On a Rigorous Proof of the Existence of Complex Waves in a Dielectric Waveguide of Circular Cross Section

Shestopalov, Yury; Kuzmina, Ekaterina

doi:10.2528/pierb18050102

Cited by 21 publications

(7 citation statements)

References 13 publications

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“…In view of Equation and the properties of tanj (Shestopalov and Kuzmina, 2018) we see that for each n = 0, 1, 2, … there is a constant M 0 > 0 and an m 0 > 1 such that

M_{0} = c o n s t = \min_{ζ \in Γ_{m}^{n}, m = 1, 2, \dots} false| tanj (ζ) false|,

M_{0} \frac{|h_{n, 2} false(κ false)|}{|ν_{m}^{n} / κ - r|} \leq \min_{ζ \in Γ_{m}, m = 1, 2, \dots} false| g_{n, 1} (ζ) false|,

which holds for m ≥ m 0 > 1. Here, function g n ,1 ( ζ ) is continuous on

Γ_{m}^{n}

; therefore the constant M 0 > 0 exists and does not depend on m .…”

Section: Series Solutionmentioning

confidence: 99%

“…Thus, determination of the resonance solution singularities reduces to the proof of existence and finding the location of zeros (real or complex) of a particular set of functions, which is actually a definite subfamily of GCPs (Shestopalov (2019)). The present approach leading to these rigorous proofs employs the technique set forth for the determination of complex waves in metal-dielectric waveguides (Shestopalov, Kuzmina, and Samokhin (2014); Shestopalov and Kuzmina (2018)).…”

Section: Introductionmentioning

confidence: 99%

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Resonance Scattering by a Circular Dielectric Cylinder

Shestopalov

2021

Radio Science

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A unified approach is developed for the analysis of singularities of the scattered field and vanishing of scattering harmonics. Rigorous proofs are presented of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder. The method employs a mathematically correct approach of the spectral theory of open structures involving generalized conditions at infinity when complex resonance frequencies may be considered. The result is obtained by verifying the existence of complex singularities of the series solution coefficients considered as functions of the problem parameters. The recently developed theory of generalized cylindrical polynomials (GCPs) is used that enables one to reduce determination of singularities (resonances) to finding zeros (real or complex) of a particular subfamily of GCPs.

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“…In view of Equation and the properties of tanj (Shestopalov and Kuzmina, 2018) we see that for each n = 0, 1, 2, … there is a constant M 0 > 0 and an m 0 > 1 such that

M_{0} = c o n s t = \min_{ζ \in Γ_{m}^{n}, m = 1, 2, \dots} false| tanj (ζ) false|,

M_{0} \frac{|h_{n, 2} false(κ false)|}{|ν_{m}^{n} / κ - r|} \leq \min_{ζ \in Γ_{m}, m = 1, 2, \dots} false| g_{n, 1} (ζ) false|,

which holds for m ≥ m 0 > 1. Here, function g n ,1 ( ζ ) is continuous on

Γ_{m}^{n}

; therefore the constant M 0 > 0 exists and does not depend on m .…”

Section: Series Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Resonance Scattering by a Circular Dielectric Cylinder

Shestopalov

2021

Radio Science

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“…Combining the first four equations of (12) and (8) leads to the set of equations (13), which is equivalent to the eigenvalue problem of a circular dielectric waveguide, as presented in [33]. This type of system of equations admits complex solutions, as demonstrated in [34]. It is numerically solved with respect to the real variable β.…”

Section: B Field Distributionmentioning

confidence: 99%

A Semi-Analytical Model of High-Permittivity Dielectric Ring Resonators for Magnetic Resonance Imaging

Moussu

Abdeddaïm

Dubois

et al. 2020

IEEE Trans. Antennas Propagat.

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Magnetic resonance imaging (MRI) is an imaging technique exploiting the magnetic resonance (MR) of specific nuclear spins, like protons. In this article, MR probes based on dielectric ring resonators are investigated from a theoretical approach. We take advantage of the high-permittivity and lowloss properties of the ceramic material used for manufacturing these probes for microscopy applications. Magnetic resonance microscopy (MRM) aims at imaging tiny samples with a sufficient resolution to distinguish small details. In this framework, compact resonators, called volume probes, contain the investigated sample and are used for both signal transmission and reception. The newly developed semi-analytical model enables the estimation of the frequency of the first transverse electric mode of a cylindrical resonator. It also provides a method to compute the corresponding magnetic field distribution, the dielectric losses contributions from the probe and the sample, and the signal-Manuscript

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“…under the same conditions when f 0 (ζ , κ) = 0. Therefore (16), (18) and (21) In general, many other cases of multiple suppression, both for DR and GL, can be established numerically which is the subject of Sections 3 and 4.…”

Section: Partial Invisibility Of Dr and Multiple Suppression Of Harmomentioning

confidence: 99%

“…Another objective is to analyze resonance scattering by benchmark structures. All these phenomena can be studied using a universal technique employing the recently developed theory of generalized cylindrical polynomials (GCPs) [14] (applied in [15,16] to study waves in GLs, in [17] to model cloaking and in [18] to study resonance scattering) which makes the present approach especially efficient. In fact, for single-and multi-layer DRs and GLs (and other obstacles with circular symmetry), the expansion coefficients in (1) have a definite structure involving GCPs which makes it possible to prove the existence, determine the localization and efficiently calculate zeros and singularities of the expansion coefficients verifying and studying thus partial cloaking and invisibility.…”

Section: Introductionmentioning

confidence: 99%

Cloaking: analytical theory for benchmark structures

Shestopalov

2020

Journal of Electromagnetic Waves and Applications

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Proceeding from the scattered field expansion in cylindrical harmonics, we define partial invisibility or partial cloaking as suppression of finitely many lowest-order field harmonics. We show that for benchmark structures (a dielectric rod and a perfectly conducting cylinder of circular cross section covered by a concentric dielectric layer), such multiple suppression can be achieved. For this purpose, we prove the solvability and explicitly determine the solution of the corresponding equation system which provide vanishing of the lowest-order field expansion coefficients and the resulting simultaneous suppression of up to five lowest-order scattered harmonics. We investigate the character and qualitative properties of partial invisibility and partial cloaking by analyzing the scattered field patterns.

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On a Rigorous Proof of the Existence of Complex Waves in a Dielectric Waveguide of Circular Cross Section

Cited by 21 publications

References 13 publications

Resonance Scattering by a Circular Dielectric Cylinder

Resonance Scattering by a Circular Dielectric Cylinder

A Semi-Analytical Model of High-Permittivity Dielectric Ring Resonators for Magnetic Resonance Imaging

Cloaking: analytical theory for benchmark structures

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