical regularisation for new frontiers of applied electromagnetics

Lucido, Mario; Kobayashi, Kazuya; Medina, F.; Nosich, Alexander I.; Vinogradova, E. D.

doi:10.1049/mia2.12182

Cited by 15 publications

(6 citation statements)

References 21 publications

(25 reference statements)

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“…The cost of this simplification is clear: after such a replacement, we lose the information of the fine details at the rim of the original disk. Nevertheless, this problem admits a unique solution provided that the boundary conditions, local power finiteness condition and Silver–Muller radiation condition are satisfied [14,31]. According to the second Green's formula, since the scattered electric and magnetic fields can be expressed as the convolution of the effective electric and magnetic current densities, respectively, with Green's functions and their normal to the disk derivatives, the equations (2.5 a ) and (2.5 b ) can be interpreted as two decoupled surface integral equations for the effective current densities [24].…”

Section: Formulation and Solution Methodsmentioning

confidence: 99%

“…Additionally, commercial codes, especially those based on the finite-difference time-domain approach, entail huge numbers of unknowns and correspondingly enormous computation times even for simple mesoscale objects, if they are in the free space, and the radiation condition is satisfied only approximately. As mentioned in [14], all these numerical troubles can be completely eliminated with either of two especially advantageous approaches—the method of analytical regularization (MAR) and the Nystrom discretization of the associated singular integral equations (ND-SIEs) [15]. These convergent techniques exploit the fact that graphene is, actually, a zero-thickness resistive sheet with frequency-dependent resistivity ( resistivit y is a short term substituting for the longer expression complex electric surface resistance ; an equivalent term is surface impedance ).…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, a preceding computer modelling, if it is trusted, fast and accurate, is important as a tool of design that enables avoiding costly and time-consuming prototyping. Here, one can see a sort of permanent competition between the general-purpose commercial codes, which have relatively low accuracy and may suffer from the convergence troubles (see [12,13] for some reviews), and mathematically sophisticated advanced in-house algorithms [14]. The latter are superior in performance because of the guaranteed convergence and controlled accuracy to machine precision, however, are normally oriented to handle a narrower class of electromagnetic geometries.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Terahertz-range plasmon and whispering gallery mode resonances in the plane wave scattering from thin microsize dielectric disk with graphene covers

Lucido

Balaban²,

Nosich³

2022

Proc. R. Soc. A.

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We analyse the scattering and absorption of a terahertz-range plane wave by a thin circular dielectric disk with two graphene covers. Assuming that the thickness of the whole composite disk is much smaller than the free-space wavelength, we reduce the complexity of the problem with the aid of the generalized boundary conditions. This yields a set of singular integral equations for the effective electric and magnetic currents, induced on an equivalent zero-thickness disk. The adopted advanced numerical solution technique is a version of the method of analytical preconditioning, which uses weighted polynomials as expansion functions in the discretization of the integral equations. Then, the resulting matrix equation has Fredholm second-kind property that enables us to control the computational error by the matrix size and reduce it to the desired level. This accurate analysis reveals resonances on several types of natural modes, best understood via visualization of in-resonance near-fields. They are the plasmon-mode resonances of the graphene disk, perturbed by the presence of the dielectric filler, and the dielectric disk modes, perturbed by the graphene covers. Additionally, quasi-full disk transparency is observed if the transverse resonance condition is fulfilled. Special attention is paid to the tunability of the found effects with the aid of graphene's chemical potential.

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Section: Formulation and Solution Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Terahertz-range plasmon and whispering gallery mode resonances in the plane wave scattering from thin microsize dielectric disk with graphene covers

Lucido

Balaban²,

Nosich³

2022

Proc. R. Soc. A.

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“…The equations arise in the scattering problems by graphene arrays can be converted to the second kind Fredholm equations by means of the methods of analytical regularization (Lucido et al 2021). In papers Zinenko et al 2017Zinenko et al , 2020 For multilayer structures, it can be efficient to consider a single layer by the method of SIE.…”

Section: Introductionmentioning

confidence: 99%

Integral equations in the H-polarized wave scattering from metasurface formed by finite multilayer graphene strip grating inside grounded dielectric slab

Kaliberda,

Pogarsky,

Sierhieieva

2023

Opt Quant Electron

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The H-polarized waves scattering and absorption by the metasurface, which consists of multilayer grating of finite number of graphene strips inside a grounded dielectric slab is considered. The problem is formulated in the domain of Fourier transform (spectral domain). The solution is obtained in two steps. At first, the scattering operators of a single graphene grating inside the infinite dielectric medium are obtained from the singular integral equations. At the second stage, the integral equations in the operator form relatively unknown Fourier amplitudes are presented for the whole structure. The kernel-functions of these equations contain singularities at the points, which correspond to the propagation constants of the natural waves of the dielectric waveguide with perfectly electric conducting wall.To eliminate the singularities and to convert the kernel-functions to the regular ones, the regularization procedure is proposed. The approach is meshless, fullwave and convergence is guaranteed by the theorems. The numerical results for the plane wave and natural wave of corresponding dielectric waveguide with perfectly electric conducting wall incidence are presented. Special attention is paid to the excitation of the plasmon and grating-mode resonances. By taking layers with different period and chemical potential, one can control the elevation angle of the main lobe and excitation frequency of the natural waves of dielectric waveguide.

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“…One way to overcome all these problems is represented by the methods of analytical regularization [11]. Such methods are aimed at individuating a suitable singular part of the integral operator, containing the most singular part of the operator itself, to be analytically inverted.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique

Lucido

2021

Applied Sciences

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In this paper, the scattering of a plane wave from a lossy Fabry–Perót resonator, realized with two equiaxial thin resistive disks with the same radius, is analyzed by means of the generalization of the Helmholtz–Galerkin regularizing technique recently developed by the author. The disks are modelled as 2-D planar surfaces described in terms of generalized boundary conditions. Taking advantage of the revolution symmetry, the problem is equivalently formulated as a set of independent systems of 1-D equations in the vector Hankel transform domain for the cylindrical harmonics of the effective surface current densities. The Helmholtz decomposition of the unknowns, combined with a suitable choice of the expansion functions in a Galerkin scheme, lead to a fast-converging Fredholm second-kind matrix operator equation. Moreover, an analytical technique specifically devised to efficiently evaluate the integrals of the coefficient matrix is adopted. As shown in the numerical results section, near-field and far-field parameters are accurately and efficiently reconstructed even at the resonance frequencies of the natural modes, which are searched for the peaks of the total scattering cross-section and the absorption cross-section. Moreover, the proposed method drastically outperforms the general-purpose commercial software CST Microwave Studio in terms of both CPU time and memory occupation.

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Guest Editorial: Method of analytical regularisation for new frontiers of applied electromagnetics

Cited by 15 publications

References 21 publications

Terahertz-range plasmon and whispering gallery mode resonances in the plane wave scattering from thin microsize dielectric disk with graphene covers

Terahertz-range plasmon and whispering gallery mode resonances in the plane wave scattering from thin microsize dielectric disk with graphene covers

Integral equations in the H-polarized wave scattering from metasurface formed by finite multilayer graphene strip grating inside grounded dielectric slab

Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique

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