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A dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency
Journal Pre-proof A dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency Chunlian Cen, Yubin Zhang, Xifang Chen, Hua Yang, Zao Yi, Weitang Yao, Yongjian Tang, Yougen Yi, Junqiao Wang, Pinghui Wu PII:
S1386-9477(19)30993-2
DOI:
https://doi.org/10.1016/j.physe.2019.113840
Reference:
PHYSE 113840
To appear in:
Physica E: Low-dimensional Systems and Nanostructures
Received Date: 7 July 2019 Revised Date:
3 November 2019
Accepted Date: 19 November 2019
Please cite this article as: C. Cen, Y. Zhang, X. Chen, H. Yang, Z. Yi, W. Yao, Y. Tang, Y. Yi, J. Wang, P. Wu, A dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency, Physica E: Low-dimensional Systems and Nanostructures (2019), doi: https:// doi.org/10.1016/j.physe.2019.113840. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Graphical abstract We present a dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency. We find the nanostructure absorption peak wavelength is flexible and adjustable by changing the graphene Fermi level EF.
A dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency Chunlian Cen1, 3, Yubin Zhang1,3, Xifang Chen1,3, Hua Yang2, Zao Yi 1,3∗∗, Weitang Yao1,3*, Yongjian Tang3, Yougen Yi4, Junqiao Wang5, Pinghui Wu6 1
Joint Laboratory for Extreme Conditions Matter Properties, Southwest University of Science and Technology, Mianyang 621010, China 2 State Key Laboratory of Advanced Processing and Recycling of Non-ferrous Metals, Lanzhou University of Technology, Lanzhou 730050, China 3
4 5
Sichuan Civil-Military Integration Institute, Mianyang 621010, China
College of Physics and Electronics, Central South University, Changsha 410083, China
School of Physics and Engineering and Key Laboratory of Materials Physics of Ministry of Education of China, Zhengzhou University, Zhengzhou 450001, China
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Photonic Technology Research & Development Center, Key Laboratory of Information Functional Material for Fujian Higher Education, Quanzhou Normal University, Quanzhou 362000, China
∗ Correspondence should be addressed to Zao Yi, Weitang Yao Tel: 86-0816-2480830; Fax: 86-0816-2480830 E-mail address: [email protected]; [email protected] 1
Abstract: In this paper, we present a dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency. We use the finite difference time domain (FDTD) method to study the absorption characteristics of the homocentric graphene ring and disk nanostructure. These simulation results show that the change of the geometrical parameters and the substrate thickness of the nanostructure can change the absorption characteristics and the emergence of dual-band absorption peaks. Moreover, we study the field distribution of nanodisks with different radius in detail. By changing the Fermi level of graphene, the wavelength of their absorption peaks can be adjusted flexibly. In addition, the proposed dual-band absorber also shows a good angle tolerance for both TE and TM polarizations. By calculation the surface-filled water (n = 1.332) and 25% aqueous glucose solution (n = 1.372) for the metamaterial absorber, the sensitivities of mode I and mode II are 5.0 µm/RIU and 15.0 µm/RIU. These research results will have broad application prospects for sensing and spatial light modulators. Keywords: surface plasmon resonance; metamaterial; graphene; dual-band absorber; FDTD 1. Introduction Terahertz (THz) technology has developed very fast in recent years, in scientific research and practical applications has broad application prospects [1-3]. However, natural materials have no light absorption at THz. There are no effective sources and detectors, efficient manipulation of the THz wave is still a great challenge. Due to the low sensitivity of THz wave detection, its application in THz wave sensors, modulators, detectors and other devices is limited. Many researchers have proposed many THz detection devices, including photon detectors [4] and metamaterials (MMs) [5] absorbers. The perfect MMs absorber was first proposed by Randy et al. [6] and caused great concern for many
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researchers. THz waves could be detected by MMs through different structures of units, so the MMs absorber promotes further development of the THz detector. However, when the structure is fixed, most MMS absorbers will work at a fixed frequency. This will limit many of its practical applicability. Therefore, the frequency adjustable design of new material system is particularly important. As a two-dimensional structure with honeycomb lattice of carbon atoms, graphene has attracted more and more attention in recent years due to its excellent electrical, mechanical and chemical properties [7-10]. The process of doping or gating can help to adjust the complex surface conductivity of graphene, which is widely used in photodetection, photovoltage and photocatalysis [11-22]. In recent years, in order to improve the absorption level of electromagnetic wave graphene under the broader spectral range comprises gigahertz (GHz), THz, infrared and optical frequencies, many researchers have been made to work [23-30]. Propagating surface plasmon polariton (PSPP) or localized surface plasmon resonance (LSPR) [31-35], guided mode resonance [36-38], Fabry Perot cavity resonance [39-41], interference effect [42], magnetic dipole resonance [43] and other physical mechanisms will enhance the absorption characteristics of graphene. Meanwhile, careful design of various characteristics of graphene electromagnetic wave absorbers, such as tunability, wide angle of incidence and polarization independence [44-47], graphene electromagnetic wave absorber as efficient and effective as possible. Either dual-band or multi-band can be regarded as an important performance indicator for graphene absorbers and people have extensive research in the THz and infrared bands [48-50]. A series of reports have been reported on the work of graphene dual-band absorber at THz wavelength in recent years, and these works are expected to be applied in sensor detection and so on [51-56]. On the basis of these studies, we hope to expand the research on the THz band graphene dual band absorber.
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Here, we propose a method by FDTD method to improve the dual-band absorption ratio of graphene in THz. The dual-band metamaterial absorber consists of a periodically placed homocentric graphene ring and disk arrays on the surface of a silica layer which is divided by a silicon substrate. The simulation results show the absorber will affect the absorption characteristics by changing the geometry. In the THz range, the resonance wavelength can be flexibly as well, which is adjusted by changes in the Fermi level. As for TM and TE polarizations, the absorber is insensitive to polarization. The surface-filled water (n = 1.332) and 25% aqueous glucose solution (n = 1.372) for the dual-band metamaterial absorber are simulated to evaluate the sensitivity of our proposed refractive index sensor. 2. Structures and methods Fig. 1 is a schematic diagram showing a periodic graphene nanoarrays. The nanoarrays consist of homocentric graphene ring and disk. The graphene arrays are attached to the surface of a silica layer, which is divided by a silicon substrate. The thickness of SiO2 and graphene are d and 1 nm, respectively. The graphene permittivity can be expressed as ε
= iσ g / ωε 0 ∆ + 1, here ∆ is the
thickness of graphene and ε0 represents the vacuum permittivity. Because doped graphene has a mainly real permittivity in the infrared region, just like the dielectric constant of the visible light region metal, it can support strong confinement and long lifetime plasmon resonance for the graphene/dielectric interface. In our calculations, by sequentially reducing the thickness of graphene, we obtained sufficient convergence at a thickness of ∆ = 1 nm. So in the next research work, we set the thickness of graphene to 1 nm. In this nanostructure, the inner radius of the nanoring is Rin, the outer radius of the nanoring is Rout and the radius of the nanodisk is R. In this paper, the reflection, transmission and absorption spectra, as well as the electric field distribution can be calculated by the utilization of the commercial software (Lumerical FDTD Solutions) based on the FDTD method. The accuracy level of
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the mesh in the nanostructures along the x-, y-, and z-axis are set to 20, 20 and 0.2 nm, respectively. The periodic boundary condition of L = 2.5 µm applies to the x as well as y directions and the propagation along the light utilizes the perfectly matched layer in the z-direction [57, 58]. The TM and TE polarizations, which are represented by the x- and y-axis show the direction of the incident electric field. Due to the symmetry of the nanostructure, the polarization direction of the incident TM plane wave is set along the x-axis. In practice, the optimized liquid precursor chemical vapor deposition method can be used to grow large area graphene films, and the graphene film can be determined by Raman measurement. Electron beams lithography is used to make graphene films into nanoring and nanodisk structures, and exposed areas are eroded away by oxygen plasma [35]. In this numerical simulation, an effective surface conductivity model can be utilized to illustrate the graphene. In the random phase approximation, the intraband σintra and interband σinter terms consist of the surface conductivity of graphene [59-62]:
σ g = σ int ra + σ int er =
2e 2 k B T i E e2 1 ln[2 cosh( F )] + [ 2 −1 2 k BT 4h 2 πh ω + iτ
+
1
π
arctan(
(1)
( hω + 2 E F ) 2 hω − 2 E F i )− ln ] 2 k BT 2π (hω − 2 EF ) 2 + 4(k BT ) 2
Here, i, ω, e, ħ, EF, τ, kB and T = 300 K are the imaginary unit, the frequency of the incident light, the electron charge, the reduced Planck’s constants, the Fermi energy, electron-phonon relaxation time, the Boltzmann constant and the temperature, respectively. In the lower THz frequency, when the EF increases to more than half of the photon energy level, due to the Pauli exclusion principle, the contribution of interband process is negligible. Here, we only consider the Fermi level of highly doped graphene, which are E F >> k BT and E F >> hω . Thus, the Eq. 1 can be approximated to the simple Drude-like model [ 55, 59]:
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σg =
e 2 EF i 2 πh (ω + i / τ )
(2)
Here the carrier relaxation time can be expressed as [56]:
τ=
µEF
(3)
evF2
In our calculations, EF = 0.6 eV, the Fermi velocity vF = 106 m/s and the carrier mobility µ = 104 cm-2/(v.s). In addition, the resonance modes supported in the nanoring should satisfy the phase matching equation [63, 64]:
2πReff . Re(neff ) = mλ
(4)
Where Reff, neff, m and λ are the effective radius is determined by (Rin + Rout)/2, the effective refractive indices of the LSPR modes supported by the nanoring, the resonance order and the resonance peak wavelength, respectively. The absorption is expressed as A(λ ) = 1 − R (λ ) − T (λ ) , the value of reflection and transmission can be represented by R(λ) and T(λ). According to Equation (2), we can obtain that the surface conductivity of graphene can be adjusted by controlling its Fermi level. Compared with chemical doping, the electrostatic tunability of graphene is a more suitable way to control the Fermi level of graphene [60, 61]. In the mid-infrared and THz bands, a large number of gate dielectric materials have been developed, such as 2D electron gas, single-layer MoS2, and ion-gel [63-65]. In this case, ion-gel with ultra-high capacitance is currently the most effective medium for realizing high Fermi energy of graphene with low top gate voltage. Good mechanical flexibility, fatigue stability, excellent electrochemical, and thermal stability make it compatible with tunable graphene plasmonic devices on various substrates. Consequently, a schematic diagram of an ion-gel top gate structure for controlling the graphene Fermi level as shown in Figure 1(B). An ion-gel layer is inserted into the graphene and the gold electrode to produce an induced carrier
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concentration and allow access to the THz spectral region. 3. Results and discussions Fig. 2 (A) shows the absorption spectra of graphene arrays with the different periods (L). The absorption maximum of the dual-band absorber changes significantly with the increase of the period, but the wavelength is almost constant. For mode I and mode II, Fig. 2(B) shows that the resonance peak wavelength and absorption maximum at different L. For both mode I and II, we can clearly see the wavelength almost keep in 23 µm and 67 µm, with the L increases. However, the maximum level of absorption decreases as the L increases. As the L increases, the unchanged resonance wavelength is because that the resonance condition remains the same level almost. Since the coupling between the adjacent nanoring and nanodisk, resulting in the resonance peak wavelength changes slightly in a small period. The reduction in the absorption maximum is attributed to a decrease in the filling ratio of graphene. Fig. 2(C) illustrates the relationship of absorption and wavelength with different thicknesses d of SiO2. In Fig. 2(C), the absorption peak wavelength is blue shifted as the SiO2 thickness d increases, for both mode I and mode II. Fig. 2(D) shows that for mode I and mode II, as the thickness of SiO2 experiences a sharp increase, from 100 nm to 500 nm, the absorption peak wavelength decreases. However, for mode I, as the SiO2 thickness d increases, the maximum level of absorption increases from 0.13 to 0.16. Conversely, for mode II, the absorption maximum is reduced from 0.13 to 0.11. For mode I and mode II, as the d increases, the shift of the resonance peak wavelength is related to change from the SP wavevector converter that changes the dielectric environment [66]. As the thickness of d increases, the equivalent refractive index of the silica-silicon composite substrate decreases, so the effective refractive index of the waveguide mode in the graphene nanoring and a nanodisk waveguide decreases. Therefore, according to formula (4), the resonance peak wavelength decreases with the
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increase of d, that is, the blue shift. Aiming to demonstrate the process of the physical mechanism of the change of absorption maximum better, in Fig. 3(A) and (B), we describe the y-component of the electric field in x-z plane for 25 µm (d = 100 nm) and 23 µm (d = 500 nm) in short wavelength (mode I). We find that the electric field of d = 500 nm is stronger than the electric field of d = 100 nm, resulting in a higher resonance absorption peak at d = 500 nm. In long wavelength (mode II), the electric field at d = 100 nm is stronger than the electric field at d = 500 nm, so the resonance absorption peak at d = 100 nm is higher, as shown in Fig. 3(C) and (D). Figures 3(E)-(G) show the z-component of the E-field distribution (Ez) in short-wave (mode I) and long-wave (mode II) at d = 100 nm and d = 500 nm. In this part, we study the effects of changing geometry parameters on the absorption characteristics. For better data comparison, Fig. 4. (A) inserts the enlarged absorption spectra of the mode I for the different inner radius of nanoring Rin. From Fig. 4(A), when the range of Rin is from 350 nm to 550 nm in intervals of 50 nm, the absorption peak wavelength of mode 1 experienced a blue shift, while that of mode II experienced a red shift. In figure 4(A) and (B), for mode I, the absorption maximum decrease with the Rin increases. The reason is that as the Rin increases, a weakened charge distribution between nanoring and nanodisk, and the coupling between nanoring and nanodisk decreases, lead to reduction of absorption efficiency. In figure 4(B), for mode II, the absorption spectra of graphene with the different inner radius of the nanoring Rin (340 nm to 400 nm). For mode II, however, as Rin increases, the absorption maximum increases first (from 340 nm to 380 nm) and then decreases (from 380 nm to 550 nm). When Rin = 380 nm, the absorption reached a maximum of 13.50%. When Rin < 380 nm, with the increase of Rin, an enhanced charge distribution on the outside of the nanoring and the coupling between nanoring and nanodisk increases, leading to increased absorption. When Rin > 380 nm, this is
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related to the ratio variance of the surface atoms to total atoms of the nanostructure. When the R and Rout is fixed, the ratio decreases sharply while the Rin increases. These free electrons will redistribute on the proposed structure, resulting in the absorption decreases. When Rin > 380 nm, with the increase of Rin, the phenomenon of decreased absorption is similar to that of metallic nanorings [67, 68]. We define the width between the nanorings as W = Rout - Rin. For mode II, when Rin increases and Rout is fixed, W decreases, and the absorption peak wavelength undergoes a red shift, as shown in Fig. 4(B). We also study the absorption spectra with the different outer radius of nanoring Rout, as shown in Fig. 4(C). In the short-wavelength (mode I), as the outer radius of the nanoring Rout increases, the absorption peak wavelength undergoes red shifted. In the long wavelength (mode II), the absorption peak wavelength undergoes blue shifted. While the absorption maximum increases as the Rout increase, for both mode I and mode II. Both of the mode I and mode II, the absorption increases because in the case of other geometrical parameters unchanged, with the increase of the Rout of the graphene arrays filling ratio increases and the interaction with light is thus enhanced, resulting in increased absorption. For mode II, when Rout increases and Rin is fixed, W increases, and the absorption peak wavelength undergoes a blue shift. We can summarize that with the decrease of W, for mode II, the absorption maximum shifted to the direction of long wavelength, namely red shift. Conversely, as W increases, the absorption maximum of mode II shifts to the short wavelength direction, that is, blue shift. The influence of the radius of nanodisk (R) on the absorption spectra is also investigated. As shown in Fig. 5(A), we find that when R changes from 250 nm to 350 nm, the absorption peak wavelength of mode I experiences a red shift and mode II has a blue shifted. However, when the radius of the nanodisk R = 150 nm and R = 450 nm, the proposed nanostructure has only one absorption peak at λ1 = 65 µm and λ4 = 33 µm, respectively. For mode I, as R increases from 250 nm to 350 nm, the absorption
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maximum is also increased. The reason is that with the increase of the R and the graphene arrays filling ratio increase, resulting in increased absorption. But for mode II, as R increases from 150 nm to 350 nm, the absorption maximum is reduced. This is the same physical mechanism as Rin > 380 nm. When the Rin and Rout of the proposed structure is fixed, the ratio decreases sharply while the R increases. These free electrons will redistribute on the proposed structure, resulting in the absorption decreases. The distribution of electric field at the different radius of the nanodisk R, as it can be witnessed in Fig. 5(B). In short wavelength, when R = 250 nm and R = 350 nm, the electric field is mainly distributed at the spacing between the nanodisk and nanoring. In long wavelength, when R = 150 nm and R = 350 nm, the distribution of electric field is mainly at the edge of nanoring. When R = 150 nm, the electric field is primarily distributed on the outside and inside of the nanoring, and there is almost no distribution of the electric field at the edge of the circle, as shown in Fig. 5(a). When R = Rin = 450 nm, the nanostructure is equivalent to a circle, which causes the electric field to be distributed at the edge of a circle, as shown in Fig. 5(f). From Eq. 2, we know that the surface conductivity of graphene is closely related to the Fermi level, which could be regulated by the adjustment of electrostatic and chemical doping [69]. The absorption spectra of different EF values as shown in Fig. 6(A). The resonance peak wavelengths are blue shifted while the maximum level of absorption increases if Fermi level of mode I and mode II shift from 0.4 eV to 1.0 eV. The reason for enhanced absorption is that the contribution of the carrier to plasma oscillation increases with the increase of EF, which leads to the increase of absorption. For both mode I and mode II, the limited electric field for the high Fermi level is stronger than that for the low Fermi level, as shown in Fig. 6(B). A stronger local electric field leads to a higher level of absorption. Fig. 6(C) indicates that the Fermi level can be regarded as a function of the resonance peak wavelength. The
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resonance peak wavelength tends to decrease monotonously with the increase of EF, mode I, and mode II can be concluded from the final results. Therefore, the adjustment of the Fermi level without changing the geometry of the absorber can help to tune the resonance peak wavelengths. The absorption of electrons in graphene is also related to the relaxation time. From Eq. 3, we can get that the changing of Fermi level by electrostatic gating or chemical doping can help to control the relaxation time directly. The changing of environment nearby, for instance, placing organic molecules on graphene, would lead to an increase of carrier mobility [70] as well as relaxation time. Fig. 7(A) illustrates the absorption spectra of different τ. Fig. 7(B) is the function of the resonance peak wavelength and the maximum level of absorption at different relaxation times. In Fig. 7(A) and (B), for mode I and mode II, the absorption maximum increases as the τ increases. Meanwhile, the resonance peak wavelength almost remains at 23 µm (for mode I) and 67 µm (for mode II). The reason why the resonance peak wavelength remains constant is that the excitation wavelength of the magnetic dipole resonance is insensitive to the τ of the nanoring and nanodisk graphene arrays. The physical mechanism can be attributed to the increase of the τ, the contribution of charge carriers plasmonic oscillations increases, resulting in higher absorption. We studied the absorption spectra from the perspectives of different incident angles for TM and TE polarizations, as shown in Fig. 8(A) and (B). For both TM and TE polarizations, as the incidence angle increases, the resonance peak wavelength almost remains at 23 µm (for mode I) and 67 µm (for mode II). The results show that the proposed nanostructure is unrelated to the incidence and polarization angle. In other words, our proposed nanostructures have good angle polarization tolerance. This is due to the high rotational symmetry of the nanoring and nanodisk graphene resonators and strong LSPR. For a single resonance SPR refractive index (RI) sensor, the dynamic range is minimal [71]. In this
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paper, the nanostructure has a two resonance SPR RI sensor. It is generally defined as the sensitivity of each refractive index units (RIU) of the peak (dip) to characterize the performance of the movement amount of the SPR sensor [72]. In Fig. 9, by changing the background index, the absorption spectra of the surface-filled water (n = 1.332) (black) and 25% aqueous glucose solution (n = 1.372) (red) for the nanostructure graphene arrays are simulated to evaluate the sensitivity of our proposed refractive index sensor. When an aqueous solution of glucose instead of water is applied to cover the coating layer, because of the slight increase of the refractive index n, the resonance peak of mode I and mode II can see moving toward longer wavelength. The sensitivities of mode I and mode II are 5.0 µm/RIU and 15.0 µm/RIU, respectively. To better explain our sensing mechanism, we calculated the electric field distributions for water (n = 1.332) and 25% aqueous glucose solution (n = 1.372) at different the absorption peak wavelength (B) λ11 = 24.5 µm, (C) λ12 = 72.2 µm, (D) λ21 = 24.7 µm, (E) λ22 = 72.8 µm. For mode I, the electric field is mainly distributed at the edge of the nanodisk. For mode II, the electric field is mainly distributed at the edge of nanoring. Moreover, we can observe that the electric field intensity at mode II (as shown in Figure 9(C) and (E)) is stronger than that of mode I (as shown in Figure 9(B) and (D)). The results show that mode II is very sensitive to the change of surrounding medium (water (n = 1.332) and 25% aqueous glucose solution (n = 1.372)), which makes the red shift of mode II much larger than that of mode I. In other words, the resonance peak wavelength shift of the mode II (∆λ2) is larger than the mode I (∆λ1). The sensitivity S = m = ∆λ/∆n, where ∆λ is the range of the resonance peak wavelength shift, ∆n is the range of the refractive index of sensing medium. For mode I and mode II, since the ∆λ2 is larger than the ∆λ1, and ∆n = 0.040 is kept constant, so the sensitivity of the mode II is greater than the sensitivity of the mode I.
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We studied the effects of different liquid thicknesses on sensor characteristics, as shown in figure 10. Figure 10(A) and (B) are the absorption spectra of the various water (n = 1.332) thickness and aqueous glucose thickness (n = 1.372). Mode I and II both show that as the liquid thickness increases, the resonance peak wavelength has a slight red shift, while the maximum absorption remains unchanged. Due to the change of the distance between the liquid and graphene, the coupling effect between them is different, resulting in the shift of the resonant peak wavelength. Moreover, the resonance shift of the mode II is larger than that of the mode I. Such as, for the mode II , the resonance peak wavelength shift of 1.3328 µm is obtained by increasing the water (n = 1.332) thickness from 100 nm to 400 nm, while the resonance peak wavelength shift of the mode I is only 0.4005 µm. Similarly, as the aqueous glucose thickness increases from 100 nm to 400 nm, the mode II the resonance peak wavelength shift is more significant than mode I. The resonance peak wavelength shift of the mode I and II is 0.4386 and 1.6176, respectively. 4. Conclusions In summary, we present a dual-band metamaterial absorber for graphene surface plasmon resonance at THz frequency. These simulation results show that the changing of the geometric parameters can help to achieve proposed nanostructure absorption enhancement characteristics. We find the adjustment of the Fermi level of graphene can affect nanostructure absorption peak wavelength, which is flexible and adjustable. As the relaxation time increase, the resonance peak wavelength almost remains at 23 µm (for mode I) and 67 µm (for mode II). For both TM and TE polarizations, the proposed nanostructure is angle-insensitive for the different incident angle. Therefore, the present dual-band absorber may have a great application prospect for sensing and spatial light modulators. Acknowledgements
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The authors are grateful to the support by National Natural Science Foundation of China (No. 51606158, 21671160; 11604311, 61705204, 21506257). Additional information Competing financial interests: The authors declare no competing financial interests. References 1
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Figure captions: Figure 1. (A) The nanostructure schematic diagram of the proposed dual-band absorber consisting of the homocentric graphene ring and disk on top of a Si layer separated by SiO2 substrate. The geometry parameters of the research system: the graphene thickness is 1 nm, the SiO2 thickness is d = 300 nm, the periodic nanostructure graphene arrays with period L = 2.5 µm, the inner and outer radius of the nanoring Rin = 450 nm and Rout = 600 nm, the radius of the nanodisk R = 300 nm. The incident electric field is along the x-axis. (B) Schematic diagram of top gate structure controlling graphene Fermi level. Figure 2. (A) and (C) the absorption spectra of graphene with the different periods (L) and thicknesses of SiO2 (d). (B) and (D) for mode I and mode II, the resonance peak wavelength and absorption maximum at various periods (L) and thicknesses of SiO2 (d). For a clearer view, Fig. 2. (A) and (C) both insert the enlarged absorption spectra of the mode I for the different periods (L) and thicknesses of SiO2 (d). Figure 3. (A)-(D) y-component of the electric field in x-z plane for 25, 75 µm (d = 100 nm) and 23, 66 µm (d = 500 nm) in short wavelength (mode I). (E)-(H) z-component of the electric field distributions (Ez = |E|) for 25, 75 µm (d = 100 nm) and 23, 66 µm (d = 500 nm) in short wavelength (mode I). Figure 4. (A) and (C) the absorption spectra of graphene with the different inner and outer radius of the nanoring Rin and Rout. (B) For mode II, the absorption spectra of graphene with the different inner radius of the nanoring Rin (340 nm to 400 nm). For a clearer view, Fig. 4. (A) and (C) both insert the enlarged absorption spectra of the mode I for different the inner and outer radius of the nanoring Rin and Rout. Figure 5. (A) The absorption spectra of graphene with the different radius of nanodisk R. (B) z-component of the electric field distributions (Ez = |E|) for the propose nanostructure at different the
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absorption peak wavelength (a) λ1 = 65 µm, (b) λ21 = 21 µm, (c) λ22 = 66 µm, (d) λ31 = 25 µm, (e) λ32 = 69 µm, (f) λ4 = 33 µm. Figure 6. (A) The absorption spectra of graphene with the different Fermi level EF. (B) z-component of the electric field distributions (Ez = |E|) at the absorption peak at EF = 0.4 eV and EF = 1.0 eV. (C) The relationship between the wavelength of the resonance absorption peak of mode I and mode II as a function of Fermi level EF. Figure 7. (A) The absorption spectra of graphene with different relaxation times (τ). (B) for mode I and mode II, the resonance peak wavelength and the absorption maximum at various relaxation times (τ). Figure 8. Absorption spectra as a function of the different incident angle for (A) TM and (B) TE polarizations. Figure 9. (A) The absorption spectra of the nanostructure graphene arrays surface filled water (n = 1.332) (black) and 25% aqueous glucose solution (n = 1.372) (red). The insertion curve is an enlarged view of the mode I absorption spectra. (B) - (E) the electric field distributions for water (n = 1.332) and 25% aqueous glucose solution (n = 1.372) at different the absorption peak wavelength (B) λ11 = 24.5 µm, (C) λ12 = 72.2 µm, (D) λ21 = 24.7 µm, (E) λ22 = 72.8 µm. Figure 10. (A) The absorption spectra of the different water thickness when surface filled water (n = 1.332). (B) The absorption spectra of the different aqueous glucose thickness when 25% aqueous glucose solution (n = 1.372). (A) and (B) the insertion curve is an enlarged view of the mode I and II absorption spectra.
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Highlights >The calculations show that by changing the geometric parameters of the proposed nanostructure, can be achieved absorption enhancement. >By changing the Fermi level of graphene, the absorption characteristics can be tuned. >As the relaxation time increases, the absorption maximum also increases, while the resonance peak wavelength remains unchanged. >For TM and TE polarizations, the absorbers are insensitive to the incident angle.
Declaration of Interest Statement
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “A dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency”.
S1386-9477(19)30993-2
DOI:
https://doi.org/10.1016/j.physe.2019.113840
Reference:
PHYSE 113840
To appear in:
Physica E: Low-dimensional Systems and Nanostructures
Received Date: 7 July 2019 Revised Date:
3 November 2019
Accepted Date: 19 November 2019
Please cite this article as: C. Cen, Y. Zhang, X. Chen, H. Yang, Z. Yi, W. Yao, Y. Tang, Y. Yi, J. Wang, P. Wu, A dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency, Physica E: Low-dimensional Systems and Nanostructures (2019), doi: https:// doi.org/10.1016/j.physe.2019.113840. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Graphical abstract We present a dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency. We find the nanostructure absorption peak wavelength is flexible and adjustable by changing the graphene Fermi level EF.
A dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency Chunlian Cen1, 3, Yubin Zhang1,3, Xifang Chen1,3, Hua Yang2, Zao Yi 1,3∗∗, Weitang Yao1,3*, Yongjian Tang3, Yougen Yi4, Junqiao Wang5, Pinghui Wu6 1
Joint Laboratory for Extreme Conditions Matter Properties, Southwest University of Science and Technology, Mianyang 621010, China 2 State Key Laboratory of Advanced Processing and Recycling of Non-ferrous Metals, Lanzhou University of Technology, Lanzhou 730050, China 3
4 5
Sichuan Civil-Military Integration Institute, Mianyang 621010, China
College of Physics and Electronics, Central South University, Changsha 410083, China
School of Physics and Engineering and Key Laboratory of Materials Physics of Ministry of Education of China, Zhengzhou University, Zhengzhou 450001, China
6
Photonic Technology Research & Development Center, Key Laboratory of Information Functional Material for Fujian Higher Education, Quanzhou Normal University, Quanzhou 362000, China
∗ Correspondence should be addressed to Zao Yi, Weitang Yao Tel: 86-0816-2480830; Fax: 86-0816-2480830 E-mail address: [email protected]; [email protected] 1
Abstract: In this paper, we present a dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency. We use the finite difference time domain (FDTD) method to study the absorption characteristics of the homocentric graphene ring and disk nanostructure. These simulation results show that the change of the geometrical parameters and the substrate thickness of the nanostructure can change the absorption characteristics and the emergence of dual-band absorption peaks. Moreover, we study the field distribution of nanodisks with different radius in detail. By changing the Fermi level of graphene, the wavelength of their absorption peaks can be adjusted flexibly. In addition, the proposed dual-band absorber also shows a good angle tolerance for both TE and TM polarizations. By calculation the surface-filled water (n = 1.332) and 25% aqueous glucose solution (n = 1.372) for the metamaterial absorber, the sensitivities of mode I and mode II are 5.0 µm/RIU and 15.0 µm/RIU. These research results will have broad application prospects for sensing and spatial light modulators. Keywords: surface plasmon resonance; metamaterial; graphene; dual-band absorber; FDTD 1. Introduction Terahertz (THz) technology has developed very fast in recent years, in scientific research and practical applications has broad application prospects [1-3]. However, natural materials have no light absorption at THz. There are no effective sources and detectors, efficient manipulation of the THz wave is still a great challenge. Due to the low sensitivity of THz wave detection, its application in THz wave sensors, modulators, detectors and other devices is limited. Many researchers have proposed many THz detection devices, including photon detectors [4] and metamaterials (MMs) [5] absorbers. The perfect MMs absorber was first proposed by Randy et al. [6] and caused great concern for many
2
researchers. THz waves could be detected by MMs through different structures of units, so the MMs absorber promotes further development of the THz detector. However, when the structure is fixed, most MMS absorbers will work at a fixed frequency. This will limit many of its practical applicability. Therefore, the frequency adjustable design of new material system is particularly important. As a two-dimensional structure with honeycomb lattice of carbon atoms, graphene has attracted more and more attention in recent years due to its excellent electrical, mechanical and chemical properties [7-10]. The process of doping or gating can help to adjust the complex surface conductivity of graphene, which is widely used in photodetection, photovoltage and photocatalysis [11-22]. In recent years, in order to improve the absorption level of electromagnetic wave graphene under the broader spectral range comprises gigahertz (GHz), THz, infrared and optical frequencies, many researchers have been made to work [23-30]. Propagating surface plasmon polariton (PSPP) or localized surface plasmon resonance (LSPR) [31-35], guided mode resonance [36-38], Fabry Perot cavity resonance [39-41], interference effect [42], magnetic dipole resonance [43] and other physical mechanisms will enhance the absorption characteristics of graphene. Meanwhile, careful design of various characteristics of graphene electromagnetic wave absorbers, such as tunability, wide angle of incidence and polarization independence [44-47], graphene electromagnetic wave absorber as efficient and effective as possible. Either dual-band or multi-band can be regarded as an important performance indicator for graphene absorbers and people have extensive research in the THz and infrared bands [48-50]. A series of reports have been reported on the work of graphene dual-band absorber at THz wavelength in recent years, and these works are expected to be applied in sensor detection and so on [51-56]. On the basis of these studies, we hope to expand the research on the THz band graphene dual band absorber.
3
Here, we propose a method by FDTD method to improve the dual-band absorption ratio of graphene in THz. The dual-band metamaterial absorber consists of a periodically placed homocentric graphene ring and disk arrays on the surface of a silica layer which is divided by a silicon substrate. The simulation results show the absorber will affect the absorption characteristics by changing the geometry. In the THz range, the resonance wavelength can be flexibly as well, which is adjusted by changes in the Fermi level. As for TM and TE polarizations, the absorber is insensitive to polarization. The surface-filled water (n = 1.332) and 25% aqueous glucose solution (n = 1.372) for the dual-band metamaterial absorber are simulated to evaluate the sensitivity of our proposed refractive index sensor. 2. Structures and methods Fig. 1 is a schematic diagram showing a periodic graphene nanoarrays. The nanoarrays consist of homocentric graphene ring and disk. The graphene arrays are attached to the surface of a silica layer, which is divided by a silicon substrate. The thickness of SiO2 and graphene are d and 1 nm, respectively. The graphene permittivity can be expressed as ε
= iσ g / ωε 0 ∆ + 1, here ∆ is the
thickness of graphene and ε0 represents the vacuum permittivity. Because doped graphene has a mainly real permittivity in the infrared region, just like the dielectric constant of the visible light region metal, it can support strong confinement and long lifetime plasmon resonance for the graphene/dielectric interface. In our calculations, by sequentially reducing the thickness of graphene, we obtained sufficient convergence at a thickness of ∆ = 1 nm. So in the next research work, we set the thickness of graphene to 1 nm. In this nanostructure, the inner radius of the nanoring is Rin, the outer radius of the nanoring is Rout and the radius of the nanodisk is R. In this paper, the reflection, transmission and absorption spectra, as well as the electric field distribution can be calculated by the utilization of the commercial software (Lumerical FDTD Solutions) based on the FDTD method. The accuracy level of
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the mesh in the nanostructures along the x-, y-, and z-axis are set to 20, 20 and 0.2 nm, respectively. The periodic boundary condition of L = 2.5 µm applies to the x as well as y directions and the propagation along the light utilizes the perfectly matched layer in the z-direction [57, 58]. The TM and TE polarizations, which are represented by the x- and y-axis show the direction of the incident electric field. Due to the symmetry of the nanostructure, the polarization direction of the incident TM plane wave is set along the x-axis. In practice, the optimized liquid precursor chemical vapor deposition method can be used to grow large area graphene films, and the graphene film can be determined by Raman measurement. Electron beams lithography is used to make graphene films into nanoring and nanodisk structures, and exposed areas are eroded away by oxygen plasma [35]. In this numerical simulation, an effective surface conductivity model can be utilized to illustrate the graphene. In the random phase approximation, the intraband σintra and interband σinter terms consist of the surface conductivity of graphene [59-62]:
σ g = σ int ra + σ int er =
2e 2 k B T i E e2 1 ln[2 cosh( F )] + [ 2 −1 2 k BT 4h 2 πh ω + iτ
+
1
π
arctan(
(1)
( hω + 2 E F ) 2 hω − 2 E F i )− ln ] 2 k BT 2π (hω − 2 EF ) 2 + 4(k BT ) 2
Here, i, ω, e, ħ, EF, τ, kB and T = 300 K are the imaginary unit, the frequency of the incident light, the electron charge, the reduced Planck’s constants, the Fermi energy, electron-phonon relaxation time, the Boltzmann constant and the temperature, respectively. In the lower THz frequency, when the EF increases to more than half of the photon energy level, due to the Pauli exclusion principle, the contribution of interband process is negligible. Here, we only consider the Fermi level of highly doped graphene, which are E F >> k BT and E F >> hω . Thus, the Eq. 1 can be approximated to the simple Drude-like model [ 55, 59]:
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σg =
e 2 EF i 2 πh (ω + i / τ )
(2)
Here the carrier relaxation time can be expressed as [56]:
τ=
µEF
(3)
evF2
In our calculations, EF = 0.6 eV, the Fermi velocity vF = 106 m/s and the carrier mobility µ = 104 cm-2/(v.s). In addition, the resonance modes supported in the nanoring should satisfy the phase matching equation [63, 64]:
2πReff . Re(neff ) = mλ
(4)
Where Reff, neff, m and λ are the effective radius is determined by (Rin + Rout)/2, the effective refractive indices of the LSPR modes supported by the nanoring, the resonance order and the resonance peak wavelength, respectively. The absorption is expressed as A(λ ) = 1 − R (λ ) − T (λ ) , the value of reflection and transmission can be represented by R(λ) and T(λ). According to Equation (2), we can obtain that the surface conductivity of graphene can be adjusted by controlling its Fermi level. Compared with chemical doping, the electrostatic tunability of graphene is a more suitable way to control the Fermi level of graphene [60, 61]. In the mid-infrared and THz bands, a large number of gate dielectric materials have been developed, such as 2D electron gas, single-layer MoS2, and ion-gel [63-65]. In this case, ion-gel with ultra-high capacitance is currently the most effective medium for realizing high Fermi energy of graphene with low top gate voltage. Good mechanical flexibility, fatigue stability, excellent electrochemical, and thermal stability make it compatible with tunable graphene plasmonic devices on various substrates. Consequently, a schematic diagram of an ion-gel top gate structure for controlling the graphene Fermi level as shown in Figure 1(B). An ion-gel layer is inserted into the graphene and the gold electrode to produce an induced carrier
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concentration and allow access to the THz spectral region. 3. Results and discussions Fig. 2 (A) shows the absorption spectra of graphene arrays with the different periods (L). The absorption maximum of the dual-band absorber changes significantly with the increase of the period, but the wavelength is almost constant. For mode I and mode II, Fig. 2(B) shows that the resonance peak wavelength and absorption maximum at different L. For both mode I and II, we can clearly see the wavelength almost keep in 23 µm and 67 µm, with the L increases. However, the maximum level of absorption decreases as the L increases. As the L increases, the unchanged resonance wavelength is because that the resonance condition remains the same level almost. Since the coupling between the adjacent nanoring and nanodisk, resulting in the resonance peak wavelength changes slightly in a small period. The reduction in the absorption maximum is attributed to a decrease in the filling ratio of graphene. Fig. 2(C) illustrates the relationship of absorption and wavelength with different thicknesses d of SiO2. In Fig. 2(C), the absorption peak wavelength is blue shifted as the SiO2 thickness d increases, for both mode I and mode II. Fig. 2(D) shows that for mode I and mode II, as the thickness of SiO2 experiences a sharp increase, from 100 nm to 500 nm, the absorption peak wavelength decreases. However, for mode I, as the SiO2 thickness d increases, the maximum level of absorption increases from 0.13 to 0.16. Conversely, for mode II, the absorption maximum is reduced from 0.13 to 0.11. For mode I and mode II, as the d increases, the shift of the resonance peak wavelength is related to change from the SP wavevector converter that changes the dielectric environment [66]. As the thickness of d increases, the equivalent refractive index of the silica-silicon composite substrate decreases, so the effective refractive index of the waveguide mode in the graphene nanoring and a nanodisk waveguide decreases. Therefore, according to formula (4), the resonance peak wavelength decreases with the
7
increase of d, that is, the blue shift. Aiming to demonstrate the process of the physical mechanism of the change of absorption maximum better, in Fig. 3(A) and (B), we describe the y-component of the electric field in x-z plane for 25 µm (d = 100 nm) and 23 µm (d = 500 nm) in short wavelength (mode I). We find that the electric field of d = 500 nm is stronger than the electric field of d = 100 nm, resulting in a higher resonance absorption peak at d = 500 nm. In long wavelength (mode II), the electric field at d = 100 nm is stronger than the electric field at d = 500 nm, so the resonance absorption peak at d = 100 nm is higher, as shown in Fig. 3(C) and (D). Figures 3(E)-(G) show the z-component of the E-field distribution (Ez) in short-wave (mode I) and long-wave (mode II) at d = 100 nm and d = 500 nm. In this part, we study the effects of changing geometry parameters on the absorption characteristics. For better data comparison, Fig. 4. (A) inserts the enlarged absorption spectra of the mode I for the different inner radius of nanoring Rin. From Fig. 4(A), when the range of Rin is from 350 nm to 550 nm in intervals of 50 nm, the absorption peak wavelength of mode 1 experienced a blue shift, while that of mode II experienced a red shift. In figure 4(A) and (B), for mode I, the absorption maximum decrease with the Rin increases. The reason is that as the Rin increases, a weakened charge distribution between nanoring and nanodisk, and the coupling between nanoring and nanodisk decreases, lead to reduction of absorption efficiency. In figure 4(B), for mode II, the absorption spectra of graphene with the different inner radius of the nanoring Rin (340 nm to 400 nm). For mode II, however, as Rin increases, the absorption maximum increases first (from 340 nm to 380 nm) and then decreases (from 380 nm to 550 nm). When Rin = 380 nm, the absorption reached a maximum of 13.50%. When Rin < 380 nm, with the increase of Rin, an enhanced charge distribution on the outside of the nanoring and the coupling between nanoring and nanodisk increases, leading to increased absorption. When Rin > 380 nm, this is
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related to the ratio variance of the surface atoms to total atoms of the nanostructure. When the R and Rout is fixed, the ratio decreases sharply while the Rin increases. These free electrons will redistribute on the proposed structure, resulting in the absorption decreases. When Rin > 380 nm, with the increase of Rin, the phenomenon of decreased absorption is similar to that of metallic nanorings [67, 68]. We define the width between the nanorings as W = Rout - Rin. For mode II, when Rin increases and Rout is fixed, W decreases, and the absorption peak wavelength undergoes a red shift, as shown in Fig. 4(B). We also study the absorption spectra with the different outer radius of nanoring Rout, as shown in Fig. 4(C). In the short-wavelength (mode I), as the outer radius of the nanoring Rout increases, the absorption peak wavelength undergoes red shifted. In the long wavelength (mode II), the absorption peak wavelength undergoes blue shifted. While the absorption maximum increases as the Rout increase, for both mode I and mode II. Both of the mode I and mode II, the absorption increases because in the case of other geometrical parameters unchanged, with the increase of the Rout of the graphene arrays filling ratio increases and the interaction with light is thus enhanced, resulting in increased absorption. For mode II, when Rout increases and Rin is fixed, W increases, and the absorption peak wavelength undergoes a blue shift. We can summarize that with the decrease of W, for mode II, the absorption maximum shifted to the direction of long wavelength, namely red shift. Conversely, as W increases, the absorption maximum of mode II shifts to the short wavelength direction, that is, blue shift. The influence of the radius of nanodisk (R) on the absorption spectra is also investigated. As shown in Fig. 5(A), we find that when R changes from 250 nm to 350 nm, the absorption peak wavelength of mode I experiences a red shift and mode II has a blue shifted. However, when the radius of the nanodisk R = 150 nm and R = 450 nm, the proposed nanostructure has only one absorption peak at λ1 = 65 µm and λ4 = 33 µm, respectively. For mode I, as R increases from 250 nm to 350 nm, the absorption
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maximum is also increased. The reason is that with the increase of the R and the graphene arrays filling ratio increase, resulting in increased absorption. But for mode II, as R increases from 150 nm to 350 nm, the absorption maximum is reduced. This is the same physical mechanism as Rin > 380 nm. When the Rin and Rout of the proposed structure is fixed, the ratio decreases sharply while the R increases. These free electrons will redistribute on the proposed structure, resulting in the absorption decreases. The distribution of electric field at the different radius of the nanodisk R, as it can be witnessed in Fig. 5(B). In short wavelength, when R = 250 nm and R = 350 nm, the electric field is mainly distributed at the spacing between the nanodisk and nanoring. In long wavelength, when R = 150 nm and R = 350 nm, the distribution of electric field is mainly at the edge of nanoring. When R = 150 nm, the electric field is primarily distributed on the outside and inside of the nanoring, and there is almost no distribution of the electric field at the edge of the circle, as shown in Fig. 5(a). When R = Rin = 450 nm, the nanostructure is equivalent to a circle, which causes the electric field to be distributed at the edge of a circle, as shown in Fig. 5(f). From Eq. 2, we know that the surface conductivity of graphene is closely related to the Fermi level, which could be regulated by the adjustment of electrostatic and chemical doping [69]. The absorption spectra of different EF values as shown in Fig. 6(A). The resonance peak wavelengths are blue shifted while the maximum level of absorption increases if Fermi level of mode I and mode II shift from 0.4 eV to 1.0 eV. The reason for enhanced absorption is that the contribution of the carrier to plasma oscillation increases with the increase of EF, which leads to the increase of absorption. For both mode I and mode II, the limited electric field for the high Fermi level is stronger than that for the low Fermi level, as shown in Fig. 6(B). A stronger local electric field leads to a higher level of absorption. Fig. 6(C) indicates that the Fermi level can be regarded as a function of the resonance peak wavelength. The
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resonance peak wavelength tends to decrease monotonously with the increase of EF, mode I, and mode II can be concluded from the final results. Therefore, the adjustment of the Fermi level without changing the geometry of the absorber can help to tune the resonance peak wavelengths. The absorption of electrons in graphene is also related to the relaxation time. From Eq. 3, we can get that the changing of Fermi level by electrostatic gating or chemical doping can help to control the relaxation time directly. The changing of environment nearby, for instance, placing organic molecules on graphene, would lead to an increase of carrier mobility [70] as well as relaxation time. Fig. 7(A) illustrates the absorption spectra of different τ. Fig. 7(B) is the function of the resonance peak wavelength and the maximum level of absorption at different relaxation times. In Fig. 7(A) and (B), for mode I and mode II, the absorption maximum increases as the τ increases. Meanwhile, the resonance peak wavelength almost remains at 23 µm (for mode I) and 67 µm (for mode II). The reason why the resonance peak wavelength remains constant is that the excitation wavelength of the magnetic dipole resonance is insensitive to the τ of the nanoring and nanodisk graphene arrays. The physical mechanism can be attributed to the increase of the τ, the contribution of charge carriers plasmonic oscillations increases, resulting in higher absorption. We studied the absorption spectra from the perspectives of different incident angles for TM and TE polarizations, as shown in Fig. 8(A) and (B). For both TM and TE polarizations, as the incidence angle increases, the resonance peak wavelength almost remains at 23 µm (for mode I) and 67 µm (for mode II). The results show that the proposed nanostructure is unrelated to the incidence and polarization angle. In other words, our proposed nanostructures have good angle polarization tolerance. This is due to the high rotational symmetry of the nanoring and nanodisk graphene resonators and strong LSPR. For a single resonance SPR refractive index (RI) sensor, the dynamic range is minimal [71]. In this
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paper, the nanostructure has a two resonance SPR RI sensor. It is generally defined as the sensitivity of each refractive index units (RIU) of the peak (dip) to characterize the performance of the movement amount of the SPR sensor [72]. In Fig. 9, by changing the background index, the absorption spectra of the surface-filled water (n = 1.332) (black) and 25% aqueous glucose solution (n = 1.372) (red) for the nanostructure graphene arrays are simulated to evaluate the sensitivity of our proposed refractive index sensor. When an aqueous solution of glucose instead of water is applied to cover the coating layer, because of the slight increase of the refractive index n, the resonance peak of mode I and mode II can see moving toward longer wavelength. The sensitivities of mode I and mode II are 5.0 µm/RIU and 15.0 µm/RIU, respectively. To better explain our sensing mechanism, we calculated the electric field distributions for water (n = 1.332) and 25% aqueous glucose solution (n = 1.372) at different the absorption peak wavelength (B) λ11 = 24.5 µm, (C) λ12 = 72.2 µm, (D) λ21 = 24.7 µm, (E) λ22 = 72.8 µm. For mode I, the electric field is mainly distributed at the edge of the nanodisk. For mode II, the electric field is mainly distributed at the edge of nanoring. Moreover, we can observe that the electric field intensity at mode II (as shown in Figure 9(C) and (E)) is stronger than that of mode I (as shown in Figure 9(B) and (D)). The results show that mode II is very sensitive to the change of surrounding medium (water (n = 1.332) and 25% aqueous glucose solution (n = 1.372)), which makes the red shift of mode II much larger than that of mode I. In other words, the resonance peak wavelength shift of the mode II (∆λ2) is larger than the mode I (∆λ1). The sensitivity S = m = ∆λ/∆n, where ∆λ is the range of the resonance peak wavelength shift, ∆n is the range of the refractive index of sensing medium. For mode I and mode II, since the ∆λ2 is larger than the ∆λ1, and ∆n = 0.040 is kept constant, so the sensitivity of the mode II is greater than the sensitivity of the mode I.
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We studied the effects of different liquid thicknesses on sensor characteristics, as shown in figure 10. Figure 10(A) and (B) are the absorption spectra of the various water (n = 1.332) thickness and aqueous glucose thickness (n = 1.372). Mode I and II both show that as the liquid thickness increases, the resonance peak wavelength has a slight red shift, while the maximum absorption remains unchanged. Due to the change of the distance between the liquid and graphene, the coupling effect between them is different, resulting in the shift of the resonant peak wavelength. Moreover, the resonance shift of the mode II is larger than that of the mode I. Such as, for the mode II , the resonance peak wavelength shift of 1.3328 µm is obtained by increasing the water (n = 1.332) thickness from 100 nm to 400 nm, while the resonance peak wavelength shift of the mode I is only 0.4005 µm. Similarly, as the aqueous glucose thickness increases from 100 nm to 400 nm, the mode II the resonance peak wavelength shift is more significant than mode I. The resonance peak wavelength shift of the mode I and II is 0.4386 and 1.6176, respectively. 4. Conclusions In summary, we present a dual-band metamaterial absorber for graphene surface plasmon resonance at THz frequency. These simulation results show that the changing of the geometric parameters can help to achieve proposed nanostructure absorption enhancement characteristics. We find the adjustment of the Fermi level of graphene can affect nanostructure absorption peak wavelength, which is flexible and adjustable. As the relaxation time increase, the resonance peak wavelength almost remains at 23 µm (for mode I) and 67 µm (for mode II). For both TM and TE polarizations, the proposed nanostructure is angle-insensitive for the different incident angle. Therefore, the present dual-band absorber may have a great application prospect for sensing and spatial light modulators. Acknowledgements
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The authors are grateful to the support by National Natural Science Foundation of China (No. 51606158, 21671160; 11604311, 61705204, 21506257). Additional information Competing financial interests: The authors declare no competing financial interests. References 1
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Figure captions: Figure 1. (A) The nanostructure schematic diagram of the proposed dual-band absorber consisting of the homocentric graphene ring and disk on top of a Si layer separated by SiO2 substrate. The geometry parameters of the research system: the graphene thickness is 1 nm, the SiO2 thickness is d = 300 nm, the periodic nanostructure graphene arrays with period L = 2.5 µm, the inner and outer radius of the nanoring Rin = 450 nm and Rout = 600 nm, the radius of the nanodisk R = 300 nm. The incident electric field is along the x-axis. (B) Schematic diagram of top gate structure controlling graphene Fermi level. Figure 2. (A) and (C) the absorption spectra of graphene with the different periods (L) and thicknesses of SiO2 (d). (B) and (D) for mode I and mode II, the resonance peak wavelength and absorption maximum at various periods (L) and thicknesses of SiO2 (d). For a clearer view, Fig. 2. (A) and (C) both insert the enlarged absorption spectra of the mode I for the different periods (L) and thicknesses of SiO2 (d). Figure 3. (A)-(D) y-component of the electric field in x-z plane for 25, 75 µm (d = 100 nm) and 23, 66 µm (d = 500 nm) in short wavelength (mode I). (E)-(H) z-component of the electric field distributions (Ez = |E|) for 25, 75 µm (d = 100 nm) and 23, 66 µm (d = 500 nm) in short wavelength (mode I). Figure 4. (A) and (C) the absorption spectra of graphene with the different inner and outer radius of the nanoring Rin and Rout. (B) For mode II, the absorption spectra of graphene with the different inner radius of the nanoring Rin (340 nm to 400 nm). For a clearer view, Fig. 4. (A) and (C) both insert the enlarged absorption spectra of the mode I for different the inner and outer radius of the nanoring Rin and Rout. Figure 5. (A) The absorption spectra of graphene with the different radius of nanodisk R. (B) z-component of the electric field distributions (Ez = |E|) for the propose nanostructure at different the
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absorption peak wavelength (a) λ1 = 65 µm, (b) λ21 = 21 µm, (c) λ22 = 66 µm, (d) λ31 = 25 µm, (e) λ32 = 69 µm, (f) λ4 = 33 µm. Figure 6. (A) The absorption spectra of graphene with the different Fermi level EF. (B) z-component of the electric field distributions (Ez = |E|) at the absorption peak at EF = 0.4 eV and EF = 1.0 eV. (C) The relationship between the wavelength of the resonance absorption peak of mode I and mode II as a function of Fermi level EF. Figure 7. (A) The absorption spectra of graphene with different relaxation times (τ). (B) for mode I and mode II, the resonance peak wavelength and the absorption maximum at various relaxation times (τ). Figure 8. Absorption spectra as a function of the different incident angle for (A) TM and (B) TE polarizations. Figure 9. (A) The absorption spectra of the nanostructure graphene arrays surface filled water (n = 1.332) (black) and 25% aqueous glucose solution (n = 1.372) (red). The insertion curve is an enlarged view of the mode I absorption spectra. (B) - (E) the electric field distributions for water (n = 1.332) and 25% aqueous glucose solution (n = 1.372) at different the absorption peak wavelength (B) λ11 = 24.5 µm, (C) λ12 = 72.2 µm, (D) λ21 = 24.7 µm, (E) λ22 = 72.8 µm. Figure 10. (A) The absorption spectra of the different water thickness when surface filled water (n = 1.332). (B) The absorption spectra of the different aqueous glucose thickness when 25% aqueous glucose solution (n = 1.372). (A) and (B) the insertion curve is an enlarged view of the mode I and II absorption spectra.
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Highlights >The calculations show that by changing the geometric parameters of the proposed nanostructure, can be achieved absorption enhancement. >By changing the Fermi level of graphene, the absorption characteristics can be tuned. >As the relaxation time increases, the absorption maximum also increases, while the resonance peak wavelength remains unchanged. >For TM and TE polarizations, the absorbers are insensitive to the incident angle.
Declaration of Interest Statement
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “A dual-band metamaterial absorber for graphene surface plasmon resonance at terahertz frequency”.