Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique
<p>Geometry of the problem.</p> "> Figure 2
<p>Relative computation error for a two stacked thin resistive disks resonator with different values of the radius of the disks (<math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mn>2</mn> <mi>λ</mi> </mrow> </semantics></math>) and of the distance between the disks (<math display="inline"><semantics> <mrow> <mrow> <mi>d</mi> <mo>/</mo> <mi>a</mi> </mrow> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>10</mn> <mo>,</mo> <mo>∞</mo> </mrow> </semantics></math>). <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>100</mn> <mo> </mo> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>200</mn> <mo> </mo> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <mo> </mo> <msub> <mrow> <munder accentunder="true"> <mi>E</mi> <mo stretchy="true">_</mo> </munder> </mrow> <mn>0</mn> </msub> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo> </mo> <mrow> <mi mathvariant="normal">V</mi> <mo>/</mo> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> <mo>°</mo> </mrow> </semantics></math>, and TE incidence: (<b>a</b>) <math display="inline"><semantics> <mrow> <mrow> <mi>d</mi> <mo>/</mo> <mi>a</mi> </mrow> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mrow> <mi>d</mi> <mo>/</mo> <mi>a</mi> </mrow> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mrow> <mi>d</mi> <mo>/</mo> <mi>a</mi> </mrow> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mrow> <mi>d</mi> <mo>/</mo> <mi>a</mi> </mrow> <mo>=</mo> <mo>∞</mo> </mrow> </semantics></math>.</p> "> Figure 3
<p>Components of the effective electric current densities on a two stacked thin resistive disks resonator for different values of the radius of the disks (<math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mn>2</mn> <mi>λ</mi> </mrow> </semantics></math>). <math display="inline"><semantics> <mrow> <mrow> <mi>d</mi> <mo>/</mo> <mi>a</mi> </mrow> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>100</mn> <mo> </mo> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>200</mn> <mo> </mo> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <mo> </mo> <msub> <mrow> <munder accentunder="true"> <mi>E</mi> <mo stretchy="true">_</mo> </munder> </mrow> <mn>0</mn> </msub> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo> </mo> <mrow> <mi mathvariant="normal">V</mi> <mo>/</mo> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> <mo>°</mo> </mrow> </semantics></math>, and TE incidence: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msub> <mi>J</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>ρ</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msub> <mi>J</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>ϕ</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mi>λ</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msub> <mi>J</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>ρ</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mi>λ</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msub> <mi>J</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>ϕ</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>2</mn> <mi>λ</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msub> <mi>J</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>ρ</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>2</mn> <mi>λ</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msub> <mi>J</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>ϕ</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>.</p> "> Figure 4
<p>Components of the effective electric current densities on the upper disk (disk 1) of a two stacked thin resistive disks resonator for different values of the distance between the disks (<math display="inline"><semantics> <mrow> <mrow> <mi>d</mi> <mo>/</mo> <mi>a</mi> </mrow> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>10</mn> <mo>,</mo> <mo>∞</mo> </mrow> </semantics></math>). <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mi>λ</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>100</mn> <mo> </mo> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>200</mn> <mo> </mo> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <mo> </mo> <msub> <mrow> <munder accentunder="true"> <mi>E</mi> <mo stretchy="true">_</mo> </munder> </mrow> <mn>0</mn> </msub> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo> </mo> <mrow> <mi mathvariant="normal">V</mi> <mo>/</mo> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> <mo>°</mo> </mrow> </semantics></math>, and TE incidence: (<b>a</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msub> <mi>J</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>ρ</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msub> <mi>J</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>ϕ</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>.</p> "> Figure 5
<p>BRCS of a two stacked thin resistive disks resonator for different values of the radius of the disks (<math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mn>2</mn> <mi>λ</mi> </mrow> </semantics></math>). <math display="inline"><semantics> <mrow> <mrow> <mi>d</mi> <mo>/</mo> <mi>a</mi> </mrow> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>100</mn> <mo> </mo> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>200</mn> <mo> </mo> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> <mo>°</mo> </mrow> </semantics></math>, and TE incidence: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mi>λ</mi> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>2</mn> <mi>λ</mi> </mrow> </semantics></math>.</p> "> Figure 6
<p>Normalized TSCS and ACS of a two stacked thin resistive disks resonator for varying values of the normalized frequency (<math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> </mrow> </semantics></math>) when a plane wave orthogonally impinges onto the structure. <math display="inline"><semantics> <mrow> <mrow> <mi>d</mi> <mo>/</mo> <mi>a</mi> </mrow> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> <mo> </mo> <mi mathvariant="sans-serif">Ω</mi> </mrow> </semantics></math>.</p> "> Figure 7
<p>Near E-field behavior in the Cartesian coordinate planes <span class="html-italic">xz</span> and <span class="html-italic">xy</span> of a two stacked thin resistive disks resonator at three resonance frequencies (<math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>9.662491</mn> <mo>,</mo> <mn>10.643395</mn> <mo>,</mo> <mn>11.998105</mn> </mrow> </semantics></math>), when a plane wave orthogonally impinges onto the structure with <math display="inline"><semantics> <mrow> <msub> <mrow> <munder accentunder="true"> <mi>E</mi> <mo stretchy="true">_</mo> </munder> </mrow> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <mover accent="true"> <mi>y</mi> <mo>^</mo> </mover> </mrow> </semantics></math>: (<b>a</b>) Near E-field in the <span class="html-italic">xz</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>9.662491</mn> </mrow> </semantics></math>; (<b>b</b>) Near E-field in the <span class="html-italic">xy</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>9.662491</mn> </mrow> </semantics></math>; (<b>c</b>) Near E-field in the <span class="html-italic">xz</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>10.643395</mn> </mrow> </semantics></math>; (<b>d</b>) Near E-field in the <span class="html-italic">xy</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>10.643395</mn> </mrow> </semantics></math>; (<b>e</b>) Near E-field in the <span class="html-italic">xz</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>11.998105</mn> </mrow> </semantics></math>; (<b>f</b>) Near E-field in the <span class="html-italic">xy</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>11.998105</mn> </mrow> </semantics></math>.</p> "> Figure 7 Cont.
<p>Near E-field behavior in the Cartesian coordinate planes <span class="html-italic">xz</span> and <span class="html-italic">xy</span> of a two stacked thin resistive disks resonator at three resonance frequencies (<math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>9.662491</mn> <mo>,</mo> <mn>10.643395</mn> <mo>,</mo> <mn>11.998105</mn> </mrow> </semantics></math>), when a plane wave orthogonally impinges onto the structure with <math display="inline"><semantics> <mrow> <msub> <mrow> <munder accentunder="true"> <mi>E</mi> <mo stretchy="true">_</mo> </munder> </mrow> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <mover accent="true"> <mi>y</mi> <mo>^</mo> </mover> </mrow> </semantics></math>: (<b>a</b>) Near E-field in the <span class="html-italic">xz</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>9.662491</mn> </mrow> </semantics></math>; (<b>b</b>) Near E-field in the <span class="html-italic">xy</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>9.662491</mn> </mrow> </semantics></math>; (<b>c</b>) Near E-field in the <span class="html-italic">xz</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>10.643395</mn> </mrow> </semantics></math>; (<b>d</b>) Near E-field in the <span class="html-italic">xy</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>10.643395</mn> </mrow> </semantics></math>; (<b>e</b>) Near E-field in the <span class="html-italic">xz</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>11.998105</mn> </mrow> </semantics></math>; (<b>f</b>) Near E-field in the <span class="html-italic">xy</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>11.998105</mn> </mrow> </semantics></math>.</p> "> Figure 8
<p>Near E-field behavior in the Cartesian coordinate planes <span class="html-italic">xz</span> and <span class="html-italic">xy</span> of a two stacked thin resistive disks resonator at three resonance frequencies (<math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>15.862148</mn> <mo>,</mo> <mn>16.503645</mn> <mo>,</mo> <mn>17.532887</mn> </mrow> </semantics></math>), when a plane wave orthogonally impinges onto the structure with <math display="inline"><semantics> <mrow> <msub> <mrow> <munder accentunder="true"> <mi>E</mi> <mo stretchy="true">_</mo> </munder> </mrow> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <mover accent="true"> <mi>y</mi> <mo>^</mo> </mover> </mrow> </semantics></math>: (<b>a</b>) Near E-field in the <span class="html-italic">xz</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>15.862148</mn> </mrow> </semantics></math>; (<b>b</b>) Near E-field in the <span class="html-italic">xy</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>15.862148</mn> </mrow> </semantics></math>; (<b>c</b>) Near E-field in the <span class="html-italic">xz</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>16.503645</mn> </mrow> </semantics></math>; (<b>d</b>) Near E-field in the <span class="html-italic">xy</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>16.503645</mn> </mrow> </semantics></math>; (<b>e</b>) Near E-field in the <span class="html-italic">xz</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>17.532887</mn> </mrow> </semantics></math>; (<b>f</b>) Near E-field in the <span class="html-italic">xy</span> plane, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mi>a</mi> <mo>=</mo> <mn>17.532887</mn> </mrow> </semantics></math>.</p> ">
Abstract
:1. Introduction
2. Formulation of the Problem and Proposed Solution
3. Numerical Results
4. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Geim, K.; Novoselov, K.S. The rise of graphene. Nat. Mater. 2007, 6, 183–191. [Google Scholar] [CrossRef] [PubMed]
- Senior, T.B.A.; Volakis, J.L. Approximate Boundary Conditions in Electromagnetics; Institution of Electrical Engineers: London, UK, 1995. [Google Scholar]
- Karam, M.A.; Fung, A.K.; Antar, Y.M. Electromagnetic wave scattering from some vegetation samples. IEEE Trans. Geosci. Remote Sens. 1988, 26, 799–808. [Google Scholar] [CrossRef] [Green Version]
- Koh, I.S.; Sarabandi, K. A new approximate solution for scattering by thin dielectric disks of arbitrary size and shape. IEEE Trans. Antennas Propag. 2005, 53, 1920–1926. [Google Scholar] [CrossRef] [Green Version]
- LeVine, D.M.; Schneider, A.; Lang, R.H.; Carter, H.G. Scattering from thin dielectric disks. IEEE Trans. Antennas Propag. 1985, 33, 1410–1413. [Google Scholar] [CrossRef] [Green Version]
- Bleszynski, E.; Bleszynski, M.; Jaroszewicz, T. Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets. IEEE Antennas Propag. Mag. 1993, 35, 14–24. [Google Scholar] [CrossRef]
- Hanson, G.W. Dyadic Green’s functions for an anisotropic, non-local model of biased graphene. IEEE Trans. Antennas Propag. 2008, 56, 747–757. [Google Scholar] [CrossRef]
- Nosich, A.I. Method of analytical regularization in computational photonics. Radio Sci. 2016, 51, 1421–1430. [Google Scholar] [CrossRef]
- Jones, D.S. The Theory of Electromagnetism; Pergamon Press: New York, NY, USA, 1964. [Google Scholar]
- Dudley, D.G. Error minimization and convergence in numerical methods. Electromagnetics 1985, 5, 89–97. [Google Scholar] [CrossRef]
- Lucido, M.; Kobayashi, K.; Medina, F.; Nosich, A.I.; Vinogradova, E. Guest editorial: Method of analytical regularisation for new frontiers of applied electromagnetics. IET Microw. Antennas Propag. 2021, 15, 1127–1132. [Google Scholar] [CrossRef]
- Lovat, G.; Burghignoli, P.; Araneo, R.; Celozzi, S. Magnetic field penetration through a circular aperture in a perfectly conducting plate excited by a coaxial loop. IET Microw. Antennas Propag. 2021, 15, 1147–1158. [Google Scholar] [CrossRef]
- Kuryliak, D.B. The rigorous solution of the scattering problem for a finite cone embedded in a dielectric sphere surrounded by the dielectric medium. IET Microw. Antennas Propag. 2021, 15, 1181–1193. [Google Scholar] [CrossRef]
- Yevtushenko, F.O.; Dukhopelnykov, S.V.; Zinenko, T.L.; Rapoport, Y.G. Electromagnetic characterization of tuneable graphene-strips-on-substrate metasurface over entire THz range: Analytical regularization and natural-mode resonance interplay. IET Microw. Antennas Propag. 2021, 15, 1225–1239. [Google Scholar] [CrossRef]
- Oğuzer, T.; Altıntaş, A. Evaluation of the E-polarization focusing ability in Thz range for microsize cylindrical parabolic reflector made of thin dielectric layer sandwiched between graphene. IET Microw. Antennas Propag. 2021, 15, 1240–1248. [Google Scholar] [CrossRef]
- Tikhenko, M.E.; Radchenko, V.V.; Dukhopelnykov, S.V.; Nosich, A.I. Radiation characteristics of a double-layer spherical dielectric lens antenna with a conformal PEC disk fed by on-axis dipoles. IET Microw. Antennas Propag. 2021, 15, 1249–1269. [Google Scholar] [CrossRef]
- Vinogradova, E.D.; Smith, P.D. Scattering of an obliquely incident E−polarised plane wave from ensembles of slotted cylindrical cavities: A rigorous approach. IET Microw. Antennas Propag. 2021, 15, 1270–1282. [Google Scholar] [CrossRef]
- Vinogradova, E.D.; Kobayashi, K. Complex eigenvalues of natural TM-oscillations in an open resonator formed by two sinusoidally corrugated metallic strips. IET Microw. Antennas Propag. 2021, 15, 1283–1298. [Google Scholar] [CrossRef]
- Koshovy, G.I. The Cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre-fractal system of impedance strips. IET Microw. Antennas Propag. 2021, 15, 1310–1317. [Google Scholar] [CrossRef]
- Doroshenko, V.O.; Stognii, N.P. Integral transforms and the regularisation method in the time-domain excitation of open PEC slotted cone scatterers. IET Microw. Antennas Propag. 2021, 15, 1360–1379. [Google Scholar] [CrossRef]
- Kantorovich, L.V.; Akilov, G.P. Functional Analysis, 2nd ed.; Pergamon Press: Oxford, UK, 1982. [Google Scholar]
- Steinberg, S. Meromorphic families of compact operators. Arch. Rational Mech. Anal. 1968, 31, 372–379. [Google Scholar] [CrossRef]
- Lucido, M. Scattering by a tilted strip buried in a lossy half-space at oblique incidence. Prog. Electromagn. Res. M 2014, 37, 51–62. [Google Scholar] [CrossRef] [Green Version]
- Corsetti, F.; Lucido, M.; Panariello, G. Effective analysis of the propagation in coupled rectangular-core waveguides. IEEE Photon. Technol. Lett. 2014, 26, 1855–1858. [Google Scholar] [CrossRef]
- Lucido, M.; Migliore, M.D.; Pinchera, D. A new analytically regularizing method for the analysis of the scattering by a hollow finite-length PEC circular cylinder. Prog. Electromagn. Res. B 2016, 70, 55–71. [Google Scholar] [CrossRef] [Green Version]
- Lucido, M.; Di Murro, F.; Panariello, G.; Santomassimo, C. Fast converging CFIE-MoM analysis of electromagnetic scattering from PEC polygonal cross-section closed cylinders. Prog. Electromagn. Res. B 2017, 74, 109–121. [Google Scholar] [CrossRef] [Green Version]
- Lucido, M.; Schettino, F.; Migliore, M.D.; Pinchera, D.; Di Murro, F.; Panariello, G. Electromagnetic scattering by a zero-thickness PEC annular ring: A new highly efficient MoM solution. J. Electromagn. Waves Appl. 2017, 31, 405–416. [Google Scholar] [CrossRef]
- Lucido, M.; Santomassimo, C.; Panariello, G. The method of analytical preconditioning in the analysis of the propagation in dielectric waveguides with wedges. J. Light. Technol. 2018, 36, 2925–2932. [Google Scholar] [CrossRef]
- Lucido, M.; Migliore, M.D.; Nosich, A.I.; Panariello, G.; Pinchera, D.; Schettino, F. Efficient evaluation of slowly converging integrals arising from MAP application to a spectral-domain integral equation. Electronics 2019, 8, 1500. [Google Scholar] [CrossRef] [Green Version]
- Lucido, M. Analysis of the propagation in high-speed interconnects for MIMICs by means of the method of analytical preconditioning: A new highly efficient evaluation of the coefficient matrix. Appl. Sci. 2021, 11, 933. [Google Scholar] [CrossRef]
- Fikioris, G. Regularised discretisations obtained from first-kind Fredholm operator equations. IET Microw. Antennas Propag. 2021, 15, 357–363. [Google Scholar] [CrossRef]
- Assante, D.; Panariello, G.; Schettino, F.; Verolino, L. Longitudinal coupling impedance of a particle traveling in PEC rings: A regularised analysis. IET Microw. Antennas Propag. 2021, 15, 1318–1329. [Google Scholar] [CrossRef]
- Assante, D.; Panariello, G.; Schettino, F.; Verolino, L. Coupling impedance of a PEC angular strip in a vacuum pipe. IET Microw. Antennas Propag. 2021, 15, 1347–1359. [Google Scholar] [CrossRef]
- Tsalamengas, J.L. Exponentially converging Nyström’s methods for systems of SIEs with applications to open/closed strip or slot-loaded2-D structures. IEEE Trans. Antennas Propag. 2006, 54, 1549–1558. [Google Scholar] [CrossRef]
- Nosich, A.A.; Gandel, Y.V. Numerical analysis of quasi-optical multireflector antennas in 2-D with the method of discrete singulari-ties. IEEE Trans. Antennas Propag. 2007, 55, 399–406. [Google Scholar] [CrossRef]
- Shapoval, O.V.; Sauleau, R.; Nosich, A.I. Scattering and absorption of waves by flat material strips analyzed using generalized boundary conditions and Nyström-type algorithm. IEEE Trans. Antennas Propag. 2011, 59, 3339–3346. [Google Scholar] [CrossRef]
- Kaliberda, M.E.; Lytvynenko, L.M.; Pogarsky, S.A.; Sauleau, R. Excitation of guided waves of grounded dielectric slab by a THz plane wave scattered from finite number of embedded graphene strips: Singular integral equation analysis. IET Microw. Antennas Propag. 2021, 15, 1171–1180. [Google Scholar] [CrossRef]
- Tsalamengas, J.L.; Vardiambasis, I.O. A parallel-plate waveguide antenna radiating through a perfectly conducting wedge. IET Microw. Antennas Propag. 2021, 15, 571–583. [Google Scholar] [CrossRef]
- Lucido, M.; Panariello, G.; Schettino, F. Scattering by a zero-thickness PEC disk: A new analytically regularizing procedure based on Helmholtz decomposition and Galerkin method. Radio Sci. 2017, 52, 2–14. [Google Scholar] [CrossRef]
- Lucido, M.; Schettino, F.; Panariello, G. Scattering from a thin resistive disk: A guaranteed fast convergence technique. IEEE Trans. Antennas Propag. 2021, 69, 387–396. [Google Scholar] [CrossRef]
- Lucido, M.; Balaban, M.V.; Dukhopelnykov, S.V.; Nosich, A.I. A fast-converging scheme for the electromagnetic scattering from a thin dielectric disk. Electronics 2020, 9, 1451. [Google Scholar] [CrossRef]
- Lucido, M. Electromagnetic Scattering from a Graphene Disk: Helmholtz-Galerkin Technique and Surface Plasmon Resonances. Mathematics 2021, 9, 1429. [Google Scholar] [CrossRef]
- Lucido, M.; Balaban, M.V.; Nosich, A.I. Plane wave scattering from thin dielectric disk in free space: Generalized boundary conditions, regularizing Galerkin technique and whispering gallery mode resonances. IET Microw. Antennas Propag. 2021, 15, 1159–1170. [Google Scholar] [CrossRef]
- Chew, W.C.; Kong, J.A. Resonance of nonaxial symmetric modes in circular microstrip disk antenna. J. Math. Phys. 1980, 21, 2590–2598. [Google Scholar] [CrossRef]
- Van Bladel, J. A discussion of Helmholtz’ theorem on a surface. AEÜ 1993, 47, 131–136. [Google Scholar]
- Lucido, M.; Di Murro, F.; Panariello, G. Electromagnetic scattering from a zero-thickness PEC disk: A note on the Helmholtz-Galerkin analytically regularizing procedure. Progr. Electromagn. Res. Lett. 2017, 71, 7–13. [Google Scholar] [CrossRef]
- Braver, I.; Fridberg, P.; Garb, K.; Yakover, I. The behavior of the electromagnetic field near the edge of a resistive half-plane. IEEE Trans. Antennas Propag. 1988, 36, 1760–1768. [Google Scholar] [CrossRef]
- Abramowitz, M.; Stegun, I.A. Handbook of Mathematical Functions; Verlag Harri Deutsch: Frankfurt, Germany, 1984. [Google Scholar]
- Gradstein, S.; Ryzhik, I.M. Tables of Integrals, Series and Products; Academic Press: New York, NY, USA, 2000. [Google Scholar]
- Wilkins, J.E. Neumann series of Bessel functions. Trans. Am. Math. Soc. 1948, 64, 359–385. [Google Scholar] [CrossRef]
- Geng, N.; Carin, L. Wide-band electromagnetic scattering from a dielectric BOR buried in a layered lossy dispersive medium. IEEE Trans. Antennas Propag. 1999, 47, 610–619. [Google Scholar] [CrossRef]
- Titchmarsh, E.C. Introduction to the Theory of Fourier Integrals; Oxford University Press: London, UK, 1948. [Google Scholar]
- Van Bladel, J. Electromagnetic Fields; IEEE Wiley: Hoboken, NJ, USA, 2007. [Google Scholar]
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Lucido, M. Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique. Appl. Sci. 2021, 11, 8173. https://doi.org/10.3390/app11178173
Lucido M. Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique. Applied Sciences. 2021; 11(17):8173. https://doi.org/10.3390/app11178173
Chicago/Turabian StyleLucido, Mario. 2021. "Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique" Applied Sciences 11, no. 17: 8173. https://doi.org/10.3390/app11178173
APA StyleLucido, M. (2021). Analysis of the Scattering from a Two Stacked Thin Resistive Disks Resonator by Means of the Helmholtz–Galerkin Regularizing Technique. Applied Sciences, 11(17), 8173. https://doi.org/10.3390/app11178173