## 3 Discussion  
The transmission spectra of RRs (with upper cladding as air) with R = 50 \(\upmu\)m, 75 \(\upmu\)m, and 100 \(\upmu\)m were meticulously captured within the wavelength range spanning from 1540 nm to 1550 nm, as shown in Figure 3a. The full width at half maximum (FWHM) of the resonance dip at 1543.84 nm is around 0.09 nm, as shown in Figure 3b. Furthermore, the measurement process includes the capture of an image of the RR structure at the resonance wavelength of precisely 1543.84 nm, facilitated by an infrared (IR) camera. At this specific wavelength, a distinct and luminous gleam of light emanates from the ring structure, vividly illustrating its on-resonance state. This captivating phenomenon is visually represented in Figure 3c, where the bright shine within the ring unequivocally signifies its resonance status. The Q factor of an optical RR is a crucial parameter that describes the efficiency and performance of the resonator in the realm of photonics [34, 35]. The Q factor represents the sharpness of the resonant peaks and is defined as follows [36]:  
\[\text{Q factor}=\frac{\lambda_{\text{res}}}{\text{FWHM}}; \tag{3}\]  
where \(\lambda_{\text{res}}\) and FWHM are the resonance wavelength and the full width at half maximum of the resonance dip, respectively. A higher Q factor in RRs signifies a more distinct and narrow resonance, making it desirable for applications like optical filters and sensors. The Q factor is affected by material losses, waveguide losses, and radiation losses. Minimalizing these losses is essential for enhancing the Q factor and improving the overall performance of RRs [17]. A high Q factor is essential for optimizing sensitivity and selectivity, enabling diverse applications in integrated photonics. The resonance dip depicted in Figure 3a for  
Figure 2: (**a**) Schematic of an RR based on Si\({}_{3}\)N\({}_{4}\) platform; (**b**) transmission spectrum of RRs with radii = 50 \(\upmu\)m, 75 \(\upmu\)m, and 100 \(\upmu\)m; (**c**) FSR versus R of the RR structure. Normalized H-field distribution in the RR with radius = 100 \(\upmu\)m in (**d**) on-resonance state and (**e**) off-resonance state. Insets show the magnified image of the coupling segment where the light transfers take place. R = 100 \(\upmu\)m occurs at precisely 1543.84 nm, exhibiting a remarkably narrow FWHM of 0.09 nm. This narrow linewidth translates into an impressive Q factor of 1.7154 \(\times\) 10\({}^{4}\), emphasizing the precision and sharpness of the resonant feature. The refractive index is a fundamental parameter that characterizes how light propagates through a medium, and changes in this index can be indicative of alterations in the composition, concentration, or physical state of the material [27]. In fields such as chemistry, biology, and environmental monitoring, refractive index sensing plays a crucial role in detecting and analyzing substances with exceptional sensitivity [37; 38; 39]. The ability to exploit minute changes in the refractive index enables advancements in diverse areas, ranging from medical diagnostics to quality control in manufacturing, underlining the versatility and importance of refractive index sensing in advancing scientific understanding and technological innovation [40]. To determine the sensitivity of the fabricated structures, certified refractive index liquids from Cargille Laboratories (series AAA) were used. These liquids are well-described high-quality standard items for sensing and quality control. The droplets of liquids were carefully deposited onto the sample each time and cleaned after the measurements with isopropyl alcohol, making sure that no residue was left. The transmission spectrum of an RR structure with R = 100 \(\upmu\)m is plotted in the presence of n = 1.295, 1.305, and 1.315 (\(\pm\)0.001). As the refractive index of the fluid increases, it modifies the n\({}_{\text{eff}}\) of the propagating mode, resulting in a redshift in the resonance wavelength, as shown in Figure 4a.