## 2 Design and Fabrication
### Wide-Spectrum, Low-Reflectance Coating Design
Under the conditions of normal incidence of light and where the optical thickness \(n_{\mathrm{f}}d=\lambda/4\), the reflectance is given as follows:  
\[R = \frac{\left(n_{\mathrm{R}}-1\right)^{2}\cos^{2}\!\left(\frac{2\pi}{ \lambda}\times\frac{\lambda}{4}\right)+\left(\frac{n_{\mathrm{R}}}{n_{ \mathrm{f}}}-n_{\mathrm{f}}\right)^{2}\sin^{2}\!\left(\frac{2\pi}{\lambda} \times\frac{\lambda}{4}\right)}{\left(n_{\mathrm{R}}+1\right)^{2}\cos^{2}\! \left(\frac{2\pi}{\lambda}\times\frac{\lambda}{4}\right)+\left(\frac{n_{ \mathrm{R}}}{n_{\mathrm{f}}}+n_{\mathrm{f}}\right)^{2}\sin^{2}\!\left(\frac{2 \pi}{\lambda}\times\frac{\lambda}{4}\right)}=\frac{\left(n_{\mathrm{R}}-n_{ \mathrm{f}}^{2}\right)^{2}}{\left(n_{\mathrm{R}}+n_{\mathrm{f}}^{2}\right)^{2}} \tag{3}\]  
When \(n_{\mathrm{f}}\) equals the square root of \(n_{\mathrm{R}}\), the reflectance is zero, i.e., complete transmission occurs. When employing the effective interface method [46] for calculations, in the case of a multilayer thin-film structure under normal incidence, the interface reflection coefficient \(r_{\rm i}\) and transmission coefficient \(t_{\rm i}\) for the \(i\) layer are given by  
\[r_{\rm i}=\frac{n_{\rm i-1}-n_{\rm i}}{n_{\rm i-1}+n_{\rm i}} \tag{4}\]  
\[t_{\rm i}=\frac{2n_{\rm i-1}}{n_{\rm i-1}+n_{\rm i}} \tag{5}\]  
where \(n_{\rm i}\) is the refractive index of the \(i\) layer. For the \(i\) layer, the effective reflection coefficient (\(R_{\rm i}\)) is given by:  
\[R_{i}=r_{\rm i}+\frac{t_{\rm i}^{2}R_{\rm i+1}e^{-2i\delta_{\rm i}}}{1-r_{\rm i }R_{\rm i+1}e^{-2i\delta_{\rm i}}} \tag{6}\]  
\[\delta_{\rm i}=\frac{2\pi}{\lambda}n_{\rm f}dcos\theta_{\rm i} \tag{7}\]  
By recursively calculating up to the first layer, the total reflection coefficient (\(R_{\rm 1}\)) of the multilayer film is obtained, and the total reflectance \(R\) is given by  
\[R=(R_{\rm 1})^{2} \tag{8}\]  
Based on the aforementioned theory, the coating layers for the output facet of the RSOA are simulated. Figure 1a shows a simulated diagram of the reflection spectrum of the output facet of the RSOA. For RSOA chips, it is best to maintain the reflectivity of the output facet at the level of \(10^{-5}\)[23]. The reflection spectrum of the Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) multilayer is V-shaped, as indicated by the blue line in Figure 1a. From the blue line in Figure 1a, it can be seen that the wavelength range where the reflection coefficient of the Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) multilayer is below 1 \(\times\)\(10^{-5}\) only covers 1534-1546 nm, a 12 nm range, which does not meet the requirement of covering the C-band from 1530 nm to 1565 nm. Therefore, the low-reflectance bandwidth of the Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) multilayer is relatively narrow, making it unsuitable for creating a wideband low-reflectance coating for the C-band. To address this limitation, a four-layer Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) film system is simulated which broadens the reflection bandwidth and provides a wide-spectrum, low-reflectance coating, as shown by the pink line in Figure 1a. For the four-layer Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) film system, the wavelength range where the reflection coefficient is below 1 \(\times\)\(10^{-5}\) spans from 1498 nm to 1582 nm, covering a total of 84 nm, covering the C-band. Thus, to achieve a wideband low-reflectance spectrum for the RSOA, the four-layer Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) film system is adopted. The thicknesses of the layers in the four-layer Nb\({}_{2}\)O\({}_{5}\) film system are Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\)/Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) = 223.61 nm/168.44 nm/105.57 nm/341.49 nm, and they are labeled as the first layer to the fourth layer, respectively. Figure 1: (**a**) Reflection spectra associated with the Nb\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) multilayer. (**b**) Reflection spectra with each individual film thickness increased by 1 nm.