High-Performance Tapered Fiber Surface Plasmon Resonance Sensor Based on the Graphene/Ag/TiO2 Layer

In this paper, a highly sensitive surface plasmon resonance sensor is proposed on the basis of a miniature tapered single-mode fiber. The sensing area of the tapered fiber is coated with graphene, silver, and titanium dioxide layer. The graphene layer is used to increase the light absorption rate, and the titanium dioxide layer is used to protect the silver layer from oxidation and improve the sensor sensitivity due to its high dielectric constant. According to the simulation results of COMSOL Multiphysics software, when the graphene is 15 layers, the silver layer is 40 nm, and the titanium dioxide is 20 nm, high-performance SPR can be obtained. The refractive index detection range of this sensor is 1.32–1.38, and its sensitivity can reach 8750 nm/RIU when the external refractive index is 1.38. The research results have potential application value for the design of high-performance SPR sensors.


Introduction
Surface plasmon resonance (SPR) is a common optical physical phenomenon, which is caused by the coupling oscillation between photons and free electrons on the metal surface, and is particularly sensitive to the medium on the metal surface. Therefore, SPR substance detection technology has been widely used and researched deeply in the fields of chemistry, biology, and medicine due to their high sensitivity, no labeling, and real-time detection [1][2][3].
The Kretschmann [4] prism-coupling structure is a more traditional way to stimulate SPR, but the sensor based on the prism structure has the disadvantages of large volume, complex system, and long-distance transmission, which limits its practical application. In 1993, Jorgenson and Yee of the University of Washington in the USA combined optical fiber with SPR technology, based on the principle of attenuated total reflection (ATR), successfully designed an optical fiber SPR sensor [5]. Comparing with the Kretschmann prism structure, the optical fiber SPR sensor has advantages such as small size, high resolution, and anti-electromagnetic interference. Since then, the optical fiber SPR sensor has been extensively studied. Its main research direction is the design of fiber structure and the choice of coating for the optical fiber sensing area. So far, many fiber structures have been proposed to realize microstructure fibers, including singlemode fiber (SMF) [6,7], multi-mode fiber (MMF) [8,9], photonic crystal fiber (PCF) [10,11], polarization maintaining fiber [12], plastic polymer fiber [13], hollow core fiber [14]. However, there are a large number of modes in MMF that can excite many SP modes, which can widen the SPR spectrum and reduce the sensing performance; the PCF process is complex and expensive; and polarization-maintaining fiber, plastic fiber, and hollow fiber are in the research stage due to their unique properties. Compared with SMF, there is only one transmission mode, so the SPR spectral line is relatively narrow, and the technology is relatively simple and mature. In this paper, the single-mode fiber is selected to build the SPR sensor. In order to excite SPR, the metal coating of the sensing area usually uses precious metals, such as gold and silver. Since the imaginary part of the dielectric constant of the silver film is larger than that of the gold film, and the real part is smaller than that of the gold film, the full width at half maximum (FWHM) and sensitivity of the silver film sensor are smaller than that of the gold film. In this paper, silver film is selected as the metal layer that excites SPR. However, silver is unstable in air, which will affect the performance of the sensor. Therefore, the silver surface is usually coated with a high dielectric constant adjusting layer (such as TiO 2 [15], ZnO [16,17]), which can not only prevent the silver layer from being oxidized, but also improve the electric field strength between the upper oxide layer and the sensing medium, so as to improve the sensitivity of the sensor. TiO 2 has been widely used because it has a stronger binding to light than other oxide dielectrics [18,19]. Twodimensional materials (graphene, Ws 2 , Wse 2 , Mos 2 , Mose 2 ) [20][21][22][23] have also been extensively studied as coating in SPR sensing due to their unique properties, especially graphene, because the absorptivity of single-layer graphene is about 2.3%, the absorptivity of graphene increases as the number of layers, and the light transmittance of graphene is as high as 97.7% [24,25]. The excellent properties of graphene can be used to improve the sensitivity of the sensor. Wang et al. proposed a photonic crystal fiber SPR sensor based on the silver/graphene structure to improve the performance of the sensor [26]. A U-shaped optic fiber SPR biosensor based on graphene/AgNPs is presented by Zhang et al. whose experimental results show that the graphene layer can improve the sensitivity of the sensor [27]. Nayak et al. covered the D-type surface with silver and graphene, and the sensitivity could reach 6800 nm/RIU [28]. All the above studies show that graphene has important applications in improving the performance of sensors.
So far, the most research on the single-mode fiber is the D-type side-polished fiber [29]. The evanescent wave of the core is revealed by polishing off the cladding of a certain thickness. Due to the fragility of the optical fiber, a high degree of controllability is required in the process of manufacturing D-type optical fiber, so the requirements for experiments are particularly high. The research in this paper is based on a cylindrical tapered single-mode fiber. The tapered fiber is divided into a sensing area and a taper transition region, which can be made by mechanical tapering or chemical etching [30,31]. This paper theoretically studies the SPR tapered single-mode sensor with graphene/ silver/titanium dioxide coating, and optimizes the parameters of each coating layer. Figure 1 shows the structure diagram and cross-sectional view of the tapered single-mode fiber proposed in this article. When the fundamental mode in the single-mode fiber is transmitted to the tapered sensing region, the mode field diameter is reduced due to the reduction of the fiber diameter, so that a part of the fundamental mode is coupled to the outside of the cladding to form evanescent wave and generate an evanescent field. Due to the effect of the evanescent field, a surface plasmon wave (SPW) is generated at the interface between metal and sensing medium. When the wave vectors of the evanescent wave and SPW are equal in the x-direction, the phase matching condition is met, and the oscillating free electrons absorb part of the transmitted light energy, resulting in an absorption peak in the resonance transmission spectrum. The dispersion formula of SPW is [32] Eq. 1:

Sensor Structure and Theoretical Modeling
where k is the number of free-space wave vectors, s s = n 2 s is the dielectric constant of the analyte, and m is the dielectric constant of the metal. The SPW wave vector changes with the dielectric constant of the analyte, causing the resonance wavelength of the SPR to shift. Therefore, we can detect the refractive index of the analyte by detecting the change in resonance wavelength.
In this simulation calculation, the cladding diameter of the sensing area is set to 7.25 μm, the core diameter is 5.25 μm, the refractive index of the cladding and core are 1.4378 and 1.4438, respectively [33], and the length of the sensing area is 0.1 mm. The dielectric constant is written as follows, according to the Drude model [34] Eq. 2: where c is the plasma wavelength and p is the collision wavelength; they are 1.7614 × 10 −5 m and 1.4541 × 10 −7 m , respectively. The dielectric constant of the dielectric layer TiO 2 can be written as [35] Eq. 3 where λ is the incident light wavelength; the unit is millimeters.
The refractive index of graphene is [36] Eq. 4: where λ is the vacuum wavelength, C 1 = 5.446 m . The thickness of a single-layer graphene is 0.34 nm; when the number of graphene layers is N, its thickness is d=0.34×N nm. The transmittance is expressed as [37] Eq. 5 where n eff represents the effective refractive index of the surface plasmon mode, Im represents its imaginary part, and L is the length of the sensing area. An important parameter that characterizes the performance of a sensor is sensitivity, which can be expressed as the ratio of resonance drift to the change in refraction of the analyte [38] Eq. 6 Another important sensor performance parameter is the FWHM, which refers to the difference between the corresponding maximum and minimum wavelengths when the resonance absorption peak is attenuated by half. The figure of merit (FOM) is the ratio of sensitivity to FWHM [39] (3) FOM is a comprehensive parameter of sensor performance. As shown in Eq. (7), FOM is directly proportional to the sensitivity and inversely proportional to FWHM.
In this paper, the finite element method software COMSOL Multiphysics is used to model the cross section of the sensing area of the tapered fiber SPR sensor. When the SPR effect is generated, the electric field intensity distribution of the cross section is shown in Fig. 2a. Figure 2b is a graph of the electric field amplitude changing with radians. When the SPR effect occurs, the energy on the two sides of the cross-section symmetry is locally strengthened, rather than the energy at the interface of the entire circle. This is because only p-polarized light can produce SPR, and s-polarized light does not produce SPR.

Silver Film Sensor
In order to optimize and determine the thickness of the Ag film, the thickness of the silver film is set to 20 nm, 30 nm, 40 nm, 50 nm, 60 nm, and 70 nm, and the external refractive index is 1.37. The simulated transmittance spectrum is shown in Fig. 3. It is shown in Fig. 3 that the resonance peak appears red-shifted as the thickness of the silver film increases. But when the thickness of silver is less than 40 nm, the shift of the resonance wavelength is more sensitive to the change of the thickness of silver, and the transmission depth gradually becomes deeper as the thickness of Ag increases. When the thickness of Ag exceeds 40 nm, the thickness of Ag has a relatively small effect on the resonance peak shift, and the depth of resonance gradually becomes shallower as the thickness of Ag increases. The reason is that the thickness of the silver layer is too large, which will reduce the evanescent wave penetrating the metal layer, resulting in SPW and evanescent wave energy coupling to decrease, which in turn leads to the reduction of the intensity of the SPR peak. Therefore, the thickness of Ag is maintained at 40 nm, which has a good SPR spectrum. Figure 4a shows the transmission spectrum of the refractive index of the sensing area from 1.32 to 1.38. It can be seen from the figure that as the sensing refractive index continues to increase, the resonance wavelength red-shifts, and the transmission depth is increasing. Figure 4b shows the fitting curve of the resonance wavelength with the change in refractive index. The fitting coefficient R 2 is 0.99956. It is shown in this figure that when the refractive index is 1.36, 1.37, and 1.38, the sensitivity reaches 3640.47 nm/RIU, 4159.5 nm/RIU, 4678.57 nm/ RIU, respectively.

Fiber-Graphene-Silver Film Sensor
Add a layer of graphene between the optical fiber and the metal layer of silver. Since graphene has light absorption and semi-metal properties; using this feature can enhance the sensitivity of the sensor. The thickness of metallic silver is 40 nm. Figure 5 shows the variation of resonance peaks with the number of graphene layers under different refractive indexes of analytes. It can be seen that as the thickness of graphene increases, the resonance peak red-shifts, and the slope of the resonance curve represents the sensitivity of the sensor. Figure 5b shows the change of sensitivity and FWHM with the number of graphene layers when the external refractive index is 1.37. It can be seen that both the sensitivity and FWHM increase with the number of graphene layers. But the increase in FWHM leads to a decrease in the detection accuracy of the sensor. Table 1 shows the specific values of sensitivity, FWHM, and quality factor varying with the number of graphene layers when the refractive index of the analyte is 1.37. Considering the influence of graphene on the quality factor and sensitivity of the sensor, 15 graphene layers are selected in the later simulation. For graphene with 0 layers and 15 layers, the refractive index is 1.32-1.38; its sensitivity is shown in Table 2. It can be seen from the table that the sensitivity of the sensor with the graphene layer has been improved.

Fiber-Graphene-Silver-TiO 2 Film Sensor
Since silver as the outermost layer is easily oxidized and affects the stability of the sensor, it can be considered to cover the outer surface of silver with TiO 2 , a material with high dielectric constant. Figure 6 shows the curve of the SPR resonance spectrum varying with the thickness of the TiO 2 when the outer layer of the optical fiber has been coated with 15-layer graphene/40 nm Ag and the analyte refractive index is 1.37. It is shown in Fig. 6a that as the thickness of TiO 2 increases, the resonance peak moves to the long-wave direction and the FWHM gradually widens. The maximum transmission depth is when TiO 2 is 5 nm. It is shown in Fig. 6b, c that FWHM exists when the thickness of TiO 2 is 20 nm, but when TiO 2 is greater than 20 nm, FWHM no longer exists. Therefore, when the thickness of TiO 2 reaches 25 nm, it is no longer suitable for sensors. Figure 7 shows that the SPR resonance peak varies with the refractive index of the analyte under different thicknesses of TiO 2 . It is shown in the figure that when the thickness of TiO 2 is the same, the resonance peak shifts to the long-wave direction with the increase of the refractive index. When the external refractive index did not change, the resonance peak red-shifts as the thickness of TiO 2 increases. We can see that the relationship between the resonance wavelength and the refractive index of the analyte is nonlinear. The obtained data points are fitted by a quadratic polynomial, and the slope of each point is used to characterize the sensor sensitivity. The relationship between sensitivity and refractive index change is shown in Fig. 8. When the refractive index of the analyte is 1.38, the sensitivity changes with the thickness of TiO 2 are 5021.4 nm/RIU, 5785.7 nm/RIU, 7578.5 nm/  In general, the sensitivity of the SPR sensor basically increases with the thickness of TiO 2 . The graphene/Ag/ TiO 2 structure of the single-mode tapered fiber SPR sensor designed in this paper has advantages in sensitivity compared with other structures, as shown in Table 3.

System Analysis
In order to systematically analyze how each layer of material affects the performance of the SPR sensor, the simulation diagram is as shown in Fig. 9. Table 4 shows the specific values of sensitivity and FWHM of each structure. Figure 9a shows the SPR transmission spectrum when the tapered single-mode fiber is only coated with Ag. When the refractive index of the analyte is 1.36, the resonance peak shift and FWHM are 60 nm and 14 nm, respectively. The sensitivity is about 3000 nm/RIU, which indicates that the sensitivity of the sensor with only one layer of Ag is not very high. Figure 9b is the transmission spectrum when 15 layers of graphene are coated between the silver film and the optical fiber. The resonance drift is about 64 nm. The sensitivity is 3200 nm/RIU, and FWHM is 20 nm. Compared with no graphene layer, the sensitivity and FWHM are slightly increased. Figure 9c shows the reflection curve of the Ag/TiO 2 sensor. From the figure, we can see that the resonance peak shift and FWHM are greatly increased compared with the sensor with 40 nm Ag film and 15-layer graphene/40 nm Ag structure; the sensitivity is about 4800 nm/RIU, and the FWHM is 115 nm when the refractive index of the analyte is 1.36. Figure 9d shows the reflection resonance curve of a 15-layer graphene/40 nm Ag/20 nm TiO 2 sensor. It is shown in Table 4 that the sensitivity of the sensor with this structure is about 5000 nm/RIU, and the FWHM is 84 nm. The sensitivity of the graphene/Ag/TiO 2 structure sensor is greatly improved compared with graphene/ Ag, and the FWHM is narrower than Ag/TiO 2 . In the comparison of structures c and d, it can be seen that the addition of graphene reduces the FWHM of the sensor and the sensitivity slightly increases. Comparing structures b and d, we can know that TiO 2 greatly improves the sensitivity of the sensor.

Optical Field Distribution of Fiber SPR Sensor
In order to further analyze how each layer of material affects the electric field intensity of the SPR sensor, the electric field distribution of three different structure sensors (Ag, graphene/Ag, graphene/Ag/TiO 2 ) is studied by COMSOL multiphysics. Figure 10 shows the TM polarization electric field intensity distribution and electric field amplitude distribution diagram when the analyte refractive index is 1.32 with different sensor structures. Figure 10a shows that the sensor structure is 40 nm Ag, and its electric field is locally enhanced at a symmetrical position, and the SPR phenomenon occurs. Figure 10b shows the electric field distribution of the 15-layer graphene/40-nm Ag structure. It is shown in the figure that the electric field intensity at the core and sensor interface is much higher than that of the 40-nm Ag sensor. This is because the strong light permeability and semi-metallic properties of graphene, a high refractive index material, increase the transmission depth of the evanescent wave, thereby increasing the electric field strength at the interface between the metal and the medium. Simultaneously, due to the extremely high electron mobility of graphene [42,43], it has a positive effect on enhancing the excitation of SPR. Thus, the performance of the sensor based on the graphene/ silver structure has been greatly improved. Figure 10c is the electric field intensity distribution curve of the 15-layer graphene/40-nm Ag/20-nm TiO 2 structure. It is shown in the figure that most of the energy is coupled to form an evanescent wave to excite SPW, and only a small part of the energy continues to be transmitted in the core in the form of the fundamental mode. This is due  to the translucency of TiO 2 in visible and near-infrared light, which can transfer the electrons from the dielectric layer to the silver film, thus greatly increasing the resonance energy coupling. Figure 11 shows the electric field intensity distribution diagram of the 15-layer graphene/40-nm Ag/20-nm TiO 2 SPR sensor under different analyte refractive indexes. We can see from the figure that the electric field intensity of interface coupling increases with the refractive index of analyte, which means that the sensor becomes more sensitive with the increase of the refractive index. The sensitivity of the sensor improves with the increase of the refractive index.

Conclusion
This paper proposes a single-mode tapered fiber SPR sensor with graphene/silver/TiO 2 coatings, and optimizes its parameters. The detection range of the sensor is 1.32 to 1.38, and the sensitivity can reach 8570 nm/RIU when the refractive index is 1.38. Simultaneously, we systematically analyzed and compared the performance of four SPR sensors with different structures, Ag, graphene/Ag, Ag/TiO 2 , graphene/Ag/ TiO 2 , and found that the overall performance of the sensor with the last structure is the best. The electric field intensity and amplitude distribution of sensors with several different structures have also been studied, showing that graphene and TiO 2 can indeed enhance the electric field coupling strength of the SPR sensor and enhance the performance of the sensor. According to the research results of this article, it has theoretical guiding significance for manufacturing highperformance SPR sensors.