Amorphous silicon has been identified as possible solution to overcome the main limitations showed by the SOI platform namely TPA and Free Carrier Absorption (FCA) effects [
28,
32,
33,
34] already discussed in the previous section. Indeed, amorphous silicon shows enhanced nonlinear performance with respect to crystalline silicon, exhibiting both an enhanced Kerr response [
28,
35,
36,
37] and a reduced TPA effect [
28,
38]. Thanks to these properties, a-Si could be used as nonlinear media at higher power levels with respect to silicon, allowing to achieve a π phase shift, even in cm-long waveguide structures. However, material stability issues have been reported [
38], which compromise the use of this compound as a nonlinear platform for optical communications. We have recently showed that CMOS compatible hydrogenated amorphous silicon waveguides can be utilized at both low and high power level regimes, showing remarkable performance and stable operation [
26,
28]. Nonlinear waveguides were fabricated and used to demonstrate low power all optical processing of phase encoded signals, such as DPSK (Differential Phase Shift Keying) and QPSK (Quadrature Phase Shift Keying) [
26]. In the following sections, we briefly report the optical characteristics of the developed amorphous silicon waveguides, and show the high speed wavelength conversion experiments using phase-encoded signals.
2.1. 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 μm 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 °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 × 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{γ} can be extracted by the measured FWM traces by using the following equation [
40]:
where
Leff is the effective nonlinear waveguide length, and η 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{γ} equal to 800 ± 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·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 and FC-related effects. As the dynamic of TPA is fast (~fs) while FC-effects are typically slower (~ps), their contributions to the overall device absorption can be discriminated by using pulsed and CW experiments [
6]. The Im{γ} 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 α
0 is the linear loss [
42].
by assuming a hyperbolic-secant pulse temporal-profile, it is possible to derive analytically the dependence of the average transmitted power,
PT, on the input pulse peak power
P0.
using the waveguide loss α
0 (estimated to be 4.7 dB/cm) and the pulse peak power that can be extracted from the experimental data, Im{γ} was evaluated by fitting the experimental curve, yielding a value of 15.5 ± 2 (Wm)
−1. In order to compare the performance of a-Si waveguides to other nonlinear material systems, it is useful to employ a figure of merit (FOM) that accounts both for the Kerr response and the nonlinear losses. This is achieved by the following FOM [
42]:
which yields a value of 4.7 for the a-Si waveguides used in this study. This is one order of magnitude higher than typical values quoted for c-Si nonlinear waveguides [
3].
The FCA coefficient (α
FC) and the carrier dynamics were assessed by performing two different experiments as described in details in [
28]. The pulse propagation in the presence of TPA can be described by the following equation [
42]:
where
NFC is the number of free carriers per unit volume and β the TPA coefficient.
The first experiment, aimed at the evaluation of free carrier recombination time, employed a pump-probe scheme as described in [
28]. Results of this experiment are reported in
Figure 3 (left panel). It can be noted that when the peak power of the pump pulses was relatively low (
P0 < 10 dBm in the waveguide), the transmission power of the probe was almost constant in time, while for
P0 > 10 dBm depletion of the probe beam was observed in the present of a pump pulse.
This can be attributed to the abrupt rise of
NFC induced by TPA and can be described through the following equation:
after the initial power drop, caused by the TPA-excited free-carriers, a two-phase recovery process can be observed: a very fast process responsible for the initial recovery of about 10% of transmission, and a second (slower) process yielding a relatively long power-recovery tail. Experimental data can be fitted by the superposition of two exponential functions with time constants τ
1 < 50 ps (fast recovery) and τ
2 = 1.87 ns.
In order to evaluate the additional loss induced by free carriers, a second experiment was carried out using a single CW beam. In this case, the beam intensity evolution along the waveguide can be written as [
42]:
α
0, β and τ parameters were previously determined. The value of α
FC can then be determined by experimentally measuring the transmission curve of a waveguide and fitting the data to Equation (7). This is shown in
Figure 3 (right), which indicates a value α
FC = 0.8 × 10
−17 cm
2. This is only slightly lower than that measured in c-Si waveguides (
αFC = 1.1 × 10
−17 cm
2) [
42].
The overall optical characteristics of the amorphous silicon waveguides are outlined in
Table 1.
a-Si has been studied by numerous research groups in the last ten years. Remarkable results have been demonstrated in terms of nonlinear optical properties [
32,
38,
43,
44] which are in accordance to what we report in this manuscript. However, the a-Si material microstructure is strongly affected by the layer deposition parameters used during the fabrication steps, therefore different performing a-Si alloys can be found in the literature. In
Table 2, we show some recent results that have been reported, mainly in terms of Kerr and TPA response.
2.2. All Optical Wavelength Conversion of DPSK and QPSK Signals
Benefitting from the nonlinear properties of the a-Si waveguides described is the previous section, wavelength conversion experiments at 20 Gb/s using either BPSK or QPSK signals were performed. The experimental set-up used for these experiments was first reported in [
26] and is shown in
Figure 4. One-millimeter-long waveguides were used for these experiments. The power of the CW pump inside the a-Si waveguide (estimated after taking into account the grating coupler losses) was set to 70 mW, well below the TPA threshold of the waveguide. An optical spectrum recorded at the waveguide output when a BPSK (Binary Phase Shift Keying) signals was used at its input is shown in
Figure 5a. The measured FWM conversion efficiency was measured to be −26 dB. Constellation diagrams for both the original BSPK signal (back to back configuration) and DPSK idler are also shown in the figure.
Figure 5b shows Bit Error Rate (BER) curves measured for the back-to-back (B2B) and the converted signal revealing that successful wavelength conversion was obtained with only 1 dB of power penalty at a BER = 10
−5.
Wavelength conversion experiments using QPSK signals were also carried out. The input signal was a 10 Gbaud QPSK signal carrying a 20 Gb/s pseudorandom data sequence. Results obtained with this signal are outlined in
Figure 6.
Figure 6a,b shows constellation diagrams for both the B2B and the converted signal, whereas
Figure 6c shows a comparison of the BER values obtained for these two signals. A penalty of 1 dB is observed at a BER = 10
−5 demonstrating that the waveguide can be used for the processing of fast, complex-modulation optical signals.
In this section, we showed the optical characteristics of the hydrogenated amorphous silicon platform [
28] and briefly reviewed the performance of fabricated waveguides when used as all-optical wavelength converters for phase-encoded telecommunication signals [
26]. Thanks to the absence of TPA in the C-band wavelength region, these devices can be considered as building blocks for applications in future all-optical networks. It is also worth noting that similar results, in terms of conversion efficiency and Optical Signal to Noise Ratio (OSNR) penalty, have been achieved in other platforms, such as crystalline silicon [
18,
46], AlGaAs on SOI [
47] or in semiconductor optical amplifiers (SOA)-based devices [
48]. Please refer to
Table 5 for a more detailed comparison between other nonlinear platforms and the a-Si pretended in here.