## 4 Application of the Proposed Structure in Temperature Sensing  
The presented system can also be used as a nanoscale temperature sensor, which is realized by using the variation of the refractive indices of the temperature sensing medium caused by an ambient temperature, with the temperature sensing material viewed as a liquid. Ethanol was chosen as the temperature sensing medium to fill the CCDRR and the MIM waveguide with a bus waveguide and two symmetrical rectangular baffles because of its high refractive-index temperature parameter of 3.94 \(\times\) 10\({}^{-4}\) (\({}^{\circ}\)C\({}^{-1}\)). The refractive-index temperature coefficients of Ag and quartz are 9.30 \(\times\) 10\({}^{-6}\) (\({}^{\circ}\)C\({}^{-1}\)) and 8.60 \(\times\) 10\({}^{-6}\) (\({}^{\circ}\)C\({}^{-1}\)), respectively, which are two orders of magnitude smaller than that of ethanol. Thus, the variation of temperature largely affects ethanol, and the effects of thermal expansion of Ag and quartz can be ignored. The schematic diagram of three-dimensional (3D) structure is shown in Figure 9. The blue part represents ethanol, the green part represents silver, and the black part represents the quartz substrate.  
Commonly, the functional connection between the refractive index, temperature coefficient, and ambient temperature of a liquid temperature sensing material can be expressed as follows [36]:  
\[n=n_{0}+\frac{dn}{dT}\;(T\;-\;T_{0}) \tag{7}\]  
where \(n_{0}=1.36048\) is the refractive index of the liquid corresponding to room-temperature, \(T_{0}\)= 20 \({}^{\circ}\)C; \(dn/dT\) =3.94 \(\times\) 10\({}^{-4}\) (\({}^{\circ}\)C\({}^{-1}\)) is the refractive index temperature coefficient; and T represents the ambient temperature. Thus, the refractive index formula, with ethanol as the filling material of the temperature sensor, and the sensitivity formula can be expressed as follows:  
\[n= 1.36048-3.94\;\times\;10^{-4}\;(\;T\;-\;20\;) \tag{8}\]  
\[S_{T}=\frac{\Delta\lambda_{T}}{\Delta T} \tag{9}\]  
The geometric arguments of the structure were fixed at \(R_{1}\) = 240 nm, \(R_{2}\) = 130 nm, \(d\) = 40 nm, \(H\) = 540 nm, \(h\) = 150 nm, \(g\) = 10 nm, and \(w\) = 50 nm. The transmission spectrum for the disparate temperatures of the sensor is plotted in Figure 10a. As the melting and boiling points of ethanol are \(-\)144.3 \({}^{\circ}\)C and 78.4 \({}^{\circ}\)C, respectively, the temperature sensor has good stability in the working range of \(-\)80-60 \({}^{\circ}\)C. As the temperature drops from 60 \({}^{\circ}\)C to \(-\)80 \({}^{\circ}\)C with an interval of 20 \({}^{\circ}\)C, the transmission spectrum displays a red-shift phenomenon and the sensitivity, which is shown as Figure 10b, has a remarkable linear fit with the value of 1.48 nm/\({}^{\circ}\)C.  
Figure 9: Three-dimensional schematic of the temperature sensor based on the MIM waveguides.  
Although the temperature sensor has some advantages, such as a high sensitivity, a simple structure, and easy integration, it still has some limitations. Due to the bounds of the boiling and melting points of ethanol, the sensor is only suitable for low-temperature sensing, and it cannot solve sensing problems when the temperature is too high. As a liquid substance, ethanol cannot meet the needs of solid-state sensing equipment under some special conditions. In some practical applications, thermal materials such as lithium niobate can be used instead of ethanol to manufacture solid-state equipment. In future research, we will also consider adding a grapheme strip into the CCDRR cavity to allow for dynamic adjustment of the sensitivity.