## 3 Results and Discussion
### Analysis of Narrow-Linewidth Laser Test Results  
After completing the tests of the RSOA's spontaneous emission spectrum and ripple, the impact of the ultra-low ripple of the four-layer Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) film system on the narrow-linewidth laser is investigated. To this end, a narrow-linewidth external cavity laser is designed. The external cavity structure integrates the FP standard cavity and filtering and optical feedback devices. The structural schematic of the system is shown in Figure 7.  
The linewidth of the laser is measured, and the output power of different currents is measured using an optical power meter. The test results are shown in Figures 8 and 9. Figure 8 presents the power spectral density (PSD) of frequency noise of a narrow-linewidth laser utilizing the RSOA chip under test conditions of 25 \({}^{\circ}\)C and 180 mA. It is noted that the frequency noise spectral density exhibits a constant level h\({}_{0}\) (Hz\({}^{2}\)/Hz) below a cutoff  
Figure 6: (**a**) Normalized ASE spectra of the RSOA at 180 mA bias current. (**b**) Magnified spontaneous-ous emission spectrum near the 1550 nm wavelength.  
frequency (\(f_{c}\)). In this case, the laser linewidth can be approximated as \(\pi\)h\({}_{0}\)[49]. As shown in Figure 8a, the extracted value of h\({}_{0}\) is 95.48 Hz\({}^{2}\)/Hz, leading to a calculated linewidth of 299.8 Hz for the narrow-linewidth laser produced by the RSOA with a normal wide-spectrum, low-reflectance coating. Figure 8b presents the test results of a narrow-linewidth laser fabricated using an RSOA chip with a less preferable wide-spectrum, low-reflectance coating (reflectance \(\approx\) 1 \(\times\) 10\({}^{-4}\)) under the same external cavity conditions and testing environment. From Figure 8b, it is evident that the linewidth of the laser produced by the chip with an inferior wide-spectrum, low-reflectance coating is significantly broader, measuring 6240.2 Hz. Therefore, the quality of the wide-spectrum, low-reflectance coating impacts the linewidth of the laser.  
Figure 8: (**a**) Linewidth, measured by PSD, of frequency noise of the RSOA with a normal wide-spectrum, low-reflectance coating. (**b**) Linewidth, measured by PSD, of frequency noise of the RSOA with an inferior wide-spectrum, low-reflectance coating.  
Figure 7: Schematic diagram of the narrow-linewidth laser structure.  
Figure 9: Light-current (L-I) curve of the narrow-linewidth laser.  
This narrow linewidth is attributed to the low ripple in the RSOA, which significantly optimizes the linewidth of the external cavity laser [18]. Figure 9 presents the light-current (L-I) curve of the narrow-linewidth laser. It can be observed that, under a test current of 180 mA, the narrow-linewidth laser made with the RSOA chip has an output power of 12.6 mW, with a threshold current around 40 mA. These results confirm that the linewidth of the narrow-linewidth laser produced by the RSOA, using the four-layer Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) film system, reaches the sub-kHz level while maintaining a certain output power, indicating relatively high performance.  
Finally, by adjusting the FP standard cavity, filtering, and other parameters of the external cavity, a wide wavelength-tuning range is achieved for the narrow-linewidth laser. The tuning range spans from 1535.83 nm to 1561.42 nm, as shown in Figure 10. This demonstrates that an RSOA with an ultra-low ripple from the four-layer Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) film system can be effectively applied to narrow-linewidth lasers requiring a wide tuning range. The four-layer Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) film system provides a wide-spectrum, low-reflectance coating, enabling flexible wavelength selection over a large wavelength range.