An Entire Domain CFVIE-CDSE Method for EM Scattering on Electrically Large Highly Inhomogeneous Gyrotropic Circular Cylinders

Katsinos, Konstantinos; Zouros, Grigorios P.; Roumeliotis, John A.

doi:10.1109/tap.2020.3026860

Cited by 11 publications

(12 citation statements)

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“…For inhomogeneous gyroelectric resonators, the complex normalized wavenumbers x l are derived through a VIE in the absence of external excitation, given by [22]:…”

Section: Vie-based Characteristic Equationsmentioning

confidence: 99%

“…where M ml , N ml , and L ml are Dini-type CVWFs [22] and Γ ml , Δ ml , and Z ml unknown expansion coefficients. For the eigenbasis defined by the M ml , N ml , and L ml vectors to be orthogonal, the sets γ M ml , γ N ml , γ L ml must satisfy certain conditions.…”

Section: Vie-based Characteristic Equationsmentioning

confidence: 99%

“…For the eigenbasis defined by the M ml , N ml , and L ml vectors to be orthogonal, the sets γ M ml , γ N ml , γ L ml must satisfy certain conditions. In particular, γ M ml and γ N ml must be selected as the roots of the eigenequations [22] (eqs A.7 and A.10):…”

Section: Vie-based Characteristic Equationsmentioning

confidence: 99%

“…For inhomogeneous gyroelectric resonators, the complex normalized wavenumbers x l are derived through a VIE in the absence of external excitation, given by [22]:

\begin{matrix} alignleft \\ right E false(ρ false) = (k_{0}^{2} I + \nabla \nabla^{T}) \int_{ρ^{'} \in S} g false(ρ, ρ^{'} false) X_{e} false(ρ^{'} false) E false(ρ^{'} false) d ρ^{'} . \end{matrix}

In Equation (), E ( ρ ) is the total electric field, ρ is the position vector in the polar coordinate system,

double-struckI

is the unity dyadic, T denotes transposition,

S = {(ρ, φ) \in {double-struckR}^{2} false| ρ \in [0, a], φ \in [0, 2 π)}

is the cross‐sectional domain of the circular cylinder, g ( ρ , ρ ′) is the two‐dimensional free space Green's function, and

{double-struckX}_{normale} (ρ) = bold-italicϵ (ρ) / ϵ_{0} - double-struckI

is the normalized tensorial electric contrast function. In particular, Equation () defines two homogeneous systems

{double-struckA}^{TE} (x_{l}) {boldu}_{l} = 0

and

{double-struckA}^{TM} (x_{l}) {boldv}_{l} = 0

...…”

Section: Inhomogeneous Gyroelectric Resonatorsmentioning

confidence: 99%

“…Eqs. 16 and 17 of [22], which were introduced earlier and contribute in

{double-struckA}^{TE, TM}

, stem from the analytical reduction of the original VIE in Equation () by expanding the unknown E ( ρ ) in Dini series as in Equation (). This means that the two‐dimensional volumetric integral in Equation () is first carried out analytically, and the

k_{0}^{2} double-struckI + \nabla \nabla^{T}

operator is then considered by using the properties ∇ T M ml ( k , ρ ) = ∇ T N ml ( k , ρ ) = 0, ∇∇ T L ml ( k , ρ ) + k 2 L ml ( k , ρ ) = 0, ∇× M ml ( k , ρ ) = k N ml ( k , ρ ), ∇ × N ml ( k , ρ ) = k M ml ( k , ρ ), and ∇× L ml ( k , ρ ) = 0 [32], where

k \equiv k_{0}, γ_{m l}^{M} / a, γ_{m l}^{N} / a, γ_{m l}^{L} / a

.…”

Section: Inhomogeneous Gyroelectric Resonatorsmentioning

confidence: 99%

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Complex WGM frequencies of gyroelectric cylindrical resonators

Katsinos

Zouros

Kolezas

et al. 2021

IET Microwaves Antenna & Prop

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Asymptotic closed-form expressions for calculating complex transverse electric (TE)/ transverse magnetic (TM) whispering gallery mode (WGM) frequencies in homogeneous gyroelectric circular cylindrical resonators of infinite length are derived. In addition, a volume integral equation (VIE)-cylindrical Dini series expansion method is extended to support the prediction of complex WGMs for continuously varying highly inhomogeneous gyroelectric circular cylindrical resonators. To this end, the entire domain orthogonal vectorial basis of VIE is extended to support very large indices of the involved Dini-type cylindrical vector wave functions via asymptotic closed-form expressions. This way, the eigenbasis required to solve the VIE becomes free of numerical instabilities arising when very large orders of the involved Bessel functions are employed. The complex frequencies obtained by the asymptotic closed-form expressions for the case of the homogeneous gyroelectric resonator, as well as those obtained by the VIE when the multilayered gyroelectric resonator is reduced to one layer, are validated by comparisons with the complex roots extracted by numerically solving the TE/TM characteristic equations obtained from the separation of variables method, using complex root finding techniques. We demonstrate the calculation of very highorder WGM frequencies for cylindrical resonators composed of homogeneous and highly inhomogeneous permittivity profiles. This asymptotic theory constitutes a rigorous tool that may serve for verifying method of analytical regularisation-based numerical solutions for other non-circular inhomogeneous cylinders, and for interpreting experimental data for applications such as WGM lasing, refractometric sensing, and magneto-optic coupling.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

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“…For inhomogeneous gyroelectric resonators, the complex normalized wavenumbers x l are derived through a VIE in the absence of external excitation, given by [22]:…”

Section: Vie-based Characteristic Equationsmentioning

confidence: 99%

Section: Vie-based Characteristic Equationsmentioning

confidence: 99%

Section: Vie-based Characteristic Equationsmentioning

confidence: 99%

“…For inhomogeneous gyroelectric resonators, the complex normalized wavenumbers x l are derived through a VIE in the absence of external excitation, given by [22]: