Electromagnetic Model of a SPR Sensor Coupled to Array of Nanoparticles by Periodic Green’s Function

Cruz, Aline; Dmitriev, Victor; Rosso, Tommaso Del; Costa, Karlo Q. da

doi:10.1155/2019/7548243

Cited by 2 publications

(11 citation statements)

References 14 publications

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“…The excitation of dipoles with length

l = λ / 50

and amplitude

I_{0} = 1 A \cdot m

was performed at frequency

f = 1.2 THz

, which is equivalent to the wavelength

λ = 250 μ m

in free space. The nanodipole array was positioned at a height

h = false(20 / 632.8 false) λ = 7.9 μ m

(value chosen based on simulations of an optical plasmonic sensor that operates with

h_{normaloptical} = 20 nm

and

λ_{normaloptical} = 632.8 nm

[12, 14]) from the first graphene surface impedance

Z_{normals 1}

, above the dielectric substrate with thickness

δ_{2} = false(50 / 632.8 false) λ = 19.75 μ m

. Parametric analyses about the effect of

Δ_{normalc}

(period of the planar array),

μ_{normalc}

(chemical potential applied to graphene impedances) and

θ^{normal′}

(orientation of the dipole array), on the electric and magnetic fields were carried out.…”

Section: Model Validation and Resultsmentioning

confidence: 99%

“…The electric and magnetic fields in the structure are defined from the solution of the Helmholtz equation, non‐homogeneous in medium 1 and homogeneous in mediums 2 and 3 [12, 21]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ - [\nabla^{2} {bold-italicA}_{1} + {k_{1}}^{2} {bold-italicA}_{1}] = μ_{1} J \\ - [\nabla^{2} {bold-italicA}_{2, 3} + {k_{2, 3}}^{2} {bold-italicA}_{2, 3}] = 0 \end{matrix}

with periodic boundary conditions at xy [12], and impedance conditions at the interfaces between the medium (

z = d_{1} = 0

and

z = d_{2} = - δ_{2}

, with

v = 1, 2

and

w = v + 1

) [19]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ {(][, A_{x v, y v})}_{z = d_{v}} = {(][, A_{x w, y w})}_{z = d_{v}} \\ {(][, \frac{1}{μ_{v}} \frac{normal∂}{\partial z} A_{x v, y v})}_{z = d_{v}} = (][, \frac{1}{μ_{w}} \frac{normal∂}{\partial z} A_{x w, y w} + j ω Z_{}) \end{matrix}

…”

Section: Equivalent Electromagnetic Modelmentioning

confidence: 99%

“…For periodic problems in xy with impedance and limit boundary conditions in z , the solution is obtained by the PGF method, defined by Fourier complex series transform in xy and closed form of the Green's function in z , resulting in the magnetic potential field (5) [12, 19, 21]

\begin{aligned} bold-italicA = \frac{1}{2 {normalΔ}_{c}^{2}} \sum_{m = - normal∞}^{normal∞} \sum_{n = - normal∞}^{normal∞} (][, \begin{matrix} right right right1em4pt \\ A_{x x}^{m n} & 0 & 0 \\ 0 & A_{y y}^{m n} & 0 \\ - normalj k_{x} A_{z x}^{m n} & - normalj k_{y} A_{z y}^{m n} & A_{z z}^{m n} \end{matrix}) bold-italicI false(θ^{'}, ϕ^{'} false) \\ \times {normale}^{- j (][, k_{x} x + k_{y} y)} \end{aligned}

with the

A_{i j}

element being the i component excited by the j component of the current source

bold-italicI false(θ^{'}, ϕ^{'} false)

, according to (6)

…”

Section: Equivalent Electromagnetic Modelmentioning

confidence: 99%

“…A conventional SPR sensor based on the surface plasmon coupled emission (SPCE) configuration consists of a multilayer structure (prism/metal/dielectric) coupled to a microfluidic channel where immobilised active particles are excited by an external electromagnetic source [12–14]. Due to the nanometric size of these particles, the radiation‐matter coupling is typically dominated by radiation in the dipolar mode [15], thus, these active particles re‐radiate waves that are coupled at the metal/dielectric interface, exciting surface plasmon polaritons (SPPs) waves, which in turn couple the dipolar radiation through the metallic material in the form of highly polarised directive TM waves in the region of the dielectric prism [16].…”

Section: Introductionmentioning

confidence: 99%

“…The sensing process is based on the electromagnetic response of the device in the form of a cone of light, whose characteristics are functions of the refractive properties of the sample in the microfluidic channel. The electromagnetic response of this device can be studied from an array of nanodipoles on the multilayer structure, where the active particles are modelled as Hertzian dipoles [12, 14, 17].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Electromagnetic model of a nanodipole array above a double‐layer graphene by periodic green's function

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“…The excitation of dipoles with length

l = λ / 50

and amplitude

I_{0} = 1 A \cdot m

was performed at frequency

f = 1.2 THz

, which is equivalent to the wavelength

λ = 250 μ m

in free space. The nanodipole array was positioned at a height

h = false(20 / 632.8 false) λ = 7.9 μ m

(value chosen based on simulations of an optical plasmonic sensor that operates with

h_{normaloptical} = 20 nm

and

λ_{normaloptical} = 632.8 nm

[12, 14]) from the first graphene surface impedance

Z_{normals 1}

, above the dielectric substrate with thickness

δ_{2} = false(50 / 632.8 false) λ = 19.75 μ m

. Parametric analyses about the effect of

Δ_{normalc}

(period of the planar array),

μ_{normalc}

(chemical potential applied to graphene impedances) and

θ^{normal′}

(orientation of the dipole array), on the electric and magnetic fields were carried out.…”

Section: Model Validation and Resultsmentioning

confidence: 99%

“…The electric and magnetic fields in the structure are defined from the solution of the Helmholtz equation, non‐homogeneous in medium 1 and homogeneous in mediums 2 and 3 [12, 21]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ - [\nabla^{2} {bold-italicA}_{1} + {k_{1}}^{2} {bold-italicA}_{1}] = μ_{1} J \\ - [\nabla^{2} {bold-italicA}_{2, 3} + {k_{2, 3}}^{2} {bold-italicA}_{2, 3}] = 0 \end{matrix}

with periodic boundary conditions at xy [12], and impedance conditions at the interfaces between the medium (

z = d_{1} = 0

and

z = d_{2} = - δ_{2}

, with

v = 1, 2

and

w = v + 1

) [19]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ {(][, A_{x v, y v})}_{z = d_{v}} = {(][, A_{x w, y w})}_{z = d_{v}} \\ {(][, \frac{1}{μ_{v}} \frac{normal∂}{\partial z} A_{x v, y v})}_{z = d_{v}} = (][, \frac{1}{μ_{w}} \frac{normal∂}{\partial z} A_{x w, y w} + j ω Z_{}) \end{matrix}

…”

Section: Equivalent Electromagnetic Modelmentioning

confidence: 99%

\begin{aligned} bold-italicA = \frac{1}{2 {normalΔ}_{c}^{2}} \sum_{m = - normal∞}^{normal∞} \sum_{n = - normal∞}^{normal∞} (][, \begin{matrix} right right right1em4pt \\ A_{x x}^{m n} & 0 & 0 \\ 0 & A_{y y}^{m n} & 0 \\ - normalj k_{x} A_{z x}^{m n} & - normalj k_{y} A_{z y}^{m n} & A_{z z}^{m n} \end{matrix}) bold-italicI false(θ^{'}, ϕ^{'} false) \\ \times {normale}^{- j (][, k_{x} x + k_{y} y)} \end{aligned}

with the

A_{i j}

element being the i component excited by the j component of the current source

bold-italicI false(θ^{'}, ϕ^{'} false)

, according to (6)

…”

Section: Equivalent Electromagnetic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electromagnetic model of a nanodipole array above a double‐layer graphene by periodic green's function

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et al. 2020

IET Microwaves, Antennas & Propagation

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Espalhamento Eletromagnético em Arranjo Periódico Linear de Nanopartículas Core-Shell

Cruz¹,

Souza²,

Silva³

et al. 2020

Anais De XXXVIII Simpósio Brasileiro De Telecomunicações E Processamento De Sinais

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Resumo-Neste artigoé apresentada uma análise do espalhamento eletromagnético produzido pela interação de uma onda plana e um arranjo de Nanopartículas metálicas do tipo Core-Shell. Para isso utilizou-se um formalismo baseado na representação espectral da Função de Green Periódica, sobre os modos de Floquet, para descrição do Campo Potencial Magnético. Os resultados mostram os perfis dos campos Elétrico e Magnético em função dos parâmetros dimensionais da estrutura, e das características da onda plana de excitação. Por fim, discussõesà respeito da convergência do método são apresentadas.

show abstract

Electromagnetic Model of a SPR Sensor Coupled to Array of Nanoparticles by Periodic Green’s Function

Cited by 2 publications

References 14 publications

Electromagnetic model of a nanodipole array above a double‐layer graphene by periodic green's function

Electromagnetic model of a nanodipole array above a double‐layer graphene by periodic green's function

Espalhamento Eletromagnético em Arranjo Periódico Linear de Nanopartículas Core-Shell

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