Tunable polarization-independent plasmonically induced transparency based on metal-graphene metasurface

Zhewei Dong; Chen Sun; Jiangnan Si; Xiaoxu Deng

doi:10.1364/OE.25.012251

1. Introduction

The photonics based on surface plasmon polaritons (SPPs) which have the unique properties of subwavelength optical confinement and significant field enhancement has attracted much attention during the past decade [1]. The plasmonic devices beyond the diffraction limit open up a wide range of nanostructures applications [2–5]. In particular, plasmonic analogues of electromagnetically induced transparency (EIT) have attracted tremendous interest due to the slow light phenomena and enhanced nonlinear properties. Plasmonically induced transparency (PIT) based on metamaterial structures [6–12], highlight the realization of EIT analogues for their effective medium characteristics, which provide great possibilities in developing novel devices, such as photonic components, integrated chip scale buffers and highly sensitive sensors [13–15]. The metallic metamaterial have been proposed to realize the PIT effect, which can modulate the PIT resonance by changing geometric parameters of the structures [16, 17]. And graphene has been introduced into the plasmonic metamaterial to obtain active tunable PIT effect at THz regime [18–22], due to its outstanding properties, like the high electron mobility, excellent ability to support surface-plasmon polaritons and tunable surface conductivity [23,24]. However, the PIT metamaterial are usually sensitive to a fixed polarization of the incident field. When the polarization of the incident electromagnetic wave is changed, the bright mode can no longer be completely excited, resulting in attenuation and even disappearance of the PIT effect. Some metallic metamaterial with center symmetric nanostructure have been proposed to realize the PIT effect [25, 26], which have identical response to various incidence polarization.

In this paper, the polarization-independent metal-graphene device are proposed to realize dual-band PIT effect at mid-infrared frequencies, which consist of two kinds of center symmetric golden structure array with different sizes and element numbers placed on the graphene interdigitated finger sets, respectively. The PIT peaks at two frequency domains are analyzed theoretically based on the coupled Lorentz oscillator model. The transmission spectra of the metal-graphene device are simulated by the finite-difference time-domain (FDTD) solutions, of which the multiple PIT peaks are independently tuned by the Fermi energy of corresponding graphene finger sets without changing the geometrical parameters of the nanostructure. By the carefully selected element numbers of the nanostructure arrays, the resonance strength of the PIT peaks at two frequency domains are nearly close. Due to the center symmetry of the nanostructure, the PIT effect of the metal-graphene device is no longer constrained by a fixed incidence polarization, which is advantageous in practical applications such as polarization-independent sensor, detector and filter.

2. Numerical results and theoretical analysis

The polarization-independent dual-band metal-graphene PIT metasurface device is composed of two kinds of golden nanostructure arrays with different sizes and element numbers separated from the dielectric substrate SiN_x by a monolayer of graphene, as shown in Fig. 1(a). The unit cell of the device consists of a 3 × 3 small size nanostructure array and a 2 × 2 big size nanostructure array, as shown in Fig. 1(b). Each element of the nanostructure array is composed of a cross and four identical split-ring-resonators(c-SRRs), and the split gap of the split-ring-resonators (SRRs) is oriented to the neighboring bars of the cross. The size of the unit cell, that is the period of the PIT device, is P = 24400nm. In the small size c-SRRs structure, the cross has length L₁ = 2200nm and width W₁ = 200nm; the SRRs have dimensions of outer radius R₁ = 400nm, width w_a₁ = 150nm and gap separation w_b₁ = 200nm; the distance between the center of the SRR and the neighboring bars of the cross is d₁; the distance between the centers of adjacent small size c-SRRs structures is P₁ = 4000nm. In the big size c-SRRs structure, the cross has length L₂ = 3600nm and width W₂ = 200nm; the SRRs have dimensions of outer radius R₂ = 650nm, width w_a₂ = 200nm and gap separation w_b₂ = 200nm; the distance between the center of the SRR and the neighboring bars of the cross is d₂; the distance between the centers of adjacent big size c-SRRs structures is P₂ = 6000nm. The thickness of golden film is 120nm. The thickness and index of the substrate SiN_x is 250nm and 2.05, respectively. The graphene layer is structured into interdigitated fingers with width W_g = 12000nm and spacing S_g = 200nm. The small and big c-SRRs structures arrays are on interdigitated finger sets G₁ and G₂, respectively. The gate voltages V₁ and V₂ are applied on the graphene interdigitated finger sets G₁ and G₂, respectively, as shown in Fig. 1(a).

Fig. 1 (a) Schematic of the polarization-independent dual-band metal-graphene PIT device. The black dashed box represents a unit cell.(b) Top view of the unit cell, containing two kinds of c-SRRs structures array(S₁ and S₂) with different sizes and element numbers.

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The characteristic of the polarization-independent dual-band metal-graphene PIT device are simulated by the FDTD solutions (Lumerical Solutions, Inc.). In the three-dimensional simulations, a linear polarized beam normally incidents on the unit cell in z direction with periodic boundary conditions in both x-z plane and y-z plane. The complex permittivity of the gold is described by the Palik model. The graphene layer is characterized using a surface conductivity rather than a volumetric permittivity. The surface conductivity of graphene σ is computed from the Kubo formula [27]

σ (ω) = \frac{i e^{2} (ω - 2 i Γ)}{π ℏ^{2}} [\frac{1}{{(ω - 2 i Γ)}^{2}} \int_{0}^{\infty} ϵ (\frac{\partial f_{d} (ϵ)}{\partial ϵ} - \frac{\partial f_{d} (- ϵ)}{\partial ϵ}) d ϵ - \int_{0}^{\infty} \frac{f_{d} (- ϵ) - f_{d} (ϵ)}{{(ω - 2 i Γ)}^{2} - 4 {(ϵ / ℏ)}^{2}} d ϵ]

where,

f_{d} (ϵ) = {(e^{(ϵ - E_{f}) / (k_{B} T)} + 1)}^{- 1}

, E_f is the Fermi energy of graphene, ω is the angular frequency, ħΓ = 0.01eV is the scattering rate [28], and T = 300K is temperature.

The resonance of plasmonic modes supported by the cross only structure array, SRRs only structure array and c-SRRs structure array are investigated by the FDTD simulation, which is shown in Fig. 2. The Fermi energies of the finger sets G₁ and G₂ are both 0.4eV. The transmission spectra of the small size cross only structure array, SRRs only structure array and c-SRRs structure array, which are shown in Fig. 2(a), are simulated with no gold structure on the graphene finger set G₂. In the transmission spectrum of the small cross only structure array, a typical localized surface plasmon (LSP) resonance is excited with the incident electric field E along the x axis, which is shown as the blue curve in Fig. 2(a). The electrical field distribution of the small cross only structure at the resonance notch is shown by the Fig. 2(b), only the golden cross bar along the x-axis couples with the incident field. An inductive-capacitive (LC) resonance is excited with the incident electric field along the x-axis in the transmission spectrum of the small SRRs only structure array, shown by the red curve in Fig. 2(a). The electrical field distribution of the SRRs only structure at resonance notch is shown in Fig. 2(c), only two diagonal SRRs couple with the incident light. The resonance notch of the cross only structure array is deeper than that of the SRRs only structure array, which means that the cross array function as bright mode and the SRRs array act as dark mode. Shown as the black curve in Fig. 2(a), the transparency peak in the resonance notch, which is the PIT effect, emerges in the transmission spectra of the c-SRRs structure array with the incident electric field E along the x axis. The electrical field distributions of the small size c-SRRs structure at the PIT peak is shown in Fig. 2(d). The resonance of the two diagonal SRRs which do not couple with the incident light are indirect excited by the near-field coupling between the bright mode and dark mode. As shown in Figs. 2(e)–2(h), the simulated transmission spectra and electrical field distribution of the big size cross only structure array, the SRRs only structure array and the c-SRRs structure array are similar with those of small size structure array. The bright mode (the cross structure) are directly excited with the incident light at the resonance frequencies, which brings out the corresponding resonance notch. The dark mode (the SRRs structure array) is indirect excited by the bright mode, which results in the emerging of transparency peak in the resonance notch. Besides, the resonance strength of the PIT peak induced by the small size c-SRRs structures is comparable to that of the big size c-SRRs structures by the carefully selected element number of each array.

Fig. 2 (a) The simulated transmission spectra of small size cross only structure array, SRRs only structure array and the c-SRRs structure array when Fermi energy E_f₁ = 0.4eV and (d₁ = 1200nm). (b) The top view of small size cross only structure array and the electric field distributions at the resonance notch of the bright mode. (c)The top view of small size SRRs only structure array and the electric field distributions at the resonance notch of the dark mode. (d) The top view of small size c-SRRs structure array and the electric field distributions at the PIT peak. (e) The simulated transmission spectra of the big size cross only structure array, SRRs only structure array and c-SRRs structure array (d₂ = 1600nm) when Fermi energy E_f₂ = 0.4eV. (f) The top view of big size cross only structure array and the electric field distributions at the resonance notch of the bright mode. (g)The top view of big size SRRs only structure array and the electric field distributions at the resonance notch of the dark mode. (h)The top view of big size c-SRRs structure array and the electric field distributions at the PIT peak.

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The transmission spectra of the metal-graphene PIT device are simulated with various distance between the SRRs and the neighboring cross bar when the Fermi energy of the finger sets G₁ and G₂ are both 0.4eV, as shown in Fig. 3. By employing two kinds of c-SRRs structure arrays with different sizes and element numbers, the multiple PIT peaks are obtained at two frequency 30.54THz and 46.08THz, respectively. As shown in Fig. 3(a), the strength of the PIT peak at frequency 46.08THz, which induced by the small size c-SRRs structure array, increases gradually with the decreasing of the distance d₁, while maintaining d₂ = 1600nm. Similarly, the transparency peak at frequency 30.54THz is enhanced by decreasing the distance d₂ of the big size c-SRRs structure array while maintaining d₁ = 1200nm, as shown in Fig. 3(b). When the SRRs get close to the neighboring cross bar, the near-field coupling between the bright mode and dark mode is enhanced, resulting in stronger PIT peak.

Fig. 3 (a) Simulated transmission spectra of the metal-graphene PIT device with different parameter d₁ when Fermi energy E_f₁/E_f₂ = 0.4eV/0.4eV and d₂ = 1600nm. (b) Simulated transmission spectra of the metal-graphene PIT device with different parameter d₂ when Fermi energy E_f₁/E_f₂ = 0.4eV/0.4eV and d₁ = 1200nm.

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The simulated transmission spectra of the metal-graphene PIT device with various Fermi energy E_f₁ and E_f₂ are shown in Fig. 4. The parameters d₁ and d₂ of the small and big c-SRRs structures array are set at 1200nm and 1600nm, respectively. As the Fermi energy E_f₁ increases from 0.2eV to 0.7eV while E_f₂ is fixed at 0.4eV, the PIT peak induced by the small c-SRRs structures is blue shifted from 44.81THz to 48.22THz, while that of the big c-SRRs structures remains nearly 30.54THz, as shown in Fig. 4(a). As the Fermi energy E_f₂ increases from 0.2eV to 0.7eV while maintaining E_f₁ at 0.4eV, the PIT peak induced by the big c-SRRs structures is blue shifted from 29.04THz to 32.51THz, while that of the small c-SRRs structures fixed at nearly 46.08THz, as shown in Fig. 4(b). The electric field distributions in the gap of the small size SRR without and with graphene layer at the PIT peak is simulated to investigate the interaction between the gold and graphene layer, which are shown as Fig. 4(c). In both situations, the electric field is enhanced in the gap of SRR. Due to the coupling of the gold structures with graphene layer, the electric field concentrates its energy near the graphene region other than gold structures. When the Fermi energy of the graphene layer increases, the electric intensity in the gap of the SRR decreases, and correspondingly the amplitude of the PIT peak is modulated. As a result of the coupling between the gold structures and graphene layer, the multiple PIT peaks of the device are modulated independently through tuning the Fermi energy of corresponding graphene finger set.

Fig. 4 (a)Simulated transmission spectra of the metal-graphene PIT device with different E_f₁ while maintaining E_f₂ at 0.4eV. (b)Simulated transmission spectra of the metal-graphene PIT device with different E_f₂ while maintaining E_f₁ at 0.4eV. (c)The electric field intensity distributions in the gap of the SRR without and with the graphene layer.

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The transmission spectra of the metal-graphene PIT device are simulated with different incidence polarization, which is shown in Fig. 5. The Fermi energy of the finger sets G₁ and G₂ are both 0.4eV. The parameters d₁ and d₂ of the small and big c-SRRs structures array are set at 1200nm and 1600nm, respectively. As polarization angle of the incident field varies from 0° to 90°, the multiple PIT peaks located at 30.54THz and 46.08THz is almost unchanged. Due to the four-fold rotational symmetry of the c-SRRs structure, the metal-graphene PIT device has identical response for any incidence polarization, exhibiting polarization-independent characteristic [29]. The performance of the metal-graphene PIT device is no longer limited by the incidence polarization, which is advantageous in practical applications for slow light and enhanced nonlinear effects.

Fig. 5 The simulated transmission spectra of the metal-graphene PIT device under various incidence polarizations ϕ from 0° to 90°, when Fermi energy E_f₁/E_f₂ = 0.4eV/0.4eV and d₁/d₂ = 1200nm/1600nm.

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The coupled Lorentz oscillator model is employed to explain the transmission characteristics of the polarization-independent dual-band metal-graphene PIT device. The external driving field is denoted as E₀e^iωt. The bright and dark modes in the c-SRRs structure arrays are expressed as $| D_{1 / 2} 〉 = {\tilde{D}}_{1 / 2} e^{i ω t}$ and $| Q_{1 / 2} 〉 = {\tilde{Q}}_{1 / 2} e^{i ω t}$ , respectively. The subscripts 1 and 2 denote the small and big c-SRRs structure array, respectively. The PIT effect induced by the c-SRRs structure array is described as a three-level system with two possible pathways of |0〉 − |D_1,2〉 and |0〉 − |D_1,2〉 − |Q_1,2〉 − |D_1,2〉 (ground state |0〉) interfering with each other destructively, which is a typical Fano resonance [30], leading to the emerging of transparency peak in the resonance notch. The field amplitude of (|D_1,2〉, |Q_1,2〉) is obtained [16]

[\begin{matrix} ω - ω_{D, 1 / 2} + i γ_{D, 1 / 2} & κ_{1 / 2} \\ κ_{1 / 2} & ω - ω_{Q, 1 / 2} + i γ_{D, 1 / 2} \end{matrix}] [\begin{array}{l} {\tilde{D}}_{1 / 2} \\ {\tilde{Q}}_{1 / 2} \end{array}] = [\begin{matrix} g_{1 / 2} {\tilde{E}}_{0} \\ 0 \end{matrix}]

where ω_D,_1/2, ω_Q,_1/2, κ_1/2, g_1/2, γ_D,_1/2, and γ_Q,_1/2 are the resonance frequencies of bright modes, the resonance frequencies of dark modes, the coupling parameters, the geometrical parameters, the damping rates of bright modes, and the damping rates of dark modes in the small and big c-SRRs structures, respectively. The amplitudes of bright modes in the small and big c-SRRs structures [16] are, respectively

{\tilde{D}}_{1 / 2} = \frac{- g_{1 / 2} {\tilde{E}}_{0} (ω - ω_{Q, 1 / 2} + i γ_{Q, 1 / 2})}{(ω - ω_{D, 1 / 2} + i γ_{D, 1 / 2}) (ω - ω_{Q, 1 / 2} + i γ_{Q, 1 / 2}) - {(κ_{1 / 2})}^{2}}

The transmission of metal-graphene PIT device is [22]

T (ω) = 1 - {| \frac{{\tilde{D}}_{1}}{{\tilde{E}}_{0}} |}^{2} - {| \frac{{\tilde{D}}_{2}}{{\tilde{E}}_{0}} |}^{2} .

The transmission spectra of the metal-graphene PIT device with d₁/d₂ = 1200/1600nm is calculated based on Eq. 4, which have multiple PIT peaks at two frequency domains, as shown in Fig. 6. The calculated transmission spectrum of the PIT device when Fermi energy E_f₁/E_f₂ = 0.4/0.4eV is shown as the black point in Fig. 6, which traces the simulated results (the black curve) well. The parameters in the theoretical calculation are ω_D,₁/ω_D,₂ = 46.91/30.84THz, ω_Q,₁/ω_Q,₂ = 46.08/30.50THz, g₁/g₂ = 2.13/1.60THz, γ_D,₁/γ_D,₂ = 2.80/2.40THz, γ_Q,₁/γ_Q,₂ = 2.10/1.50THz and κ₁/κ₂ = 2.45/1.58THz. The calculated transmission spectrum of the PIT device when Fermi energy E_f₁/E_f₂ = 0.5/0.3eV is shown as the red asterisk. which have a good agreement with the simulated results (the red curve). The corresponding parameters in the theoretical calculation are ω_D,₁/ω_D,₂ = 47.81/29.84THz, ω_Q,₁/ω_Q,₂ = 46.72/29.41THz, g₁/g₂ = 2.12/1.59THz, γ_D,₁/γ_D,₂ = 2.72/2.30THz, γ_Q,₁/γ_Q,₂ = 2.10/1.35THz and κ₁/κ₂ = 2.45/1.66THz. The resonance frequencies of the bright modes ω_D,_1/2 and dark modes ω_Q,_1/2 are modulated by changing the corresponding Fermi energy E_f₁/E_f₂, leading to the shifting of PIT peaks in different directions, which fit well with the simulated results.

Fig. 6 The black point and red asterisk are theoretical calculated transmission spectrum of the metal-graphene PIT device at E_f₁/E_f₂ = 0.4/0.4eV and E_f₁/E_f₂ = 0.5/0.3eV, respectively. The black curve and red curve are the corresponding simulated results. The parameters d₁/d₂ = 1200/1600nm.

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By employing two kinds of gold c-SRRs structure arrays with different sizes and element numbers, the PIT peaks are obtained at two frequency domains in the mid-infrared region. The PIT resonance of the small size c-SRRs structure is comparable to that of the big size c-SRRs structure by the carefully selected element number of the c-SRRs structure array. By integrating the gold nanostructures with the graphene finger sets, the multiple transparency peaks are independently modulated by changing the Fermi energy of corresponding graphene finger set. Due to the center symmetry of the c-SRRs structure, the metal-graphene PIT device is independent of the incidence polarization.

3. Conclusion

In summary, a dynamically tunable polarization-independent dual-band PIT device is proposed at mid-infrared frequencies by integrating the center symmetric c-SRRs structure arrays with different sizes and element numbers into separate graphene interdigitated finger sets. The dual-band PIT effect of the metal-graphene device is explained by employing the coupled Lorentz oscillator model. The spectral locations of multiple transparency peaks are simulated by FDTD solutions, which are independently and dynamically modulated through the Fermi energy by tuning the voltages applied on corresponding graphene finger sets. As a result of careful selection of the element numbers of the structure arrays, the response strength of the PIT device at two different frequency domain are nearly close. Due to the center symmetric structure, the proposed device have identical response to different incidence polarization, which have good performance for randomly polarized light in optical information processing and integrated optics.

Funding

National Natural Science Foundation of China (61378067, 61675131).

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Tunable polarization-independent plasmonically induced transparency based on metal-graphene metasurface

Abstract

1. Introduction

2. Numerical results and theoretical analysis

3. Conclusion

Funding

References and links

Cited By

Figures (6)

Equations (4)

Optics Express