High-sensitivity refractive index sensors using coherent perfect


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High-sensitivity refractive index sensors using coherent perfect absorption on graphene in the Vis-NIR region Chawei Li, Jinlin Qiu, Jun-Yu Ou, Qing Huo Liu, and Jinfeng Zhu ACS Appl. Nano Mater., Just Accepted Manuscript • DOI: 10.1021/acsanm.9b00523 • Publication Date (Web): 29 Apr 2019 Downloaded from http://pubs.acs.org on April 30, 2019

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High-sensitivity refractive index sensors using coherent perfect absorption on graphene in the VisNIR region Chawei Li1,2, Jinlin Qiu1, Jun-Yu Ou3, Qing Huo Liu4 and Jinfeng Zhu1,2* 1School

of Electronic Science and Engineering, Xiamen University, Xiamen 361005, China

2Shenzhen

Research Institute of Xiamen University, Shenzhen 518057, China

3Optoelectronics

Research Centre and Centre for Photonic Metamaterials, University of

Southampton, Highfield, Southampton, SO17 1BJ, UK 4Department

of Electrical and Computer Engineering, Duke University, Durham, North

Carolina 27708, USA

KEYWORDS: graphene, nanophotonics, refractive index sensing, coherent perfect absorption, plasmonics, metamaterial

ABSTRACT: Plasmonic structures with sophisticated nanofabrication have revolutionized the ability to trap light on the nanoscale and enable high-sensitivity refractive index sensing. Previous theoretical research has indicated that the sensitivity and figure of merit around the wavelength of

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1μm for a plasmonic sensing system can be up to 13,000 nm/RIU and 138, respectively. In order to improve the sensing performance, we propose a graphene-based non-plasmonic sensor with the sensitivity over 440,000nm/RIU at the wavelength of 1μm, which is 33 times more than the theoretical result of plasmonic sensors. Our graphene sensor is a nanofabrication-free design with perfect light confinement within a monolayer of graphene. Meanwhile, its figure of merit is up to the scale of thousands, which is also much higher than plasmonic sensors. Our scheme uses a simple dielectric structure with a monolayer of graphene and shows a great potential for low-cost sensing with high performance.

1. INTRODUCTION Optical refractive index sensors with high sensitivity are widely used in the fields of chemistry, biology, medicine and material engineering, and they have attracted a plenty of attention in the nanotechnology community. In the past decade, optical sensors using various plasmonic nanostructures have been extensively studied due to their high sensitivity.1-3 The basic mechanism of plasmonic sensing is to excite charge density oscillations propagating along the dielectric/metal interface.4 The spectral response related to these oscillations is sensitive to the environmental refractive index, so that plasmonic sensors can detect a very tiny variation of the refractive index. Theoretical research on a plasmonic sensing system has demonstrated the sensitivity and figure of merit (at the wavelength of 1μm) up to 13,000 nm/RIU and 138, respectively.5 With the aim to improve the performance of plasmonic sensing systems, the scheme based on metamaterials has

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been adopted with the development of micro- and nano-fabrication in nanophotonics. A. V. Kabashin et al. has used plasmonic nanorod metamaterials for a high sensitivity over 30,000nm/RIU and a FOM up to 330 at the wavelength of 1.28μm.6 K. V. Sreekanth et al has reported a plasmonic sensing platform based on hyperbolic metamaterials, which has the sensitivity and FOM up to 30,000nm/RIU and 590 around the wavelength of 1.3μm, respectively.7 Even though the use of metamaterial concept has efficiently elevated the sensitivity and FOM of plasmonic sensors, their preparation often requires a sophisticated and expensive micro- or nanofabrication. In addition, other non-plasmonic structures have also been investigated to improve the sensing performance, like slot waveguide ring resonators, photonic crystal cavities and slabs.8-10 These systems have obviously increased the FOM or quality factor, but they hardly obtain higher sensitivity than the plasmonic systems. Therefore, high performance optical sensors with a simple structure and a lower cost are still quite in demand. Recently, 2D materials have become an important role for developing future optical devices due to their unique light-matter interaction.11,12 As the most popular 2D material, graphene has attracted a lot of optical investigations from ultraviolet (UV) to terahertz.13-16 A promising optical property of graphene is that it can support surface plasmon polaritons (SPP) and near-field enhancement for the spectral range from mid-infrared to terahertz, which enable graphene to replace metals in plasmonic applications.17-20 The mid-infrared spectra for graphene are well suited for optical sensing because they reflect many molecular fingerprints which can identify different biochemical building blocks of life, such as proteins, lipids, and DNA,21 and there have been plentiful efforts made by using graphene plasmonic effects to realize various sensing applications in mid-infrared range.22-24 However, in the range from the visible to near infrared (NIR), intrinsic graphene is unable to support plasmonic effects, and it can be regarded as a lossy conductive

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surface.25 In this condition, utilizing plasmonic effects of graphene for high performance optical sensing is no longer feasible for the visible and NIR region, in which the optical detecting configurations are usually simpler and much more economical than in the mid-infrared range. Therefore, in order to realize graphene-based optical sensing with high performance in the visible and NIR region, an innovative design based on nanophotonics of 2D materials has become a quite important research topic. In this work, a simple all-dielectric photonic structure for high performance optical sensing has been proposed, in which graphene is sandwiched between a lossless dielectric and a liquid sample. By utilizing optical total reflection and single-channel coherent perfect absorption, the use of metallic materials is not necessary and the complicated nanofabrication is also avoided. By a series of systematic design and optimization, we have achieved multiple extremely sensitive coherence modes with a maximum sensitivity of 440,000nm/RIU around the wavelength of 1μm and a maximum FOM up to the scale of thousands, which indicate that the proposed optical sensor is more advanced and promising than conventional plasmonic sensors due to its nanofabrication-free configuration and ultra-sensitive performance. 1. METHODOLOGY In this study, we propose an ultra-sensitive refractive index sensor with a coating of monolayer graphene. The proposed configuration consists of a lossless dielectric hemispherical prism, a liquid sample layer, and a graphene layer sandwiched between them. The liquid sample is injected through a microfluidic channel and confined in a circular container, as shown in Figure 1. The sample liquid is exposed to the air. The refractive index of the air, prism and sample liquid are nair, n1 and n2, respectively. The light beam obliquely illuminates from the prism to the central region of the prism/graphene interface at an incident angle θ1. Based on our previous work,26 when the

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conditions of nairarcsin(nair/n1) are satisfied, the total optical reflection will happen and block the transmission.

Figure 1. Schematic drawing of the graphene-based sensing system. For the optical structure with multiple layers, the reflectance can be calculated by the method of characteristic matrix.27 The electric and magnetic fields in the first layer (prism layer) can be determined as below,

éE1 ù ê ú= êH1 ú ë û

L- 1

ÕM k= 2

k

éEL ù ê ú= êH L ú ë û

é cos bk Mk = ê êjhk sin bk ë

ém11 ê êm21 ë

m12 ùéEL ù úê ú, ê ú m22 ú ûëH L û

( j sin bk )/hk ù ú cos bk ú û

(1)

where βk and ηk are the phase factor and tilted admittance in the kth layer, respectively. The phase factor can be expressed as βk=2πNkdkcosθk/λ, where Nk, dk and θk represent the complex refractive index of material, thickness and light angle in the kth layer. EL and HL denote the electric field and magnetic field in the last layer (air).The tilted admittance relies on the light polarization, and it can be expressed as below,

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 yk cos k TE wave 

k  

 yk cos k TM wave 

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(2)

where yk=Nkyair denotes the admittance in the kth layer and yair represents the admittance in the air. Equation (1) can be normalized through dividing by EL as shown below,

éE1 EL ù éB ù ém11 ê ú= ê ú= ê êH1 EL ú ê û ê ë û ëC ú ëm21

m12 ùé1 ù úê ú ê ú m22 ú ûëhL û

(3)

The effective admittance for the assembly of layers except the first layer can be defined as below,

Y=

H1 C m21 + m22hL = = E1 B m11 + m12hL

(4)

The multilayer system can be simplified into a simple interface between two media with the tilted admittance η1 for the first layer (prism) and the effective admittance Y for the assembly of layers except the first layer, respectively. The reflection coefficient can be expressed as below,

r=

h1 - Y h1 + Y

(5)

and the reflectance of the system can be expressed as below,

R= rr*

(6)

On the condition of total reflection at the sample/air interface, the absorbance in graphene can be calculated by A=1-R. As observed from Equation (5) and Equation (6), if η1 equals to Y, the reflectance is zero leading to the perfect absorbance A=100%. In the optical study, graphene can be regarded as a 2D conductive surface. We use a scheme in combination with the Fano model and Kubo formalism to describe the optical conductivity of graphene in the visible and NIR range, which can be expressed as below,

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 Fano   =

 CB        1 hc /   Er , = 1  2 Γr / 2 2

(7)

 Kubo   , c , , T    int ra   int er  intra 

  f   ,  , T  f   , c , T   je 2 c  d  d d 2  0 2 h  c  j     

 inter  

2 je2  c  j   f d   , c , T   f d  , c , T  0 4  c  j 2 /  2  4  h2 d  h2



f d   ,  c , T   e

   c  k BT



1

1

(8)

In Equation (7), σCB(λ) denotes the continuum background for the Fano model, Гr=0.78eV is the energy width, Er=5.02eV is the resonance energy of the perturbed exciton, and ɛ represents the normalized energy.28 In Equation (8), the optical conductivity includes the contributions from the interband transition σinter and intraband transition σintra based on the Kubo formalism; ħ, T and e denote the reduced Plank constant, Kelvin temperature and electron charge, respectively; μc, kB and ξ represent the chemical potential, Boltzmann constant and electron energy, respectively; Γ denotes the scattering rate and fd is the Fermi-Dirac distribution function.29,30 We also assume the monolayer graphene as lossy dielectric material with a thickness of 0.35nm.31 Since the thickness of monolayer graphene is extremely small compared with that of the liquid sample layer, its influence on the phase change of propagating light wave can be neglected for further discussion. Therefore, we mainly focus on investigating the phase factor of sample layer β2=2πn2d2cosθ2/λ, which depends on the light angle in layer 2, applied wavelength, refractive index and thickness of the liquid sample layer. In the proposed structure, we get the use of single-channel coherent perfect absorption in graphene at a critical incident angle for high performance sensing.32-36 The optical absorbance of graphene depends on the dispersive optical conductivity σ(λ) and the in-plane electric field component Ei(λ) on the graphene surface, which can be expressed as below,

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A(  ) 

 ( ) 2

Ei (  )

2

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(9)

as demonstrated by Equation (9), the TM light wave does not support the perfect absorption because its in-plane electric field amplitude reduces with the increased θ1. In contrast, the TE light wave always keeps the maximum electric field amplitude in the graphene surface for the possibility of perfect light absorption. Hence, the TE light wave is adopted for the next sensing study. The characteristic matrix method is used to optimize the performance of graphene-based optical sensors. Additionally, we use a commercial numerical software (Comsol Multiphysics 5.3a) for full wave simulation and validation.37,38 2. RESULTS AND DISCUSSION On the condition of perfect absorption, the tilted admittance in the first layer almost perfectly matches with the effective admittance of the assembled layers according to Equation (5). The lightgraphene interaction is maximized at a coherent wavelength and a critical angle, which corresponds to the condition where the complete round-trip phase accumulation within the sample layer is some multiple of 2π.39 The phase condition to achieve zero-reflectance (i.e. unity absorbance in graphene) can be written as below,

2b2 - f half = 2mp (m = 0,1,2K ) where

(10)

f half denotes the phase shift due to the half-wave loss at the prism/graphene interface, m

represents the order of coherence. The phase factor in the sample layer can be calculated as β2=(2m+1)π/2, in which m determines the coherence order for perfect absorption. Such lightmatter interaction perfectly traps the optical energy in a monolayer of graphene, which originates from the optical phase manipulation by a single channel. This mechanism is entirely different from

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the near field effects of plasmonic sensing, in which the electromagnetic decay length is usually utilized. We next investigate the parameter conditions for n1, n2 and d2 to obtain a considerable value of optical sensitivity. Based on Snell's law and the phase factor β2=2πn2d2cosθ2/λ, we can calculate the wavelength shift Δλ of perfect absorption induced by Δn (the refractive index change of the sample) for the fixed values of θ1 and d2, and furthermore, we can deduce the sensitivity formula as below, Dl =

S= =

2pd 2

b2

( (n + D n) - n sin q 2

Dl 2p d 2 = D n b 2D n 2p d 2

b2

2 1

2

n22 - n12 sin 2 q1

2

1

( (n + D n) - n sin q 2

2

2 1

2

1

)

(11)

)

(12)

n22 - n12 sin 2 q1

f (n1 , n2 , D n, q1 )

(

d 2 =b2l / 2p n22 - n12 sin 2 q1

)

(13)

where the sensitivity S is a function of d2, β2, n1, n2, Δn and θ1. When the coherent perfect absorption happens, the zero reflectance can be achieved in detection measurement, and the conditions for β2=(2m+1)π/2 and a specific critical angle θ1 should be satisfied. The function f (n1, n2, Δn, θ1) is determined by θ1 when other parameters are fixed. We change θ1 from 0° to 89°and find f (n1, n2, Δn, θ1) is also increasing with θ1, as observed in Fig. S1 of the supplementary material. So θ1=89° is used in the following discussion. As shown in Figure 2, we fix n2=1.405, Δn=0.001 and θ1=89° for the testing wavelength around 1μm, and evaluate the conditions of n1 and d2 for high sensitivity. Figure 2(a) indicates that d2 and f are the two monotone increasing functions of n1, which are also two multiplier factors to influence the sensitivity S. As observed in Figure 2(b), both the thickness and sensitivity increase slowly as the value of n1 gradually changes from 1.1 to 1.35, but the increment becomes exceptionally striking as n1 gets close to the value of

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n2. As the value of n1 approaches the value of n2, the sensitivity increases dramatically. When n1 is 1.4, the sensitivity is over 100,000nm/RIU. The high sensitivity from 1.35 to 1.4 corresponds to the high function values of d2 and f as shown in Figure 2(a). When n1 is gradually approaching n2, both of d2 and f(n1, n2, Δn, θ1) increase, and the increment becomes extremely significant as n1 gets close to n2. Therefore, when the values of n1 and n2 are close, the sensitivity will increase dramatically. In view of this, n1=1.404 (e.g. PDMS) will be utilized for the next discussion. In fact, PDMS has an extremely small imaginary part of the refractive index (<0.00001 normally), so the influence of realistic material damping on sensing performance can be neglected, as shown in Fig. S2.

Figure 2. (a) The sample thickness d2 and f(n1, n2, Δn, θ1) as functions of n1 regardless of the use of monolayer graphene. (b) The sample thickness d2 and sensitivity S as functions of n1 in view of the use of monolayer graphene. For both cases, β2, n2, Δn, θ1 and λ are π/2, 1.405, 0.001, 89° and 1μm, respectively. We next investigate the graphene-coated photonic structure for further optical sensing applications. As observed in Figure 3(a) and Figure 3(b), the sensing performance for θ1=89° and d2=4.2μm is calculated by both the analytical method and numerical simulation, and they show prominent consistency, which validates the accuracy and reliability for our next discussion. By

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gradually increasing n2 from 1.405 to 1.4054, the coherent wavelength for zero reflectance (i.e. unity absorbance) shows a remarkable red shift from 995nm to 1160nm. Therefore, the deduced sensitivity S is 440,000nm/RIU, which is an exceptional high value compared with many other sensing methods. The zero reflectance is attributed to the single-channel coherent perfect absorption at a critical incident angle.26 Such perfect absorption can be further revealed by comparing the electric field intensities. As observed in Figure 3(c), the amplitude of electric field at λ=1000nm is maximized because the condition for Equation (10) is satisfied for m=0, and this leads to the perfect absorption (i.e. zero reflection). In contrast, the amplitude of electric field at λ=500nm is minimized to zero owing to the π phase difference of coherent light waves on graphene, which results in perfect reflection (i.e. zero absorption). The electric field distributions also illuminate that the perfect light absorption results from the electric field enhancement on the graphene surface, according to Equation (9). We also calculate the figure of merit (FOM) for this sensing structure as expressed below,40

FOM =

S Gm

(14)

where Гm denotes the resonance bandwidth (around the wavelength of the mth order coherent perfect absorption) for the reflectance values below the average of the maximum and minimum reflectance ratios in the spectrum. As observed in Figure 3(d) for the first coherence order (m=0), when the sample refractive index n2 increases from 1.4051 to 1.4054, the FOM slightly changes from 390 to 366, and the sensitivity is higher than 412,500nm/RIU and also slightly changed. For m=0, the sensitivity is extremely high, but the FOM is still relatively low due to a large value of the corresponding absorption bandwidth. As we increase n2 from 1.405 to 1.41, we find that there are other different perfect absorption bands due to the coherence of higher orders and their

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bandwidth is much smaller than the low order coherence, as shown in Figure 3(e). This implies that one can improve the FOM by using the high order coherence.

Figure 3. Sensing performance of the proposed graphene-based structure calculated by (a) the method of characteristic matrix and (b) the FEM simulation, where n1=1.404, d2=4.2μm and θ1=89°. (c) Corresponding electric field distributions, where for n2=1.405. (d) Sensitivity and FOM (m=0) as functions of n2. (e) Reflectance as a function of n2 and λ. In order to reduce the absorption bandwidth for an enhanced FOM, we can introduce the high order coherent perfect absorption by increasing d2 based on Equation (10) and (13). As shown in Figure 4(a), by increasing d2 to 12.8μm, we find three kinds of reflectance dips in the visible and NIR range, which originate from three types of high order coherence (m equals to 1, 2 and 3, respectively). All these three coherences have a much narrower bandwidth compared with the zero order coherence shown in Figure 3(a) and (b). As n2 increase from 1.405 to 1.4051, there is an obvious red shift for the three absorption bands, which implies that one can obtain a high sensitivity

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in the broadband range from visible to NIR. Moreover, the sensitivity and FOM for different coherence orders are calculated and plotted in Figure 4(b). For the coherence orders from 1 to 3, the sensitivities reach 420,000nm/RIU, 250,000nm/RIU and 170,000nm/RIU, respectively; meanwhile, the FOM values are 1372, 2193 and 2787, respectively. These results illuminate that the FOM can be significantly improved by using the coherent absorption with a higher order, while the sensitivity can be kept at a very high value. For the fixed sample thickness, one can get a higher FOM by partially sacrificing the sensitivity level, and there can be a trade-off between these two parameters of sensing performance. With the purpose of achieving high sensing performance around λ=1μm, we can assume increase β2 for a high order coherence with a high FOM while keeping the high value of sensitivity. Based on Equation (12) and (13), when n1, n2, Δn, θ1 and λ are fixed, the sensitivity is determined by d2/β2 and β2 is proportional to d2. In practice, we can increase d2 for a high FOM as well as a high sensitivity, as shown in Figure 4(c). Along with the sample thickness increasing from 4.2μm to 64μm, the sensitivity value slightly changes above 410,000nm/RIU, but the FOM is significantly improved from 390 to 6833.

Figure 4. (a) Reflectance ratio as a function of λ and n2, where n1=1.404, d2=12.8μm and θ1=89°. (b) The sensitivity and FOM for different orders of coherent absorption. (c) The sensitivity and FOM as functions of d2, where the absorption wavelengths of different coherence orders for sensing are fixed around λ=1μm.

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Finally, we discuss the influence of incident angle on the sensitivity of the proposed structure. One might argue that the incident angle of 89° for coherent perfect absorption might be too large in practical sensing applications for optical engineering. In view of this, we investigate the use of a smaller incident angle, as can be seen in Figure 5(a). When the incident angle is reduced to 86°, the wavelength of coherent absorption (i.e. minimum reflection) for the first order (m=1) shows an obvious red shift from 1000nm to 1938nm, and the reflectance around λ=1938nm is not 0 but 40.2%. This is because the coherent wavelength λ= 2πn2d2cosθ2/β2 can be determined by the light angle θ2, when other parameters are fixed. When the incident angle θ1 declines from 89° to 86°, θ2 also decreases and leads to a red shift of the coherent wavelength. Furthermore, the sensitivity for the first order coherent absorption is decreased from 420,000nm/RIU to 230,000nm/RIU, and this can be explained by Equation (12). As shown in Equation (12) and Fig. S1, f(n1, n2, Δn, θ1) is the monotone increasing function of θ1. Decreasing θ1 from 89° to 86° partially reduces the sensitivity. Figure 5(b) provides the electric field distributions of these two incident angles for the first order coherent absorption. The use of θ1=86° partially deviates from the perfect match condition shown in Equation (5), and results in the reduction of electric field on graphene and less optical loss for the entire sensing structure. Despite of this, the sensitivity of 230,000 nm/RIU for θ1=86° in the NIR range is still much higher than conventional optical sensors, which indicates the feasibility of our sensing scheme in practical applications. At last, a comparison of the performance between the proposed sensor and some other recently reported sensors is summarized in Table 1. As observed in Table 1, both of the sensitivity and FOM of our proposed sensing structure have been improved dramatically compared with previous sensing research based on plasmonics, metamaterials and other optical schemes, which indicates that our design is very promising for ultrahigh sensing performance.

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Figure 5. (a) Reflectance ratio as a function of λ, n2 and θ1, where n1=1.404 and d2=12.8μm. (b) Corresponding electric field distributions for coherent absorption (m=1) in graphene, where n2 is 1.405.

Table 1. Performance comparisons between recent reported optical sensors and our work Methods and

Sensitivity

FOM

Central λ (μm)

References

(nm/RIU)

plasmonics 5

~13000

138

1

metamaterial 6

~30000

330

1.28

metamaterial 7

~30000

590

1.3

graphene 24

2500

10.7

7.3

plasmonics 40

1010

108

0.9

graphene 41

7023

196

1.55

plasmonics 42

559

38

0.9

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This work

440000

6833

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1

3. CONCLUSION In this study, a graphene-based all-dielectric photonic structure has been proposed to realize ultrahigh sensitivity optical sensing. This structure prevents the use from metallic materials and facilitates low-cost fabrication. By a systematic theoretical study, the sensitivity as high as 440,000nm/RIU is achieved using the single-channel coherent perfect absorption. In addition, the FOM is also dramatically enhanced compared with plasmonic sensors. By adopting graphene, we demonstrate the unprecedented potential of sensing performance based on 2D materials. Our method is promising for future high performance refractive index sensing, and explores a new solution for realizing various optical sensors using graphene and other 2D materials.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

ACKNOWLEDGMENTS This work was supported by NSAF (Grant No. U1830116), Natural Science Foundation of Guangdong Province (Grant No. 2018A030313299), Fujian Provincial Department of Science and Technology (Grant No. 2017J01123), Shenzhen Science and Technology Innovation Commision

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(Grant No. JCYJ20170306141755150), and the fund of Key Laboratory of THz Technology, Ministry of Education, China.

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