## 3 Results and Discussion
### SiOC Optical Waveguides  
The channel waveguides are fabricated in silicon oxycarbide (SiOC) using UV photolithography and reactive ion etching (RIE) techniques as described in Section 2.2. The channel waveguides are realized because they provide high confinement of electromagnetic light wave in two dimensions. The light confinement in the SiOC core region can be enhanced by increasing waveguide core dimensions (width and height). After each step during the whole process, the optical chips were analyzed under optical microscope to check for the quality, defects, and residual of photoresist. The photomask used to define waveguide patterns with photolithography has a set of hundreds of waveguides with different widths ranging from 1.8 to 4.5 \(\upmu\)m. Figure 7a shows micrograph of the SiOC waveguides (black strips) captured with optical microscope at the end of the waveguide fabrication process (after photoresist lift-off, before upper cladding deposition). The width of the waveguides increases from top to bottom (arrow direction). The waveguides definition is clear and free from defects. High resolution SEM image of one of the SiOC channel waveguides with refractive index n\({}_{\text{e}}\) = 1.578 and dimensions of 4400 nm by 400 nm is shown in Figure 7b before the deposition of the silica upper cladding. The SiOC waveguides were buried under 8 \(\upmu\)m thick upper SiO\({}_{2}\) cladding (n = 1.444) and provide an index contrast \(\Delta\)n of 8.2%. The index contrast between core and clad is calculated using the relation [21],  
\[\Delta\text{n}=\frac{\left(\text{n}_{\text{core}}^{2}-\text{n}_{\text{clad}}^{ 2}\right)}{2\text{n}_{\text{core}}^{2}} \tag{3}\]  
Based on the defined geometry of SiOC waveguides, electromagnetic simulations were performed to understand the mode of operation (single- or multi-mode) of the waveguides and compute the effective refractive index n\({}_{\text{eff}}\) values of the propagating TE and TM modes. Figure 8a shows the fundamental TE ad TM modes of the SiOC waveguide with dimensions 4400 \(\times\) 400 nm\({}^{2}\) (see Figure 7b) and their calculated n\({}_{\text{eff}}\) values are 1.458 and 1.4602 at \(\lambda\) = 1550 nm. The confinement factor of the SiOC waveguides for the fundamental TE and TM modes is around 30%. In Figure 8b, n\({}_{\text{eff}}\) of TE and TM modes of the SiOC waveguide are computed as a function of width (2-4.4 \(\upmu\)m). The SiOC waveguides are single mode as no higher order TE or TM modes appear when the width is varied from 2 to 4.4 \(\upmu\)m. The n\({}_{\text{eff}}\) of fundamental TM modes is larger than TE modes due to the anisotropy exhibited by columnar structure in SiOC film that is on the order of 10\({}^{-2}\). Figure 7: **(a)** Optical micrograph of straight SiOC waveguides with different widths (increasing from top to bottom with arrow) captured with optical microscope after photoresist lift-off, (**b**) high resolution SEM image of SiOC channel waveguide with dimensions (width W = 4400 nm by height H = 400 nm). Figure 9 shows the experimental analyses of losses of single mode SiOC channel waveguides for different widths (2-4.4 \(\upmu\)m) by using a cut-back technique. This technique enables to identify both the propagation losses of the waveguide and the coupling losses due to mismatch between fiber and waveguide modes overlap. As shown in Figure 9a, the propagation losses of SiOC optical waveguides having dimensions of W = 4400 nm by H = 400 nm are estimated to be 4 \(\pm\) 0.5 dB/cm from the data slope versus waveguide length. The excited TE and TM polarizations (shown with black right and red left triangles, respectively) exhibit similar propagation losses. The coupling losses due to the mismatch between fiber and waveguide modes are estimated around 1.5 dB/facet, and are in good agreement with numerical simulations, which predict 80% coupling efficiency. In general, the coupling efficiency varies between fiber and waveguide modes with waveguide core size.