# Ultra-Low-Loss Silicon Waveguides for Heterogeneously Integrated Silicon/III-V Photonics
## 3 Passive Device Demonstrations  
### Long Waveguide Delay-Line  
We designed 52.2 cm long spiral delays (illustrated in Figure 4a) to characterize the propagation loss. Waveguide widths were 1.8, 3.0 and 8.0 \(\upmu\)m and the minimum bend radius used in all spirals was 800 \(\upmu\)m. We use the coherent optical frequency domain reflectometry (OFDR) technique with  
Figure 3: (**a**) Experimental data (circular markers) and theoretical curve (solid line) for the propagation loss of 1 \(\upmu\)m wide waveguide at varying etch depth. (**b**) Theoretical calculations (solid lines) of the waveguide loss at varying waveguide width at three different etch depth (500 nm, 231 nm and 56 nm). The experimentally measured results are plotted in circular markers.  
a commercially available system (Luna Inc. OBR 4400, Roanoke, VA, USA) [34] to quantify the propagation loss of the fabricated Si rib waveguides. The technique has been proven to calculate the propagation loss with high accuracy independent of the fiber-waveguide coupling loss uncertainty [21]. Figure 4b shows the data measured for the 52.2 cm long spiral of 1.8 \(\upmu\)m wide ULL silicon waveguide. The peaks on the left hand side (near 0 m distance) and right hand side (near 0.5 m distance) are the reflections at the waveguide facets. The linearity of the trace verifies that the waveguide loss is not bend-loss limited. The measured mean and deviation of spectral dependence of the propagation loss of the three waveguide widths are plotted in Figure 4c. A single mode 1.8 \(\upmu\)m wide waveguide achieves an average of 16 dB/m propagation loss over C + L band. The propagation loss in multimode ULL waveguide with 3.0 \(\upmu\)m and 8.0 \(\upmu\)m widths are lower, at 10 dB/m and 4 dB/m, respectively.  
The measured loss of the ULL waveguides show a relatively large discrepancy to the values predicted by the \(n_{w}\) approximation method described in Section 2.2 (Figure 2b). The model had several simplifications such as ignoring the surface roughness of the etched slab surfaces. For fully etched (500 nm) or halfway etched (231 nm) waveguides, the optical field that interacts with the etched surface is small enough to be neglected in the total loss calculation. However, with the very shallow rib (56 nm) waveguides, the optical field expands laterally (similar to a slab mode) and the interaction between the mode field and the etched surface cannot be ignored. The roughness rms of the etched surface is typically in order of several nanometers, which is more than one order of magnitude larger than the unetched waveguide top surface roughness (\(\sim\)0.1 nm). The scattering due to the etched surface roughness is therefore significant and results in the discrepancy between the experimental and theoretical waveguide loss.  
Figure 4: (**a**) Mask layout of spiral delay lines with 52.2 cm total length and 850 \(\upmu\)m minimum bend radius (**b**) Optical Backscatter Reflectometry (OBR) data from the spiral with 1.8 \(\upmu\)m width. A linear fit of the waveguide backscatter is shown with the dashed red line. The propagation loss of the waveguide can be approximated as 1/2 of the slope of the fitted line. (**c**) Wavelength dependence of the propagation loss (mean and standard deviation) of waveguides with different widths (1.8 \(\upmu\)m, 3.0 \(\upmu\)m and 8.0 \(\upmu\)m).