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Abstract
Tunable multi-function metasurfaces have become the latest research frontiers in planar optics. In this study, a dynamically tunable plasmon-induced transparency (PIT) structure based on a graphene split-ring resonator and graphene ribbon is proposed. The influences of the structural parameters and graphene Fermi energy on the PIT response were investigated both analytically and numerically simulations. The inclusion of an additional vanadium dioxide (VO2) substrate layer enables the metasurface to achieve dynamic switching between PIT and perfect absorption using the phase change property of VO2. The new metasurface device exhibits the PIT effect when the VO2 layer is in an insulating state and acts as a perfect absorber when it is in a metallic state. Moreover, the response of the two functions can be easily adjusted dynamically by changing the Fermi energy of graphene. In addition, both functions were highly sensitive to changes in the ambient refractive index. The results of this work have potential applications in slow-light devices, optical switches, modulators, perfect absorbers, highly sensitive sensors, and multifunctional devices.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces are artificial array structures comprising a large number of sub-wavelength units arranged periodically or non-periodically on a two-dimensional plane, which can control electromagnetic waves flexibly [1]. Over the past few decades, metasurfaces have rapidly developed into powerful electromagnetic field regulation tools to realize various novel optical phenomena, such as electromagnetically induced transparency (EIT) [2–4] and perfect absorption [5,6], which have important application value in many fields because they possess a sub-wavelength ultrathin structure and are highly amenable to design. EIT refers to a phenomenon in which a narrow transparency window is formed within a broad absorption spectrum. It was first discovered in a three-atom system under harsh experimental conditions, including extremely low temperature, high-intensity lasers, and appropriate atomic energy level systems [7]. In contrast, plasmon-induced transparency (PIT), an analog of EIT, has no strict implementation conditions and can be simulated using metamaterials. Therefore, metasurface-based PIT has attracted great attention from researchers and has been widely used for realizing optical switches [8], modulators [9], and slow optical devices [10]. Perfect absorption refers to the complete absorption of incident light of a certain wavelength by the material. A metasurface-based perfect absorber can be achieved when the impedance of the absorber matches that of free space, which can be realized by designing metasurface cells of the appropriate structure and shape. Until now, metasurface-based perfect absorbers have been widely used in sensors [11,12] and thermal radiation detectors [13] for various wavebands.
The latest research frontier in the fields of PIT/EIT and perfect absorption is designing tunable metasurfaces to achieve tunable PIT/EIT devices [14,15] and perfect absorbers [16,17], which can significantly improve the practicability and compatibility of the devices in practical applications. This can be achieved by including materials with adjustable properties such as phase change materials [18], Dirac semimetals [19–21], and graphene [22,23]. Significant efforts have been made by researchers in this regard. For example, Wei et al. realized a dual- polarization PIT metasurface design based on graphene and black phosphorus, and both polarizations can be tuned [15]. Yao et al. studied the broadband absorption of two-layer graphene under electrical modulation and obtained an absorption bandwidth that is 1.7 times higher than that of single-layer graphene [24]. Song et al. proposed a VO2 based dual-function device, which can switch from EIT to broadband absorption when VO2 transitions from an insulator to a metal [25]. However, some of these studies focused only on the tunability of a single function [26–29], while the others studied only the switching of dual functions [30–32]. Therefore, designing devices that can simultaneously switch between PIT and perfect absorption and adjust the response frequency of the two functions separately is the next important step in this field, which motivated our work.
We propose a simple metasurface structure comprising a monolayer graphene split-ring resonator (GSRR) and graphene ribbon (GR) to realize PIT. The mechanism of PIT and the influences of the structural parameters and the Fermi energy of graphene on the PIT are analyzed and discussed. The inclusion of an additional VO2 substrate layer enables the metasurface to dynamically switch between PIT and perfect absorption by using the phase change property of VO2. When the conductivity of VO2 is low, the device can realize the PIT. When the conductivity of VO2 is high enough to block the transmission, the device acts as a perfect absorber. The response frequency of both functions can be adjusted dynamically by changing the Fermi energy of graphene. Furthermore, since the proposed bifunctional metasurface is highly sensitive to changes of the ambient refractive index, it can be used for sensing. Our work achieves switching between different functions and the dynamic modulation of each function. This may positively influence research of multifunctional devices and be used in slow-light devices, sensing, and perfect absorption.
2. Material models
The monolayer graphene was modeled as an equivalent two-dimensional impedance layer, whose impedance is Z(ω) = 1/σ(ω). According to the Pauli Exclusion Principle, the complex surface conductivity of graphene, in the THz band and at room temperature, is given by [33]
The permittivity of VO2 in the THz band can be obtained using the Drude model [34]:
3. Graphene-based PIT structures
In this section, we describe the study of the graphene-based PIT structure. The schematic of the proposed PIT structure is shown in Fig. 1. GSRR and GR are deposited on a silicon dioxide (SiO2) substrate whose thickness and permittivity are 0.2 µm and 3.9 [28,37], respectively. A layer of ion-gel (whose thickness and permittivity are 0.1 µm and 1.82, respectively) on the surface of graphene is used to deposit electrodes (Au) to control the carrier density of graphene [29,38]. The structural parameters are R = 2.4 µm, l = 3 µm, W1 = 0.8 µm, W2 = 0.9 µm, and P = 6 µm. The distance between GSRR and GR is d, and the opening angle of the GSRR is α. CST Microwave Studio, a full-wave electromagnetic simulation software based on a finite integration technique, was used to simulate the proposed structure. In the simulation, the boundary conditions in the x and y directions are provided by the unit cells, and the z direction is open (add space). The incident wave is plane wave and polarized along the x-axis throughout this study. The transmission can be obtained from T=|S21|2, where S21 represents transmission coefficient. Unless emphasized, the incident electromagnetic waves are incident normally.
Fig. 1. Three-dimensional schematic diagram and top view of the proposed graphene-based PIT structure.
The simulated transmission curves of a single GSRR (dashed red line), single GR (dashed blue line) and their combination (solid black line) corresponding to EF, α, and d of 0.6 eV, 90°, 0.7 µm, respectively, are shown in Fig. 2(a). Compared to those for the single GSRR and GR structures, the frequency of dip1 in the combined structure red shifts, while that of dip2 blue shifts owing to the coupling between GSRR and GR. A high transmission window appears between dip1 and dip2 in the combined structure. To explore the physical mechanism of this phenomenon, we simulated the z-components of the electric field (Ez) distributions at the frequencies corresponding to dip1 (3.6 THz), dip2 (4.42 THz), and the transmission peak (3.96 THz), as shown in Figs. 2(b)–(d). At 3.6THz, a strong electric dipole resonance occurs at both arms of GSRR, and GR has a weak response to THz wave, as shown in Fig. 2(b). By contrast, at 4.42 THz, GR exhibits a strong electric dipole response, and GSRR has a weak response, as shown in Fig. 2(d). At 3.96THz, due to resonance detuning, GSRR and GR have a very weak response at the same time and their induce currents are out of phase, which is the characteristic of the electromagnetic-trapped mode [14]. Due to the opposite current oscillations of GSRR and GR, the scattered field at 3.96THz is very weak. Therefore, the high transmission peak appears at 3.96 THz, as shown in Fig. 2(c). Figures 2(c) and (f) are the electric field distributions of a single GSRR and GR at 3.96THz, respectively. GSRR has a strong response while the GR response is not obvious. However, the response of their combination is suppressed, as shown in Fig. 2(c). This proves our conclusion: the anti-phase current oscillations of GSRR and GR at 3.96 cause the electric dipole moments of the two structures to cancel each other.
Fig. 2. (a) Transmission of a single GSRR (red dashed line), single GR (blue dashed line), and their combination (black solid line). Electric field (Ez) distribution of the graphene layer at (b) 3.6 THz, (c) 3.96 THz, and (d) 4.42 THz. (e) and (f) Electric field (Ez) distribution of GSRR and GR at 3.96THz, respectively.
The two-particle model which can be used to describe the coupling between GSRR and GR treats them as two particles interacting with the incident wave. The interaction between them can be expressed as [37,40]:
In the fitting, the transmittance is defined as T = 1-Im(χ) (using the Kramer–Kronig relations). γ1, γ2 can be obtained from the linewidths of the separate GSRR and GR transmission curves. The coupling strength κ is obtained by solving the equations ${\omega _1} = \sqrt {\omega _0^2 - {\kappa ^2}} {\; }$and ${\omega _2} = \sqrt {\omega _0^2 + {\kappa ^2}} $, where ω1 and ω2 represent the band-stop frequencies. Finally, as shown in Fig. 3(a), the transmission curves of the analytic model with EF of 0.4 eV, 0.6 eV, and 0.8 eV are obtained. The curve obtained using the analytic model is evidently consistent with the simulated curve. As EF increases, the transmission window undergoes a blue shift and widens. This phenomenon is more evident in Fig. 3(b). The fitting parameters, such as the coupling strength and damping rates, are plotted in Fig. 3(c). As EF increases, γ1 and γ2 remain almost unchanged, while κ shows an obvious increase. These imply that increasing the Fermi energy strengthens the coupling between GSRR and GR.
Fig. 3. (a) Transmission curves of simulation (black solid line) and analytic model (red dashed line) when EF = 0.4 eV, 0.6 eV, and 0.8 eV, respectively. (b) Transmission as a function of EF and frequency. (c) Fitting parameters of the analytic model with different EF.
We then discuss the influences of the structural parameters d and α on the transmission curve. Changing d essentially changes the coupling strength between GSRR and GR. When compared to the single GSRR and GR structures, the transmission curve of the combined structure exhibits the effect of the coupling between GSRR and GR via red shifts and blue shifts in the frequencies of dip1 and dip2, respectively. Therefore, when the coupling strength is enhanced by reducing d, the frequencies of dip1 and dip2 will be further red shifted and blue shifted, respectively. However, when the coupling strength is reduced by increasing d, the frequencies of dip1 and dip2 will undergo blue shifts and red shifts, respectively. A change in α affects the resonance frequency of GSRR. According to the formula of the plasmon resonance frequency for graphene f = e/(2πћ)(EF/πD)1/2 [41], when α increases, the effective length D of graphene parallel to the polarization direction decreases, leading to an increase in f, that is, the dip1 blue shifts when α increases. The increase in α does not affect the coupling between GSRR and GR; therefore, dip2 is expected to remain unchanged when α changes. To verify this, we simulated the transmission curves using different parameters. The transmission curves corresponding to different values of d at α= 90° are shown in Fig. 4(a). The figure shows that when d decreases from 1.1 µm to 0.3 µm, dip1 exhibits a red shift and its transmission increases, while dip2 exhibits a blue shift and its transmission decreases. This observation is consistent with our expectations. The transmission curves corresponding to different values of α at d= 0.7 µm are shown in Fig. 4(b), where an increase in α is observed to produce a blue shift in dip1. During this process, dip2 remains unchanged. These phenomena are also consistent with our analysis.
Since electromagnetic waves are not always normally incident into the structure, we simulated the transmission curve at different incident angles θ (in the y-z plane) assigning the values of 0.6 eV, 90°, and 0.7 µm to EF, α, and d, respectively. As shown in Figs. 5(a) and (b), the frequencies of the transmission peak and transmission valleys remain unchanged as θ increases, while the transmission decreases. This can be attributed to two factors. First, the change in the incident angle does not change the electric field component in the x-direction, so it does not affect the resonance frequencies and coupling strength of GSRR and GR, and the frequencies of the transmission peak and the transmission valleys remain unchanged. Second, an increase in the incident angle increases the reflection of the incident wave resulting in decreased transmission. Moreover, when the incident angle is less than 30°, the maximum change in transmission (3%) indicates insensitivity to small incident angles, which is beneficial for practical applications.
Fig. 5. (a) Transmission curves for different θ (in the y-z plane). (b) Transmission as a function of θ and frequency.
It is worth noting that PIT is accompanied by strong dispersion and slow light effect, which makes it important for applications including slow optical devices and optical routing. The group delay (τd) is used to quantify the slow-light effect. It is defined as the derivative of the transmission phase φ(ω) as a function of angular frequency ω, that is,
Figure 6(a) clearly demonstrates that as EF increases from 0.4 eV to 0.8 eV, the peak value of τd increases from 0.28 ps to 0.32 ps. When EF is fixed at 0.6 eV, τd increases monotonously from 0.30ps to 1.02ps with the incident angle θ increases from 0° to 85°, as shown in Fig. 6(b). Because a larger incident angle leads to a longer propagation distance in the structure resulting in a larger group delay. In sum, active tuning of the group delay can be achieved by controlling the EF of graphene and incident angle. Moreover, when θ increases from 0° to 30°, the group delay only increases by 1.2%, showing insensitivity to small incident angles. These tunable features are essential for developing integrated devices.
4. Tunable and switchable bifunctional metasurface for PIT and perfect absorption
In this section, we describe the effect of adding an additional VO2 substrate layer to realize a switchable PIT and perfect absorption bifunctional device. The optimized thickness of VO2 is 0.8 µm while the SiO2 layer is 4 µm thick. The other parameters remain unchanged. The new structure is shown in Fig. 7. The conductivity of VO2 can be adjusted independently by the applied voltage [27,31].
Fig. 6. (a) Group delay for different EF at normal incidence. (b) Group delay for different θ when EF =0.6 eV.
In this structure, three tunable parameters, the graphene Fermi energy, incident angle, and conductivity of VO2, can be used to actively adjust the transmission curve. The transmission curves and group delay curves under different graphene Fermi energies and incident angles obtained when VO2 is in the insulating state (σ =10 S/m), are shown in Figs. 8(a)–(d). In this case, the device exhibits PIT. The transmission peak blue shifts and decreases, the group delay of the transmission peak increases as EF increases. This behavior can be explained in two factors. First, the resonant frequency f positively related to the EF of graphene. Secondly, the transmission of THz waves pass through VO2 gradually decreases with the frequency increases. The transmission of the transmission peak decreases, and the group delay of the transmission peak increases with an increase in θ under EF = 0.3 eV, as shown in Figs. 8(c) and (d). This can be attributed to the increase in the incident angle increases the propagation distance of THz waves in the structure, which is equivalent to increasing the thickness of the structure, so the transmission decreases and group delay increases. The transmission curves and group delay curves under different σ when EF = 0.3 eV and θ=0° are shown in Figs. 8(e)–(f). It can be seen that the transmission and group delay decrease as σ increases, but the frequency of the peak remains unchanged. When σ=200000 S/m, VO2 becomes metallic, and blocks the transmission of electromagnetic waves.
Fig. 8. (a) Transmission and (b) group delay for different EF when σ=10 S/m. (c) Transmission and (d) group delay for different θ when EF =0.3 eV. (e) Transmission and (f) group delay for different σ when EF =0.3 eV.
As the transmission of electromagnetic waves is blocked when VO2 is in the metallic state, we simulated the absorption curves at EF = 1.2 eV. The absorption is defined as A = 1-|S11|2-|S21|2 = 1-|S11|2, where S11 and S21 represent complex reflection and transmission coefficients, respectively (|S21|=0 when VO2 is in the metallic state). Two nearly perfect absorption peaks at 3.94 THz and 5.04 THz can be clearly observed. We introduce the coupled mode theory (CMT) and compare it with the simulation results [28,43].
where a is the amplitude of resonance with the resonance frequency ${\omega _0}$. $\gamma $ and $\delta $ are the radiation loss and intrinsic loss rates of the resonance, respectively. ${S_ + }$ and ${S_ - }$ are amplitudes of the input and output THz waves, respectively. Finally, the absorption can be expressed as:Next, we studied the tunability of the absorber. When EF is fixed at 1.2 eV, the absorption in the frequency range 2-6 THz increases significantly as the conductivity of VO2 decreases, except for the two peaks, as shown in Figs. 10(a) and (b). We attribute this to the decrease in conductivity, which weakens the metallicity of VO2, resulting in the increased absorption of electromagnetic waves by VO2. As shown in Fig. 10(c), the absorption peak blue shifts with the increase in EF and absorption gradually increases because the resonance frequency is positively correlated with the graphene Fermi energy. In addition, the tolerance to the incident angle θ is discussed, as shown in Fig. 10(d). When EF= 1.2 eV is fixed and the incident angle θ is gradually increased, it is surprising to note that the absorption peaks remain unchanged at 0°-80° and maintain more than 90% absorption between 0°-58°. This demonstrates that our structure has a high tolerance to the incidence angle, which is very important for practical applications.
Fig. 9. (a) Absorption curves of simulation (black solid line), CMT1 for GSRR (red dashed line), and CMT2 for GR (blue dashed line). Surface current distribution of the graphene layer at (b) 3.94 THz and (e) 5.04 THz. Electric field (|E|) distribution of the graphene layer at (c) 3.94 THz and (f) 5.04 THz. Magnetic field (|H|) distribution of the graphene layer at (d) 3.94 THz and (g) 5.04 THz. (h) Real part and imaginary parts of the relative impedance z with EF = 1.2 eV.
Fig. 10. (a) Absorption and (b) transmission as a function of σ. (c) Absorption as a function of EF and frequency. (d) Absorption as a function of θ and frequency.
It is well known that the transmission peak of PIT is strongly dispersive and very sensitive to the refractive index. Therefore, we explored the influence of the ambient refractive index on PIT and perfect absorption. The response frequencies of the two functions vary with the refractive index n, as shown in Fig. 11. The sensing performance is quantified by calculating the sensitivity S, which is defined as the ratio of the variation of the wavelength to the refractive index ($S = {\Delta }\lambda /{\Delta }n$). We calculated the sensitivity S of the PIT as S= 18219 nm/RIU, while those of the two absorption peaks are S1= 20541 nm/RIU and S2= 23166 nm/RIU. The subscripts 1 and 2 correspond to peaks 1 and 2, respectively. For comparison, we list similar published studies in Table 1, which indicate that our proposed structure can switch between the two functions and also exhibit better sensing performance than other graphene sensors. This can be attributed to two factors. First, our structure is composed of graphene split-ring resonator and graphene ribbon. The response of an isolated structure is intense than that in other references. Secondly, our graphene structure occupies a larger proportion of the entire unit structure. Combined with our previous analysis, it can be found that our structure is highly sensitive to the refractive index and insensitive to the incident angle, and we believe that it will have good application potential in refractive index sensors.
Fig. 11. PIT curves (a) and peak frequency (b) vary with n when EF =0.2 eV, σ=10 S/m. Absorption curves (c) and peak frequency (d) vary with n when EF =1.2 eV, σ=200000 S/m.
Table 1. Comparison with similar published works
5. Conclusion
In summary, a graphene-based PIT structure in the THz range is proposed. The influences of the structural parameters, graphene Fermi energy, and incident angle on the PIT response and group delay are investigated in detail. The proposed structure is then turned into a bifunctional device by including a VO2 substrate. The new structure can switch between PIT and perfect absorber using the phase change property of VO2. PIT occurs when the VO2 is in an insulating state, and two perfect absorption peaks occur when the VO2 is in the metallic state. The responses of the two functions can be adjusted dynamically by changing the Fermi energy of graphene. Moreover, the responses of the two functions are insensitive to the incident angle, which is suitable for practical applications. The influence of the ambient refractive index on PIT and absorber was also explored. It offers potential applications for refractive index sensing. We expect our work to promote research on multifunctional metasurfaces and their applications.
Funding
National Natural Science Foundation of China (62075047, 61965006, 61975038, 61964005,62065006); Natural Science Foundation of Guangxi Province (2020GXNSFDA297019, 2020GXNSFAA238040, 2021GXNSFAA075012); Science and Technology Project of Guangxi (AD19245064); Guangxi Key Laboratory of Automatic Detecting Technology and Instruments (YQ20107); and the Innovation Project of GUET Graduate Education (2020YCXS089).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data on the relaxation time of graphene underlying the results presented in this paper are available in Ref. [26]. Data on the conductivity of VO2 underlying the results presented in this paper are available in Ref. [28,29]. The data of the permittivity of SiO2 underlying the results presented in this paper are available in Ref. [21,30].
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