Glycerol concentration sensor based on the MIM waveguide structure

Glycerol is widely used in medicine, industry and skin care products. This study investigated a high-sensitivity glycerol concentration sensor based on double Fano resonances in a metal-insulator-metal (MIM) waveguide structure, established a coupling model of a baffle waveguide (BW) and a circular split ring resonator (CSRR), and generated asymmetric double Fano resonances in the waveguide structure. The Fano resonance transmittance reached 0.82, and the linear relationship between the refractive index (RI) and the glycerol concentration was obtained using the sensitivity of the Fano resonance spectrum. The application of the proposed sensor for glycerol concentration detection revealed that the Fano resonance wavelength was redshifted with the RI and that the sensing sensitivity reached 1153.85 nm/refractive index unit (RIU); therefore, the quick detection of the corresponding glycerol concentration can be realized. This proposed structure has significance in the research of optical sensors and optical switches.


Introduction
The Fano resonance spectrum is very sensitive [1,2], and the research on the sensing characteristics [3], especially the interaction between surface plasmons and light, can be used to develop new nanoscale photonic devices [4][5][6]; Based on the physical properties of surface plasmas such as strong binding force, low loss, low power consumption, small size and easy integration, SPP and Fano MIM waveguide devices can be manufactured for optical sensors and filters. It is very promising to study the sensitivity of Fano resonance spectral lines to fabricate MIM waveguide structures for concentration sensors [7]. At present, the MIM waveguide sensor based on Fano resonance have become a hot topic that people continue to overcome [8]. Surface plasmon resonance-based high-sensitivity refractive index sensors have been proposed, and biosensors have been studied to perform better in the infrared region than graphene-based biosensors, with a sensitivity exceeding 970/RIU [9]. Based on the multiple Fano resonance characteristics in the surface plasmon resonance sensor, it has been shown that multiple Fano resonances can be generated by changing the structure, and the quality factor of high sensitivity is 4 times higher than that of the general surface plasmon resonance sensor [10]. A refractive index sensor composed of nanoring arrays and Fabry-Perot (FP) resonators based on multiple Fano resonances has been proposed, with corresponding sensing sensitivities up to 621.5 nm/RIU and 906.9 nm/RIU [11]. Based on Fano resonance, an optical refractive index sensor based on the "lucky knot" nanostructure in the mid-infrared region has been proposed, with a sensitivity of 986 nm/RIU and a maximum quality factor of 32.7, which is superior to the sensor based on metal materials [12]. The super surface device based on nano metal medium metal plasma cavity array has been proposed. The super surface is sensitive to the environmental refractive index, and the sensitivity of the refractive index temperature sensor studied is 667 nm/RIU [13].
In this paper, based on the research on the sensing characteristics of SPP, an MIM waveguide structure composed of BW and a CSRR was proposed, and the application of SPPbased sensor was studied. The detection method of glycerol concentration was proposed, i.e., the glycerol concentration has a linear relationship with the RI, and RI can affect the Fano resonance spectrum; therefore, the relationship between the glycerol concentration and Fano resonance spectrum can be established, and a concentration sensor based on surface plasmon can be achieved. The glycerol concentration sensor we proposed is a better method to process samples, which is uncommon in the current glycerol concentration sensor. The sensitivity is up to 1153.85 nm/RIU calculated through experiments. Compared with other similar studies, the sensitivity of this structure in optical sensors has been improved. This structure is of great significance in the research of optical sensors.
2 Propagation characteristics and numerical calculation

Propagation analysis
In this paper, the waveguide structure method is used to excite the SPP, and the principle is that the incident light generates an evanescent wave in the waveguide structure. Since it matches the wave vector of the surface SPP, the SPP can be activated when the evanescent wave passes through the metal layer [14]. In the waveguide, P out PoavxdS 2 and P in PoavxdS 1 are output power and input power, and define the transmittance T P out /P in [15,16].
The dielectric constant is modeled using the Drude model [17]: where, γ 0.018 [eV], ω is the angular frequency, ε ∞ 3.7 and ω p 9.1 [eV] are the permittivity and plasma frequency, respectively. The dispersion relation in the TM mode waveguide structure is as follows [18]: Where, the dielectric constant of the medium is ε i , and the dielectric constant of the metal is ε m (ω), β n eff *k 0 are the complex propagation constants of SPPs, n eff is the effective RI of the mode, k 0 2π/λ is the wave vector in vacuum [19]. According to standing wave theory, the resonance wavelength can be obtained [20]: Effective length D is the length of resonant cavity of the waveguide structure, ψ is the phase shift after boundary reflection, and R e (n eff ) is the real part of the effective ). The formulas of the three parameters, the sensitivity S, the quality factor FOM, and quality factor Q, which reflect the sensing characteristics of the waveguide structure, are as follows: [21][22][23][24].
FWHM represents the full width half maximum of the spectral line [25,26]. R 2 reflects the fitting degree of the fitting curve to the predicted value, where n i ∧ represents the predicted value of the sample, n represents the average value of the true value, and the larger R 2 represents the better fitting degree. The formula is as follows:

Model calculation and analysis
The MIM waveguide structure is shown in Figure 1A, which is composed of a BW and a CSRR. For the two-dimensional (2D) structure diagram, its simulation is fast, it can reflect the overall structure, and its final result reaches the expectations, so it was selected for the simulation in this paper. The waveguide structure to be measured is the yellow region. The BW and CSRR can be etched by electron beam etching, and the material to be measured can be filled with capillary attraction, and finally, the structure was sealed with a transparent insulator. In the waveguide structure, Pin is the input power, Pout is the output power [27], g represents the distance between BW and CSRR, w represents the height of the straight waveguide, d and y denote the width of the main waveguide baffle and the ring waveguide baffle, respectively, the width of the middle baffle is f, the height of the waveguide is L, r and R are the radius of the small and big circles, respectively.
Fano resonance is a kind of scattering resonance phenomenon that produces asymmetric line shape, which is formed by the mutual coupling of continuous state energy level and discrete state energy level. The incident light is TM polarization mode, because the excited surface plasmon polaritons can only exist in TM polarization mode. Figure 1B shows the transmission lines when the waveguide structure is in discrete state, continuous state, and coupled state, respectively [28]. As shown in Figure 1C, when the CSRR is not coupled with a baffle, the spectrum can be viewed as a discrete state, when the CSRR is coupled with a baffle, a continuous state can be formed, and the magnetic field distribution can be viewed as an energy distribution [29,30]. In this waveguide structure, two lowest points are formed at 800 nm and 1200 nm through the mutual coupling of the continuous state and the discrete state, thereby forming the double Fano resonances [31]. Further study of the resulting asymmetric line spectral shape, especially the variation of parameters, affects the sensing properties of Fano resonance [32].
The waveguide structure directly affects the Fano resonance lines [33]. Figure 2 shows the transmission lines of different geometric parameters. Table 1 is the value of the corresponding geometric parameters for the FOM [34]. Figure 2A shows the transmission lines of the BW and CSRR coupling distances g from 8 nm to 17 nm. First, the other variables are controlled,  i.e., d = 10 nm, y = 20 nm, f = 10 nm, r = 110 nm, R = 165 nm, and L = 40 nm. In Figure 2A, with the increase of g, the Fano resonance spectrum appears redshifted, and the transmission peak decreases from 0.841 to 0.696. Table 1 shows that, at Peak 1 and Peak 2, the FOM reaches the maximum, but the transmission peak is the lowest, and the FOM at Peak 2 is generally greater than that at Peak 1. Figure 2B shows the transmission lines when the L of middle waveguide of the CSRR increases from 30 nm to 60 nm. The other fixed variables are as follows: d = 10 nm, y = 20 nm, f = 10 nm, r = 110 nm, R = 165 nm, and g = 8 nm. With the increase of L of middle waveguide of the CSRR, the Fano resonance spectrum exhibits a blueshift, the transmittance at Peak 1 increases with the increase of L to reach 0.82, and the transmittance at Peak 2 changes slightly from 0.57 to 0.55. Table 1 shows that the FOM reaches the highest value of 58.252 at Peak 2. Figure 2C shows the transmission lines when the r changes from 110 nm to 115 nm. The other fixed variables are as follows: d = 10 nm, y = 20 nm, f = 10 nm, R = 160 nm, L = 60, and g = 8 nm. Figure 2C shows that as r increases, the Fano resonance spectrum appears redshifted, and the transmission peak reaches 0.809 at Peak 1.  Figure 2D shows the transmission lines when the d changes from 8 nm to 14 nm. The other fixed variables are as follows: y = 20 nm, f = 10 nm, r = 110, R = 165 nm, L = 60 nm, and g = 8 nm. Figure 2D shows that as d increases, the Fano resonance spectrum appears redshifted, and the transmission peak at Peak 1 reaches 0.844. According to the data in Table 1, the FOM at Peak 2 increases  Transmission spectrum as a function of refractive index n.
Frontiers in Physics frontiersin.org from 50.999 to 56.338. Finally, the reference literature shows that the quality factor combined with the transmittance can reflect the sensing characteristics of the waveguide [35,36]. In summary, the appropriate geometric parameters selected in this paper are as follows: r = 110 nm, y = 20 nm, f = At 10 nm, R = 165 nm, d = 10 nm, L = 40 nm, and g = 10 nm.

Sensing performance analysis
In this paper, the influence of the Fano transmission spectrum on the RI was further studied, which provides the possibility for the study on optical sensors [37,38]. Figure 3A shows the Fano transmission lines of the waveguide with different RI (n = 1-1.08). Table 2 shows the FOM and RI at Peak 1 and Peak 2. In Figure (a), the transmission peak at Peak 1 is redshifted from 753 nm to 813 nm, and the peak at Peak 2 is redshifted from 1185 nm to 1281 nm. According to Eqs. 4, 5, The maximum S and FOM are 1200 nm/RIU and 53, respectively. This is because the coupling electric field at peak 2 decreases and the transmissivity decreases, and the Fano resonant transmission peak narrows. The calculated FWHM ratio at peak 1 decreases, and because the sensitivity at peak 2 is greater than that at peak 1, according to formula (5), the FOM at peak 2 is usually greater than that at peak 1.
As shown in Table 3 comparing the results of this study with those of other studies, it shows that the sensing performance of the studied structure is significantly improved.

Glycerol concentration detection
Glycerol is widely used in medicine, industry and skin care. When glycerol is used in different types of preparations in our daily life, there are strict requirements on its concentration. Especially when glycerol is used on humans, the use of different glycerol concentrations requires our attention. As shown in Table 4, the actual application of several different glycerol concentrations.
In this paper, a glycerol concentration sensor with MIM waveguide structure is proposed by taking advantage of the sensitivity of Fano resonance lines [46][47][48]. In this study, the sensitivity S Δλ/Δn(nm/RIU) was defined to measure the sensing characteristics [49-51]. The Abbe refractometer was used to measure the RI of the liquid, which is simple to operate and does not require a specific light source, the measurement accuracy is high, with an accuracy of the RI at 1 × 10 −4 , the measurement reproducibility is excellent, and the required liquid samples are less [52]. In this study, liquid glycerol was selected as the experimental object. Glycerol can be miscible with water at any ratio. In this study, a pure glycerol was mixed with water to prepare different concentrations of glycerol. An Abbe refractometer was used to measure the RI of different concentrations of glycerol at a room temperature of 25°C, the measurement was repeated multiple times, and the average value was obtained, with the concentration error of ± 1% [53].   The experimental results are shown in Table 5. There is a linear relationship between concentration and RI as shown in Figure 4. The linear fitting shows that n = 0.01297C + 1.3408 (n is the RI, and c is the concentration) Table 6 shows the comparison between the actual measured value and the fitted refractive index, According to (Eq. 7), R 2 = 0.999,998 proves that the fitting curve we get is well fitted. The refractive index of glycerin measured by Abbe refractometer can be accurate

FIGURE 5
Transmission lines of different concentrations of glycerol.

FIGURE 6
Fitting relationship between glycerol concentration and the Fano resonance wavelength. to four decimal places, and the accuracy of 0.1% concentration of the solution to be measured can be theoretically detected. Figure 5 shows that the Fano resonance wavelengths generated by filling multiple glycerol samples with different concentrations into the waveguide cavity are different, and the transmission spectrum exhibits a redshift phenomenon as the concentration of glycerol increases. The data are shown in Table 7, and the fitting curves of different concentrations of glycerol and Fano resonance wavelength were made at Peak 1 and Peak 2 respectively as shown in Figure 6. The results show that λ Peak1 93.455C + 999.87 at Peak 1, and λ Peak2 150.55C + 1585.1 at Peak 2 (λ is the resonance wavelength, and C is the glycerol concentration), and the fitting quality is as high as 99.9%. Based on Eq. 4, the S at Peak 1 and Peak 1 is calculated to be 719.23 and 1153.85, respectively, and the FOM is as high as 38.2.

Conclusion
In this paper, based on the research on the sensing characteristics of SPP, an MIM waveguide structure composed of BW and a CSRR was proposed. The finite element method and simulation show that the transmission spectrum of this structure is a double Fano resonance spectrum. The effect of geometric parameters on the Fano resonance lines was investigated, and the results showed that the Fano resonance transmittance was as high as 0.8, the sensitivity reached 1200 nm/RIU, and the quality factor was 53. This study found that when the MIM waveguide structure was filled with glycerol, the RI of glycerol with different concentrations was different, and the Fano resonance spectrum was affected by the RI; therefore, based on the relationship between the RI and Fano resonance spectrum, the glycerol concentration could be detected according to the change in the Fano resonance wavelength.

Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.