Smart Graphene-Based Frequency Selective Surface Designed to Act as Single or Dual Band Device with Reconfigurable Operation Bands

Oliveira, Rodrigo M. S. de; Paiva, Rodrigo R.; Rodrigues, Nilton R. N. M.; Elias, Manoel R.

doi:10.1590/2179-10742019v18i41685

Rodrigo M. S. de Oliveira

Universidade Federal do Pará (UFPA), Rua Augusto Corrêa 01, Belém, Pará, Brasil, rmso@ufpa.br, rods.paiva26@gmail.com, niltonrodolfo@gmail.com

http://orcid.org/0000-0001-7178-6387

Rodrigo R. Paiva

Universidade Federal do Pará (UFPA), Rua Augusto Corrêa 01, Belém, Pará, Brasil, rmso@ufpa.br, rods.paiva26@gmail.com, niltonrodolfo@gmail.com

http://orcid.org/0000-0001-5346-902X

Nilton R. N. M. Rodrigues

Universidade Federal do Pará (UFPA), Rua Augusto Corrêa 01, Belém, Pará, Brasil, rmso@ufpa.br, rods.paiva26@gmail.com, niltonrodolfo@gmail.com

http://orcid.org/0000-0002-7219-601X

Manoel R. Elias Filho

Universidade do Estado do Pará (UEPA), Travessa Djalma Dutra S/N, Belém, Pará, Brasil, reinaldo@uepa.br

http://orcid.org/0000-0001-5128-0282

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Fig.1
Subcellular FDTD modeling of graphene sheet in the Yee cell (i,j,k) based on specific updating equations for tangential components of

\vec{E}

and

\vec{J}

under influence of

\vec{B} = B_{0} {\hat{a}}_{z}

.

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Fig. 2
The real part of the conductivity of graphene

{\tilde{σ}}_{d}

is illustrated in (a), its imaginary part in (b) and λ_SPP in (c), for B = 0 T, as functions of the chemical potential μ_c.

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Fig. 3
Geometry of the FSS of [¹⁰10 [10] L. Lin, L. S. Wu, W. Y. Yin, and J. F. Mao, “Modeling of magnetically biased graphene patch frequency selective surface (FSS),” in 2015 IEEE MTT-S International Microwave Workshop Series on Advanced Materials and Processes for RF and THz Applications (IMWS-AMP), Jul. 2015, pp. 1-3.] (perspective view of part of the periodic structure).

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Fig. 4
Validation of the developed FDTD methodology: co-polarization transmission coefficient.

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Fig. 5
The unit cell of the FSS proposed in this work for dynamic change of the state of operation and smart tuning of rejection band(s).

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Fig. 6
Comparison between FDTD and HFSS results: FSS co-polarization transmission coefficient for the graphene ring with rectangular aperture with dimensions d = 0.25 μm and l = 2.25 μm, without the internal graphene sheet. For the graphene ring, μ_ce is set to 1 eV.

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Fig. 7

{\vec{J}}_{s}

(A/m²) for the following FSSs: (a) square ring only, μ_ce = 1 eV and d = l = 2.25 μm at f = 3.29 THz and (b) square ring with the graphene sheet in its aperture, μ_ce = 0.75 eV, μ_ci = 1 meV and a = 100 nm, for f = 2.65 THz (first resonance).

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Fig. 8

{\vec{J}}_{s}

for the FSSs configured with μ_ce = 1 eV and with the following parameters: (a) d = 0.25 μm and l = 2.25 μm for f = 3.39 THz (first resonance, with no graphene sheet in the ring aperture), (b) d = 0.25 μm and l = 2.25 μm for f = 6.93 THz (second resonance, with no graphene sheet in the ring aperture) (c) μ_ci = 1 eV and a = 100 nm, for f = 2.78 THz (first resonance of the proposed FSS), (d) μ_ci = 1 eV and a = 100 nm, for f = 6.21 THz (second resonance of the proposed FSS).

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Fig. 9
Mesh generated in HFSS for modeling the FSS with a = 100 nm. Mesh details are highlighted.

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Fig. 10
Co-polarization transmission coefficient for a = 100 nm: (a) the two proposed FSS operation configurations, (b) validation of FDTD model for the off mode and (c) validation of FDTD model for the on mode.

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Fig. 11
Transmission coefficient for the analyzed configurations.

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Fig. 12
Distribution of surface current density

{\vec{J}}_{s} (A / m^{2})

for the μ_ce = μ_ci = 1 eV configuration: (a) at the first resonance (2.78 THz) and (b) at the second resonance (6.21 THz).

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Fig. 13
Distribution of

{\vec{J}}_{s} (A / m^{2})

for μ_ce = 1 eV / μ_ci = 0.6 eV configuration at: (a) 2.73THz and (b) 5.09 THz.

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Fig. 14
Transmission coefficients illustrating the shift of both rejection bands of mode on due to regulation of μ_ce.

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Fig. 15
Transmission coefficients for the two illustrative initial configurations, displaying shifting of both bands.

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Fig. 16
Transmission coefficient for the configurations analyzed, illustrating controlled shifting of the lower rejection band.

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Fig. 17
Distribution of surface current density

{\vec{J}}_{s} (A / m^{2})

for the μ_ce = 1 eV / μ_ci = 0.55 eV configuration: (a) at the first resonance (2.71THz) (a) and (b) at the second resonance (4.91 THz).

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Fig. 18
Distribution of surface current density

{\vec{J}}_{s} (A / m^{2})

for the μ_ce = 0.55 eV / μ_ci = 0.65 eV configuration: (a) at the first resonance (2.07 THz) (a) and (b) at the second resonance (4.88 THz).

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Fig. 19
Transmission coefficient illustrating the shifting of the rejection band of mode off by tuning μ_ce.

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Fig. 6
Comparison between FDTD and HFSS results: FSS co-polarization transmission coefficient for the graphene ring with rectangular aperture with dimensions d = 0.25 μm and l = 2.25 μm, without the internal graphene sheet. For the graphene ring, μ_ce is set to 1 eV.

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Fig. 7

{\vec{J}}_{s}

(A/m²) for the following FSSs: (a) square ring only, μ_ce = 1 eV and d = l = 2.25 μm at f = 3.29 THz and (b) square ring with the graphene sheet in its aperture, μ_ce = 0.75 eV, μ_ci = 1 meV and a = 100 nm, for f = 2.65 THz (first resonance).

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Fig. 8

{\vec{J}}_{s}

for the FSSs configured with μ_ce = 1 eV and with the following parameters: (a) d = 0.25 μm and l = 2.25 μm for f = 3.39 THz (first resonance, with no graphene sheet in the ring aperture), (b) d = 0.25 μm and l = 2.25 μm for f = 6.93 THz (second resonance, with no graphene sheet in the ring aperture) (c) μ_ci = 1 eV and a = 100 nm, for f = 2.78 THz (first resonance of the proposed FSS), (d) μ_ci = 1 eV and a = 100 nm, for f = 6.21 THz (second resonance of the proposed FSS).

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Fig. 9
Mesh generated in HFSS for modeling the FSS with a = 100 nm. Mesh details are highlighted.

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Fig. 10
Co-polarization transmission coefficient for a = 100 nm: (a) the two proposed FSS operation configurations, (b) validation of FDTD model for the off mode and (c) validation of FDTD model for the on mode.

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Fig. 11
Transmission coefficient for the analyzed configurations.

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Fig. 12
Distribution of surface current density

{\vec{J}}_{s} (A / m^{2})

for the μ_ce = μ_ci = 1 eV configuration: (a) at the first resonance (2.78 THz) and (b) at the second resonance (6.21 THz).

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Fig. 13
Distribution of

{\vec{J}}_{s} (A / m^{2})

for μ_ce = 1 eV / μ_ci = 0.6 eV configuration at: (a) 2.73THz and (b) 5.09 THz.

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Fig. 14
Transmission coefficients illustrating the shift of both rejection bands of mode on due to regulation of μ_ce.

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Fig. 15
Transmission coefficients for the two illustrative initial configurations, displaying shifting of both bands.

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Fig. 16
Transmission coefficient for the configurations analyzed, illustrating controlled shifting of the lower rejection band.

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Fig. 17
Distribution of surface current density

{\vec{J}}_{s} (A / m^{2})

for the μ_ce = 1 eV / μ_ci = 0.55 eV configuration: (a) at the first resonance (2.71THz) (a) and (b) at the second resonance (4.91 THz).

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Fig. 18
Distribution of surface current density

{\vec{J}}_{s} (A / m^{2})

for the μ_ce = 0.55 eV / μ_ci = 0.65 eV configuration: (a) at the first resonance (2.07 THz) (a) and (b) at the second resonance (4.88 THz).

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Fig. 19
Transmission coefficient illustrating the shifting of the rejection band of mode off by tuning μ_ce.

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Fig. 20
Schematic diagram of the experiment conducted in [¹²12 [12] A. C. Tasolamprou, A. D. Koulouklidis, C. Daskalaki, C. P. Mavidis, G. Kenanakis, G. Deligeorgis, Z. Viskadourakis, P. Kuzhir, S. Tzortzakis, M. Kafesaki, E. N. Economou and C. M. Soukoulis, “Experimental demonstration of ultrafast THz modulation in a graphene-based thin film absorber through negative photoinduced conductivity,” ACS photonics, vol. 6, no. 3, pp. 720-727, 2019.] for measuring graphene absorption of THz incident wave.

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Fig. 21
Comparison among absorption spectra obtained experimentally and numerically in [¹²12 [12] A. C. Tasolamprou, A. D. Koulouklidis, C. Daskalaki, C. P. Mavidis, G. Kenanakis, G. Deligeorgis, Z. Viskadourakis, P. Kuzhir, S. Tzortzakis, M. Kafesaki, E. N. Economou and C. M. Soukoulis, “Experimental demonstration of ultrafast THz modulation in a graphene-based thin film absorber through negative photoinduced conductivity,” ACS photonics, vol. 6, no. 3, pp. 720-727, 2019.] and the spectra calculated in this work using CST and COMSOL.

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Table I
REJECTION BANDS OF FSSs

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Table II
λ₀ (WAVELENGTH IN VACUUM) AND λ_SPP (WAVELENGTH ON GRAPHENE) FOR SEVERAL CONDITIONS OF INTEREST

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Table III
RELATIVE BANDWIDTHS OF THE REJECTION BANDS PRODUCED BY THE FSS OPERATING IN THE ON MODE, FOR EACH CONFIGURATION OF CHEMICAL POTENTIALS.

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Table IV
RELATIVE BANDWIDTH FOR THE REJECTION BANDS PRODUCED BY THE FSS OPERATING IN THE OFF MODE, FOR EACH CONFIGURATION OF THE CHEMICAL POTENTIAL.

(1)

(2)

(3)

(4)

(5.1)

(5.2)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

	Lower rejection band	Higher rejection band
FSS based on Graphene ring with rectangular aperture	40 % (2.70 – 4.05 THz)−10.05 dB (3.39 THz)	13.76 % (6.43 – 7.38 THz)−7.71 dB (6.93 THz)
Smart FSS dual-band mode	29.30 % (2.36 – 3.17 THz)−7.19 dB (2.78 THz)	23.30 % (5.50 – 6.95 THz)−10.37 dB (6.21 THz)
Smart FSS single-band mode	37.50 % (2.21 – 3.23 THz) −7.76 dB (2.65 THz)	–

Chemical Potential	Frequency	λ₀ (μm)	λ_SPP (μm)
μ_c = 1 eV	2.71 THz	110.70	88.38
	2.73 THz	109.89	87.49
	2.78 THz	107.91	85.32
	4.91THz	61.10	35.74
	5.09 THz	58.94	33.65
	6.21 THz	48.31	23.90
μ_c = 0.65 eV	2.07 THz	144.92	108.88
μ_c = 0.65 eV	4.88 THz	61.47	26.20
μ_c = 0.6 eV	2.73 THz	109.89	67.80
μ_c = 0.6 eV	5.09 THz	58.94	22.67
μ_c = 0.55 eV	2.07 THz	144.92	100.32
	2.71 THz	110.70	64.88
	4.88 THz	61.47	22.75
	4.91 THz	61.10	22.50

	Chemical potentials	Lower rejection band	Higher rejection band
Shifting of the lower rejection band in mode on	μ_ce = 0.43 eV, μ_ci= 0.73 eV	1.83 THz only	—
	μ_ce = 0.55 eV, μ_ci = 0.65 eV	16.42 % (1.90 – 2.24 THz)	—
	μ_ce = 0.75 eV, μ_ci = 0.58 eV	22.6 % (2.12 – 2.66 THz)	—
	μ_ce = 1 eV, μ_ci = 0.55 eV	25.50 % (2.36 – 3.05 THz)	—
Shifting of the higher rejection band in mode on	μ_ce = 1 eV, μ_ci = 0.4 eV	—	25.55 % (3.79 – 4.90 THz)
	μ_ce = 1 eV, μ_ci = 0.6 eV	—	23.09 % (4.52 – 5.70 THz)
	μ_ce = 1 eV, μ_ci = 0.7 eV	—	22.80 % (4.82 – 6.06 THz)
	μ_ce = 1 eV, μ_ci = 0.8 eV	—	23.04 % (5.07 – 6.39 THz)
	μ_ce = 1 eV, μ_ci = 1eV	—	23.30 % (5.5 – 6.95 THz)
Shifting of the both rejection bands	μ_ce = 0.45 eV, μ_ci = 0.6 eV	1.87 THz only	17.8% (4.20 – 5.02 THz)
	μ_ce = 0.6 eV, μ_ci = 0.6 eV	18.1% (1.96 – 2.35 THz)	19% (4.38 – 5.3 THz)
	μ_ce = 0.8 eV, μ_ci = 0.6 eV	23.93 % (2.17 – 2.76 THz)	20.97 % (4.48 – 5.53 THz)
	μ_ce = 1 eV, μ_ci = 0.6 eV	26.48 % (2.36 – 3.08 THz)	23.04 % (4.52 – 5.7 THz)

	Configurations of chemical potentials	Rejection band
Shifting of the rejection band in mode off	μ_ce = 0.3 eV, μ_ci = 1 meV	1.76 THz only
	μ_ce = 0.5 eV, μ_ci = 1 meV	28.7 % (1.91 – 2.55 THz)
	μ_ce = 0.85 eV, μ_ci = 1 meV	39.16% (2.32 – 3.45 THz)
	μ_ce = 1 eV, μ_ci = 1 meV	41.41% (2.47 – 3.76 THz)

\tilde{σ} (ω) = [\begin{matrix} {\tilde{σ}}_{x x} (ω) & {\tilde{σ}}_{x y} (ω) \\ {\tilde{σ}}_{y x} (ω) & {\tilde{σ}}_{y y} (ω) \end{matrix}] = [\begin{matrix} {\tilde{σ}}_{d} (ω) & - {\tilde{σ}}_{p} (ω) \\ {\tilde{σ}}_{p} (ω) & {\tilde{σ}}_{d} (ω) \end{matrix}],

\tilde{J} (ω) = \tilde{σ} (ω) \cdot \tilde{E} (ω) = [\begin{matrix} \begin{matrix} {\tilde{σ}}_{d} (ω) {\tilde{E}}_{x} (ω) - {\tilde{σ}}_{p} (ω) {\tilde{E}}_{y} (ω) \\ {\tilde{σ}}_{p} (ω) {\tilde{E}}_{x} (ω) + {\tilde{σ}}_{d} (ω) {\tilde{E}}_{y} (ω) \end{matrix} \\ 0 \end{matrix}] .

{J_{x} |}_{i + \frac{1}{2}, j, k}^{n + \frac{1}{2}} = A \cdot [\begin{matrix} {J_{x} |}_{i + \frac{1}{2}, j, k}^{n - \frac{1}{2}} \\ {J_{y} |}_{i + \frac{1}{2}, j, k}^{n - \frac{1}{2}} \end{matrix}] + 2 σ_{0} Γ B \cdot [\begin{matrix} {E_{x} |}_{i + \frac{1}{2}, j, k}^{n} \\ {E_{y} |}_{i + \frac{1}{2}, j, k}^{n} \end{matrix}]

{J_{y} |}_{i, j + \frac{1}{2}, k}^{n + \frac{1}{2}} = A \cdot [\begin{matrix} {J_{x} |}_{i, j + \frac{1}{2}, k}^{n - \frac{1}{2}} \\ {J_{y} |}_{i, j + \frac{1}{2}, k}^{n - \frac{1}{2}} \end{matrix}] + 2 σ_{0} Γ B \cdot [\begin{matrix} {E_{x} |}_{i, j + \frac{1}{2}, k}^{n} \\ {E_{y} |}_{i, j + \frac{1}{2}, k}^{n} \end{matrix}] .

{J_{x} |}_{i, j + \frac{1}{2}, k}^{n - \frac{1}{2}} = \frac{1}{4} ({J_{x} |}_{i + \frac{1}{2}, j, k}^{n - \frac{1}{2}} + {J_{x} |}_{i + \frac{1}{2}, j + 1, k}^{n - \frac{1}{2}} + {J_{x} |}_{i - \frac{1}{2}, j, k}^{n - \frac{1}{2}} + {J_{x} |}_{i - \frac{1}{2}, j + 1, k}^{n - \frac{1}{2}})

{J_{y} |}_{i + \frac{1}{2}, j, k}^{n - \frac{1}{2}} = \frac{1}{4} ({J_{y} |}_{i, j + \frac{1}{2}, k}^{n - \frac{1}{2}} + {J_{y} |}_{i + 1, j + \frac{1}{2}, k}^{n - \frac{1}{2}} + {J_{y} |}_{i, j - \frac{1}{2}, k}^{n - \frac{1}{2}} + {J_{y} |}_{i + 1, j - \frac{1}{2}, k}^{n - \frac{1}{2}}) .

{E_{x} |}_{i + \frac{1}{2}, j, k}^{n + 1} = {E_{x} |}_{i + \frac{1}{2}, j, k}^{n} + \frac{Δ t}{ε} (\frac{{H_{z} |}_{i + \frac{1}{2}, j + \frac{1}{2}, k}^{n + \frac{1}{2}} - {H_{z} |}_{i + \frac{1}{2}, j - \frac{1}{2}, k}^{n + \frac{1}{2}}}{Δ y} - \frac{{H_{y} |}_{i + \frac{1}{2}, j, k + \frac{1}{2}}^{n + \frac{1}{2}} - {H_{y} |}_{i + \frac{1}{2}, j, k - \frac{1}{2}}^{n + \frac{1}{2}}}{Δ z} - \frac{{J_{x} |}_{i + \frac{1}{2}, j, k}^{n + \frac{1}{2}}}{Δ z}) .

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Smart Graphene-Based Frequency Selective Surface Designed to Act as Single or Dual Band Device with Reconfigurable Operation Bands

Abstract