# Ultra-Low-Loss Silicon Waveguides for Heterogeneously Integrated Silicon/III-V Photonics
## 3 Passive Device Demonstrations
### Narrow Bandwidth Bragg Gratings  
Another useful component that can be utilized with low-loss waveguides is a low-kappa (\(\kappa\)) Bragg grating. These gratings are widely used in filters, sensors, and semiconductor lasers as a wavelength selective element, much like the ring resonator. The bandwidth of the grating is directly proportional to power coupling coefficient \(\kappa\), and therefore can be minimized by reducing the perturbation strength of the grating [39]. At the same time, the length (\(L\)) of the grating should be long enough (\(\kappa L\) \(\sim\)1) and the loss of the waveguide must be low in order to obtain sufficient reflection. Care must be taken in the design of the grating in order to achieve weak \(\kappa\) as conventional sidewall or top surface gratings tend to have stronger \(\kappa\). Instead, we utilize \"post\" (or inversely, \"hole\") gratings in which small areas of the waveguiding material are placed (removed) periodically on either side of the waveguide. The dimensions of the posts (holes) and proximity to the waveguide can be lithographically defined, and tailored to achieve the desired \(\kappa\). This approach has been successful for low loss silicon nitride gratings [40]. For our waveguides, it is simpler to etch holes on either side of the waveguide, as shown in Figure 6a. The resulting \(\kappa\) of the grating is directly controlled by the hole-to-waveguide distance, while the period of the grating is set to be 240 nm, corresponding to a stopband at 1563 nm for an unperturbed waveguide \(n_{\mathit{eff}}=3.2560\).  
We fabricate uniform gratings with lengths of 0.5 and 1.0 cm. The waveguide width is 1.8 \(\upmu\)m, and the length is 2.2 cm. We used an e-beam lithography to write the grating teeth, although DUV immersion lithography can also resolve 120 nm features. Transmission and reflection spectra are measured, and fitted using a transfer matrix model in Lumerical Interconnect. This approach also accounts for Fabry-Perot cavities formed by the waveguide facets, which affects the grating shape. From this, we extract the bandwidth and peak reflectivity of the grating, which can then be used to estimate \(\kappa\). A few selected gratings are depicted in Figure 6b along with the predicted grating bandwidth. Using 1 cm long gratings, we were able to achieve a 50 pm FWHM bandwidth with roughly 70% reflectivity, with potential to further reduce the bandwidth with a longer grating. Figure 6c and d show two examples of the measured reflection and transmission spectra of the 1 cm long grating waveguides with \(\kappa=1.25\) cm\({}^{-1}\) and \(\kappa=4.0\) cm\({}^{-1}\), respectively. Finally, Figure 6e shows the relation between the distance between the holes to the core waveguide's edge and \(\kappa\) strength. The measured data was fitted well with an exponential curve. The right y-axis of Figure 6e shows the calculated effective index difference between the waveguide with and without the hole gratings.  
Figure 6: (**a**) An SEM image of the fabricated low \(\kappa\) Bragg grating waveguide with a close-up of the holes on both sides of the waveguide. (**b**) Theoretical calculations of gratings’ full width half max (FWHM) versus varying \(\kappa L\) for 0.5, 1 and 2 cm long grating waveguides. Circular blue markers show the measured data. (**c,d**) Spectra of reflection and transmission of 1 cm long grating waveguides with \(\kappa=1.25\) cm\({}^{-1}\) and \(\kappa=4.0\) cm\({}^{-1}\), respectively. The ripples are caused by reflections off the waveguide facets. (**c**) The extracted \(\kappa\), \(\Delta n\), and exponential fit as a function of waveguide to hole distance.