## Abstract

Based on the transmission characteristics of surface plasmon polaritons (SPPs) in sub-wavelength structures, this paper proposes a metal-insulator-metal (MIM) waveguide structure composed of a main waveguide with glass (SiO_{2}) branches (WWGB) coupled with an elliptical split-ring resonance cavity (ESRRC). WWGB has a broadband continuous transmission spectrum, while ESRRC has a narrow-band discrete transmission spectrum. The coupling and interference between the two can generate excited dual-Fano resonance, with sensitivities and figures of merits (FOM) of 800 nm/RIU, 1150 nm/RIU, and 9.88, 104.55, respectively. After adding SiO_{2} branches to both sides of the main waveguide, the FOM are enhanced to 28.57 and 127.78, representing increases of 189% and 22.15%, respectively. This structure can be applied as a temperature sensor. After filling the cavity of the to-be-tested material with 75% ethanol, as the temperature increases, the Fano resonance wavelength to drift, therefore, the corresponding temperature can be calculated by the Fano resonance wavelength. Experiments show that the proposed MIM waveguide has a maximum sensitivity of 1406.25 nm/RIU, an FOM of 156.25, and a temperature sensitivity of 0.45 nm/℃. Ultimately, the results demonstrate that incorporating SiO_{2} branches enhances the sensing characteristics of the MIM waveguide, after adding ethanol, the MIM can be applied to temperature sensors, with a high sensitivity of 1406.25 nm/RIU, thereby providing a new design strategy for producing high-performance waveguides.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

The rapid development of modern information technology and big data has led to increasing demand for accurate transmission equipment capable of handling the corresponding increase in information transmission volume [1,2]. However, the diffraction limit of traditional optics has restricted the development of integrated optics, nano-optics, and other modern optics [3,4], with many devices struggling to deliver satisfactory performance. The concept of surface plasmon polaritons (SPPs) [5] has inspired many breakthroughs in optical devices. An SPP is an electromagnetic wave caused by the collective charge oscillation generated by the coupling of incident light to free electrons on the metal surface. The resultant wave propagates along the metal-dielectric interface and decays exponentially in the direction perpendicular to the interface [6–8]. Fano resonance manifests as asymmetric spectral lines formed by the mutual interference between the wide continuous state and narrow discrete state [9]. Compared with symmetrical Lorentz spectral lines, Fano resonance spectral lines exhibit a larger slope [10]. By leveraging the physical characteristics of SPPs—such as low power consumption, low loss, strong binding force, and easy structural integration—metal-insulator-metal (MIM) waveguide devices based on SPPs and Fano resonance can be manufactured, which demonstrate great promise as temperature sensors and optical switches, with additional applications in other fields [11–13].

The ability of SPPs to overcome the diffraction limit and confine electromagnetic waves to sub-wavelength dimensions has resulted in Fano resonance-based MIM waveguide sensors becoming a prevalent research topic [14–16]. For example, Haffar et al. proposed an SPP waveguide with a double split-ring resonator. Various resonance modes have been observed in the transmission spectrum of this structure; however, despite exhibiting several novel features, this design achieved a maximum sensitivity of only 586.8 nm/RIU [17]. Bazgir et al. presented a switchable SPP polarized light coupled waveguide made by exploiting a DNA composite, demonstrating that the DNA composite switch can be used for optical gates, which exhibit high switching coefficients [18]. Ouyang et al. proposed a MIM waveguide with independently tunable Fano resonances based on coupled hetero-cavities. The structure was formed by coupling a rectangular cavity and a circular cavity with a metal-strip core, which modulated the Fano resonance through the rotation of the latter [19]. A MIM structure based on a triangular cavity resonator proposed by Jankovic excited four sharp Fano resonances; nevertheless, its maximum sensitivity was limited to 986 nm/RIU [20]. Lotfiani et al. proposed a high-sensitivity surface plasmon resonance biosensor based on Fano resonances, which proved that the Fano-like photocurrent curve can be modulated by changing the refractive index [21]. Although each of the aforementioned papers proposed a waveguide structure, the waveguide materials lacked variety, and the waveguide performance depended entirely on adjusting its geometric parameters. Therefore, this paper proposes a new method to improve sensor performance that is to introduce other materials (such as SiO2) into the structure.

This paper proposes a MIM waveguide structure comprising a main waveguide with glass (SiO_{2}) branches (WWGB) and an elliptical split-ring resonance cavity (ESRRC). Using the finite element method, COMSOL software is used to numerically calculate the transmittance and magnetic field distribution of the structure. COMSOL is a multi-physics direct coupling numerical analysis software with powerful simulation functions. The modeling process in this paper is as follows: firstly define the solution domain, then set the boundary conditions and perfect matching layer, and then set the electromagnetic field of the solution domain. Finally, divide the cell, solve the Maxwell equations of each cell node, and obtain the electromagnetic field distribution and light absorption.

## 2. Structure model and analysis method

The MIM waveguide structure proposed in this paper consists of a WWGB coupled with an ESRRC. The structure is shown in Fig. 1 (where (a) three-dimensional view, (b) top view). Incident light (port input power ${\textrm{P}_{\textrm{in}}}$ = 1W) enters from the left, propagates in the waveguide, and is fully reflected, producing an evanescent wave. When the wave vector of the evanescent wave matches the SPP wave vector, an SPP is excited. The waveguide substrate was SiO_{2}, with Ag used to excite SPPs [22]. In this structure, *w* represents the width of the main waveguide; *w*_{1} and *h* represent the width and height of SiO_{2}, respectively; *g* represents the coupling distance between WWGB and ESRRC; *a* and *b* represent the major and minor axes, respectively, of the elliptical split ring; *L* and *d* represent the width and split-length of the ESRRC, respectively. The preparation method is as follows: firstly, a silver layer is deposited on a quartz substrate by a vapor deposition method, and the substrate provides a mechanical buffer effect. Then the middle structure is etched by the electron beam etching method, including the resonant cavity, the main waveguide, etc., finally, the cavity of the to-be-tested material is filled with ethanol by capillary attraction and sealed with highly transparent medium.

In general, air has a refractive index (*n*) of 1, while its relative dielectric constant is ${\varepsilon _d}$ = 1. The relative dielectric constant of Ag is determined by the Drude model [23]:

The transmittance *T* at the output port is the ratio of the output power, ${\textrm{P}_{\textrm{out}}}$, and the input power, ${\textrm{P}_{\textrm{in}}}$, ${\textrm{P}_{\textrm{in}}} = \smallint \textrm{Poavx d}{\textrm{S}_1}$ and ${\textrm{P}_{\textrm{out}}} = \smallint \textrm{Poavx d}{\textrm{S}_2}$, where $\textrm{Poavx}$ is the $\textrm{x}$-axis component of the time-averaged power and ${\textrm{S}_1}$ and ${\textrm{S}_2}$ are the cross-sectional areas of ${\textrm{P}_{\textrm{in}}}$ and ${\textrm{P}_{\textrm{out}}}$, respectively [29,30].

## 3. Simulation and results

#### 3.1 Analyze the characteristics of Fano

For the analysis of the sensing characteristics of the structure, the initial geometric parameters of the structure were *w* = 70 nm, *w*_{1} = 65 nm, *h* = 60 nm, *g* = 10 nm, *L* = 35 nm, and *d* = 25 nm. Figure 2 shows the transmission spectra corresponding to the separate ESRRC (blue line), the separate WWGB (green line), the all system (red line) (Fig. 2(a)), and the magnetic field distribution of the corresponding structure (Fig. 2(b)). As shown in Fig. 2(b), after adding ESRRC, within the wavelength range of about 760 nm, due to the coupling effect, the magnetic field is concentrated in ESRRC, resulting in the lowest point of the transmission spectrum at 760 nm, thus forming a sharp Fano.

The transmission spectrum representing the separate WWGB exhibits a stable transmittance and can be regarded as a wide-band continuous state, while the transmission spectrum of the ESRRC alone resembles a Lorentz function, and can be regarded as a narrow-band discrete state. For the combined structure, the transmission spectrum features a Fano resonance due to the mutual coupling and interference of the narrow discrete and wide continuous states.

#### 3.2 Structural parameters analysis

Beyond the sensitivity ($\textrm{S} = \Delta \lambda /\mathrm{\Delta }n({\textrm{nm}/\textrm{RIU}} )$), the sensing characteristics of a sensor is also evaluated using the full width at half maximum (FWHM) and FOM. To improve the sensing characteristics of the structure, SiO_{2} branches were added to the original structure. The transmission spectra of Fano resonance for three structures are shown in Fig. 3, The S, FWHM and FOM of the resonance spectrum of the three structures are shown in Table 1. In structure II (Fig. 3(b)), a rectangular SiO_{2} branch has been added to the ESRRC, resulting in triple-Fano resonance (Fig. 3(e)). Although the FWHM of the triple-Fano resonance spectrum is improved, the sensitivity is reduced. In structure III (Fig. 3(c)), SiO_{2} branches with length *w*_{1} and height *h* have been added on both sides of the main waveguide. The results show that when there is no SiO_{2} branch on either side of the main waveguide (Figs. 3(a) and 3(d), Table 1), the sensitivities of the dual-Fano resonance are 800 nm/RIU and 1150 nm/RIU, the FWHM values are 81 and 11, and the FOM are 9.88 and 104.55 for Peak I and Dip I, respectively. After adding the SiO2 branches to each side of the main waveguide, the FWHM values of the dual-Fano resonance of the MIM change to 28 and 9 for Peak I and Dip I, respectively, corresponding to decreases of 65.43% and 18.18%, while the respective FOM are 28.57 and 127.78, representing increases of 189% and 22.15%, respectively. The results show that adding SiO_{2} branches to both sides of the MIM main waveguide can improve its sensing performance. As such, structure III was selected for further analysis.

After finalizing the structure, we investigated the influence of several important parameters on the Fano resonance spectrum in order to obtain the optimal geometric parameters. Figure 4 shows the transmission spectra and the changes in FWHM in response to increasing the height of the SiO_{2} branches from 40 nm to 80 nm. The left peak in the Fano resonance spectra is marked as Peak I, with the valley on the right denoted as Dip I. As the height of the branches was increased, the other parameters were set as follows: *w* = 70 nm, *w*_{1} = 65 nm, *g* = 10 nm, *L* = 35 nm, and *d* = 25 nm. Figure 4(b) shows that, as h increases, the FWHM of Peak I first decreases and then increases, while its transmittance decreases from 0.85 to 0.76. After careful evaluation of the FWHM maximum transmittance values for Peak I and Dip I, *h* = 60 nm was selected as the optimum branch height.

Figure 5 shows the transmission spectra and the changes in the FWHM and transmittance values of the Fano resonances as the coupling distance, *g*, between the WWGB and the ESRRC was increased from 5 nm to 20 nm. The other parameters were set as *w* = 70 nm, *w*_{1} = 65 nm, *h* = 60 nm, *L* = 35 nm, and *d* = 25 nm. Figure 5(a) shows that as *g* increases, both Peak I and Dip I of the Fano resonance spectrum are blue shifted; additionally, the transmittance decreases rapidly, and the intensity of Peak I decreases from 0.86 to 0.64. As shown in Fig. 5(b), the FWHM values of both Peak I and Dip I decrease rapidly from initial values of 47 and 44 before stabilizing at 17 and 9, respectively. This change is clearest when *g* increases from 5 nm to 10 nm. Careful consideration of the FWHM and transmittance values of Peak I and Dip I led to a final coupling distance of *g* = 10 nm being selected.

Next, the influences of the width and split-length of the ESRRC structure on the Fano transmission spectrum were explored. The width, *L*, of the elliptical ring was increased from 25 nm to 45 nm (in 5-nm intervals), with the resulting transmission spectra shown in Fig. 6(a). As *L* increases, the Fano transmission spectrum exhibits a blue shifted, with Dip I undergoing a greater shift than Peak I. Furthermore, although the transmittance of Peak I decreases as *L* increases, the opposite occurs for Dip I. Figure 6(b) shows that the FWHM values of both Peak I and Dip I decrease as *L* is increased, with the FWHM of Dip I showing minimal change when *L* was increased from 35 nm to 40 nm. Following this analysis, an ESRRC width of 35 nm was selected.

Figure 7 shows the Fano transmission spectra, FWHM values, and transmittances in response to varying the split-length, *d*, of the elliptical split ring. Figure 7(a) reveals that both Peak I and Dip I of the Fano transmission spectrum undergo a blue shifted as *d* increases. Peak I exhibits a greater blue shifted, while the transmittance decreases from 0.81 to 0.7; in contrast, Dip I shows a considerably smaller blue shifted, with little variation between the different spectra. Figure 7(b) shows the variation in the FWHM of the resonance line spectrum: increasing the split-length causes the FWHM of both Peak I and Dip I to decrease, with the rate of decrease reducing as *d* increases. Consequently, a split-length of 25 nm was selected. Comparing the relative influence of each parameter shows that *g* and *h* have a greater impact on the transmittance of the Fano resonance. Increasing either or both of *L* and *d* induces a blue shifted in the Fano resonance. In summary, the final geometric parameters selected for the structure III design were *w* = 70 nm, *w*_{1} = 65 nm, *h* = 60 nm, *g* = 10 nm, *L* = 35 nm, and *d* = 25 nm.

## 4. Sensitivity calculation and temperature detection

#### 4.1 Sensitivity calculation

After determining the optimal structure and geometric parameters of the MIM waveguide, we investigated its sensing characteristics. In addition to measuring the sensing characteristics of the structure in terms of sensitivity, we used the $\textrm{FOM}$ to evaluate the sensing performance of the MIM waveguide. The refractive index sensitivity and FOM are defined [31–33] as:

where, RIU is the abbreviation of Refractive Index Unit. and A higher FOM indicates better sensing performance [24,34,35].Figure 8(a) shows the Fano transmission spectra as the refractive index, *n*, of the to-be-tested material increases from 1 to 1.08.

The features of the transmission spectra are redshifted as the refractive index increases, with Peak I redshifted from 757 nm to 821 nm, Peak II from 1045 nm to 1137 nm, and Dip I from 1060 nm to 1152 nm. Figure 8(b) tracks the wavelengths of the dual-Fano resonance features as a function of *n*. Equation (4) yields a sensitivity of 800 nm/RIU for Peak I, with Peak II and Dip I both having a sensitivity 1150 nm/RIU. In addition, from Eq. (5), the FOM of Peak I calculated as 28.57, while the FOM of Peak II and Dip I are both 127.78.

#### 4.2 Temperature detection

Based on the redshift observed for the wavelength of the Fano resonance of the MIM waveguide in response to increasing the refractive index, we investigated its performance as a temperature sensor. To deploy the MIM waveguide as a temperature sensor, the nanocavity was filled with ethanol, which has a relatively high thermo-optic coefficient [36]. The refractive index can then be expressed as:

where ${T_0} =$ 20 ℃ and*T*is the ambient temperature [37,38].

The temperature sensitivity [39] is defined as:

The ethanol with the original concentration of 75% was mixed with water in proportion to produce ethanol with the concentration of 50% and 25% respectively. An Abbe refractometer, which uses the total internal reflection to measure the refractive index and average dispersion of transparent and translucent liquids or solids [40], was used to measure the refractive indices of these ethanol solutions over a temperature range of 12–32 °C (in intervals of 5 °C). The average of measurement data are listed in Table 2. As ethanol volatilization is an endothermic process, there is a temperature error of 0.5 °C in this experiment. The temperature dependence of the refractive index of each concentration of ethanol is shown in Fig. 9, where the black line is the trend line. Various concentrations of ethanol and refractometer are shown in Fig. 10: There are different concentrations of ethanol in the three test tubes on the left, and the Abbe refractometer on the other side. It can be concluded from the experimental data and the broken line graph: First, as the temperature increases, the refractive index of ethanol decreases. Secondly, the refractive index of ethanol increases as its concentration increases. The conclusion is quite similar to the results of similar studies [41]. However, only the refractive index of 75% ethanol has a good linear relationship with temperature. The fitting curve is very close to the trend line, and the linear equation of the trend line is: n = -0.0016 T + 1.3674, leading to its selection as the temperature-detection liquid.

Figure 11 shows the transmission spectra of the 75% ethanol at temperatures between 0 °C and 60 ℃. It can be seen from the transmission spectrum that as the temperature increases, the Fano resonance wavelength exhibits an overall blue shift. Peak II and Dip I are both blue-shifted by 135 nm, from 1440 nm to 1305 nm and from 1460 nm to 1325 nm, respectively. Using Eq. (4), the sensitivity of Dip I was calculated to be 1406.25 nm/RIU, while from Eq. (5), the FOM of Dip I was calculated to be 156.25. And, the temperature sensitivity of Dip I was calculated to be 0.45 nm/℃ from Eq. (7).

Finally, this paper also compared with other similar Fano resonance works, as listed in Table 3. It can be observed that the proposed structure has improved the sensitivity value by 19.17%, 17.18%, and 11.45%, respectively.

The information of refractometer and ethanol used in this experiment is shown in Table 4.

## 5. Conclusions

This paper proposes a new type of highly sensitive MIM structure that can excite dual-Fano resonance, and the quality factor of the structure is improved by adding SiO2 branches. Then it is applied to temperature detection and adopts optical detection method; this is a better non-destructive detection method. Compared with other methods, it is obviously a better method for processing samples. It is not common in current temperature sensing. Finally, experiments show that the sensitivity of the proposed MIM waveguide as a temperature sensor can reach 1406.25** **nm / RIU, the FOM is 156.25, and the temperature sensitivity is 0.45** **nm / ℃. As such, this study provides a theoretical basis for a new type nano-temperature sensor design template and ideas for improving sensor performance.

## Funding

Middle-aged and Young Teachers' Basic Ability Promotion Project of Guangxi; National Natural Science Foundation of China (51965007).

## Disclosures

No conflict of interest exits in the submission of this manuscript

## Data availability

Data underlying the results presented in this paper can be obtained from the authors upon reasonable request.

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