# An Introduction to Nonlinear Integrated Photonics: Structures and Devices
## 4 Nonlinear Photonics Devices
### All-Optical Processing
#### 4.2.2 Frequency Conversion
Advanced modulation formats, such as multiple (M)-order QAM (quadrature amplitude modulation), are fundamental for design of modern high-capacity optical transport networks [171]. In order to enable bandwidth efficient, high-speed transmission on a chip level, integrated optical components that can operate on these modulation formats providing fundamental optical functionalities, such as wavelength routing, wavelength conversion, format conversion, etc., are required. As an example, wavelength conversions of high-order OFDM m-QAM signal based on degenerate four-wave mixing (FWM) process has been demonstrated in a silicon waveguide [172]. [PERSON] et al. [173] also used a silicon waveguide: a continuous-wave (CW) pump and a four-channel WDM 16-QAM signal were simultaneously fed into the waveguide through a grating coupler. Owing to the FWM process, the idler takes the information carried by the input WDM 16-QAM signal at the output port. In this way, wavelength conversion of WDM 16-QAM signal using a silicon waveguide was achieved. In [34], four-wave mixing (FWM)-based wavelength conversion of binary phase shift-keyed (BPSK) and quadrature phase shift-keyed (QPSK) signals at 20-Gb/s bit-rate in a 1-mm long amorphous silicon waveguide was demonstrated with a maximum FWM-efficiency of \(-\)26 dB. The first demonstration of wavelength conversion of higher-order QAM signals at data rates above 100 Gb/s in silicon was reported by [PERSON] et al. [174]. Error-free wavelength conversion of 28 Gbaud 16-QAM single polarization (112 Gb/s) signals using FWM in a dispersion-engineered silicon nanowire (SNW) was demonstrated. In XPM converters, a phase shift is induced on a signal by a pump when it propagates through a nonlinear device. The method is commonly applied along with an interferometric approach, which is able to translate at its output phase variations into amplitude variations. XPM-based wavelength conversion has the advantage of broadband operation, but the limitation is that it can applied only to amplitude modulation formats. As an example, wavelength conversion in chalcogenide planar waveguides (As\({}_{2}\)S\({}_{3}\)) was achieved in the telecommunications C-band wavelength range via cross-phase modulation, with 5.4 ps optical pulses near 1550 nm [175]. In this device, a pulsed pump source, potentially containing digital data, is directed though the nonlinear medium along with \begin{table}
\begin{tabular}{c c c c c c} \hline
**Geometry** & **Material** & **On Chip Power (mW)** & **Footprint (\(\mu\)m\({}^{2}\))** & **Qavg** & \(\eta_{\text{NL}}\)**(dB)** \\ \hline PhC on SOI [165] & InGaP & 3 & 39 & 55,000 & –12 \\ \hline Ring [166] & AlGaAs-O-I & 7 & 929 & 44,000 & –12 \\ \hline Ring-CROW(\({}^{\star}\)) [167] & Si & 100 & 4140 & x & –21 \\ \hline Ring [168] & Graphene oxide on Hydex glass & 158 & x & 50,000 & –35 \\ \hline Ring [169] & Hydex & 6 & 5730 & \(10^{6}\) & –36 \\ \hline Ring [170] & Grahene & 8 & 314 & 9000 & –37 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of continuous-wave FWM nonlinear efficiency conversion \(\eta\)NL in some integrated devices. a CW probe beam. The pump beam, inducing a transient chirp on the probe beam via XPM through Kerr nonlinearity, broadens the probe spectra generating sidebands. Using an optical filter, a single sideband can be selected so the output signal at the converted wavelength is modulated in time similarly to the pump pulse. [PERSON] et al. presented tunable wavelength conversion of a 10-Gb/s return-to-zero on-off-keyed (RZ-OOK) signal over a range of 20 nm, carried out in a silicon nanowire waveguide using cross-phase modulation (XPM), followed by a tunable filter [176]. All-optical four-channel format conversion from non-return-to-zero on-off-keyed (NRZ-OOK) to return-to-zero on-off-keyed (RZ-OOK) formats, based on semiconductor optical amplifiers (SOAs), was demonstrated in Ref. [177].