High-Sensitivity Goos-Hänchen Shifts Sensor Based on BlueP-TMDCs-Graphene Heterostructure

Surface plasmon resonance (SPR) with two-dimensional (2D) materials is proposed to enhance the sensitivity of sensors. A novel Goos–Hänchen (GH) shift sensing scheme based on blue phosphorene (BlueP)/transition metal dichalogenides (TMDCs) and graphene structure is proposed. The significantly enhanced GH shift is obtained by optimizing the layers of BlueP/TMDCs and graphene. The maximum GH shift of the hybrid structure of Ag-Indium tin oxide (ITO)-BlueP/WS2–graphene is −2361λ with BlueP/WS2 four layers and a graphene monolayer. Furthermore, the GH shift can be positive or negative depending on the layer number of BlueP/TMDCs and graphene. For sensing performance, the highest sensitivity of 2.767 × 107λ/RIU is realized, which is 5152.7 times higher than the traditional Ag-SPR structure, 2470.5 times of Ag-ITO, 2159.2 times of Ag-ITO-BlueP/WS2, and 688.9 times of Ag-ITO–graphene. Therefore, such configuration with GH shift can be used in various chemical, biomedical and optical sensing fields.


Introduction
The Goos-Hänchen (GH) shift refers to the lateral spatial shift of the center of mass of the bounded beam relative to the geometric prediction [1]. The GH migration results from the role dispersion of the Fresnel reflection coefficient [2,3]. When the phase of reflection coefficient changes significantly near the critical angle of total reflection, GH effect can be enhanced [4][5][6]. Due to the advantages of GH shift in precision measurement and optical sensing, new attention has been observed [7][8][9]. In the fields of optics, chemistry and sensors, GH shift has been widely discussed [10,11] and there is always a goal for researchers to obtain large GH shifts.
The GH shift at the interface of two homogeneous materials with different optical properties is usually very small, almost equal to the incident wavelength [12]. Leveraging on metal to excite surface plasmon polaritons (SPP) is an effective way to improve GH shift [13]. SPPs are kinds of vertically constrained evanescent electromagnetic waves [14,15]. According to Snell's law, if the incident angle is larger than the total reflection angle, the total reflection phenomenon will appear when a beam of light is transmitted from a dense medium to a sparse medium [16]. When total reflection occurs, if there is no energy loss, it is called total internal reflection (TR), if there is energy loss, it is called attenuated total reflection (ATR). From the point of view of physical optics, a more in-depth study of total reflection shows that when total reflection occurs, the beam enters a wavelength-level depth in the optical medium, and its amplitude decays exponentially along the direction perpendicular to the interface. At the same time, in the incident plane, it transmits for a certain distance along the interface direction, and then returns to the optical dense medium. From the point of view of physical

Design Consideration and Mathematical Model
The hybrid structure of Ag-ITO-BlueP/TMDCs-graphene based on the Kretschmann structure is shown in Figure 1. The p-polarized He-Ne laser emitted at 632.8 nm is collimated by a Glan-Taylor prism. Under the Kretschmann structure, the glass slide coated with metal film is fixed on the base of equilateral prism made of high refractive index (RI) glass with refractive index matching solution [43]. The incident light is irradiated on the SPR sensor through the side of the equilateral triangular coupling prism. The prism coupling device is controlled by a mobile rotary table, so as to change the angle of the incident light.
In the following description of the refractive index (RI) in each layer, λ is the wavelength of the incident light, and its unit is um. In the first layer, the SF11 prism with RI (n 1 ) is obtained [43]: Sensors 2020, 20, 3605

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Then, in the second layer, BK7 glass with RI (n 2 ) is obtained [44]: The third layer is Ag thin film and its RI (n 3 ) is obtained through the Drude model [45]: The ITO film as fourth layer with RI (n 4 ) is [46]: Subsequently, the 2D material of BlueP/TMDCs and graphene with monolayer and RI is shown as Subsequently, the 2D material of BlueP/TMDCs and graphene with monolayer and RI is shown as Table 1 [47,48]. The sensing medium is used for deionized (DI) water and its RI (n7) is obtained [43]: Therefore, the RI is n1 = 1.7786, n2 = 1.5151, n3 = 0.1350 + 3.9850i, n4 = 1.858 + 0.058i, n7 = 1.332 + nbio. The nbio represents the RI change of DI water. The thickness of BK7 glass and sensing medium is both 100 nm. In order to compare the properties of 2D materials, we set the thickness of Ag and ITO to 45 nm and 10 nm, respectively. When the number of graphene layers n ≤ 5, it is reasonable to treat monolayer as a non-interacting [49]. Hence, we only use graphene and BlueP/TMDCs with 5 layers or less, and ignore the interaction between them.  The sensing medium is used for deionized (DI) water and its RI (n 7 ) is obtained [43]: where the Sellmeier coefficients A 1 = 0.5666959820, Therefore, the RI is n 1 = 1.7786, n 2 = 1.5151, n 3 = 0.1350 + 3.9850i, n 4 = 1.858 + 0.058i, n 7 = 1.332 + n bio . The n bio represents the RI change of DI water. The thickness of BK7 glass and sensing medium is both 100 nm. In order to compare the properties of 2D materials, we set the thickness of Ag and ITO to 45 nm and 10 nm, respectively. When the number of graphene layers n ≤ 5, it is reasonable to treat monolayer as a non-interacting [49]. Hence, we only use graphene and BlueP/TMDCs with 5 layers or less, and ignore the interaction between them.
In order to analyze the reflectivity (R p ) and phase (ψ p ), the transfer matrix method (TMM) and the Fresnel equation based on n-layer model are used [47]. The SPR sensor is composed of parallel stacking in Z direction perpendicular to the sensing interface. The M is the structure of the transmission matrix (TM), and p-polarized light is gained through the following relationship [43]: where and The total reflection coefficient (r p ) of p-polarized light is related to the matrix as follows: where p 1 corresponds to the SF11 prism layer and p 7 to the water layer. The R p and ψ p of the p-polarized light are shown as [17]: We can use the fixed phase method to calculate the GH shift as followed: where the θ 1 is the incident angle.

Result and Discussion
As shown in Figure 2, the reflectance, phase and GH shift of conventional Ag and Ag-ITO structure are compared and analyzed. The reflectivity (red dot line) and phase (blue dot line) are shown in Figure 2a. The SPR curve shows that there is a narrow reflection angle near 52.71 • and 55.22 • respectively, and the minimum reflectivity is 0.068 a.u for Ag structure and 0.014 a.u for Ag-ITO structure, respectively. In Figure 2b, the highest GH shift with Ag = 45 nm is 60.21λ. With Ag = 45 nm and ITO = 10 nm, the maximum GH shift attains 62.11λ indicating ITO can increase the GH shift and other performance.
Although ITO plays a certain role in the increase of GH shift, the enhancement is still relatively small. Next, we study the influence of the graphene layer, as shown in Figure 3. For the graphene monolayer, the reflectivity is 0.0024 a.u at 55.44 • and the GH shift is 125.7λ. When the graphene bilayer is added to the Ag-ITO structure, the best performance is obtained with the largest GH shift of −439.7λ.
Sensors 2020, 20, 3605 5 of 12 We can observe that the phase change from Z-shaped-like to Lorentzian-like, and GH shift change from positive to negative. Then, with the increase of graphene layers, the GH shift is −67.56λ, −33.46λ, −20.19λ, respectively. Although ITO plays a certain role in the increase of GH shift, the enhancement is still relatively small. Next, we study the influence of the graphene layer, as shown in Figure 3. For the graphene monolayer, the reflectivity is 0.0024 a.u at 55.44° and the GH shift is 125.7λ. When the graphene bilayer is added to the Ag-ITO structure, the best performance is obtained with the largest GH shift of −439.7λ. We can observe that the phase change from Z-shaped-like to Lorentzian-like, and GH shift change from positive to negative. Then, with the increase of graphene layers, the GH shift is −67.56λ, −33.46λ, −20.19λ, respectively. Similarly, the BlueP/TMDCs is added to the Ag-ITO structure, as shown in Figure 4. In Table 2, the optimal GH shift (S/λ) with different number of BlueP/TMDCs is obtained. Hence, In the BlueP/TMDCs, we can understand that the BlueP/MoSe2 has the greatest contribution to Ag-ITO structure. Although ITO plays a certain role in the increase of GH shift, the enhancement is still relatively small. Next, we study the influence of the graphene layer, as shown in Figure 3. For the graphene monolayer, the reflectivity is 0.0024 a.u at 55.44° and the GH shift is 125.7λ. When the graphene bilayer is added to the Ag-ITO structure, the best performance is obtained with the largest GH shift of −439.7λ. We can observe that the phase change from Z-shaped-like to Lorentzian-like, and GH shift change from positive to negative. Then, with the increase of graphene layers, the GH shift is Similarly, the BlueP/TMDCs is added to the Ag-ITO structure, as shown in Figure 4. In Table 2, the optimal GH shift (S/λ) with different number of BlueP/TMDCs is obtained. Hence, In the BlueP/TMDCs, we can understand that the BlueP/MoSe2 has the greatest contribution to Ag-ITO structure. Similarly, the BlueP/TMDCs is added to the Ag-ITO structure, as shown in Figure 4. In Table 2, the optimal GH shift (S/λ) with different number of BlueP/TMDCs is obtained. Hence, In the BlueP/TMDCs, we can understand that the BlueP/MoSe 2 has the greatest contribution to Ag-ITO structure. From Figures 2-4, there are four important features. First, at a certain thickness of Ag-ITO film, due to the large real-part value of BlueP/TMDCs and graphene dielectric function, with the increase of BlueP/TMDCs and graphene layers, the SPR resonance angle has a large red shift. Second, the imaginary part of dielectric function of graphene layer is larger than that of BlueP/TMDCs layer, which leads to a large loss of electronic energy. Third, the resonance depth (i.e., the minimum reflectivity) strongly Sensors 2020, 20, 3605 6 of 12 depends on the number of BlueP/TMDC and graphene layers deposited on Ag-ITO films. The light energy absorbed by Ag-ITO film is not enough to excite strong SPR. By further coating BlueP/TMDCs and graphene on the surface of Ag-ITO film, the light absorption of the hybrid structure can be enhanced effectively, thereby promoting a stronger SPR excitation.
Sensors 2020, 20, 3605 6 of 13   From Figures 2-4, there are four important features. First, at a certain thickness of Ag-ITO film, due to the large real-part value of BlueP/TMDCs and graphene dielectric function, with the increase of BlueP/TMDCs and graphene layers, the SPR resonance angle has a large red shift. Second, the imaginary part of dielectric function of graphene layer is larger than that of BlueP/TMDCs layer, which leads to a large loss of electronic energy. Third, the resonance depth (i.e., the minimum reflectivity) strongly depends on the number of BlueP/TMDC and graphene layers deposited on Ag-ITO films. The light energy absorbed by Ag-ITO film is not enough to excite strong SPR. By further coating BlueP/TMDCs and graphene on the surface of Ag-ITO film, the light absorption of the hybrid structure can be enhanced effectively, thereby promoting a stronger SPR excitation. Figure 5 shows the GH shift relative to the incident angle when graphene is monolayer and the number of BlueP/TMDCs layers changes from monolayer to five layers. The optimal GH shift and resonance angle with different number of BlueP/TMDCs and graphene monolayer are obtained as Table 3. We know that with the increase of the optimal GH shift of each BlueP/TMDCs, the corresponding resonance angle also increases.  Figure 5 shows the GH shift relative to the incident angle when graphene is monolayer and the number of BlueP/TMDCs layers changes from monolayer to five layers. The optimal GH shift and resonance angle with different number of BlueP/TMDCs and graphene monolayer are obtained as Table 3. We know that with the increase of the optimal GH shift of each BlueP/TMDCs, the corresponding resonance angle also increases. Subsequently, the BlueP/TMDCs monolayer and different number of graphene layers are added to the Ag-ITO structure of SPR, as shown in Figure 6. The optimal GH shift with a different number of graphene and BlueP/TMDCs monolayer are obtained, as shown in Table 4.  Subsequently, the BlueP/TMDCs monolayer and different number of graphene layers are added to the Ag-ITO structure of SPR, as shown in Figure 6. The optimal GH shift with a different number of graphene and BlueP/TMDCs monolayer are obtained, as shown in Table 4.   In Table 5, the optimal GH shift with a different number of BlueP/TMDCs and graphene layers are summarized, where the bold indicates the highest GH shift value under the structure. In the BlueP/MoS2 and graphene, the highest GH shift is −385.8λ in BlueP/MoS2 bilayer and graphene monolayer. Then, the maximum GH shift with BlueP/WS2 four layers and graphene monolayer is -2361λ. Subsequently, the largest GH shift with BlueP/WSe2 three layers and graphene monolayer of -655.5λ is obtained. Finally, the highest GH shift of 456.9λ is obtained for both BlueP/MoSe2 and graphene monolayer. Therefore, in the Ag-ITO-BlueP/TMDCs-graphene structure, BlueP/WS2 has the greatest contribution to GH shift. The monolayer of graphene has the best performance.  In Table 5, the optimal GH shift with a different number of BlueP/TMDCs and graphene layers are summarized, where the bold indicates the highest GH shift value under the structure. In the BlueP/MoS 2 and graphene, the highest GH shift is −385.8λ in BlueP/MoS 2 bilayer and graphene monolayer. Then, the maximum GH shift with BlueP/WS 2 four layers and graphene monolayer is -2361λ. Subsequently, the largest GH shift with BlueP/WSe 2 three layers and graphene monolayer of -655.5λ is obtained. Finally, the highest GH shift of 456.9λ is obtained for both BlueP/MoSe 2 and graphene monolayer. Therefore, in the Ag-ITO-BlueP/TMDCs-graphene structure, BlueP/WS 2 has the greatest contribution to GH shift. The monolayer of graphene has the best performance. In our study, the RI of the sensing medium (∆n 7 ) is changed, then and the GH shift is shown a giant red shift. Hence, the proposed new SPR heterostructure is used as a high sensitivity sensor based on shift variation. ∆GH is defined as highest value of the varying GH shift and the sensitivity is defined as S' p = ∆GH/∆n 7 . We define the traditional SPR Ag, Ag-ITO, Ag-ITO-BlueP/WS 2 (monolayer), Ag-ITO-graphene (monolayer), Ag-ITO-BlueP/WS 2 (monolayer)-graphene (monolayer), Ag-ITO-BlueP/WS 2 (four layers)-graphene (monolayer) structure as Structure I to Structure VI and show as Figure 7. In Table 6, the optimal S' P with ∆GH and ∆n 7 for Structure I to Structure VI are gained. Therefore, Structure VI is 5152.7 times higher than Structure I, 2470.5 times higher than Structure II, 2159.2 times higher than Structure III, and 688.9 times higher than Structure IV. In our study, the RI of the sensing medium (∆n7) is changed, then and the GH shift is shown a giant red shift. Hence, the proposed new SPR heterostructure is used as a high sensitivity sensor based on shift variation. ∆GH is defined as highest value of the varying GH shift and the sensitivity is defined as S'p = ∆GH/∆n7. We define the traditional SPR Ag, Ag-ITO, Ag-ITO-BlueP/WS2 (monolayer), Ag-ITO-graphene (monolayer), Ag-ITO-BlueP/WS2 (monolayer)-graphene (monolayer), Ag-ITO-BlueP/WS2 (four layers)-graphene (monolayer) structure as Structure I to Structure VI and show as Figure 7. In Table 6, the optimal S'P with ΔGH and ∆n7 for Structure I to Structure VI are gained. Therefore, Structure VI is 5152.7 times higher than Structure I, 2470.5 times higher than Structure II, 2159.2 times higher than Structure III, and 688.9 times higher than Structure IV. Better compared with previous research results, Table 7 summarizes the GH shift and sensitivity based on SPR sensor. In references [9], the GH shift of 12.5λ is obtained by traditional Au thin film. In reference [50], when MoS 2 of 2D material and air was added to the SPR biosensor, the GH shift was improved to 40.5λ. We can find that 2D material and air can improve the GH shift of SPR sensor. In reference [51], when the graphene replaced MoS 2 , the GH shift increased to 61.1λ. Therefore, compared with MoS 2 , graphene improves the performance of the SPR sensor more significantly. However, when graphene and MoS 2 were added to the Au film of SPR sensor, the GH shift increased to 235.8λ for reference [36], and the highest sensitivity was obtained as 5.545 × 10 5 λ/RIU. In reference [37], when the ITO and MoSe 2 replaced MoS 2 , the GH shift increased to 801.7λ, and the maximum sensitivity was 8.02 × 10 5 λ/RIU. In this work, we use BlueP/TMDCs instead of TMDCs, and change metal into Ag, so as to construct the SPR sensor with Ag-ITO-BlueP/WS 2 -graphene hybrid structure. The optimal GH displacement is 2361λ and the maximum sensitivity is 2.767 × 10 7 λ/RIU. Based on the analysis, we can see that our novel SPR sensor improves the GH shift and sensitivity significantly.

Conclusions
In this paper, the GH shift of the Kretschmann configuration combined with SPR-based 2D nanomaterials is studied. When SPPs were excited, we theoretically proved the influence of the number of graphene and BlueP/TMDCs layers on the GH shift, and obtained a huge GH shift by using the mixed structure of BlueP/WS 2 four layers and graphene monolayer. The maximum GH shift is 2361 times that of the incident wavelength. Compared with the traditional SPR structure, the shift of the structure is increased by more than 39.21 times. In addition, by changing the number of BlueP/TMDCs layers, we can control the positive and negative shift of GH in the structure of BlueP/TMDCs-graphene. The maximum GH shift corresponding to the highest sensitivity is 2.767 × 10 7 λ/RIU, which is 5152.7 times higher than the traditional SPR of Ag, 2462.8 times of Ag-ITO, 2159.2 times of Ag-ITO-BlueP/WS 2 , and 688.9 times of Ag-ITO-graphene. The sensing layer we use is deionized water, therefore, it is suitable as a sensing medium with a refractive index close to 1.332, to gain a higher sensitivity. This structure is expected to be a candidate for high-performance sensors.

Conflicts of Interest:
The authors declare no conflict of interest.