## 3 Silicon Germanium Waveguides and Nonlinear Applications
### Wavelength Conversion of 16-QAM and 64-QAM Signals:  
The performance of SiGe waveguides as nonlinear processors for telecommunication signals was tested in wavelength conversion experiments. These demonstrations (detailed in [57]) used 10 Gbaud 16- and 64-QAM signals and were conducted in the 1550 nm wavelength region. The SiGe device used featured a strip air-clad structure with a 0.6 \(\upmu\)m width and a 1.6 \(\upmu\)m height and whose fabrication process was similar to that described in [31; 55]. The experimental setup used for the wavelength converter is similar to that implemented for the DSPK and QPSK wavelength conversion in the amorphous silicon waveguide (Section 2.2, Figure 4). Figure 9a depicts a typical optical spectrum obtained at the output of the waveguide after converting a 10-Gbaud 16-QAM signal. As can be seen, an idler with a large OSNR exceeding 36-dB was generated with a conversion efficiency of \(-\)9.7 dB. Furthermore, a uniform FWM CE exhibiting less than 0.5 dB variation was observed in the signal detuning range between 1548.39 nm and 1564 nm (Figure 9b). Figure 10a shows the constellation diagrams and BER curves assessed before and after the wavelength conversion process for both the 16-QAM (Figure 10a) and 64-QAM signals (Figure 10b). The 16-QAM measurements showed an almost identical rms error vector magnitude (EVM) between the B2B signal (8.6%) and the idler (8.7%). Furthermore, a negligible BER penalty of less than 0.3 dB at a BER of \(10^{-3}\) was obtained. For the 64-QAM case, a similar performance level was achieved. The rms EVM figures of both the B2B and the idler were similar, with 15.5% measured for the B2B and 15.8% for the idler. Furthermore, the two BER curves are similar with an error floor developing on the converted signal at high values of received power (note that the BER of the 64-QAM signal (5.9 \(\times\)\(10^{-2}\)) was limited by the bandwidth (9.6 GHz at \(-\)20 dB) and effective number of bits of our Arbitrary Waveform Generator (AWG). Both sets of results in Figure 10 demonstrate that the wavelength converter results in almost no \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Re[\(\gamma\)] (Wm)\({}^{-1}\)** & **Im[\(\gamma\)] (Wm)\({}^{-1}\)** & **FOM** \\ \hline \(W=1000\) nm, Ge (10\%) & 16 & 0.76 & 1.67 \\ \(W=1000\) nm, Ge (20\%) & 25 & 1.16 & 1.71 \\ \(W=1000\) nm, Ge (30\%) & 35 & 1.98 & 1.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Nonlinear parameters for three selected SiGe waveguides. Figure 9: (a) Output optical spectrum of the wavelength converter; and (b) normalized FWM conversion efficiency (dB) as a function of pump-signal detuning (nm). loss in quality in the converted signal (idler) in comparison to the original B2B signal and highlight the potential of the SiGe platform in implementing a wide range of state-of-art all-optical signal processing applications. In Table 5, we compare both a-Si and SiGe wavelength converters and their key performance against other similar devices already presented in the literature, showing conversion of complex, phase encoded telecom signals:  
Crystalline silicon has been widely used to realize all optical wavelength converters as shown for example in [7; 46]. In Table 5, we only report the most advanced result (in terms of signal complexity), showing the wavelength conversion of a 112 Gb/s 16 QAM signal. Although the efficiency of these devices can be improved, we believe that their main limitation is represented by the combination of TPA and FC's effects, which limit the maximum pump power that can be injected in the waveguide, thus reducing the achievable conversion efficiency. A biased waveguide can be used to mitigate the impact of FCA as shown in [19], however this approach requires additional fabrication steps that might be not desirable. Impressive results have been recently shown by using AlGaAs waveguides [47], however this platform is not CMOS compatible and may require high temperature fabrication steps [20; 21] to reduce the propagation losses.