## 2 Experimental Details  
### Layer Fabrication and Characterizations Techniques  
SiOC films were deposited with reactive RF magnetron sputtering of a silicon carbide (SiC) target in presence of argon (Ar) and oxygen (O\({}_{2}\)) gases at room temperature. The SiOC films are deposited on a 4 inches Si (100) wafer with 8 \(\upmu\)m SiO\({}_{2}\) buffer layer that isolates SiOC core from high index Si substrate. To achieve the desired refractive index, an optimized sputtering recipe with the following parameters is used: rf power = 350 W, Ar flow = 60 sccm, and O\({}_{2}\) flow = 2.6 sccm. The sputtering was run for around three minutes to obtain a SiOC layer with a thickness of 400 nm. Further details on deposition process, obtained deposition rate of sputtering, and optical parameters of SiOC films are provided in [14]. The surface roughness of the deposited SiOC layer was determined with atomic force microscope (5600 LS AFM system, Keysight, CA, USA) at five different places on the four-inch wafer. The SiOC layer was probed in contact mode over an area of 10 by 10 \(\upmu\)m\({}^{2}\) at each location. Cross-sectional images of SiOC film and waveguides were obtained with scanning electron microscope (SEM LEO 1525, One Zeiss Drive, NY, USA) to investigate the morphology and verify the profile and thickness. Since SiOC is a dielectric material, a thin layer of platinum (\(\approx\)2 nm) was deposited on the SiOC films to avoid electrons charging effect. The high-resolution images were captured by accelerating electrons at a voltage of 20 kV and the signal was collected from in-lens detector while keeping a distance of around 6 mm between the SiOC sample and the electron gun. The optical properties of the deposited SiOC film on SiO\({}_{2}\)/Si wafer are measured with variable angle spectroscopic ellipsometer (VASE J.A. Woollam Inc., Lincoln, NE, USA). The ellipsometric data were acquired at multiple incidence angles (65\({}^{\circ}\), 70\({}^{\circ}\), and 75\({}^{\circ}\)) in the spectral range from 1200 to 1600 nm with a step size of 10 nm between two wavelengths. The ellipsometry measures the change in polarization state of the light reflected from the surface of the film/substrate under investigation. The measured quantities are psi (\(\psi\)) and del (\(\Delta\)) which are angles defining the ratio of Fresnel reflection coefficients \(R_{p}\) and \(R_{s}\) for parallel (\(p\)) and normal (\(s\)) polarized light as [15],  
\[\frac{R_{p}}{R_{s}}=\tan\psi exp(i\Delta) \tag{1}\]Ellipsomteric measurements were performed taking in to account the possible depolarization originated by thickness non-uniformity and surface roughness. Since ellipsometry is an indirect technique, an optical model is necessary to obtain the optical constants (n, k) of film/substrate. A four-layer film/substrate stack including surface-roughness, SiOC film, SiO\({}_{2}\) layer, and Si substrate as shown in Figure 1a was used as a model to extract the optical constants n and k of the SiOC film. The surface roughness layer is based on Bruggeman EMA [16; 17] that is AFM equivalent and provides peak-to-valley roughness. The SiOC film index was represented by Cauchy dispersion model,  
\[\text{n}(\lambda)=A+\frac{\text{B}}{\lambda^{2}}\left(\lambda\text{ in }\mu\text{m}\right) \tag{2}\]  
where A and B constants are the fit parameters in modelling the measured ellipsometric \(\uppsi\) and \(\Delta\) data. The SiOC film was modeled as anisotropic layer by introducing uniaxial anisotropy in the Cauchy model. The optical axis was considered perpendicular to the surface as illustrated in Figure 1b. From the frame of reference of ellipsometry, ordinary axis n\({}_{\text{o}}\) corresponds to transverse electric (TE) polarization and extra-ordinary axis n\({}_{\text{e}}\) to transverse magnetic (TM) polarization as shown in Figure 1b. The data was fitted by the commercial WVASE32 software [17] using the optical model given in Figure 1a.