A Fast-Converging Scheme for the Electromagnetic Scattering from a Thin Dielectric Disk

Lucido, Mario; Balaban, M.V.; Dukhopelnykov, Sergii V.; Nosich, Alexander I.

doi:10.3390/electronics9091451

Cited by 18 publications

(22 citation statements)

References 35 publications

(48 reference statements)

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“…Assuming that τ = λ and τ = a, the field inside the disk can be neglected and the disk approximated with a flat F I G U R E 1 Geometry of the problem zero-thickness median surface, S, located at z = 0 for ρ ≤ a and ϕ ∈ [0, 2π], on which the following GBC have to be satisfied [12,13,25]:…”

Section: Background: Formulation Of the Problem And Regularizing Discretization Schemementioning

confidence: 99%

“…is the proper selection of the sets of basis functions to be used. Suitable expansion series for the nonvanishing components of the contributions in Equation ( 10) are shown in the following [19,24,25]…”

Section: Background: Formulation Of the Problem And Regularizing Discretization Schemementioning

confidence: 99%

“…Assuming that τ = λ and τ = a , the field inside the disk can be neglected and the disk approximated with a flat zero‐thickness median surface, S , located at z = 0 for ρ ≤ a and ϕ ∈ [0, 2 π ], on which the following GBC have to be satisfied [12, 13, 25]:

\frac{1}{2} \hat{z} \times (\underset{true̲}{E} (ρ, ϕ, 0^{+}) + \underset{true̲}{E} (ρ, ϕ, 0^{-})) \times \hat{z} = R_{normale} {\underset{J}{true}}_{normale} (ρ, ϕ)

\frac{1}{2} \hat{z} \times (\underset{true̲}{H} (ρ, ϕ, 0^{+}) + \underset{true̲}{H} (ρ, ϕ, 0^{-})) \times \hat{z} = R_{normalm} {\underset{J}{true}}_{normalm} (ρ, ϕ)

where the currents are the field jumps across S ,

{\underset{J}{true}}_{normale} (ρ, ϕ) = \hat{z} \times ({\underset{H}{true}}^{sc} (ρ, ϕ, 0^{+}) - {\underset{H}{true}}^{sc} (ρ, ϕ, 0^{-}))

{\underset{J}{true}}_{normalm} (ρ, ϕ) = - \hat{z} \times ({\underset{E}{true}}^{sc} (ρ, ϕ, 0^{+}) - {\underset{E}{true}}^{sc} (ρ

…”

Section: Background: Formulation Of the Problem And Regularizing Disc...mentioning

confidence: 99%

“…In order to guarantee the convergence, the key point is the proper selection of the sets of basis functions to be used. Suitable expansion series for the nonvanishing components of the contributions in Equation () are shown in the following [19, 24, 25]:

{\overset{J}{true}}_{r, T}^{(n)} (w) = \sum_{h = - 1 + δ_{n, 0}}^{+ \infty} γ_{r, T, h}^{(n)} {\overset{f}{true}}_{T, h}^{(n)} (w)

{\overset{f}{true}}_{T, h}^{(n)} (w) = \sqrt{2 η_{T, h}^{(n)}} \frac{J_{η_{T, h}^{(n)}} (a w)}{w^{p_{T}}}

η_{T, h}^{(n)} = | n | + 2 h + p_{T} + 1

where δ n , m is the Kronecker delta and

γ_{r, T, h}^{(n)}

denotes the general expansion coefficient, which are complete and nonredundant Neumann series of the weighted Bessel functions, orthonormal on the interval (0, +∞) with the weight function

w^{2 p_{T} ‐ 1}

[30], and have closed form spatial domain counterparts. With such a choice, the physical behaviour of the components of the cylindrical harmonics of the currents around the centre of the disk is reconstructed.…”

Section: Background: Formulation Of the Problem And Regularizing Disc...mentioning

confidence: 99%

“…On substitution into GBC Equation () on S , two decoupled surface IEs for the effective currents can be readily obtained [12]. Taking advantage of the revolution symmetry of the problem, these equations can be reduced to two infinite sets of independent one‐dimensional IEs in the Hankel transform domain [25]:

\int_{0}^{+ \infty} {\underset{\underset{H}{true}}{true}}^{(n)} (w ρ) [{\underset{true̲}{\underset{\tilde{boldG}}{true}}}_{r} (w) - R_{r} \underset{\underset{true̲}{I}}{true}] {\underset{\overset{J}{true}}{true}}_{r}^{(n)} (w) w d w = - {\underset{F}{true}}_{r}^{inc (n)} (ρ, 0)

for ρ ≤ a and with r = e, m, F e = E and F m = H , where the apex n denotes the n ‐th term of the Fourier series, the symbol

{\underset{P}{true}}^{(n)} (\cdot) = (\begin{matrix} left \\ left P_{ρ}^{(n)} (\cdot) \\ left - normalj P_{ϕ}^{(n)} (\cdot) \end{matrix})

has been introduced,

{\underset{\tilde{boldJ}}{true}}_{r}^{(n)} (w) = \int_{0}^{+ \infty} {\underset{true̲}{\underset{H}{true}}}^{(n)} (w ρ) {\underset{J}{true}}_{r}^{(n)} (ρ) ρ d ρ

are the vector Hankel transform of order n (VHT n ) of ...…”

Section: Background: Formulation Of the Problem And Regularizing Disc...mentioning

confidence: 99%

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Plane wave scattering from thin dielectric disk in free space: Generalized boundary conditions, regularizing Galerkin technique and whispering gallery mode resonances

Lucido

Balaban²,

Nosich³

2021

IET Microwaves Antenna & Prop

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Considered is the plane-wave scattering from and absorption by a thin circular dielectric disk. The analysis uses a set of the singular integral equations for the effective electric and magnetic currents, derived using the generalized boundary conditions on the disk median section. Following the recently developed analytical preconditioning procedure, these equations are discretized by the Galerkin technique with judiciously chosen expansion functions, which provide for the Fredholm second-kind nature of the resulting matrix equations. This guarantees the code convergence and high efficiency. It is demonstrated that the developed technique delivers the most important features of thin dielectric disksthe resonances on the natural modes. In the resonances on the slab modes, the disk can be well-transparent and the shadow is created only by its rim; in the whispering gallery mode resonances, the scattering occurs mainly in the disk plane.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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Section: Background: Formulation Of the Problem And Regularizing Discretization Schemementioning

confidence: 99%

Section: Background: Formulation Of the Problem And Regularizing Discretization Schemementioning

confidence: 99%

\frac{1}{2} \hat{z} \times (\underset{true̲}{E} (ρ, ϕ, 0^{+}) + \underset{true̲}{E} (ρ, ϕ, 0^{-})) \times \hat{z} = R_{normale} {\underset{J}{true}}_{normale} (ρ, ϕ)

\frac{1}{2} \hat{z} \times (\underset{true̲}{H} (ρ, ϕ, 0^{+}) + \underset{true̲}{H} (ρ, ϕ, 0^{-})) \times \hat{z} = R_{normalm} {\underset{J}{true}}_{normalm} (ρ, ϕ)

where the currents are the field jumps across S ,

{\underset{J}{true}}_{normale} (ρ, ϕ) = \hat{z} \times ({\underset{H}{true}}^{sc} (ρ, ϕ, 0^{+}) - {\underset{H}{true}}^{sc} (ρ, ϕ, 0^{-}))

{\underset{J}{true}}_{normalm} (ρ, ϕ) = - \hat{z} \times ({\underset{E}{true}}^{sc} (ρ, ϕ, 0^{+}) - {\underset{E}{true}}^{sc} (ρ

…”

Section: Background: Formulation Of the Problem And Regularizing Disc...mentioning

confidence: 99%

{\overset{J}{true}}_{r, T}^{(n)} (w) = \sum_{h = - 1 + δ_{n, 0}}^{+ \infty} γ_{r, T, h}^{(n)} {\overset{f}{true}}_{T, h}^{(n)} (w)

{\overset{f}{true}}_{T, h}^{(n)} (w) = \sqrt{2 η_{T, h}^{(n)}} \frac{J_{η_{T, h}^{(n)}} (a w)}{w^{p_{T}}}

η_{T, h}^{(n)} = | n | + 2 h + p_{T} + 1

where δ n , m is the Kronecker delta and

γ_{r, T, h}^{(n)}

denotes the general expansion coefficient, which are complete and nonredundant Neumann series of the weighted Bessel functions, orthonormal on the interval (0, +∞) with the weight function

w^{2 p_{T} ‐ 1}

Section: Background: Formulation Of the Problem And Regularizing Disc...mentioning

confidence: 99%

\int_{0}^{+ \infty} {\underset{\underset{H}{true}}{true}}^{(n)} (w ρ) [{\underset{true̲}{\underset{\tilde{boldG}}{true}}}_{r} (w) - R_{r} \underset{\underset{true̲}{I}}{true}] {\underset{\overset{J}{true}}{true}}_{r}^{(n)} (w) w d w = - {\underset{F}{true}}_{r}^{inc (n)} (ρ, 0)

for ρ ≤ a and with r = e, m, F e = E and F m = H , where the apex n denotes the n ‐th term of the Fourier series, the symbol

{\underset{P}{true}}^{(n)} (\cdot) = (\begin{matrix} left \\ left P_{ρ}^{(n)} (\cdot) \\ left - normalj P_{ϕ}^{(n)} (\cdot) \end{matrix})

has been introduced,

{\underset{\tilde{boldJ}}{true}}_{r}^{(n)} (w) = \int_{0}^{+ \infty} {\underset{true̲}{\underset{H}{true}}}^{(n)} (w ρ) {\underset{J}{true}}_{r}^{(n)} (ρ) ρ d ρ

are the vector Hankel transform of order n (VHT n ) of ...…”

Section: Background: Formulation Of the Problem And Regularizing Disc...mentioning

confidence: 99%

See 3 more Smart Citations

Plane wave scattering from thin dielectric disk in free space: Generalized boundary conditions, regularizing Galerkin technique and whispering gallery mode resonances

Lucido

Balaban²,

Nosich³

2021

IET Microwaves Antenna & Prop

Self Cite

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Second‐kind Fredholm integral‐equation analysis of scattering by layered dielectric gratings

Tsitsas

2021

IET Microwaves Antenna & Prop

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Scattering of the E-polarised plane electromagnetic wave from two different but of the same-period all-dielectric rectangular bar gratings on substrates is analysed using a volume-integral-equation (VIE) method. Here, VIE is a Fredholm integral equation of the second kind with unknown function being the electric field in the gratings regions. Discretisation of the VIE is performed by applying an entire-domain Galerkin technique. The developed algorithm possesses guaranteed convergence, provides accuracy, and is easily controlled by the order of discretisation. Numerical results for frequency-selective reflection, manipulation of light to propagate in prescribed directions, and the ultrahigh-Q lattice-modes resonances are presented and discussed.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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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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A Fast-Converging Scheme for the Electromagnetic Scattering from a Thin Dielectric Disk

Cited by 18 publications

References 35 publications

Plane wave scattering from thin dielectric disk in free space: Generalized boundary conditions, regularizing Galerkin technique and whispering gallery mode resonances

Plane wave scattering from thin dielectric disk in free space: Generalized boundary conditions, regularizing Galerkin technique and whispering gallery mode resonances

Second‐kind Fredholm integral‐equation analysis of scattering by layered dielectric gratings

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

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