High-Sensitivity Angle Modulation Biosensor Based on Surface Plasmon Resonance of Metasurface

Metasurface is a popular artificial layered material. In this paper, a sensor based on surface plasmon resonance with a new type of symmetrical triangular structure is designed. This paper designs a metasurface structure, the highest sensitivity of 364 °/RIU is achieved by adopting angle modulation. We used COMSOL simulation software, the metal layer structure and size parameters are optimized to obtain the best reflectivity curve, and the accuracy of the simulation is improved through the linear interpolation method. Compared with the traditional gold layer structure, the sensitivity of 135 °/RIU is increased by 1.7 times. We believe that this design can have potential application value in the field of biosensing.


I. INTRODUCTION
S URFACE Plasmon Resonance (SPR) is a promising technology that has been widely used in many fields such as new drug development, medical diagnosis, food safety, and environmental monitoring [1], [2]. The implementation of SPR technology relies on surface plasmons (SPs) and evanescent waves. When the wave vector of the evanescent wave matches the wave vector of the SPs, SPR appears, which results in a sharp drop in the reflectance curve. The reflectivity curve depends on the incident angle, working wavelength, prism refractive index, medium, metal, and analyte [1], [3]. SPR technology is high sensitivity and label-free, which allows real-time and on-site monitoring, electromagnetic interference prevention, and determination of interaction dynamics [4], [5], [6], [7], [8].
Due to these features, SPR technology is often applied in biosensors. Metasurface is a kind of artificial material. Its thickness is less than wavelength. Metamaterials have unique properties. Therefore, metasurface have been largely used in super-lens [9], super-resolution, invisibility [10], negative refraction [11], polarization rotation, source imaging [12], energy Manuscript  harvesting [13], biomedical sensors [14]. With the development of nanofabrication technology, nanostructured metal stimulation SPR has received more and more attention [15], [16]. Butterflyshaped structure enhances dipole resonance and electrical excitation [17], [18]. Among several instruments of SPR biosensing platforms, the angle modulation is a widely used modulation method, in which the reflectivity of monochromatic light is monitored as a function of the incident angle. This method is considered reliable and sensitive, partly because commercially available instruments allow angular resolutions as low as 0.001°. This article studied the change of SPR resonance angle caused by the change of refractive index of the upper solution on the metal metasurface at an incident wavelength of 632.8 nm.
First, we studied the effect of gold structure changes on the sensitivity of angular modulation. Then, we added a silver symmetrical triangle structure to the gold layer array and scan the thickness of these two layers as well as the gap width between them using COMSOL simulation. After decreasing errors with the interpolation function approach, we got multiple results with the optimal sensitivity, and determined the optimal range of angle modulation sensitivity.

A. Schematic Diagram of Sensor Based on Prism Structure
The schematic diagram of the sensor based on the prism structure is shown in Fig. 1. Passing through the polarizer and collimator, x-direction-polarized laser with 632.8 nm wavelength enters the prism at a certain incident angle, interacts with the sensing medium in the sensing structure, and finally reflects  into the power meter. By measuring the reflectance, according to the change of the resonance angle, the change of the refractive index of the solution in the range of 1.33 to 1.34 can be obtained. Fig. 2 shows the SPR structure of the symmetrical triangular metasurface. Because a lower refractive index prism can achieve higher sensitivity, the gold nano-layer with a thickness of H (43-51 nm) is deposited on the BK-7 glass (1000 nm) following the Kretschmann model. On the gold layer, a silver layer with a diagonal length equal to the unit side length of gold layer and a thickness of D (8-12 nm) is deposited. an opening with a width of W (8-12 nm) is opened in the y-axis direction of the silver layer. By scaning the combination of the above parameters, the sensor performance can be optimized. The incident light, a TM wave with a wavelength of 632.8 nm, come from the y-axis of the glass below and form a total reflection. the evanescent field generated by total reflection passes through the nano-thick metal film and excites surface plasmon resonance at the interface between metal film and sample. When the thickness of the metal film is less than the skin depth of the material, the evanescent field couples with the SPW at the metal film-sample interface.

B. Metasurface SPR Structure
In this work, we propose Symmetric triangle configurations which provide a strong SPP mode confinement in the narrow region. As a result, there is a high light-mater interaction which results in the enhanced sensitivity of the sensor. The transmission spectrum and E-field distributions are simulated using COM-SOL 5.1 software by utilizing a 3D (three-dimension) finite element method (3D-FEM). The structure is a periodic structure, so we used periodic boundary conditions. The EM-wave frequency domain (ewfd) is chosen as the physics interface and the modal analysis is added to the study. In COMSOL simulations, the subdomains of the sensor design are divided into triangular mesh element with a fine mesh grid size for the air medium and waveguide geometries. This allows us to obtain precise simulation results within the available computational resources. When solving EM wave problems, it is advantageous to model a domain with open boundaries that is a boundary of the computational domain through which an EM wave can pass without reflection. To approximate an open geometry, scattering boundary conditions (SBC) are used at the outer edges of the FEM simulation window.

C. Principles and Formulas
The incident light enters from the lower glass and is totally reflected at the glass-metal interface. The horizontal component of the light wave vector.
In the above formula, k r is the wave vector of the horizontal component of the incident light, ω is the frequency of the incident light, c is the speed of light in vacuum, and ε r is the dielectric constant of the lower glass.
The wave vector of the surface plasma wave generated at the interface between the metal medium and the dielectric is expressed as: In the above formula, k spr is the wave vector of the incident light, and ε 1 is the dielectric constant of the detection solution When the wave vector of the incident light along the interface direction is the same as the plasma wave vector of the excited surface, the sonic wave of all emitted light and the surface plasmon wave generated by the metal layer-solution layer resonate, so the energy of the reflected light reaches the minimum. That is how surface plasmon resonance occurs: The structure is an angle-modulated SPR structure. The expression is: Where θ is the angle of change, n r is the refractive index of the lower glass, and n 1 is the refractive index of the upper solution.
Calculation of SPR sensitivity: In the above formula, S is the sensitivity of angle modulation, Δθ is the angle of change, Δn is the change of the refractive index of the solution III. RESULTS

A. The Sensitivity of Metal Array Structure Compared With the Ordinary Gold Layer
To explore whether the material of the metasurface can enhance the surface plasmon resonance of the structure, the SPR material generally is made of gold or silver. These two materials can stimulate a better SPR effect. In this section We chose gold as the structural material. The metal film with a thickness of 10 nm to 70 nm can achieve the best coupling effect with the visible light. Next, we study the sensitivity of a single gold layer of 60 nm and compare it with the sensitivity of a 50 nm thick gold layer plusing a 10 nm thick square array.
In order to increase the sensitivity, we replace the upper layer of gold material with silver and replace the original square structure with a symmetrical triangle structure in the following subsequent.
As shown in Fig. 4(a), the sensitivity of the SPR structure with a 60 nm thick gold layers is 135°/RIU when the refractive index is in the range of 1.33 to 1.34. in order to verify whether the SPR is successfully excited, we add a field monitor to observe the electric field distribution of the sensing element during simulation when the metasurface structure is applied. The electric field distribution of the longitudinal section of the sensor is shown in Fig. 4(b), and the electric field distribution of the cross section of a square row is shown in Fig. 5(b). It can be clearly seen that when the refractive index is 1.33 and the incident angle is 76°, it successfully cause resonance, and the energy of the light is highly localized near the upper and lower discontinuities. At this time, most of the incident light is caused by resonance. It is consumed and cannot be reflected back into the incident medium, resulting in the appearance of resonant peaks on the reflection spectrum. This local field strength can reach 9 10 V/m when the port output power is 1 W. This is of great benefit to the detection work, because the highly localized electric field helps to enhance the interaction between the object to be measured and the incident light, which can make the sensor more sensitive to changes in the refractive index of the detected sample. Fig. 4(b) shows that the sensitivity of the metal array can reach 220°/RIU. although the full width at half maximum is increased, the quality factor will decrease accordingly, As shown in Fig. 5(a). In subsequent research, we found that the structure can reach 250°/RIU When the upper gold layer is 12 nm and the lower gold layer is 45 nm. From the above results, we can conclude that compared with the traditional structure, although the quality factor will decrease due to the increase in the full width at half maximum, the hypersurface structure has a greater sensitivity to angle modulation. In the above study, we compared the commonly used model with the metasurface structure, and determined the sensitivity of the surface structure to SPR under the condition of the enhanced local electric field. Next, we will open the upper square metal in the y direction when the upper metal is replaced by silver, as for more local electric field enhancement can be generated and better results can be obtained.

B. The Effect of Metal on Structural Sensitivity
In this section, we need to adjust three structural parameters, but we are adjusting the structural parameters. If the controlled variable method is used, the results are not too rigorous for the study of the parameters one by one. Therefore, we use COMSOL to perform simulation calculations for the upper silver layer gap(D) at 8-13 nm, the upper gold layer(W) at 8-13 nm, and the lower structure(H) at 45-53 nm. The results are obtained from the above, and the sensitivity of angle modulation is improved to obtain an optimal gap, in which we also use the algorithm of interpolation function to further improve the sensitivity of the simulation.
In the parameter optimization process, the grid optimization method is adopted to scan the four parameters and obtain 225 sets of data. Due to the limitation of computing resources, the incident angle step size is only set to 0.2°. Therefore, the sensitivity error is about 40°/RIU in this work. In order to improve the accuracy of the sensitivity, we use quadratic interpolation  I  THE REFRACTIVE INDEX OF EACH LAYER OF THE STRUCTURE   TABLE II  THE 5 MOST SENSITIVE PARAMETERS to post-process the incident angle-reflectivity curve, thereby effectively improving the sensitivity.
By observing the incident angle-reflectivity curve, it can be found that the lines at adjacent angles have the characteristics of a parabola. Therefore, if we assume that multiple adjacent points satisfy a specific quadratic function, the refractive index at the corresponding angle can be expressed as: Among this, let θ n+2 − θ n+1 = θ n+1 − θ n = Δθ, and θ i = θ n + nΔθ, n ∈ (0, 1), we can get the reflectivity r i of any angle θ i between the n angle θ n and the n + 1 angle θ n+1 : Through the above method, we effectively reduce the original sensitivity error from 40°/RIU to 0.4°/RIU. It is worth noting that, using this method to post-process the data, the accuracy of the sensitivity depends on the number of interpolation points, which can be manually controlled. Here we believe that an error of 0.4°/RIU can already meet our needs for parameter optimization.
The results obtained by the quadratic interpolation function are shown in the following table. Among the 225 groups of data, we have selected the 5 groups with the highest angle modulation sensitivity, as shown in the following Table II. As can be seen in the table, in the 225 sets of simulation data, it can be seen that when the silver layer gap is 12 nm, the sensitivity will be significantly improved, and the sensitivity of the first 5 sets of parameters all exceed 340°/RIU. Next, we simulated the most sensitive parameter combination. The data when the sensitivity is 364°/RIU is shown in Fig. 6(a), and the  electric field diagram is as follows. It can be seen that the energy is concentrated in one corner. Compared with the electric field in the previous section, the energy is more concentrated, and it is also better for the improvement of sensitivity. Effect. When the port output power is 1 W, the electric field strength can reach 9 10 V/m, as shown in Fig. 6(b).
From the point of view of the refractive index, this mechanism is more susceptible to the influence of the metal complex permittivity value given by ε = ε r + iε i [17]. ε r is the real part, and ε i is the imaginary part of the dielectric function of the metal. The real part of the dielectric constant of the metal determines the position of the SPR, and the imaginary part determines the bandwidth.
To further investigate the role of structural alterations, we considered the intensity changes of the magnetic resonances of the two structures. As shown in the inset of Fig. 8, Because of the coupling structure formed by the symmetrical triangular structure, the intensity of the magnetic resonance decreases. there is a clear increase in magnetic resonance intensity, about 23%. In the structure, the dipolar−dipolar and charge−charge interaction are missing and dipolar−charge interaction is strengthened alongside the strengthening of near field array effect. Such nearly coherent interaction can pump more charges into the active components and boost up the intensity of resonance.
According to the current research on metal structure SPR, the angle modulation sensitivity of the two structures in this paper is traditional times, the most sensitive result is 4.6 times that of traditional SPR, as shown in Table III.  In order to test the detection performance of the sensor, we set the refractive index of the detection medium to 1.33 + Δθ with a step size of 0.002 to simulate the change in the refractive index of the sensor surface from 1.33 to 1.34 during actual measurement. The configuration of the sensor is the structure in Table III when covering 1. Fig. 8(b) shows the change in the absorption peak when the refractive index increases from 1.33 to 1.34. After calculation, the resonance angle change under this structure has a very good linear relationship with the refractive index change. The correlation coefficient is 0.99. But the figure of merit dropped to 22.3. The relationship between the refractive index of the solution n and the resonance angle θ can be expressed as follows: IV. DISCUSSION The current ways to improve the sensitivity of SPR mainly lie in a multilayer structure and a structure using a grating. In this paper, starting from the structure of the metal, by changing the relative permittivity of the overall model, the local electric field energy is increased to achieve the effect of improving the sensitivity. In the next work, we will also try to reduce the full width at half maximum and increase the sensitivity by adding two-dimensional materials.

V. CONCLUSION
This paper proposes a new SPR biosensor based on metasurface. The traditional SPR structure is optimized to a symmetrical triangle structure. The highest sensitivity can reach 364°/RIU, which is about 170% higher than the traditional SPR sensor. However, as the sensitivity increases, the full width at half the maximum of the reflectance curve becomes larger, resulting in a corresponding decrease in the quality factor compared with traditional sensors. However, due to its high sensitivity, it also has great potential in biosensing, which can be applied in the fields of bioassay, food safety, medical diagnosis etc.
Disclosures: The authors declare that there is no conflict of interests regarding the publication of this paper.