Dynamically Tunable Electromagnetically Induced Transparency in Graphene and Split-Ring Hybrid Metamaterial

Transcription

1 DOI /s Dynamically Tunable Electromagnetically Induced Transparency in Graphene and Split-Ring Hybrid Metamaterial Zhong Huang 1 & Yunyun Dai 2 & Guangxu Su 1 & Zhendong Yan 1 & Peng Zhan 1,3 & Fanxin Liu 4 & Zhenlin Wang 1,3 Received: 19 October 2016 /Accepted: 3 February 2017 # Springer Science+Business Media New York 2017 Abstract In this letter, a novel hybrid metamaterial consisting of periodic array of graphene nano-patch and gold split-ring resonator has been theoretically proposed to realize an active control of the electromagnetically induced transparency analog in the mid-infrared regime. A narrow transparency window occurs over a wide absorption band due to the coupling of the high-quality factor mode provided by graphene dipolar resonance and the low-quality factor mode of split-ring resonator magnetic resonance, which is interpreted in terms of the phase change and surface charge distribution. In addition to the obvious dependence of the spectral feature on the geometric parameters of the elements and the surrounding environmental dielectric constant, our proposed metamaterial shows great tunabilities to the transparency window by tuning the Fermi energy of the graphene nano-patch through electric gating and its electronic mobility without changing the geometric parameters. Furthermore, our proposed metamaterial combines low losses with very large group index associated with the resonance response in the transparency window, showing * Peng Zhan zhanpeng@nju.edu.cn * Zhenlin Wang zlwang@nju.edu.cn School of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing , China Department of Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Key Laboratory of Surface Physics, Fudan University, Shanghai , China Collaborative Innovation Center of Advanced Microstructures, Nanjing , China Department of Applied Physics, Zhejiang University of Technology, Hangzhou , China it suitable for slow light applications and nanophotonic devices for light filter and biosensing. Keywords Graphene. Electromagnetically induced transparency. Split-ring resonator. Near-field coupling. Slow light Introduction Electromagnetically induced transparency (EIT), which is generated when a narrowband discrete state destructively interferes with a broadband continuum, is a quantum effect in atomic systems giving rise to a sharp peak within a broad transmittance dip [1]. Recently, many studies have demonstrated the asymmetric Fano line-profile resonances due to the coupling or hybridization of surface plasmon and photonic modes in metallic plasmonic microstructure, leading to sorts of EIT-like phenomena [2, 3]. In the past decade, various metallic plasmonic sub-wavelength microstructures have been employed to generate EIT-like effect in the visible and infrared regime because of its flexible design and easy implementation [4 6]. However, most of these metallic microstructures have to be tuned to work in different frequency regimes only by varying their geometrical parameters because the properties of the surface plasmon in metals are greatly limited by the difficulty or impossibility in dynamically tuning their plasma frequencies. Therefore, the active manipulation of the plasmonic EIT-like effect consisting of the sub-wavelength constitutive elements without requirement of any change of their geometries has been attracting great attentions. Recently, two-dimensional (2D) materials have received a great deal of attention due to their exceptional optical and electronic properties. In particular, the outstanding carrier mobility and the tunable conductivity (permittivity) of graphene

2 are beneficial in active optical devices. As an atomically monolayer plasmonic platform, it has been confirmed that both propagating and localized surface plasmon modes could be excited in a graphene with nanostructures, [7, 8]makingit potential in the fields of nanophotonics and optoelectronics [9 12]. Due to its 2D nature similar to the 2D free electron gas and its specific linear dispersion band structure, the surface plasmon in graphene exhibit essential properties of deep sub-wavelength and tight electric field confinement in the broad wavelength regime from terahertz to infrared, while maintaining relatively lower loss [13], which might open up a new gateway for designing and engineering novel plasmonic nanostructures and metamaterials with ultra-deep sub-wavelength feature sizes. More importantly, graphene shows strong tunability of electromagnetic properties through manipulating its Fermi energy level by electrical gating or chemical doping [14], allowing it to be a good candidate for active tunable plasmonic nanostructures and their corresponding functionalized electro-optic devices. Herein, we purposed a graphene-gold complex metamaterial working at mid-infrared regime, which is a double-layer nanostructure with its unit cell consisting of a gold split-ring resonator (SRR) and a graphene rectangular resonator, separated by a dielectric layer. Graphene rectangular resonator used here works as a Bdark^ mode with high-quality factor (narrow linewidth), while the gold SRR works as a Bbright^ mode with low-quality factor (large linewidth). The gold SRR are called Bartificial magnetic atom^ whichhaveanenhanceddiamagnetic response to magnetic fields. Such magnetic resonances have enabled the magnetic light-matter interaction, and have been investigated for the possible realization of negative index of refraction [15]. The induced surface charge distribution of the metamaterial at different wavelengths suggests that the EIT-like effect is obtained from the destructive interference between the narrowband graphene dipolar resonance and the broadband magnetic resonance of the SRR, resulting in transmitting spectra with an EIT-like window. The active control of the EITlike effect is demonstrated by tuning the Fermi energy of the graphene, the structure s geometrical parameters and the environmental dielectric constant. Recently, the verylong-wavelength infrared (VLWIR) optics in the wavelength regime of μm, has been a very important topic of wide concern due to their perceived potential for applications in remote environmental monitoring, infrared earth sensing, meteorological information, and astronomy research [16]. In addition, this regime is particularly suitable for biosensing to detect various molecular vibrations such as proteins, lipids, and DNA [17, 18]. Furthermore, the large group index can be achieved with the proposed structures suggest potential applications in slow light devices, switches, and modulators [19]. Structure Design and Simulation As is showninfig. 1a, the purposed double-layer metamaterial is constructed with a square array by a unit cell composed of upper layer of a gold SRR resonator and lower layer of a graphene resonator. The resonators are excited by the electric field of a normally incident plane wave. The electric field E in, magnetic field H in and the wave vector K in of the incidence are along the x, y,andz axis, respectively. As shown in the Fig. 1b (front view), the vertical distance (d) between the graphene resonator and the SRR is 1 μm. The height of the SRR h is 30 nm. Figure 1c displays the bottom view of a unit cell of the proposed structure with detailed geometrical parameters. The array periodicity p along the x- and y-directions are identical and set as 6 μm. The arm length l of the SRR is 3 μm, and the arm width w is 0.75 μm. The graphene resonator has the same length as the arm length of the SRR, and its width is defined as w g. The whole nanostructure is purposed to be embedded in a homogeneous dielectric environment with a dielectric constant ε d to neglect the effects of the substrate. For simplicity, the dielectric environment is firstly considered as air or vacuum which means ε d = 1. In our simulations, the permittivity of gold is described by the Drude model: ε gold ðωþ ¼ 1 ω 2 p ωωþ ð iγþ ð1þ where ω p is the plasma frequency and γ is the damping constant, which is set as s 1 and s 1,respectively [20]. For monolayer graphene, here assumes the thickness (t g ) is 0.5 nm, suggested in the literature [21]. Thus, the dielectric constant of the graphene ε g can be derived from: ε g ¼ ε 0 þ iσ g ωt g ð2þ where ε 0 is the electric permittivity of the vacuum. Here, σ g represents the complex surface conductivity of graphene, Fig. 1 a Three-dimensional schematic view of the hybrid structure, b the front view of a unit cell, and c the bottom view of a unit cell

3 which involves the intraband and interband transitions contributions, and it can be calculated through the local limit of random-phase approximation (RPA) [22] as: σ g ðωþ ¼ þ e2 4ħ 2ie 2 k B T πħ 2 ðω þ iτ 1 Þ ln 2cosh E f 2k B T ( 1 2 þ 1 π arctan ħω 2E " f i 2 #) 2k B T 2π ln ħω þ 2E f 2 ħω 2E f þ ð 2kB TÞ 2 ð3þ where k B is the Boltzmann constant, T is the temperature, ω is the frequency of the incident light, τ is the carrier relaxation time from the impurities in graphene, E f is the Fermi energy of the graphene, and μ is the carrier mobility in graphene. Numerical simulations in this letter were performed using a commercial finite element method (FEM) based software package (COMSOL Multiphysics). Periodic boundary conditions are applied to the four side boundaries located in the xz and yz planes. The top and bottom boundaries are terminated with perfectly matched layers to absorb reflected and transmitted light in the z axis. Results and Discussions To demonstrate the nature of the EIT-like effect clearly, we firstly study the transmission spectra under the normal incidence with TM polarization (its magnetic field is perpendicular to the x-z plane) for the pure gold SRR array with different l and the pure graphene rectangular nano-patch array with different w g,asshowninfig.2a, c, respectively. As an example, when the arm length l of the SRR equals to 3.0 μm while the other parameters are used as mentioned above, a broad transmission dip centered at 15 μm is observed for the pure gold SRR array, which corresponds to an excitation of magnetic resonant mode. Figure 2b plots the magnetic field marked as red-arrows on the xy plane showing a current loop that induces a magnetic moment. Furthermore, since the electric field couples to the SRR magnetic resonance, the distribution of the H z component magnetic field at the half-height plane of the SRR (which is normalized by the magnetic intensity of incident light) shows a strong enhancement of the magnetic field mainly confined within the inner area of the SRR, and its corresponding enhancement reaches up to a value of 182. On the other hand, for the pure graphene nano-patch array, we also perform the calculations for its optical response. One kind of EIT phenomenon was demonstrated by using well-designed metallic microstructures in which two intrinsic electric dipolar resonances with very near spectral positions but quite different line-widths were excited simultaneously and strongly coupled with each other, and it s worthwhile to note that these two resonances actually are both Bbright modes^ [23]. For a typical example of our design with the width of the graphene ribbon being 650 nm, a transmission dip with a very narrow linewidth centered at 15 μm is shown in Fig. 2c, which is arising from the excitation of a coupled electric dipole resonant mode recognized by the normalized electric field distribution (( E/E in ) 2 ), illustrated in Fig. 2d. Here, the Femi energy being 0.7 ev, and the graphene s electron mobility being 10,000 cm 2 /Vs (previous reports showed that the carrier mobility of the graphene could reach 4000 cm 2 /Vs at room temperature (T = 300 K) and that of high-quality suspended graphene could even be 23,000 cm 2 /Vs [24]). It is obvious that a strongly localized electric fields can be concentrated firmly on the long edges of the graphene resonator with an enhancement of Particularly, in this case, the width of the graphene resonator is only 650 nm, just being about 1/ 20 of the incident light wavelength in vacuum, which exhibits the deep-subwavelength property of mode confinement. Generally, an analogous EIT effect in metamaterials was implemented based on Fano-resonance arising from a destructive interference between broad radiative (bright) and narrow sub-radiative (dark) modes [25], and mostly, the dark mode could not be directly excitable [26]. In our proposed doublelayer metamaterial, the upper gold SRR serves as an artificial magnetic dipole with low-quality factor of Q = 5.36 (Fig. 2a red line) leading to a relative broad resonant spectral response in the mid-infrared regime, which could be considered as a Bbright atom^ in EIT-like plasmonic system. On the other hand, utilizing the nature of very small absorption loss and strong optical confinement (small leaky radiation) of graphene, the lower graphene nano-patch could serve as a Bdark atom^, sustaining a dipole mode with higher quality factor of Q = 37.5 (Fig. 2c, red line). Both these two modes are actually excitable in their own right. When these two modes have near perfect spectral overlap with strong linewidths contrast and comparable resonant amplitudes, a conspicuous coupled resonant mode with Fano line-shape will be formed, creating a narrow transparency window in the wavelength center of the bright mode. As verified by the corresponding simulated transmission spectra in Fig. 3a, the interference of the resonant modes leads to an evident narrow transparency window with a transmission peak frequency at 15.1 μm and two dips at 14.2 μm and 15.9 μm. Complimentarily, in Fig. 3b the transmission phase data exhibits a typical anomalous dispersion associated with the Fano-resonance region, and an abrupt phase change of rad is observed. To further understand the mechanism of the EIT phenomenon, the normalized surface charge distributions of the unit cell at the wavelengths of 14.2, 15.1, and 15.9 μm marked as I, II, and III are plotted in Fig. 3c, respectively. From that, at the transmission dips (points II and III), apparently the strong surface currents around SRR and charge distributions along the graphene nano-patch are induced. Note that the induced dipole-like electric moments in these two

4 Fig. 2 a Transmittance of the pure gold SRR array for different l, b magnetic field distribution at the half-height plane of the SRR under 15 μm light illumination, c transmittance of the pure graphene resonator for different w g and d electric field distribution of the graphene resonator under 15 μm light illumination cases are in opposite direction coinciding with the transmission phase spectral trend, which identifies the mode hybridization. However, it s obvious that, for the narrow transmission window centered at 15.1 μm (at point I), the induced current in the SRR is almost suppressed, while a relative stronger dipole-like charge distribution of the graphene resonator appears. This phenomenon arises from the electromagnetic nearfield coherent coupling between the radiative and dark modes, leading to a dominant dark mode resonance of the graphene nano-patch consequently. As mentioned above, the coupling strength of bright and dark modes is strongly influenced by their spectral overlap. However, the optical response of the gold SRR is almost determined by their geometric parameters, and in practical it is very difficult to change the physical structure after fabrication of the metallic SRR array. Alternatively, one of the major advantages of the graphene compared to the noble metals (such as gold, silver, and copper) is its active broadband tunability of Fermi energy (E f ) by electrostatic gating and chemical doping, which opens up a new gateway to enable continuously tunable plasmonic elements. From the quasi-static analysis, the plasmonic resonance wavelength of graphene nano-patch could be expressed roughly as λ res (ε eff w g / E f ) 1/2,whereε eff is the effective dielectric constant of the media surrounding the whole structure [27]. Figure 4a shows the infrared response of our proposed graphene-based hybrid metamaterials to the graphene s Fermi energy. In this simulation, E f is changed from 0.7 to 0.9 ev by applying different bias voltages, while the other parameters are set as w g = 650 nm, μ =10,000cm2/Vs and ε d =1.0.It s clear that the transparency window is tunable within a large range and shows an obvious blue-shift with the increase of E f. Besides, the intrinsic loss of graphene will strongly influence its plasmonic properties. Normally, the graphene s intrinsic loss (i.e., the electron Fig. 3 a Transmittance and transmission phase of the hybrid structure, the full wavelength of the transmission phase is shown in the inset, b the surface charge distribution at the half-height plane of the SRR and the surface of the graphene patch respectively

5 Fig. 4 a Transmittance for the hybrid metamaterial with different Fermi energy and b transmittance for the hybrid structure with different electronic mobility in the graphene patch mobility μ) could be tuned by controlling the electrical contact [28] or different dielectric substrate, such as boron nitride and suspended graphene [29, 30]. The Q-factor degradation of graphene resonator would occur as the electron mobility decreases, which is expected to lead to the gradually weaker EITlike responses. Figure 4b shows the evolution of the calculated transmission spectra of our proposed double-layers metamaterial when μ is varied from 10,000 cm 2 /Vs to 1000 cm 2 /Vs, with other parameters being E f = 0.7 ev, w- g =650nm,andε d = 1. The energy dissipation tends to be dominant for the graphene with smaller μ, and thus the efficiency of EIT-like resonance is visibly deteriorated. As the electron mobility of graphene increases to 5000 cm 2 /Vs, the transmittance efficiency will gradually reach up to more than 50% and the transparency window is becoming distinguishable. It is worthwhile to note that during this process the Q- factor of EIT-like resonance will be higher, however the corresponding wavelength will not shift at all. Just analogous to the conventional plasmonic elements such as metallic cut nanowire, the wavelength of plasmonic dipole resonance of the graphene nano-patch will determine by its physical dimension. As shown in Fig. 5a, an obvious red-shift of the transparency window is demonstrated with the width of the graphene nano-patch (w g )increasingfrom450to 650 nm, which is due to the size-dependence of the dipole resonance of the graphene resonator. And when w g is selected as 550 nm, the balance of near-perfect spectral overlap of bright/dark resonant modes and stronger absorption of graphene led by the increase of its width can result in an optimized EIT-like window. Here, E f = 0.7 ev, μ = 10,000 cm 2 /Vs, and ε d = 1.0. On the other hand, the environmental index offers us another degree of freedom to tune the EIT-like effect of our proposed graphene-based metamaterial. Practically, the whole structure could be immersed or embedded in different dielectric background. Here, we assume the refractive index of the background ε d changing from 1 to 1.4 with w g = 650 nm, E f =0.7eV, μ =10,000cm 2 /Vs, and the corresponding EIT-like responses demonstrate a gradual red-shift as ε d increases, as shown in Fig. 5b. This range of ε d covers the achievable materials such as ion gel and electro-optic polymers. EIT-like system has been demonstrated to greatly slow down the speed of light [31] which is potential for routing optical information. In order to demonstrate the slow-light effect in our proposed double-layer metamaterial, we firstly calculate the effective refractive index n e (ω) of the structure through extracting the transmission and reflection coefficients by using the retrieval method described in reference [32]. Figure 6a displays the retrieved real and imaginary part of n e (ω) for a typical proposed structure with w g = 650 nm, E f = 0.7 ev, μ =10,000cm 2 /Vs, and ε d = 1.0. Because the intrinsic loss of gold is much higher than that of graphene, one Fig. 5 a Transmittance for the hybrid metamaterial with different width of graphene patch and b transmittance for the hybrid metamaterial with different background relative permittivity

6 Fig. 6 a Real and imaginary part of the effective refractive index of the designed hybrid structures and b group index of the designed hybrid structures would expect a larger imaginary part of effective refractive index. However, inside the transparency window, the imaginary part of the n e is very small, indicating there is no loss in the gold SRR due to the magnetic resonance is suppressed. Then, the effective group index n g (ω) dispersiondetermined from the slope of the real part of the effective refractive index (Re [n e (ω)]), could be computed using the following equation: n g ðωþ ¼ n e ðωþþω n eðωþ ω ð4þ The calculated group index n g for the transparency window exceeds 75 as shown in Fig. 6(b), implying that the electromagnetic wave passing through the same thickness of the metamaterial with a group velocity 75 times slower than that in vacuum. Positive and negative group index n g corresponds to slow and fast light, respectively [33]. According to the above simulation results, the group index could be further increased by tuning the Fermi energy and electron mobility of graphene as well as optimizing the other physical parameters of the proposed metamaterials, but possibly facing the cost of bandwidth and increased losses. Conclusion In conclusion, we numerically proposed a novel electrically tunable EIT-like metamaterial consisting of top-layer gold SRR array and bottom-layer graphene nano-patch array. The destructive interference between the low-quality factor magnetic resonance of the SRR and the high-quality factor dipolar resonance of the graphene resonator, which can be both directly excited by the incident light, leads to the EIT-like effect. The related physical mechanism is studied by inspecting the phase change and induced surface charge distributions at different wavelengths within the transparency window. The transparency window of the metamaterial can be actively controlled in the range of 10 to 20 μmbytuningthefermienergy and the electron mobility of the graphene, the geometry parameters and the environmental dielectric constant. Besides, the large effective group index and small loss of the metamaterial within the transparency window may offer new possibilities for applications in the mid-infrared regime, e.g., in slow light, spectral filtering, and biosensing. Acknowledgments This work was supported by the State Key Program for Basic Research of China (Grant No. 2013CB632703), and by the National Nature Science Foundation of China (Grant Nos , , , and ). References 1. Miroshnichenko AE, Flach S, Kivshar YS (2010) Fano resonances in nanoscale structures. Rev Mod Phys 82: Chiam SY, Singh R, Rockstuhl C, Lederer F, Zhang W, Bettiol AA (2009) Analogue of electromagnetically induced transparency in a terahertz metamaterial. Phys Rev B 80: Lukyanchuk B, Zheludev NI, Maier SA, Halas NJ, Nordlander P, Giessen H (2010) The Fano resonance in plasmonic nanostructures and metamaterials. Nat Mater 9: Gu J, Singh R, Liu X, Zhang X, Ma Y, Zhang S (2012) Active control of electromagnetically induced transparency analogue in terahertz metamaterials. Nat Commun 3: Zhu Z, Yang X, Gu J, Jiang J, Yue W, Tian Z (2013) Broadband plasmon induced transparency in terahertz metamaterials. Nanotechnology 24: Yin X, Feng T, Yip S, Liang Z, Hui A, Ho J (2013) Tailoring electromagnetically induced transparency for terahertz metamaterials: From diatomic to triatomic structural molecules. Appl Phys Lett 103: Gao W, Shu J, Qiu C, Xu Q (2012) Excitation of plasmonic waves in graphene by guided-mode resonances. ACS Nano 6: Gao W, Shi G, Jin Z, Shu J, Zhang Q, Vajtai R (2013) Excitation and active control of propagating surface plasmon polaritons in graphene. Nano Lett 13: Avouris P, Freitag M (2014) Graphene photonics, plasmonics, and optoelectronics. IEEE J Quantum Elect 20: García de Abajo FJ (2014) Graphene plasmonics: challenges and opportunities. ACS Photonics 1: Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV (2004) Electric field effect in atomically thin carbon films. Science 306:

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