1. 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 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 [
17]. You et al. proposed a long-range surface plasmon resonance (SPR) mode, in which gold (Au) is the excitation layer of SPPs, so as to improve the GH shift [
18]. The sliver (Ag) film layer of SPR can easily adjust the position of the minimum reflection and the maximum GH shift [
19]. The sensitivity of GH shift to the refractive index of the surrounding medium is obtained by optimizing the incident angle and the thickness of Au [
20].
Compared with other metal oxides, Indium tin oxide (ITO) has the characteristics of anti-corrosion, high transmittance, good conductivity, etc., which are widely used in the field of optical sensing [
21,
22]. The GH shift of p-polarized laser beam reflected from ITO surface under complex field has been studied [
23]. In addition, two-dimensional (2D) nanomaterial with high thermal conductivity, carrier mobility, wide band optical response spectrum and strong nonlinear optical properties have attracted more and more attention [
24,
25]. The 2D materials include graphene [
26,
27], black phosphorus (BP) [
28,
29], and transition metal dichalcogenides (TMDCs) [
30,
31]. Graphene is the most representative 2D material widely used in optical sensors [
32]. Luo studied the electro-optical modulation and magneto-optical modulation of GH shift in the double graphene coated waveguide [
33]. Zhou et al. researched the GH effect in graphene substrate system by transfer matrix method [
34]. Zhao et al. theoretically proposed the GH shift of light beam in a defect photonic crystal composed of dielectric multilayer and graphene [
35]. By optimizing the thickness and layers number of the Au-MoS
2–graphene hybrid, You et al. gained the highest GH shift of 235.8λ [
36]. Through the optimization and comparative analysis of the Au-ITO-TMDCs–graphene hybrid structure, Han et al. obtained the highest GH shift of 801.7λ with MoSe
2 monolayer and graphene bilayer [
37]. Zhu et al. discovered another promising 2D material, Blue phosphorene (BlueP) [
38]. The BlueP has the same thermal stability as BP with a band width of 2 eV, so it has a broad application prospect for sensing applications [
39]. In addition, because the monolayer of BlueP and TMDCs have the same hexagonal crystal structure, it is easy to construct the heterstructure of BlueP/TMDCs [
40]. Srivastava obtained the SPR sensor of BlueP/MoS
2 heterostructure to improve the sensitivity [
41]. Sharma et al. proposed to use the BlueP/TMDCs molybdenum disulfide heterostructure, and compared with the traditional graphene SPR sensors [
42].
In this paper, the hybrid structure of BlueP/TMDCs (Blue/WS2, BlueP/MoS2, BlueP/MoSe2, BlueP/WSe2) and graphene coated with ITO and Ag thin film is proposed. The maximum GH shift achieved was −2361λ for four layers BlueP/WS2 and monolayer graphene. In addition, the highest sensitivity for index sensing reached 2.767 × 107λ/RIU, which is 5152.7 times higher than the traditional Ag structure. We believe that this scheme with 2D materials has potential in highly sensitive sensors.
2. 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 (
n1) is obtained [
43]:
Then, in the second layer, BK7 glass with RI (
n2) is obtained [
44]:
The third layer is Ag thin film and its RI (
n3) is obtained through the Drude model [
45]:
The ITO film as fourth layer with RI (
n4) is [
46]:
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]:
where the Sellmeier coefficients
A1 = 0.5666959820,
A2 =0.1731900098,
A3 =0.02095951857,
A4 = 0.1125228406,
t1= 0.005084151894,
t2 = 0.01818488474,
t3 = 0.02625439472,
t4 = 10.73842352.
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 thickness and dielectric constant of each layer are set as
dk and
εk (
εk =
nk2) (
k = 1,2,…7). In order to analyze the reflectivity (
Rp) and phase (
ψp), 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 (
rp) of
p-polarized light is related to the matrix as follows:
where
p1 corresponds to the SF11 prism layer and
p7 to the water layer. The
Rp and
ψp 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
θ1 is the incident angle.
3. 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. 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/MoSe
2 has the greatest contribution to Ag-ITO structure.
From
Figure 2,
Figure 3 and
Figure 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.
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/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 (∆
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/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 Δ
GH 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
5λ/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
5λ/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
7λ/RIU. Based on the analysis, we can see that our novel SPR sensor improves the GH shift and sensitivity significantly.