Giant Goos-Hänchen Shifts in Au-ITO-TMDCs-Graphene Heterostructure and Its Potential for High Performance Sensor

In order to improve the performance of surface plasmon resonance (SPR) biosensor, the structure based on two-dimensional (2D) of graphene and transition metal dichalcogenides (TMDCs) are proposed to greatly enhance the Goos-Hänchen (GH) shift. It is theoretically proved that GH shift can be significantly enhanced in SPR structure coated with gold (Au)-indium tin oxide (ITO)-TMDCs-graphene heterostructure. In order to realize high GH shifts, the number of TMDCs and graphene layer are optimized. The highest GH shift (−801.7 λ) is obtained by Au-ITO-MoSe2-graphene hybrid structure with MoSe2 monolayer and graphene bilayer, respectively. By analyzing the GH variation, the index sensitivity of such configuration can reach as high as 8.02 × 105 λ/RIU, which is 293.24 times of the Au-ITO structure and 177.43 times of the Au-ITO-graphene structure. The proposed SPR biosensor can be widely used in the precision metrology and optical sensing.


Introduction
Surface plasmon resonance (SPR) is a kind of highly sensitive real-time spectral phenomenon, which can be used to measure the refractive index change on the surface of the metal film [1]. The optical biosensor based on SPR technology has many advantages, such as high sensitivity, real-time monitoring of the dynamic process of the reaction, label the biological sample, and no background interference [2][3][4].
In the past few years, SPR-based biosensors have developed rapidly in environmental monitoring, medical diagnosis, food safety detection, and so on [5][6][7]. Many researchers use new materials [8,9] and optimized structures [10,11] to improve the performance of SPR biosensors.
As we know, when total reflection occurs at the interface of two kinds of media, a small lateral displacement occurs between the incident light and the reflected light, which is called the Goos-Hänchen (GH) shift [12,13]. Artmann gives a theoretical explanation of the effect of GH shift based on the stationary phase method [14]. In the past year, GH shift has applied to optical measurement [15], chemical sensors [16], and other important fields [17]. Researchers are using various methods to enhance GH shift, one of which is to excite surface plasmon polaritons (SPPs). SPPs are a special physical phenomenon, which occurs in the coupling of electromagnetic wave and charge excitation at Sensors 2020, 20, 1028 3 of 14 refractive index [44]. The Au thin film coated BK7 glass slide is attached to the base of an equilateral prism made of high refractive index glass through index matching fluid [45].
For the first layer, the SF11 glass with refractive index is obtained as following relation [45]: where λ is the wavelength of incident light in um. The second layer is BK7 glass with the refractive index as following [45]: According to the Drude-Lorentz mode, the third layer is the Au film with refractive index as following [46]: The fourth layer is the ITO film with refractive index as [29]: The fifth layer of TMDCs with the refractive index and thickness of monolayer at λ = 632.8 nm is shown in Table 1 [47,48]. In the sixth layer, the refractive index of graphene at visible range is obtained by the relation [49]: where the constant C 1 ≈ 5.446 µm −1 . The thickness of monolayer of graphene is 0.34 nm. For the last layer, the sensing medium is water. In the λ = 632.8 nm, the refractive indices are n 1 = 1.7786, n 2 = 1.5151, n 3 = 0.181 + 3.068i, n 4 = 1.858 + 0.058i, n 6 = 3.000 + 1.149i, n 7 = 1.330 [50], respectively. The change of the refractive index of the sensing medium caused by the adsorption of biomolecules on the surface of graphene is characterized by n bio . The dielectric constant of each layer is set to ε k (k = 1,2,...,7). The thickness (d k ) of SF11 glass, BK7 glass, and sensing medium are d 1 = 200 nm, d 2 = 100 nm, and d 7 =100 nm, respectively. For this SPR biosensor, we use the thickness of Au (d 3 ) 50 nm and ITO (d 4 ) 10 nm to excite the SPR. It is reasonable to take the individual graphene sheet as a non-interacting monolayer if the number of layers N ≤ 5 [51]. Therefore, in this article, we discuss graphene layers and TMDCs less than or equal to 5.

Result and Discussion
The curve of reflectivity changing with incident angle is called SPR curve, once SPPs are excited, there will be a reflection angle and a corresponding sharp change of reflection phase. According to Equations (11)-(13), we can know that the SPR reflectivity (Rp), phase (ψp), and GH shift of Au-ITO film coated BK7 and SF11 glass, as shown in Figure 2. In Figure 2a, we can see that the SPR curve has a narrow reflection angle near 59.47°, the minimum reflectivity of 0.0313 a.u., and the corresponding phase changes sharply, which indicates that a strong SPR based on the traditional Kretschmann-Raether structure is excited. In Figure 2b, the GH shift as of incidence is obtained, the GH shift at the resonance angle increases obviously. When the Au and ITO are 50 nm and 10 nm, respectively, the highest GH shift of this structure is S = 51.95 λ. Then, the different layers of graphene and TMDCs are used to increase GH shift. First, the different layers of graphene are added to the Au-ITO structure. In Figure 3, the reflectivity, phase and GH shift under different graphene layers are shown. For monolayer, the minimum reflectivity is 0.0154 a.u. at resonance angle of 59.83°, the phase change to Z-shaped-like at resonance, and the GH In order to study the changes of the GH shift and reflectivity in SPR biosensors, we use the transfer matrix method (TMM) and the Fresnel equation based on N-layer model to perform a detailed analysis. The M is the characteristic TM of n-layer composite structure, which is obtained from the following relation of P-polarized light [45]: where M k is expresses as: where p k and α k are written as: where, d k is the thickness of the kth layer. The matrix of the total reflection polarized light (γ p ) can be expressed as [18]: where p 1 and p N are the corresponding terms for the first layer and the Nth layer. The reflectivity (Rp) and phase (ψ p ) is shown as: Sensors 2020, 20, 1028 5 of 14 Therefore, the GH shift is obtained by the stationary phase method, and it can be expressed as [14]: where the θ 1 is the angle of incidence.

Result and Discussion
The curve of reflectivity changing with incident angle is called SPR curve, once SPPs are excited, there will be a reflection angle and a corresponding sharp change of reflection phase. According to Equations (11)-(13), we can know that the SPR reflectivity (Rp), phase (ψp), and GH shift of Au-ITO film coated BK7 and SF11 glass, as shown in Figure 2. In Figure 2a, we can see that the SPR curve has a narrow reflection angle near 59.47 • , the minimum reflectivity of 0.0313 a.u., and the corresponding phase changes sharply, which indicates that a strong SPR based on the traditional Kretschmann-Raether structure is excited. In Figure 2b, the GH shift as of incidence is obtained, the GH shift at the resonance angle increases obviously. When the Au and ITO are 50 nm and 10 nm, respectively, the highest GH shift of this structure is S = 51.95 λ.

Result and Discussion
The curve of reflectivity changing with incident angle is called SPR curve, once SPPs are excited, there will be a reflection angle and a corresponding sharp change of reflection phase. According to Equations (11)-(13), we can know that the SPR reflectivity (Rp), phase (ψp), and GH shift of Au-ITO film coated BK7 and SF11 glass, as shown in Figure 2. In Figure 2a, we can see that the SPR curve has a narrow reflection angle near 59.47°, the minimum reflectivity of 0.0313 a.u., and the corresponding phase changes sharply, which indicates that a strong SPR based on the traditional Kretschmann-Raether structure is excited. In Figure 2b, the GH shift as of incidence is obtained, the GH shift at the resonance angle increases obviously. When the Au and ITO are 50 nm and 10 nm, respectively, the highest GH shift of this structure is S = 51.95 λ. Then, the different layers of graphene and TMDCs are used to increase GH shift. First, the different layers of graphene are added to the Au-ITO structure. In Figure 3, the reflectivity, phase and GH shift under different graphene layers are shown. For monolayer, the minimum reflectivity is 0.0154 a.u. at resonance angle of 59.83°, the phase change to Z-shaped-like at resonance, and the GH Figure 2. The change of (a) reflectivity and phase respect to angle of incidence; (b) Goos-Hänchen (GH) shift with respect to angle of incidence for Au-ITO structure.
Then, the different layers of graphene and TMDCs are used to increase GH shift. First, the different layers of graphene are added to the Au-ITO structure. In Figure 3, the reflectivity, phase and GH shift under different graphene layers are shown. For monolayer, the minimum reflectivity is 0.0154 a.u. at resonance angle of 59.83 • , the phase change to Z-shaped-like at resonance, and the GH shift of this structure is S = 63.89 λ. For bilayer and 3 layers, the GH shifts of this Au-ITO-graphene structure are 89.06 λ and 168.5 λ, respectively. For 4 layers, the minimum reflectivity is 1.9829 × 10 −6 a.u. at resonance angle of 61.01 • , the phase change to Lorentzian-like at resonance angle, and the highest GH shift of SPR biosensor structure is −241.2 λ. Therefore, when the phase change is Lorentzian-like, the GH shift is negative, and the greater the change of phase, the larger the value of GH shift. The GH shift of −134.7 λ is obtained by 5 layers. Hence, when the thickness of graphene is 4 layers, the GH shift reaches the maximum value S = −241.2 λ. Subsequently, different layers of MoSe 2 are added to the Au-ITO structure, as demonstrated in Figure 4. For monolayer, SPR curve has a narrow reflection angle near 61.09 • , the minimum reflectivity of 0.0313 a.u, the phase change to Z-shaped-like at resonance angle, and the GH shift of this structure is S = 90.19 λ. For bilayer, the minimum reflectivity is 6.75 × 10 −5 a.u. at resonance angle of 63.02 • . The phase change to Lorentzian-like at resonance angle, and the highest GH shift of SPR biosensor is S = −492.6 λ. From 3 layers to 5 layers, the GH shift is −53.41 λ, −28.01 λ, and 20.14 λ, respectively. Therefore, the maximum GH shift of −492.6 λ is obtained by the MoSe 2 bilayer. From Figures 3 and 4, we can find four important features. First of all, when increasing the number of graphene layer or MoSe 2 layer, the SPR resonance angle will show a larger GH shift, and the GH shift of MoSe 2 is larger than that of graphene. Secondly, the bandwidth of the reflection curve will be broadened rapidly with the increase of the number of MoSe 2 /graphene layers, because the electronic energy loss of MoSe 2 layer is related to its imaginary part of dielectric function. The increment of MoSe 2 layer leads to a large electron energy loss [45]. narrow reflection angle near 61.09°, the minimum reflectivity of 0.0313 a.u, the phase change to Zshaped-like at resonance angle, and the GH shift of this structure is S = 90.19 λ. For bilayer, the minimum reflectivity is 6.75 × 10 −5 a.u. at resonance angle of 63.02°. The phase change to Lorentzianlike at resonance angle, and the highest GH shift of SPR biosensor is S = −492.6 λ. From 3 layers to 5 layers, the GH shift is −53.41 λ, −28.01 λ, and 20.14 λ, respectively. Therefore, the maximum GH shift of −492.6 λ is obtained by the MoSe2 bilayer. From Figures 3 and 4, we can find four important features. First of all, when increasing the number of graphene layer or MoSe2 layer, the SPR resonance angle will show a larger GH shift, and the GH shift of MoSe2 is larger than that of graphene. Secondly, the bandwidth of the reflection curve will be broadened rapidly with the increase of the number of MoSe2/graphene layers, because the electronic energy loss of MoSe2 layer is related to its imaginary part of dielectric function. The increment of MoSe2 layer leads to a large electron energy loss [45].  In order to enhance the GH shift, the different layers of graphene and TMDCs are used to increase GH shift. Firstly, we investigate the angle of incidence for different number of graphene layers with monolayer of MoSe 2 . In Figure 5, the reflectivity, phase, and GH shift of graphene from monolayer to 5 layers added to Au-ITO-MoSe 2 (monolayer) hybrid structure change with angle of incidence. For monolayer, the GH shift of this structure is S = 186.4 λ at resonance angle of 61.53 • . For the bilayer of graphene, the minimum reflectivity is 3.29 × 10 −5 a.u. at resonance angle of 61.97 • , the phase change to Lorentzian-like at resonance angle, and the highest GH shift of SPR biosensor is S = −801.7 λ. For the 3, 4, 5 layers, the GH shift is −114.1 λ, −58.14 λ, and −37.68 λ, respectively. Therefore, when the graphene and MoSe 2 are bilayer and monolayer, respectively, the maximum GH shift of −801.7 λ is obtained by Au-ITO-MoSe 2 -graphene hybrid structure. Secondly, the different number of MoSe 2 layers added to the Au-ITO-graphene (monolayer) structure. In Figure 6, with the increase of MoSe 2 from layer 2 to layer 5, the lowest point of the reflection curve is more and more far away from zero, and the phase change is smaller, which shows that the light absorption is gradually weakened, and the SPR excitation are also weakened. In order to enhance the GH shift, the different layers of graphene and TMDCs are used to increase GH shift. Firstly, we investigate the angle of incidence for different number of graphene layers with monolayer of MoSe2. In Figure 5, the reflectivity, phase, and GH shift of graphene from monolayer to 5 layers added to Au-ITO-MoSe2 (monolayer) hybrid structure change with angle of incidence. For monolayer, the GH shift of this structure is S = 186.4 λ at resonance angle of 61.53°. For the bilayer of graphene, the minimum reflectivity is 3.29 × 10 −5 a.u. at resonance angle of 61.97°, the phase change to Lorentzian-like at resonance angle, and the highest GH shift of SPR biosensor is S = −801.7 λ. For the 3, 4, 5 layers, the GH shift is −114.1 λ, −58.14 λ, and −37.68 λ, respectively. Therefore, when the graphene and MoSe2 are bilayer and monolayer, respectively, the maximum GH shift of −801.7 λ is obtained by Au-ITO-MoSe2-graphene hybrid structure. Secondly, the different number of MoSe2 layers added to the Au-ITO-graphene (monolayer) structure. In Figure 6, with the increase of MoSe2 from layer 2 to layer 5, the lowest point of the reflection curve is more and more far away from zero, and the phase change is smaller, which shows that the light absorption is gradually weakened, and the SPR excitation are also weakened.   Subsequently, different number of other TMDCs (MoS 2 /WS 2 /WSe 2 ) are added to the monolayer of graphene. As shown in Figure 7a, with MoS 2 monolayer, the highest GH shift is 409.9 λ. With the increment of MoS 2 layers, the GH shift changes from positive to negative. However, the GH shift that become negative are smaller, which are −56.57 λ, −24.23 λ, −16.12 λ, and −13.03 λ, respectively. Therefore, the maximum GH shift of 409.9 λ is obtained with both monolayer of MoS 2 and graphene. In Figure 7b, when the WS 2 is from monolayer to 5 layer, the GH shift is 43.09 λ, 29.92 λ, 21.82 λ, 17.0 λ, and 14.28 λ, respectively. In Figure 7c, with the increment of WSe2, the GH shift is less than 47.98 λ in monolayer WSe 2 .
Overall, with larger number of TMDCs/graphene layers, the bandwidth of the reflection curve widens rapidly. This is because the electronic energy loss of TMDCs layer is related to the imaginary part of the dielectric function. Through the above analysis, MoSe 2 shows the best performance in Au-ITO-TMDCs-graphene hybrid structure of SPR biosensor. When the thickness of Au, ITO, MoSe 2 , and graphene are 50 nm, 10 nm, bilayer and monolayer, respectively, the best GH shift of −801.7 λ is obtained. λ in monolayer WSe2.
Overall, with larger number of TMDCs/graphene layers, the bandwidth of the reflection curve widens rapidly. This is because the electronic energy loss of TMDCs layer is related to the imaginary part of the dielectric function. Through the above analysis, MoSe2 shows the best performance in Au-ITO-TMDCs-graphene hybrid structure of SPR biosensor. When the thickness of Au, ITO, MoSe2, and graphene are 50 nm, 10 nm, bilayer and monolayer, respectively, the best GH shift of −801.7 λ is obtained. With the increase of layers of TMDCs/graphene, the GH shift increases gradually. However, further increasing the layers, the absorbed energy will not be completely transferred to the enhanced evanescent field, which leads to the decrease of GH shift. This can be analyzed from the depth and width of the SPR curve. The closer the reflectance to zero the higher the modulation depth, and the With the increase of layers of TMDCs/graphene, the GH shift increases gradually. However, further increasing the layers, the absorbed energy will not be completely transferred to the enhanced evanescent field, which leads to the decrease of GH shift. This can be analyzed from the depth and width of the SPR curve. The closer the reflectance to zero the higher the modulation depth, and the greater the loss the broader the resonance [28]. Therefore, based on those impacts, the combination of monolayer MoSe 2 and bilayer graphene can offer the optimal GH shift. In Table 2, the optimal GH shift with different number of graphene and TMDCs layers are summarized. It can be seen from the Table that the largest GH shift (−801.7 λ) is obtained when the MoSe 2 is monolayer and the graphene is bilayer, and the optimal GH shift is at θ = 61.97 • . With MoS 2 and graphene monolayer the best GH shift (404.9 λ) can be obtained. With WS 2 , the highest GH shift 382.4 λ is gained by WS 2 monolayer and graphene 5 layers. Finally, the largest GH shift of −454.3 λ is obtained when the WSe 2 is monolayer and graphene is 5 layers. We found that when we change the refractive index of sensing medium (n 7 ), the GH shift will appear with a large variation. Hence, the structure can be used as a high sensitivity biosensor by monitoring the change of GH and the sensitivity (S P ) is defined as [18]: where the ∆GH is the change of GH shift, ∆n 7 is the change of refractive index of sensing medium. In Figure 8a, the change of GH shift of Au-ITO structure with the change of n 7 is plotted. When the n 7 increases from 1.330 to 1.332, the maximum of GH shift reaches ∆GH = 5.47 λ (all "λ" are calculated numerically only). Therefore, we can calculate the sensitivity to be S P = 2735 λ/RIU. Similarly, in Figure 8b, the GH shift reaches ∆GH = 9.04 λ leading to sensitivity of S P = 4520 λ/RIU. In Figure 8c, the highest of GH shift reaches ∆GH = 42.84 λ in Au-ITO-MoSe 2 (monolayer)-graphene (monolayer) structure, so the sensitivity is S P = 2.142 × 10 4 λ/RIU. In Figure 8d, the Au-ITO-MoSe 2 (monolayer) -graphene (bilayer) offers the maximum of GH shift ∆GH = 160.4 λ, when the n 7 increases from 1.3300 to 1.3302, resulting in the highest sensitivity of 8.02 × 10 5 λ/RIU, which is 293.24 times larger than the Au-ITO structure and 177.43 times larger than the Au-ITO-graphene (monolayer) structure. For comparison, the performances of previously reported 2D-material-assisted GH shift sensors based on SPR sensors are summarized in Table 3. Significant enhancements on both GH shift and sensitivity can be obtained in the proposed sensors.  For comparison, the performances of previously reported 2D-material-assisted GH shift sensors based on SPR sensors are summarized in Table 3. Significant enhancements on both GH shift and sensitivity can be obtained in the proposed sensors.

Conclusions
In this paper, the high GH shift in SPR biosensor based on Au-ITO-TMDCs-graphene hybrid structure is analyzed. We theoretically prove the influence of the number of graphene and TMDCs layers on the GH shift, and a large GH shift is obtained by using the mixed structure of monolayer MoSe 2 and bilayer of graphene. The maximum displacement is 801.7 times of the incident wavelength. Compared with the traditional SPR structure, the shift of the structure is increased by more than 2 orders of magnitude. Moreover, the GH shift can be positive or negative depending on the layer number of TMDCs and graphene. The sensitivity corresponding to the maximum GH shift can reach as high as 8.02 × 10 5 λ/RIU, which is 293.24 times of the Au-ITO structure and 177.43 times of the Au-ITO-graphene structure. Such configuration could pave the way to high precision optical sensing.