## 3 Results and Discussion  
The performance of the ring resonator thermometer is shown in Figure 5. The probe laser scanned the wavelength around 1550 nm, and the transmission spectrum was obtained. Figure 5a shows the transmission of an unpackaged device. The overall envelope shows a maximum value at a wavelength of around 1545 nm, close to the expected value in Figure 3. The power ratio of transmitted light to incident light is 9.73%, indicating a single coupling efficiency of 31.13%, below the simulated value; this may be due to the difference between the real geometric structure and the designed parameters as well as due to material absorption loss. The full-width-at-half-maximum (FWHM) of resonating mode is 0.021 nm as measured in an atmospheric environment, indicating a Q-factor of 73,400. After the packaging, the transmission is as shown in Figure 5b: the Q-factor dropped to 21,400, and the FSR is reduced from 8.64 to 6.59 nm, which results from the fact that the adhesives change the refractive index environment around the resonator. Figure 4: Diagram of experimental setup for device performance characterization. Blue lines represent optical paths, and black lines represent electrical paths. Laser: Toptica, CTL1550; WM (wavemeter): High Finesse, WSU10-IR2; DAQ (data acquisition card): National Instrument, USB-6361; PA (power amplifier): Mini-circuits, ZHL-1-2W-S+; AOM: AA opto-electronic, MT200-IIR30-Fio; RF: Rigol, DSG815; PI: New Focus, LB1005; Polarizer: Thorlabs, ILP1550 PM-APC; PD: Thorlabs, PDA20 CS-EC; FPC (fiber polarization controllers): Thorlabs, FPC032; Bath: Fluke, 7341; OSC (oscilloscope): Keysight DSOX3054T. When the environment temperature changes, the peak wavelength of resonating mode shifts, approximately following the equation:  
\[\Delta\lambda=\frac{\lambda\Delta T}{n_{g}}\bigg{(}\frac{\partial n_{eff}}{ \partial T}+\frac{n_{eff}}{L}\frac{\partial L}{\partial T}\bigg{)}, \tag{1}\]  
where \(\lambda\), \(\Delta\lambda\), \(T\), \(\Delta T\), \(n_{g}\), \(n_{eff}\), and \(L\) are wavelength, wavelength variation, temperature, temperature variation, group index, effective refractive index, and ring perimeter, respectively. Given that the thermal expansion coefficient of silicon (3.57 \(\times\) 10\({}^{-6}\)/K) is two orders of magnitude smaller than the thermo-optic coefficient (2 \(\times\) 10\({}^{-4}\)/K), an environment temperature change has a negligible impact on the result. The wavelength shifting from \(-\)30 to 120 K does not exceed the FSR (Figure 5c), indicating a temperature range over 150 K with a sensitivity of 42 pm/K (Figure 5d). It should be pointed out that the reason why this sensitivity is quite different from the values previously reported (\(\sim\)70 pm/K) is that the adhesives change the effective thermo-optic coefficient, similar to the effect reported in [23]. The above wavelength scanning method is suitable for the measurement of a relatively wide temperature range, but for a small temperature change (<1 K), the wavelength locking method should be applied, where the wavelength of the laser source is locked at the blue detuning fringe of the resonating mode, and the power of the transmission laser is recorded to represent the small temperature change. This method requires a high stability for both the power and polarization of the laser source. Figure 6a shows the results of the power stabilization; the relative fluctuations over a period of 20 min are reduced from 5% (red line) to 2% (blue line) after implementing the power stabilization. In order to show the  
Figure 5: The transmission spectrum of (**a**) unpackaged device and (**b**) packaged device. (**c**) The transmission spectra under various temperatures. (**d**) Peak wavelength of resonating mode versus various temperatures. effect of the polarization stabilization, the output laser from the feedback loop is given access to an additional polarizer, and then the power is recorded under two conditions: with and without polarizers in the loop, as shown in Figure 6b.