Applied Sciences

Research

37 pages, 888 KiB

Open AccessArticle

Spectral Analysis of Electromagnetic Diffraction Phenomena in Angular Regions Filled by Arbitrary Linear Media

by Vito G. Daniele and Guido Lombardi

Appl. Sci. 2024, 14(19), 8685; https://doi.org/10.3390/app14198685 - 26 Sep 2024

Cited by 2 | Viewed by 436

A general theory for solving electromagnetic diffraction problems with impenetrable/penetrable wedges immersed in/made of an arbitrary linear (bianistropic) medium is presented. This novel and general spectral theory handles complex scattering problems by using transverse equations for layered planar and angular structures, the characteristic [...] Read more.

A general theory for solving electromagnetic diffraction problems with impenetrable/penetrable wedges immersed in/made of an arbitrary linear (bianistropic) medium is presented. This novel and general spectral theory handles complex scattering problems by using transverse equations for layered planar and angular structures, the characteristic Green function procedure, the Wiener–Hopf technique, and a new methodology for solving GWHEs. The technique has been proven effective for analyzing problems involving wedges immersed in isotropic media; in this study, we extend the theory to more general cases while providing all necessary mathematical tools and corresponding validations. We obtain generalized Wiener–Hopf equations (GWHEs) from spectral functional equations in angular regions filled by arbitrary linear media. The equations can be interpreted with a network formalism for a systematic view. We recall that spectral methods (such as the Sommerfeld–Malyuzhinets (SM) method, the Kontorovich–Lebedev (KL) transform method, and the Wiener–Hopf (WH) method) are well-consolidated, fundamental, and effective tools for the correct and precise analysis of electromagnetic diffraction problems constituted by abrupt discontinuities immersed in media with one propagation constant, although they are not immediately applicable to multiple-propagation-constant problems. To the best of our knowledge, the proposed mathematical technique is the first extension of spectral analysis to electromagnetic problems in the presence of angular regions filled by complex arbitrary linear media, thereby providing novel mathematical tools. Validation through fundamental examples is proposed. Full article

(This article belongs to the Special Issue Challenge of Guaranteed Convergence in Applied Electromagnetics: Recent Progress in the Methods of Analytical Regularization)

► Show Figures

Figure 1

12 pages, 3655 KiB

Open AccessArticle

Controlling the Focusing Ability of the Parabolic Graphene Reflector in Free Space at Microwave Frequencies

by Taner Oğuzer

Appl. Sci. 2024, 14(4), 1520; https://doi.org/10.3390/app14041520 - 14 Feb 2024

Viewed by 891

Abstract

The studied configuration is a two-dimensional, very thin parabolic reflector made of graphene and illuminated by an H-polarized electromagnetic plane wave. We present basic scattering and focusing properties of such a graphene reflector depending on the graphene parameters at microwave frequencies, using the [...] Read more.

The studied configuration is a two-dimensional, very thin parabolic reflector made of graphene and illuminated by an H-polarized electromagnetic plane wave. We present basic scattering and focusing properties of such a graphene reflector depending on the graphene parameters at microwave frequencies, using the resistive boundary condition for very thin sheets. The scattering is formulated as an electromagnetic boundary-value problem; it is transformed to a singular integral equation that is further treated with the method of analytical regularization (MAR) based on the known solution of the Riemann–Hilbert Problem (RHP). The numerical results are computed by using a Fredholm second-kind matrix equation that guarantees convergence and provides easily controlled accuracy. Compared to THz range, in microwaves, the scattering pattern of reflector and the field level at geometrical focus can be controlled in a wide range by adjusting the chemical potential of graphene. Even though here no dielectric substrate supporting the graphene is considered, the practical realization can also be possible as a thin layer graphene material in GHz range. As we demonstrate, the variation of the chemical potential from 0 to 1 eV can improve the focusing ability within the factor of three. The high accuracy of the used method and the full wave formulation of the problem support our findings. Full article

(This article belongs to the Special Issue Challenge of Guaranteed Convergence in Applied Electromagnetics: Recent Progress in the Methods of Analytical Regularization)

► Show Figures

Figure 1

13 pages, 12744 KiB

Open AccessArticle

Tunability of Radiation Pattern of the H-Polarized Natural Waves of Dielectric Waveguide with Infinite Graphene Plane and Finite Number of Graphene Strips at THz

by Mstyslav E. Kaliberda and Sergey A. Pogarsky

Appl. Sci. 2023, 13(19), 10563; https://doi.org/10.3390/app131910563 - 22 Sep 2023

Cited by 2 | Viewed by 791

Abstract

We investigate the radiation of the THz natural waves of the dielectric waveguide with graphene plane scattered by finite number of graphene strips. Our mathematically accurate analysis uses the singular integral equations method. The discretization scheme employs the Nystrom-type algorithm. The complex-valued propagation [...] Read more.

We investigate the radiation of the THz natural waves of the dielectric waveguide with graphene plane scattered by finite number of graphene strips. Our mathematically accurate analysis uses the singular integral equations method. The discretization scheme employs the Nystrom-type algorithm. The complex-valued propagation constants of the natural waves and corresponding fields are determined numerically from the equation, which also involves the kernel-function of the singular integral equation. The method we use is meshless and full-wave. The convergence is provided by the mathematical theorems. By varying the chemical potential of graphene and structural geometrical parameters, we examine the elevation angle of the main lobe of the radiation pattern and the radiated power. Full article

(This article belongs to the Special Issue Challenge of Guaranteed Convergence in Applied Electromagnetics: Recent Progress in the Methods of Analytical Regularization)

► Show Figures

Figure 1

23 pages, 878 KiB

Open AccessArticle

Wave Diffraction from a Bicone Conjoined with an Open-Ended Conical Cavity

by Dozyslav B. Kuryliak and Oleksiy M. Sharabura

Appl. Sci. 2023, 13(14), 8517; https://doi.org/10.3390/app13148517 - 23 Jul 2023

Cited by 2 | Viewed by 1113

Abstract

The problem of axially symmetric TM-wave diffraction from a bicone conjoined with an open-ended conical cavity is analysed rigorously. The scatterer is formed by the perfectly conducting semi-infinite and truncated semi-infinite conical surfaces; the spherical termination of an internal area of the truncated [...] Read more.

The problem of axially symmetric TM-wave diffraction from a bicone conjoined with an open-ended conical cavity is analysed rigorously. The scatterer is formed by the perfectly conducting semi-infinite and truncated semi-infinite conical surfaces; the spherical termination of an internal area of the truncated cone creates the open-ended cavity. In this paper the certain physical aspects of diffraction which are known to cause mathematical difficulties are considered. It includes an accurate analysis of the wave-mode transformation phenomena at the open end of the cavity, as well as a study of wave radiation from the cavity into the biconical waveguide. The primary outcome of this paper is a precise treatment of the wave diffraction problem mentioned above using new techniques and establishing new properties of resonance modes’ penetration into the biconical waveguide region. Full article

(This article belongs to the Special Issue Challenge of Guaranteed Convergence in Applied Electromagnetics: Recent Progress in the Methods of Analytical Regularization)

► Show Figures

Figure 1

14 pages, 5841 KiB

Open AccessArticle

Plane-Wave Diffraction from Resistive-Filled Circular Hole in Infinite Resistive Plane: An Analytically Regularizing Approach

by Mario Lucido, Gaetano Chirico, Marco Donald Migliore, Daniele Pinchera and Fulvio Schettino

Appl. Sci. 2023, 13(13), 7465; https://doi.org/10.3390/app13137465 - 24 Jun 2023

Cited by 1 | Viewed by 1017

Abstract

The study of the electromagnetic diffraction from penetrable screens with apertures and/or inhomogeneities is of great relevance today due to the huge number of modern applications in which they are involved. In this paper, the analysis of the plane wave scattering from a [...] Read more.

The study of the electromagnetic diffraction from penetrable screens with apertures and/or inhomogeneities is of great relevance today due to the huge number of modern applications in which they are involved. In this paper, the analysis of the plane wave scattering from a resistive-filled circular hole in a resistive plane is addressed. The uniquely solvable boundary value problem for the Maxwell equations, obtained via imposing generalized boundary conditions, power boundedness condition, and Silver–Muller radiation condition, is equivalently formulated in terms of an infinite set of singular dual integral equations in the vector Hankel transform domain. The Helmholtz–Galerkin technique allows for the discretization and, simultaneously, analytical regularization of the obtained integral equations. Fast convergence is guaranteed by a suitable choice of the basis functions reconstructing the physical behavior of the fields at the discontinuity between the two involved media. Moreover, the full-wave nature of the proposed approach allows the direct assessment of near-field and far-field parameters. Full article

(This article belongs to the Special Issue Challenge of Guaranteed Convergence in Applied Electromagnetics: Recent Progress in the Methods of Analytical Regularization)

► Show Figures

Figure 1

13 pages, 446 KiB

Open AccessFeature PaperArticle

A Dual Integral Equation Approach for Evaluating the Shielding of Thick Circular Disks against a Coaxial Loop

by Giampiero Lovat, Paolo Burghignoli, Rodolfo Araneo and Salvatore Celozzi

Appl. Sci. 2023, 13(9), 5819; https://doi.org/10.3390/app13095819 - 8 May 2023

Cited by 1 | Viewed by 1346

Abstract

The electromagnetic interaction between a circular disk with finite conductivity and finite thickness and a coaxial circular loop of constant current is addressed here. The finite conductivity and thickness of the material disk lead to the adoption of suitable generalized boundary conditions, and [...] Read more.

The electromagnetic interaction between a circular disk with finite conductivity and finite thickness and a coaxial circular loop of constant current is addressed here. The finite conductivity and thickness of the material disk lead to the adoption of suitable generalized boundary conditions, and the problem is thereby reduced to the solution of two sets of dual integral equations in the Hankel transform domain. Such equations are then solved by expanding the spectral unknowns in Neumann series of Bessel functions. An alternative formulation that is valid for purely conductive screens with no magnetic properties, which is computationally much faster, is proposed as well. The magnetic shielding effectiveness of the structure is studied in detail, pointing out its dependencies and possible critical situations. Full article

(This article belongs to the Special Issue Challenge of Guaranteed Convergence in Applied Electromagnetics: Recent Progress in the Methods of Analytical Regularization)

► Show Figures

Figure 1

11 pages, 880 KiB

Open AccessArticle

The Regularization Technique in Modeling of the Plane E-Polarized EM Wave Scattering by Coplanar System of Electrically Conducting Flat Strips

by George I. Koshovy and Andrii G. Koshovy

Appl. Sci. 2023, 13(9), 5488; https://doi.org/10.3390/app13095488 - 28 Apr 2023

Cited by 2 | Viewed by 978

Abstract

The integral equations technique has been successfully modified for studying the plane E-polarized electromagnetic wave scattering by multilevel coplanar systems of zero-thickness impedance strips. Reformulation of the scattering problem in the form of the second-kind regular integral equations has been realized on [...] Read more.

The integral equations technique has been successfully modified for studying the plane E-polarized electromagnetic wave scattering by multilevel coplanar systems of zero-thickness impedance strips. Reformulation of the scattering problem in the form of the second-kind regular integral equations has been realized on the base of the Carleman regularization technique. Two novel and original classes of specific Cantor functions have been presented and analyzed. Using new Cantor functions, it is easy to create a lot of non-classical orderings for specific multilevel coplanar strips systems. That sort of system can be useful for modeling irregular natural processes and zones in the future. Considerable attention was focused on the plane E-polarized electromagnetic wave scattering by sparsely filled coplanar systems of electrically narrow impedance strips. An explicit solution of the scattering problem has been obtained for such case of strips system. Full article

(This article belongs to the Special Issue Challenge of Guaranteed Convergence in Applied Electromagnetics: Recent Progress in the Methods of Analytical Regularization)

► Show Figures

Figure 1

22 pages, 9578 KiB

Open AccessArticle

Diffraction by a Semi-Infinite Parallel-Plate Waveguide with Five-Layer Material Loading: The Case of H-Polarization

by Kewen He and Kazuya Kobayashi

Appl. Sci. 2023, 13(6), 3715; https://doi.org/10.3390/app13063715 - 14 Mar 2023

Cited by 2 | Viewed by 1418

Abstract

In this paper, the plane wave diffraction from a semi-infinite parallel-plate waveguide with five-layer material loading is rigorously analyzed for H-polarization using the Wiener–Hopf technique. The Fourier transform of the scattered field is introduced and boundary conditions are applied in the transform domain [...] Read more.

In this paper, the plane wave diffraction from a semi-infinite parallel-plate waveguide with five-layer material loading is rigorously analyzed for H-polarization using the Wiener–Hopf technique. The Fourier transform of the scattered field is introduced and boundary conditions are applied in the transform domain to formulate the problem as simultaneous Wiener–Hopf equations, which are solved by the factorization and decomposition procedure leading to exact and approximate solutions. The scattered field in real space is explicitly derived by taking the Fourier inverse of the solution in the transform domain. For the region inside the waveguide, the scattered field is represented by the waveguide TM modes, and the field outside the waveguide is evaluated asymptotically by applying the saddle-point method to obtain a far-field expression. Numerical examples of the radar cross section (RCS) for various physical parameters are presented, and far-field scattering characteristics of the waveguide are discussed in detail. Full article

(This article belongs to the Special Issue Challenge of Guaranteed Convergence in Applied Electromagnetics: Recent Progress in the Methods of Analytical Regularization)

► Show Figures