Construction and Evaluation of Plasmonic Refractive Index Sensor Based on Changing the Number of Resonators and Changing Their Dimensions

In this paper, a plasmonic refractive index sensor based on MIM waveguide (metal_insulation_metal) with two plasmonic waveguides and five rings and two teeth and four rectangular cavities is proposed and designed. The refractive index of the resonators as well as the resonant wavelengths will be investigated by the time difference finite difference method. To achieve an optical sensor with excellent quality and performance, we change the number and type of amplifiers and their dimensions. In each stage of the simulation, we will only change the refractive index of the middle ring located in the middle of the two waveguides, and the refractive index of the other amplifiers remains the same. This challenge will help to form a more appropriate structure for optical sensors. The sensor built in this simulation has a balanced and suitable function for integrated circuits and helps researchers to better understand the design of plasmonic structures. It also has important applications in medical research, health care, drug manufacturing, security monitoring and environmental protection, internal security of countries and the battlefield.


Drawing the structure of the plasmonic sensor and analyzing its structural model
The structure of our proposed sensor consists of two plasmonic waveguides, five rings, two teeth and four rectangular cavities (Fig.1). The two waveguides have a height of W1 = 50 nm. The middle ring, which is located between the two waveguides, has an outer radius of R1 = 125 nm and an inner radius of r1 = 90 nm. Also, two teeth are connected to the middle ring, which has a length of 40 nm and a height of 20 nm. There are four rings in the upper and lower parts of the waveguides, which have an inner radius of r2 = r3 = r4 = r5 = 91 nm and outer radius R2 = R3 = R4 = R5 = 126 nm, respectively. The two monitors Pin and Pout are input and output monitors, respectively, which are used to measure the input and output waves. The wave transmission is calculated by the following equation: T = Pout / Pin (1) Also, the simulation substrate is made of silver metal and the waveguides and amplifiers are made of air . To show the optical properties of metals in simulation, we use the greeting model: Here ωp = 1.37 × 1016 refers to bulk frequency for plasma, ɛ∞ =1 gives the medium constant for the infinite frequency, γ = 3.21 × 1013 means damping frequency for electron oscillation, and ω shows incident light angular frequency. Because the wavelength of the radiant light is greater than the height of the waveguides, only TM mode can be present in the sensor structure and participate in simulations. The TM wave starts moving from the left and goes through the left waveguide to the resonators. Each resonators reflects or allows a portion of the input wave signal to pass through. Eventually the wave reaches the output waveguide, the intensity of which decreases at the end of the path relative to the beginning of its motion. To explain the electric field distribution, it can be said that energy loss is reduced when the field distribution in structures is equal and similar (Fig.  2). Therefore, in order to achieve the maximum field distribution in the designed sensor structure, all dimensions must be optimal. Using the time domain finite difference method, we examine and analyze the sensor performance (numerical analysis) and using the transmission line model method, we theoretically examine the performance of the sensor. Summarizing these two methods, we analyze the proposed structure resonance behavior and get a functional plasmonic sensor. For the numerical approach, we use the finite difference time domain method with exactly the same boundary conditions. Consider the mesh size for both x and y directions, 8 nm. To reduce the simulation time and create a suitable space, we do the simulation in two dimensions. To measure the performance of the sensor and to technically test the designed structure, we examine each of the cavities separately, and in the last step, we examine all the components of the structure as shown in Fig.1. That is, first we analyze this sensor in detail and then in general.

Simulation and design of the sensor using two waveguides and a ring with two tooth.
In the first stage, only the middle ring and its two tooth are present, which are placed in the middle of two plasmonic waveguides (Fig.3). We see the transmission spectrum from the sensor device in Fig.4. We change the refractive index of the middle ring with a step of 0.01 nm from 1.14 to 1.2 nm. This will change the resonance spectra and wavelengths. Here we come to the first characteristic of measuring the performance of a sensor, namely S sensitivity: S = Δλ / Δn (nm / RIU) (3) In the above equation, Δn is the refractive index change and Δλ is the resonance wavelength change. By changing the refractive index, the plasmon scattering changes and the resonance point of the structure changes. The graph of the sensitivity coefficient of a plasmonic sensor is shown in Fig.5. According to the figure, the highest sensitivity is related to the refractive index n = 1.2 (in mode 3), which is equal to 1298 nm / RIU. According to Fig.6, the maximum the figure of merit (FOM) for the refractive index is n = 1.2 (in mode2), which is equal to 17.629 nm / RIU. The last criterion for measuring the designed sensor is Q quality factor: Q = λres / FWHM (5) According to Fig.7, the maximum value of the quality factor Q is for the refractive index n = 1.15 (in mode1), which is equal to 24.124 nm / RIU.

Simulation and design of the sensor using two waveguides and five rings with two tooth
In this step, we seek to improve the performance of the proposed sensor by increasing the number of amplifiers and changing their dimensions and coordinates (Fig.8). We see the transmission spectrum of the designed sensor device in Fig.9. This transmission spectrum has three peaks. The left peak has a narrower FWHM and the right peak has a wider FWHM. The middle peak has the highest height. But the right peak will perform better than the other two peaks because it has the highest amount of wavelength change per refractive index change. We will now change the refractive index of the middle ring by 0.01 nm from 1.14 to 1.2 nm and calculate the sensitivity of the proposed sensor. As shown in Fig.10, the highest sensitivity is related to the refractive index n = 1.18 (in mode3), which is equal to 1692 nm / RIU.  In the continuation of the discussion, we will calculate the figure of merit (FOM) and the quality factor Q and draw the diagrams related to them (Fig.11). According to the figure, the highest figure of merit (FOM) is related to refractive index n = 1.18 (in mode2) which is equal to 14.168 nm / RIU and also, the highest quality factor Q is related to refractive index n = 1.18 (in mode1) Which is equal to 19.994 nm / RIU. Fig.11. Diagram of figure of merit (FOM) and quality coefficient diagram of Q refractive index sensor with five rings and two tooth .

.Simulation and design of the sensor using two waveguides and four cavities and a ring with two tooth
At this stage of the simulation, there are four cavities and a middle ring and two tooth (Fig.12). We see the transmission spectrum of the designed sensor device in Fig.13. The transmission spectrum has three peaks. As in the previous sensor structure (Fig.9), the left peak has a narrower FWHM and the courier on the right has a wider FWHM. But a change has been made compared to the previous structure and the highest height belongs to the left peak. But again, the right peak will perform better than the other two peaks because it has the highest amount of wavelength change per refractive index change. We will now change the refractive index of the middle ring by 0.01 nm from 1.14 to 1.2 nm and calculate the sensitivity of the sensor. As shown in Figure 14, the highest sensitivity is related to the refractive index n = 1.19 (in mode3), which is equal to 1692 nm / RIU. We will now calculate the values of the figure of merit (FOM) and the quality factor Q and draw diagrams related to them (Fig.15). According to the figure, the highest figure of merit (FOM) is related to the refractive index n = 1.16 (in mode2), which is equal to 14.475 nm / RIU. The value obtained has a higher FOM value than the previous structure (Fig.11). Also, the highest quality factor Q is related to the refractive index n = 1.18 (in mode1), which is equal to 23.99 nm / RIU, which has a higher value of Q than the previous structure (Fig.11).

.Simulation and design of the sensor using two waveguides and four cavities and five rings with two tooth
In this step of the simulation, we design a plasmonic sensor whose structure is the sum of the two structures of Figures 8 and 12. To use it to reach a general conclusion about the sensor we want. The structure of this sensor will include two waveguides, four cavities and five rings and two tooth ( Figure 16). We see the transmission spectrum of the designed sensor device in Fig.17. This transmission spectrum has two peaks. The courier on the left has a narrower FWHM and the courier on the right has a wider FWHM. The highest height belongs to the peak on the left. But the right peak will perform better than the other peak because it has the highest amount of wavelength change per refractive index change. We will now change the refractive index of the middle ring by 0.01 nm from 1.14 to 1.2 nm and calculate the sensitivity of the sensor. According to Fig.18, the highest sensitivity is related to the refractive index n = 1.2 (in mode2), which is equal to 1714 nm / RIU. We will now calculate the values of the figure of merit (FOM) and the quality factor Q and draw diagrams related to them (Fig.19). According to the figure, the highest competence figure (FOM) for the refractive index is n = 1.2 (in mode2), which is equal to 10.407 nm / RIU. Also, the highest quality factor Q is for the refractive index n = 1.15 (in mode1), which is equal to 19.55 nm / RIU.

Conclusion
Refractive index sensors are divided into six categories based on structure (plasmonic and photonic). The dimensions and coordinates of the sensor structure have a great effect on increasing the sensor performance. In this paper, we evaluate sensor performance by changing the coordinates and structure of the sensor and changing the refractive index of the resonators. The resonant wavelength spectrum will change evenly, helping to better design the sensor. Due to its small size and balanced performance, this configuration is suitable for use in integrated circuits.