Giant and controllable Goos-H&#x00E4;nchen shifts based on surface plasmon resonance with graphene-MoS<sub>2</sub> heterostructure

Qi You; Youxian Shan; Shuaiwen Gan; Yuting Zhao; Xiaoyu Dai; Yuanjiang Xiang

doi:10.1364/OME.8.003036

1. Introduction

Goos-Hänchen (GH) effect refers to a lateral spatial shift that an electromagnetic wavepacket experiences in its incidence plane when it is reflected from a surface. It can be traced back as early as the era of Newton, but until 1947 was confirmed in experiment by Goos and Hänchen [1-2]. The GH shift has received great attention since its discovery and has become a hotspot in academic research. During the last decade, a large number of theoretical [3–9] and experimental [10–13] works have been devoted to the study of the GH shift, and it can be applied in various important fields such as biomedicine [14], chemical sensors [15], and optical measurements [16].

At a single dielectric interface, the lateral shift is usually small, almost comparable to the wavelength of the incident beam. Especially in metal reflection, GH shift is particularly small, as shown by the experiments of Merano and others [17]. And if 2D crystals are concerned theoretical expectations of a free standing crystal predict an even smaller effect [18]. However, large positive and negative lateral shifts could be achieved by exciting surface plasmon resonance (SPR). As described by Yin et al [19], a lateral spatial displacement that is greater than 50 wavelengths for the reflected beam due to the surface plasmon polaritons (SPPs), was observed experimentally. The SPP is a special physical phenomenon that occurs at the metal-dielectric interface, where electromagnetic waves are coupled to charge excitations. Typically SPPs can be excited via evanescent waves in attenuated total reflection (ATR) structure, where the wave vector mismatch between vacuum and SPPs is compensated by using high-index prism. When SPPs are excited at the metal-dielectric interface, there will be a reflectance dip in the reflectance-angle/wavelength curve, and the electromagnetic fields near the interface will become very strong, which can lead to a larger lateral shift. Therefore, the enhancement of SPR is one of the effective methods to increase GH displacement. In the traditional ATR configuration, gold (Au) and silver (Ag) are considered as the best metals to stimulate SPPs, but the loss of noble metal configuration is large, which limits GH shift research and application in the future. As a result, how to solve this problem has become a current challenge for researchers.

In recent years, more and more two-dimensional (2D) nanomaterials have attracted considerable attention due to their excellent performance [20–22]. The most representative of 2D materials are graphene and semiconductor molybdenum disulfide (MoS₂). Graphene, a single layer of carbon atoms arranged in a hexagonal lattice, was first discovered in 2004 and attracted great attention due to its extraordinary properties, such as high electronic mobility, low ohmic loss, high surface area and adjustable bandgap [23–28]. But the reason for limiting the development of graphene in optics is that the intrinsic optical responsivity of graphene is usually poor [29-30]. Thus, this has led to the appearance of hybrid or composite structure containing graphene that enhance carrier multiplication or gain by creating multiple charge carriers with a single photon [31-32]. Molybdenum disulfide (MoS₂), a new type of semiconductor 2D material belonging to transition-metal dichalcogenide (TMDC), makes a natural partner to graphene for optically active heterostructures [33]. The heterostructure formed by graphene and MoS₂ has many advantages, for example, a photoconductive antenna with high input impedance and reconfigurability was proposed by Zangeneh-Nejad et al [34], the heterostructure reported by Loan et al provides an excellent and ultrasensitive platform for the detection of DNA hybridization [35]. In addition, graphene-MoS₂ heterostructures in the electronics [36], sensors [37], optics [38], and other fields have also been widely studied. Recently, Britnell et al [39] have found that the formation of heterostructures by graphene and TMDC can enhance the absorption of light, improve the quantum efficiency and maintain the high carrier mobility of graphene.

Thus, inspired by these above, in this paper, we have proposed a graphene-MoS₂ hybrid structure to enhance the GH shift. SPR is excited through the ATR configuration, graphene and MoS₂ layers are used to improve the absorption efficiency of incident beams and to enhance SPR. When the 2-layer MoS₂ and the 3-layer graphene are combined, the maximum GH shift is 235.8λ. By adjusting the layers of graphene and MoS₂, GH shift can be positive or negative. Moreover, our structure can be used as a GH shift sensor, the optimal sensitivity as high as 5.545*10⁵λ can be obtained. Compared with the traditional GH shift sensor based on SPR, the sensitivity is greatly improved. The reflectivity and GH shift of the configuration are systematically investigated by varying the number of graphene layers and number of MoS₂ layers using transfer-matrix analysis.

2. Theoretical model and method

The structure analyzed here is shown in Fig. 1, which is a typical Kretschmann-Raether configuration [40]. The prism we adopted is SF11 because of its high refractive index. Under the prism is a glass slide (BK7), an Au thin film coated glass slide is attached to the base of an equilateral prism made of high refractive index glass through index matching fluid [41]. Below the Au thin film is a MoS₂-graphene hybrid structure. The bottom layer we adopt is deionized (DI), it can act as a sensing layer when we use the configuration as a sensor based on changing GH shifts. Here, the wavelength of the excitation light is λ = 632.8 nm.

Fig. 1 Modified Kretschmann-Raether configuration with MoS₂-graphene hybrid structure for surface plasmon excitation. A beam is incident on the structure with incident angle θ, giving rise to a reflected wave with the GH shift.

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In this configuration, the refractive index of SF11 is given by the relation [42]:

n_{1} = {(\frac{1.73759695 λ^{2}}{λ^{2} - 0.013188707} + \frac{0.313747346 λ^{2}}{λ^{2} - 0.0623068142} + \frac{1.89878101 λ^{2}}{λ^{2} - 155.23629} + 1)}^{\frac{1}{2}},

where λ is the wavelength of incident light in μm. And second layer is BK7 glass slide and its refractive index is determined by the following relation [42]:

n_{2} = {(\frac{1.03961212 λ^{2}}{λ^{2} - 0.00600069867} + \frac{0.231792344 λ^{2}}{λ^{2} - 0.0200179144} + \frac{1.01046945 λ^{2}}{λ^{2} - 103.560653} + 1)}^{\frac{1}{2}},

where λ is the wavelength of incident light in μm. The third layer is the Au film and its dielectric constant follows the Drude-Lorentz mode as follow [43]:

n_{3} = {(1 - \frac{λ^{2} λ_{c}}{λ_{p}^{2} (λ_{c} + i λ)})}^{\frac{1}{2}},

where λ_c and λ_p are the collision and plasma wavelengths of the metal, respectively. For Au film, λ_c = 8.9342*10⁻⁶ m and λ_p = 1.6826*10⁻⁷ m. The refractive index of MoS₂ is n₄ = 5.9 + 0.8i at λ = 632.8 nm, which is obtained from the experimental measurement data [44]. The refractive index of graphene at visible range is given by the relation [45]:

n_{5} = 3 + i \frac{C_{1}}{3} λ,

where the constant C₁≈5.446μm⁻¹, λ is the wavelength of incident light in μm. And the for the deionized (DI) water (n₆), its refractive index is 1.332 at λ = 632.8 nm [46]. Therefore, based on the above parameters and equations, we finally get the refractive index of each layer as follows: n₁ = 1.7786, n₂ = 1.5151, n₃ = 0.1838 + 3.4313i, n₄ = 5.9 + 0.8i, n₅ = 3 + 1.149i, n₆ = 1.332, respectively. Permittivity of each layer is set to be ε₁, ε₂, ε_3, ε₄, ε₅ and ε₆, and the relationship between dielectric constant and refractive index is

ε_{k} = n_{k}^{2}

, where k = 1,2,3,4,5,6. We use 45nm Au (d₃) to excite the SPR, the thickness of the BK7 slide is d₂ = 100 nm. Single-layer MoS₂ thickness is d₄ = 0.65 nm [47], the fifth layer is graphene, which has a monolayer thickness of d₅ = 0.34 nm [48]. In the discussion, we analyze the influence of graphene and MoS₂ layers on GH shift. Taking individual graphene sheet as non-interacting monolayer, which is reasonable if layer number N<6 [49]. In the following analysis, the number layer of graphene we used is less than 6, so we can ignore their interaction. The same goes for MoS₂. The incident filed is assumed to be transverse magnetic (TM) polarized to analyze the GH shift and reflectance (R_p).

For the multilayer system, we can use the transfer matrix method (TMM) and Fresnel equations based on an N-layer model to analysis the phase (ϕ_p) and reflectivity (R_p) [48, 50]. The total transfer matrix is the multiple multiplication of the transfer matrix for each layer,

M = \prod_{K = 2}^{N - 1} M_{K} = [\begin{matrix} M_{11} & M_{12} \\ M_{21} & M_{22} \end{matrix}],

where N refers to the total number of layers in the structure, and

M_{K} = [\begin{matrix} \cos β_{k} & (- i \sin β_{k}) / q_{k} \\ - i q_{k} \sin β_{k} & \cos β_{k} \end{matrix}],

with

q_{k} = {(\frac{u_{k}}{ε_{k}})}^{1 / 2} \cos θ_{k} = \frac{{(ε_{k} - n_{1}^{2} \sin θ_{1})}^{1 / 2}}{ε_{k}},

and

β_{k} = \frac{2 π}{λ} n_{k} \cos θ_{k} (z_{k} - z_{k - 1}) = \frac{2 π d_{k}}{λ} {(ε_{k} - n_{1}^{2} \sin^{2} θ_{1})}^{1 / 2},

where ε_k, n_k and d_k represent the dielectric constant, refractive index and thickness of the kth layer. θ₁ is the incident angle, and λ represents the wavelength at the base of SF11 prism. Then we need to calculate the total reflection coefficient (r_p) for p-polarization from the following expression:

r_{p} = \frac{(M_{11} + M_{12} q_{N}) q_{1} - (M_{21} + M_{22} q_{N})}{(M_{11} + M_{12} q_{N}) q_{1} + (M_{21} + M_{22} q_{N})},

where q₁ and q_N are the corresponding terms for the first layer (SF11 prism) and the Nth layer. Finally, the phase (

ϕ

_p) and reflectivity (R_p) of reflection coefficient r_p are obtained from the formulae:

ϕ_{p} = \arg (r_{p}), R_{p} = {| r_{p} |}^{2},

After obtaining the phase (

ϕ

_p) and reflectivity (R_p), we can calculate the GH shift by the stationary phase method, and it can be expressed as [51]:

S = - \frac{1}{k_{0}} \frac{d ϕ_{p}}{d θ_{1}},

3. Results and discussion

The curve of reflectivity with respect to the incident angle is called the SPR curve, once the SPPs are excited, there will be a reflection dip and the corresponding sharp changing reflectance phase. According to Eq. (7), the sharper the phase jump, the larger the GH shift we will obtain. Here we plot Fig. 2(a) to show the reflectivity (solid red line) and phase (solid blue line) with respect to the incident angle when the structure with only Au thin film. As we can see, the SPR curve shows a narrow reflection dip around 53.6° and the corresponding phase changes sharply indicating that a strong SPR based on the traditional Kretschmann-Raether structure is excited. At the same time, we plot the GH shift as a function of the incident angle in Fig. 2(b), the GH shift at the resonance angle is significantly increased as expected. The GH shift S in this structure (prism-gold-water) attains 14λ, which is the largest GH shift we can obtain in this system for 45 nm Au thin film.

Fig. 2 Variation of (a) reflectivity, phase and (b) GH shift with respect to angle of incidence for only 45 nm Au thin film at wavelength 632.8 nm.

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To systematically investigate the influence of the number of graphene layers and MoS₂ layers on the structure, we plot Fig. 3 (four-layer system with prism-gold-graphene-water) and Fig. 4 (four-layer system with prism-gold-MoS₂-water) to show the reflectivity, phase and GH shift with respect to the incident angle. There are two important features that can be found from Figs. 3 and 4: (i) when we increase the number of graphene layers or MoS₂ layers, the SPR resonance angle will show a large red shift, and the red shift of MoS₂ grows faster than graphene. The reason for this is that MoS₂ has a larger real part of permittivity than graphene, increasing the real part of the MoS₂ dielectric function will lead to larger incident angle to excite the SPR [52]; (ii) the bandwidth of reflectance curves broadening rapidly with the increasing number layers of MoS₂/graphene, and this is caused by the electron energy loss of MoS₂ layers associated with their imaginary part of the dielectric function. The imaginary part of dielectric function of Au thin film is smaller than that of MoS₂, so it leads to a larger electron energy loss [39]. From Fig. 3(c) and 4(c), the GH shift strongly depends on the number of graphene or MoS₂ layers, in this case, the largest GH shift we can obtain is 116λ.

Fig. 3 Variation of (a) reflectivity, (b) phase and (c) GH shift with respect to angle of incidence for different number of graphene layers at wavelength 632.8 nm. The thickness of the gold layer is 45 nm.

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Fig. 4 Variation of (a) reflectivity, (b) phase and (c) GH shift with respect to angle of incidence for different number of MoS₂ layers at wavelength 632.8 nm. The thickness of the gold layer is 45 nm.

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Figures 5 and 6 show the reflectivity, phase and GH shift with respect to the incident angle when the graphene or MoS₂ layer is fixed to 1 layer and the number of MoS₂ or graphene layers varies from 1 to 5 layers. It can be further analyzed and compared the effects of graphene layers and MoS₂ layers on the GH shift under different structure. In Fig. 5, with the increase of MoS₂ from 1 to 3 layers, the lowest point of the reflection curve is getting closer to zero, the phase also changes sharper, which indicates that the light absorption can be enhanced and a stronger SPR excitation is promoted. When MoS₂ is increased to 4 layers, the phase curve changes from “decrement” to “increment”, while the corresponding GH shift is changed from positive to negative. Moreover, a Heaviside step-like phase jumps occur at resonance dip where the reflectivity is the lowest point at a fixed graphene layer, and the sharpest phase changes at the point of lowest reflectivity where 3-layer MoS₂ and 1 layer graphene coated on the 45 nm Au thin film.

Fig. 5 Variation of (a) reflectivity, (b) phase and (c) GH shift with respect to angle of incidence for different number of MoS₂layers at wavelength 632.8 nm. The number of graphene is 1 layer and the thickness of the gold layer is 45nm.

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Fig. 6 Variation of (a) reflectivity, (b) phase and (c) GH shift with respect to angle of incidence for different number of graphene layers at wavelength 632.8 nm. MoS₂ is 1 layer and the thickness of the gold layer is 45 nm.

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When we fixed MoS₂ layer to monolayer, and change graphene layer from 1 to 5 layers, as shown in Fig. 6, the reflection curve is becoming lower with the increase of graphene layer, which also indicates that increasing the graphene layers can enhance the excitation of SPR. And in this structure, the phase curve jumps when the number of layers of graphene changes from 4 to 5 layers. The sharpest phase and maximum shift occurs when monolayer MoS₂ and 4-layer graphene coated on the 45 nm Au thin film. Also, the largest GH shift in this case we calculated attains 85.62λ. Compared with Fig. 5, it is obvious that the red shift of this system grows more slowly than Fig. 5. The reason for which is that the imaginary part of graphene is smaller than that of MoS₂, so the bandwidth of GH shift curves broadening slowly. And it can be considered as an adjustment to positive and negative GH shift at different incident angle. These results can be considered to obtain positive or negative GH shifts at different incident angles. Since increasing the number of layers of graphene or MoS₂ in the 5-layer system (prism-gold-MoS₂-graphene-water) can enhance the excitation of SPR, we can predict that the largest GH shift can be obtained when the multilayer MoS₂ and multilayer graphene are combined to form a heterogeneous structure. Therefore, to obtain the largest GH shift, we adjust the number of MoS₂ and graphene from 0 to 5 layers in the proposed 5-layer system (prism-gold-MoS₂-graphen-water) where the MoS₂ and graphene coated on 45 nm Au thin film. And we can obtain the largest GH shift, the results are shown in Table 1. It can be seen from the table that the largest GH shift (−235.8λ) is obtained when the MoS₂ is 2 layers and the graphene is 3 layers, and the optimal GH shift obtained by calculation occurs at θ = 56.8°.

Table 1. Value of optimal GH shift (S/λ) with different number of graphene and MoS₂ layers.

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In order to fully understand and confirm the above analysis, we use the finite element method (FEM) for simulation. The incident light is considered to be a Gaussian beam of finite width, and its half-width is 25λ. Figure 7(a) shows the results of the simulation when graphene and MoS₂ are both 0 layers, the lateral shift of the reflective beam S is about 13.8λ due to the excitation of the SPPs, which is lower than the theoretical value 13.99λ, the difference is caused by the influence of Gaussian beam width on simulation, so this deviation is acceptable. Similarly, when graphene is 3 layers and MoS₂ is 0 layers, the results are shown in Fig. 7(b), the lateral shift S≈19.7λ, which is less than the theoretical value of 19.96λ, is also considered reasonable. Therefore, the simulation results can verify that our theoretical calculation is correct.

Fig. 7 Numerical simulates the GH shift of the Gaussian beam when (a) graphene and MoS₂ are both 0 layers, (b) 3-layer graphene and 0-layer MoS₂. The half-width of the incident beam is 25λ. The angle of incidence is 53.6° and 54.2°, respectively.

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In our theoretical research, we find that the GH shift will appear a great red shift when we change the refractive index of bottom layer (n₆). Therefore, based on this change of red shift, the proposed structure can be used as a highly sensitive sensor to use. We define ΔGH as the change of GH shift with the changing of the refractive index of bottom layer, the sensitivity we defined as S' = ΔGH/Δn, where Δn refers to the change of refractive index of bottom layer. The results are shown in Fig. 8, here we compare the S' based on the structures only Au thin film, Au-graphene (1 layer), Au-graphene (1 layer)-MoS₂ (1 layer) and Au-graphene (3-layer)-MoS₂ (2-layer), respectively, corresponding to Fig. 6 (a)-(d). From Fig. 6 (a), one can see that in the structure of Au film only, the GH shift changes relatively little when we change the refractive index of the bottom layer by 0.002, which is about 1.76λ (all “λ” are calculated numerically only), thus, we can calculate the sensitivity to be S' = 880λ/RIU. In the Au-graphene structure, ΔGH is 2.2λ for Δn = 0.002, and the sensitivity is S' = 1100λ/RIU. Similarly, in the Au-graphene-MoS₂ structure, we can obtain the sensitivity is S' = 1655λ/RIU. However, when the graphene increases to 3 layers and MoS₂ increases to 2 layers, ΔGH is enhance to 110.9λ, and the Δn is only 0.0002, so the sensitivity is S' = 5.545*10⁵λ/RIU, which is nearly 350 times larger than the sensitivity in the SPR structure with only Au coating or graphene coating.

Fig. 8 Variation of GH shift with respect to the incident angle when changing the refractive index of the sensing medium in (a) only Au thin film, (b) l layer graphene coated with Au thin film (c) 1 layer graphene and 1 layer MoS₂ coated with Au film, (d) 3-layer graphene and 2-layer MoS₂ coated with Au film. The thickness of Au film is 45 nm.

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In the calculated results in Fig. 8 (d), the GH shift shows a huge change with the slight change of the underlying refractive index. In order to verify this huge change of GH shift, we conduct a further simulation of this. We assume that a Gaussian beam is incident into the structure shown in Fig. 1. In the plane of z = 0, the electric field expression of the incident beam can be expressed in integral form [52]: $E_{x}^{(i)} {|_{z = 0} = (1 / 2 π)}^{1 / 2} \int A (k_{y}) \exp (i k_{y} y) d k_{y}$ , where $A (k_{y}) = (w_{y} / \sqrt{2}) \exp [- w_{y}^{2} {(k_{y} - k_{y 0})}^{2} / 4]$ is the initial angular spectrum distribution of Gaussian beam, $k_{y 0} = k_{0} \sin θ$ , $w_{y} = W / \cos θ$ , $w_{y} = W / \cos θ$ is the half-width of the beam of incident plane. And the electric field of the reflected beam can be expressed as: $E_{x}^{(r)} {|_{z = 0} = (1 / 2 π)}^{1 / 2} \int r (k_{y}) A (k_{y}) \exp (i k_{y} y) d k_{y}$ . Finally, the lateral shift can be expressed as:

Δ y = \frac{\int_{- \infty}^{+ \infty} {| r |}^{2} A^{2} \frac{\partial ϕ_{r}}{\partial k_{y}} d k_{y}}{\int_{- \infty}^{+ \infty} {| r |}^{2} A^{2} d k_{y}} .

According to the above formulas, we can get the GH shift of the simulated reflected beam [53]. The result is shown in Fig. 9. Here, the half-width of incident beam is set as W = 1000λ, and other parameters are the same as in Fig. 8(d). It can be seen from the figure that the reflected beams of both Fig. 9(a) and (b) have a large negative shift when the angle of incidence is 56.8°, and the value of lateral shift is approximately equal to the shift value in Fig. 8(d) at θ = 56.8°. After calculation, we can get that the difference of the reflected light offset value is

Δ S = 290.9 u m - 162.73 u m = 128.17 u m

when the bottom layer refractive index is 1.332 and 1.3322, respectively. And the lateral shift value of Fig. 8(d) we calculate is

Δ S = 110.9 λ = 110.9 * 632.8 * 10^{- 3} / \cos ({56.8}^{\circ}) = 128.16 u m

, the results of the comparison are very close, which proves the correctness of our conclusion: the GH shift is very sensitive to the change of bottom layer refractive index, when we change the bottom layer refractive index, there exist a huge change of GH shift in the structure we proposed.

Fig. 9 Numerical simulations of the reflected beam from the MoS₂-graphene heterostructure under different refractive index of sensing layer. The blue curve refers to the incident beam, the red curve and the green curve denote the reflected light corresponding to different refractive index. Other parameters are the same as in Fig. 8(d) in the manuscript.

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As is well known, in the Kretschmann-Raether configuration, the thickness of noble metal is crucial for exciting SPPs. Usually, the best thickness is 40 nm to 50 nm when Au is used to stimulate the SPPs. Thus, we plot Fig. 10 to determine the optimal thickness of Au thin film so that we can obtain the highest sensitivity in the proposed configuration, and the result shows that sensitivity as high as 5.545*10⁵λ can be obtained when the thickness of Au film is 45 nm. Thus, we can conclude that 2 layers of MoS₂ and 3 layers of graphene with 45 nm Au thin film are the best parameters to realize the optimal sensitivity of the proposed sensing system.

Fig. 10 Variation of peak sensitivity with respect to the thickness of Au layer for the proposed system, when the MoS₂ is 2 layers and the graphene is 3 layers.

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4. Conclusion

In conclusion, the lateral shift in the Kretschmann-Raether configuration combined with 2D nanomaterials based on SPR is researched. When SPPs is excited, we have theoretically shown the influence of the number of graphene and MoS₂ layers on the GH shift, and obtain a giant GH shift when using a hybrid structure of 2-layer MoS₂ and 3-layer graphene. The largest shift is nearly 235.8 times the incident wavelengths, the shift of our structure is increased by more than 2 orders compared with the traditional SPR structure. Moreover, by changing the number of MoS₂ layers, we can control the positive and negative GH shift in graphene-MoS₂ system. As a SPR sensor based on the changing GH shift, our structure can obtain the maximum sensitivity with 5.545*10⁵λ/RIU when Au thin film is 45 nm, which indicates that the proposed configuration can be used in the field of high-sensitivity sensor. It should be pointed out that since the sensing layer we used is DI water, it is suitable for sensing medium with refractive index near 1.332 to obtain superior sensitivity.

Funding

National Natural Science Foundation of China (Grant Nos. 61505111 and 11604216); China Postdoctoral Science Foundation (Grant No.2016M600667); Science and Technology Planning Project of Guangdong Province (Grant No. 2016B050501005); Educational Commission of Guangdong Province (Grant No. 2016KCXTD006); Guangdong Natural Science Foundation (Grant No. 2015A030313549).

References and links

1. F. Goos and H. Hanchen, “Ein neuer und fundamentaler Versuchzur Totalreflexion,” Ann. Phys. 436(7-8), 333–346 (1947). [CrossRef]

2. F. Goos and H. Lindberghanchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” Ann. Phys. 440(3-5), 251–252 (1949). [CrossRef]

3. C. Y. Luo, X. Y. Dai, Y. J. Xiang, and S. Wen, “Enhanced and tunable Goos–Hänchen shift in a cavity containing colloidal ferrofluids,” IEEE Photonics J. 7(4), 6100310 (2015). [CrossRef]

4. L. Y. Jiang, Q. K. Wang, and Y. J. Xiang, “Electrically tunable Goos–Hänchen shift of light beam reflected from a graphene-on-dielectric surface,” IEEE Photonics J. 5(3), 6500108 (2013). [CrossRef]

5. Y. J. Xiang, X. Y. Dai, and S. C. Wen, “Negative and positive Goos-Hänchen shifts of a light beam transmitted from an indefinite medium slab,” Appl. Phys., A Mater. Sci. Process. 87(2), 285–290 (2007). [CrossRef]

6. C. Luo, J. Guo, Q. Wang, Y. Xiang, and S. Wen, “Electrically controlled Goos-Hänchen shift of a light beam reflected from the metal-insulator-semiconductor structure,” Opt. Express 21(9), 10430–10439 (2013). [CrossRef] [PubMed]

7. T. Tang, J. Qin, J. Xie, L. Deng, and L. Bi, “Magneto-optical Goos-Hänchen effect in a prism-waveguide coupling structure,” Opt. Express 22(22), 27042–27055 (2014). [CrossRef] [PubMed]

8. Z. Zheng, L. F. He, Y. H. Wan, J. S. Liu, “Goos-Hänchen one kind of method and system for measuring displacement sensor,” CN patent 103148787 B (2016).

9. C. A. Valagiannopoulos, “On examining the influence of a thin dielectric strip posed across the diameter of a penetrable radiating cylinder,” Prog. Electromagn. Res. C 3, 203–214 (2008). [CrossRef]

10. C. Bonnet, D. Chauvat, O. Emile, F. Bretenaker, A. Le Floch, and L. Dutriaux, “Measurement of positive and negative Goos--Hänchen effects for metallic gratings near Wood anomalies,” Opt. Lett. 26(10), 666–668 (2001). [CrossRef] [PubMed]

11. H. Gilles, S. Girard, and J. Hamel, “Simple technique for measuring the Goos-Hänchen effect with polarization modulation and a position-sensitive detector,” Opt. Lett. 27(16), 1421–1423 (2002). [CrossRef] [PubMed]

12. J. Unterhinninghofen, U. Kuhl, J. Wiersig, H.-J. Stöckmann, and M. Hentschel, “Measurement of the Goos–Hänchen shift in a microwave cavity,” New J. Phys. 13(2), 023013 (2011). [CrossRef]

13. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 20(12), 27 (2009).

14. S. Hayashi, D. V. Nesterenko, and Z. Sekkat, “Fano resonance and plasmon-induced transparency in waveguide-coupled surface plasmon resonance sensors,” Appl. Phys. Express 8(2), 022201 (2015). [CrossRef]

15. Z. Salamon, H. A. Macleod, and G. Tollin, “Coupled plasmon-waveguide resonators: a new spectroscopic tool for probing proteolipid film structure and properties,” Biophys. J. 73(5), 2791–2797 (1997). [CrossRef] [PubMed]

16. X. Liu, Z. Cao, P. Zhu, Q. Shen, and X. Liu, “Large positive and negative lateral optical beam shift in prism-waveguide coupling system,” Phys. Rev. E 73(5), 056617 (2006). [CrossRef] [PubMed]

17. M. Merano, A. Aiello, G. W. ’t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express 15(24), 15928–15934 (2007). [CrossRef] [PubMed]

18. M. Merano, “Optical beam shifts in graphene and single-layer boron-nitride,” Opt. Lett. 41(24), 5780–5783 (2016). [CrossRef] [PubMed]

19. X. B. Yin, L. Hesselink, Z. W. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85(3), 372–374 (2004). [CrossRef]

20. M. Mattheakis, C. A. Valagiannopoulos, and E. Kaxiras, “Epsilon-near-zero behavior from plasmonic Dirac point: Theory and realization using two-dimensional materials,” Phys. Rev. B 94(20), 201404 (2016). [CrossRef]

21. K. S. Thygesen, “Calculating excitons, plasmons, and quasiparticles in 2D materials and van der Waals heterostructures,” 2D Mater. 4(2), 022004 (2017). [CrossRef]

22. C. A. Valagiannopoulos, M. Mattheakis, S. N. Shirodkar, and E. Kaxiras, “Manipulating polarized light with a planar slab of black phosphorus,” J. Phys. Commun. 1(4), 045003 (2017). [CrossRef]

23. A. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]

24. Y. C. Fan, N. H. Shen, F. L. Zhang, Z. Y. Wei, H. Q. Li, Q. Zhao, Q. H. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4(11), 1824–1828 (2016). [CrossRef]

25. Y. C. Fan, N. H. Shen, F. L. Zhang, Q. Zhao, Z. Y. Wei, P. Zhang, J. J. Dong, Q. H. Fu, H. Q. Li, and C. M. Soukoulis, “Photoexcited graphene metasurfaces: significantly enhanced and tunable magnetic resonances,” ACS Photonics 5(4), 1612–1618 (2018). [CrossRef]

26. Y. C. Fan, N. H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2(1), 151–156 (2015). [CrossRef]

27. Y. C. Fan, L. Q. Tu, F. L. Zhang, Q. H. Fu, Z. R. Zhang, Z. Y. Wei, and H. Q. Li, “Broadband terahertz absorption in graphene-embedded photonic crystals,” Plasmonics (published online 2017).

28. Y. C. Fan, Z. Y. Wei, H. Q. Li, H. Chen, and C. M. Soukoulis, “Photonic band gap of a graphene-embedded quarter-wave stack,” Phys. Rev. B 88(24), 241403 (2013). [CrossRef]

29. T. Mueller, F. Xia, and P. Avouris, “Graphene photo detectors for high-speed optical communications,” Nat. Photonics 4(5), 297–301 (2010). [CrossRef]

30. M. Freitag, T. Low, F. Xia, and P. Avouris, “Photoconductivity of biased graphene,” Nat. Photonics 7(1), 53–59 (2013). [CrossRef]

31. G. Konstantatos, M. Badioli, L. Gaudreau, J. Osmond, M. Bernechea, F. P. Garcia de Arquer, F. Gatti, and F. H. L. Koppens, “Hybrid graphene-quantum dot phototransistors with ultrahigh gain,” Nat. Nanotechnol. 7(6), 363–368 (2012). [CrossRef] [PubMed]

32. M. Kim, N. S. Safron, C. Huang, M. S. Arnold, and P. Gopalan, “Light-driven reversible modulation of doping in graphene,” Nano Lett. 12(1), 182–187 (2012). [CrossRef] [PubMed]

33. K. Roy, M. Padmanabhan, S. Goswami, T. P. Sai, G. Ramalingam, S. Raghavan, and A. Ghosh, “Graphene-MoS₂ hybrid structures for multifunctional photoresponsive memory devices,” Nat. Nanotechnol. 8(11), 826–830 (2013). [CrossRef] [PubMed]

34. F. Zangeneh- Nejad and R. Safian, “Significant enhancement in the efficiency of photoconductive antennas usinga hybrid graphene molybdenum disulphide structure,” J. Nanophotonics 10(3), 036005 (2016). [CrossRef]

35. P. T. K. Loan, W. Zhang, C. T. Lin, K. H. Wei, L. J. Li, and C. H. Chen, “Graphene/MoS₂ heterostructures for ultrasensitive detection of DNA hybridisation,” Adv. Mater. 26(28), 4838–4844 (2014). [CrossRef] [PubMed]

36. L. Yu, Y. H. Lee, X. Ling, E. J. Santos, Y. C. Shin, Y. Lin, M. Dubey, E. Kaxiras, J. Kong, H. Wang, and T. Palacios, “Graphene/MoS₂ hybrid technology for large-scale two-dimensional electronics,” Nano Lett. 14(6), 3055–3063 (2014). [CrossRef] [PubMed]

37. Z. G. Nejad and S. Reza, “Hybrid graphene–molybdenum disulphide based ring resonator for label-free sensing,” Opt. Commun. 371, 9–14 (2016). [CrossRef]

38. D. Kufer, I. Nikitskiy, T. Lasanta, G. Navickaite, F. H. Koppens, and G. Konstantatos, “Hybrid 2D-0D MoS₂ -PbS quantum dot photodetectors,” Adv. Mater. 27(1), 176–180 (2015). [CrossRef] [PubMed]

39. L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov, “Strong light-matter interactions in heterostructures of atomically thin films,” Science 340(6138), 1311–1314 (2013). [CrossRef] [PubMed]

40. U. Schroter and D. Heitmann, “Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration,” Phys. Rev. B 60(7), 4992–4999 (1999). [CrossRef]

41. X. Li, Y. Zhu, W. Cai, M. Borysiak, B. Han, D. Chen, R. D. Piner, L. Colombo, and R. S. Ruoff, “Transfer of large-area graphene films for high-performance transparent conductive electrodes,” Nano Lett. 9(12), 4359–4363 (2009). [CrossRef] [PubMed]

42. S. W. Zeng, S. Y. Hu, J. Xia, T. Anderson, X. Q. Dinh, X. M. Meng, P. Coquet, and K. T. Yong, “Graphene-MoS₂ hybrid nanostructures enhanced surface plasmon resonance biosensors,” Sensor Actuat. Biol. Chem. 207, 801–810 (2015).

43. H. Raether, “Surface plasmons on smooth and rough surfaces and on gratings,” Springer Tr. in Mod. Phys. 111, 1–133 (1988).

44. A. Castellanosgomez, N. Agrait, and G. Rubiobollinger, “Optical identification of atomically thin dichalcogenide crystals,” Appl. Phys. Lett. 96(21), 213116 (2010). [CrossRef]

45. M. Bruna and S. Borini, “Optical constants of graphene layers in the visible range,” Appl. Phys. Lett. 94(3), 031901 (2009). [CrossRef]

46. M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl. Opt. 46(18), 3811–3820 (2007). [CrossRef] [PubMed]

47. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, “Single-layer MoS₂ transistors,” Nat. Nanotechnol. 6(3), 147–150 (2011). [CrossRef] [PubMed]

48. L. Wu, H. S. Chu, W. S. Koh, and E. P. Li, “Highly sensitive graphene biosensors based on surface plasmon resonance,” Opt. Express 18(14), 14395–14400 (2010). [CrossRef] [PubMed]

49. C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101(11), 111609 (2012). [CrossRef]

50. B. Gupta and A. K. Sharma, “Sensitivity evaluation of a multi-layered surface plasmon resonance-based fiber optic sensor: a theoretical study,” Sensor. Actuat. Biol. Chem. 107(1), 40–46 (2005).

51. K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 2(1-2), 87–102 (1948). [CrossRef]

52. I. Pockrand, “Surface plasma oscillations at silver surfaces with thin transparent and absorbing coatings,” Surf. Sci. 72(3), 577–588 (1978). [CrossRef]

53. L. G. Wang, M. Ikram, and M. S. Zubairy, “Control of the Goos-Hänchen shift of a light beam via a coherent driving field,” Phys. Rev. A 77(2), 023811 (2008). [CrossRef]

MoS₂/Graphene	0 layer	1 layer	2 layer	3 layer	4 layer	5 layer
0 layer	13.99	15.02	16.8	19.96	26.25	43.16
1 layer	14.03	16.4	20.93	31.78	85.62	−83.79
2 layer	16.47	23.31	46.8	-235.8	−29.14	−14.42
3 layer	26.73	96.62	−47.12	−17.35	−10.7	−6.827
4 layer	116	−38.21	−15.38	−9.28	−6.489	−4.92
5 layer	69.08	−67.15	−22.81	−14.08	−10.54	−8.791

Giant and controllable Goos-Hänchen shifts based on surface plasmon resonance with graphene-MoS₂ heterostructure

Abstract

1. Introduction

2. Theoretical model and method

3. Results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (10)

Tables (1)

Equations (12)

Optical Materials Express