## 2 Design and Fabrication  
### Wide-Spectrum, Low-Reflectance Coating Design  
The key to achieving high-performance in an RSOA lies in ensuring that the output end facet exhibits an extremely low reflectance. To maintain stable operating conditions for the RSOA, the reflectance of the output end facet should ideally be on the order of \(10^{-5}\)[23; 26; 27; 28]. Achieving such low reflectance requires careful selection of coating materials and precise optimization of the coating layer thickness on the output end facet. TiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) thin films are widely used in optical multilayer coatings due to their excellent optical transmittance in the visible and near-infrared wavelength ranges, as well as their high refractive indices [29; 30; 31]. Extensive research has been conducted on the structure, optical properties, and fabrication conditions of TiO\({}_{2}\) and Nb\({}_{2}\)O\({}_{5}\) films, aiming to produce high-quality optical coatings [32; 33; 34; 35; 36; 37; 38; 39; 40; 41]. It has been observed that amorphous materials are typically preferred for the multilayer optical films on facets. TiO\({}_{2}\) films, however, exhibit poor refractive index stability during fabrication and significant absorption, which further increases under ultraviolet exposure. Additionally, at a 300 \({}^{\circ}\)C annealing condition, TiO\({}_{2}\) films undergo a transition from an amorphous to a crystalline state, which facilitates the formation of a crystalline structure during fabrication. In contrast, Nb\({}_{2}\)O\({}_{5}\) films offer better chemical stability compared to TiO\({}_{2}\). The transition temperature from the amorphous to crystalline state for Nb\({}_{2}\)O\({}_{5}\) films is above 450 \({}^{\circ}\)C, making it relatively easier to prepare high-quality amorphous Nb\({}_{2}\)O\({}_{5}\) films. After careful comparison, Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) multilayer coatings were ultimately selected as the film layer for the RSOA, as they provide a broadband, low-reflectance solution. There have been numerous reports on optimizing the parameters of low-reflection coatings for the end facet [42; 43; 44; 45]. For multilayer coating structures [46], the effective interface method is commonly used for calculations. Any optical multilayer structure can be replaced by a virtual equivalent interface, which allows the characteristics of a single-layer film to be extended to the multilayer case [46]. Taking a single-layer film with an exit medium of air as an example, the reflectance is given as described in [46]:  
\[R = \frac{\left(n_{0}\!-\!n_{\mathrm{R}}\right)^{2}\cos^{2}\delta_{1}+ \left(\frac{n_{\mathrm{R}}n_{0}}{n_{\mathrm{I}}}-n_{\mathrm{f}}\right)^{2} \sin^{2}\delta_{1}}{\left(n_{0}+n_{\mathrm{R}}\right)^{2}\cos^{2}\delta_{1}+ \left(\frac{n_{\mathrm{R}}n_{0}}{n_{\mathrm{f}}}+n_{\mathrm{f}}\right)^{2} \sin^{2}\delta_{1}} \tag{1}\]  
\[\delta_{1} = \frac{2\pi}{\lambda}n_{\mathrm{f}}d\cos\theta_{1} \tag{2}\]  
where \(R\) is the optical intensity reflectance; \(n_{\mathrm{R}}\) is the refractive index of the incident medium, i.e., the refractive index of the waveguide mode; \(n_{\mathrm{f}}\) is the refractive index of the film material; \(n_{0}\) is the refractive index of the surrounding medium, generally referring to air; \(\delta_{1}\) is the phase thickness; \(d\) is the film thickness; and \(\theta_{1}\) is the incidence angle. When the refractive index of the film layer is designed to lie between that of the incident medium and air, the single-layer film exhibits anti-reflection properties.