## 2 Amorphous Silicon Waveguides
### Linear and Nonlinear Optical Characterization  
Nonlinear waveguides were fabricated at CEA-Leti laboratories on standard thermal oxide 200 mm wafers and their nonlinear properties were demonstrated in [28] for the first time. The thickness and width of the waveguides were set to 220 nm and 480 nm respectively. The sample under test was fabricated starting from a 1.7 \(\upmu\)m thick SiO\({}_{2}\) layer. The a-Si layer was deposited by means of the Plasma Enhanced Chemical Vapour Deposition (PECVD) technique at a temperature of 350 \({}^{\circ}\)C. A first etching step was used to define grating coupler patterns with an etching depth of 70 nm. The couplers were designed in such a way to only couple the transverse electric mode (TE-mode). After deposition of a silica hard mask, a full etch step (etching depth of 220 nm) was performed to define the waveguide layout. Several straight and serpentine waveguides (with a fixed 480 \(\times\) 220 nm cross-section) were obtained with lengths varying from 1 mm to 82.6 mm. Finally, a protective 500 nm oxide upper cladding was deposited on the top of the waveguides. A schematic of the waveguide cross-section is shown in Figure 1. Details of the fabrication process can be found in [26; 28]. The Kerr response of the a-Si waveguides were evaluated by means of continuous wave (CW) degenerate Four Wave Mixing (FWM) experiments, performed in the C-band wavelength region using waveguides of various lengths as shown in details in [28]. A CW pump beam and a weaker CW signal were combined together and sent to the waveguide under test using a vertical coupling scheme [39]. A typical recorded spectrum, after propagation along the structure under test, is shown in Figure 2 (inset). The Re[\(\gamma\)] can be extracted by the measured FWM traces by using the following equation [40]:  
\[\text{Re}\{\gamma\}=\frac{\sqrt{P_{i}(L)/P_{s}(L)}}{\text{n}P_{p}(0)L_{\text{eff }}} \tag{1}\]  
where \(L_{\text{eff}}\) is the effective nonlinear waveguide length, and \(\eta\) accounts for the phase-mismatch induced by waveguide dispersion. By considering spectra obtained from waveguides of different lengths, measured at various pump power levels, a Re[\(\gamma\)] equal to 800 \(\pm\) 50 (Wm)\({}^{-1}\) was obtained, which is three times larger with respect to values commonly measured in channel crystalline silicon (c-Si) waveguides [41]. The waveguide dispersion was also evaluated by measuring the FWM efficiency while increasing the pump-signal detuning, as reported in Figure 2. By fitting the curve, a dispersion coefficient D = \(-\)380 ps/(nm\(\cdot\)km) was obtained. TPA and Free Carrier Absorption (FCA) coefficients were determined by means of pulsed experiments, as described in detail in [28]. TPA and FCA effects occur when the optical power inside the waveguide is higher than the TPA-threshold, thus triggering the multiple photon absorption  
Figure 1: Amorphous silicon waveguide cross section. The thickness of the SiO\({}_{2}\) layer is 1.7 \(\upmu\)m [28]. Figure 2: Normalized FWM (Four Wave Mixing) efficiency as a function of pump-signal detuning. The waveguide length was 2.26 cm. Inset: Spectrum recorded after propagation along the waveguide [26; 28]. and FC-related effects. As the dynamic of TPA is fast (\(\sim\)fs) while FC-effects are typically slower (\(\sim\)ps), their contributions to the overall device absorption can be discriminated by using pulsed and CW experiments [6]. The Im\(\{\gamma\}\) coefficient was assessed through the use of ultra-short pulses (120 fs pulse duration at 82.5 MHz repetition rate) and its value calculated starting from the following differential equation, where \(P(z)\) is the pump power and \(\alpha_{0}\) is the linear loss [42]. \[\frac{d}{dz}P(z)=-a_{0}P(z)-2|\text{Im}(\gamma)|P^{2}(z) \tag{2}\]  
by assuming a hyperbolic-secant pulse temporal-profile, it is possible to derive analytically the dependence of the average transmitted power, \(P_{T}\), on the input pulse peak power \(P_{0}\).