We present a characterization of the spectral modulation and wavelength shifting induced via cross-phase modulation (XPM) in a hydrogenated amorphous silicon (a-Si:H) core optical fiber. Pump-probe experiments using picosecond and femtosecond signal pulses are shown to be in good agreement with numerical simulations of the coupled nonlinear propagation equations. The large 10nm red-shifts obtained with the femtosecond probe pulses are attributed to the high Kerr nonlinearity of the a-Si:H material. Extinction ratios as high as 12dB are measured for the conversion process at telecommunications wavelengths, indicating the potential for high-speed nonlinear optical control in a-Si:H fibers and waveguides.
© 2012 OSA
The large Kerr nonlinearity of silicon offers great potential for the development of high-speed, all-optical signal processing components. Many devices have already been demonstrated in crystalline silicon (c-Si) waveguides including cross-phase modulation (XPM) induced optical switching , signal regeneration based on self-phase modulation (SPM) , and demultiplexing via four-wave mixing (FWM) . However, within the telecommunications band, nonlinear absorption mechanisms such as two-photon absorption (TPA) and TPA induced free-carrier absorption (FCA) act to reduce the nonlinear figure of merit FOMNL = n2/βTPAλ, where n2 is the nonlinear index and βTPA is the TPA parameter, which ultimately degrades the device performance . Recently there has been increased interest in hydrogenated amorphous silicon (a-Si:H) as a platform for ultrafast telecoms applications owing to its large n2, typically more than twice that of c-Si, and modest βTPA that is associated with the larger bandgap (i.e., shorter TPA cut-off wavelength) of the amorphous material [5, 6, 7, 8]. As a result, continued advancements in the growth conditions of the a-Si:H material have led to the FOMNL being routinely reported in the range FOMNL ∼ 1– 5 [6,8,9]. These values are significantly larger than that for c-Si where FOMNL ∼ 0.4 , so that Kerr effects can prevail over the nonlinear absorption and free carrier refraction during short pulse propagation.
a-Si:H waveguides are typically fabricated on-chip using the CMOS compatible plasma enhanced chemical vapor deposition technique to have very similar geometries and dimensions to their c-Si counterparts, thus allowing for a direct comparison in device performance. Two notable results based on FWM wavelength conversion have shown that a-Si:H waveguides can yield higher conversion efficiencies  and fast pattern-free operation speeds , clearly highlighting some of the material benefits. In parallel to this, we have presented an alternative platform for the construction of a-Si:H devices based on the semiconductor fiber technology . This approach is advantageous as it offers a route to incorporating silicon processing functionality directly within fiber architectures, reducing integration costs as well as allowing for the construction of robust devices with novel waveguiding properties [11, 12]. Furthermore, the high pressure technique used to deposit the a-Si:H core material inside the silica capillary templates is conducted at low temperatures, and uses minimal precursor volumes, thus reducing the cost and complexity of the waveguide fabrication . It is worth noting that although there have been some reports of this material being optically unstable , the micron sized a-Si:H core fibers fabricated to date have exhibited excellent stability for input peak powers of several hundreds of watts, and such stability has also recently been demonstrated for similar intensity levels in a-Si:H waveguides grown on-chip . Significantly, despite the large core sizes, these fibers have been shown to guide light with most of the power in the fundamental mode for near-single-mode operation, which is important for signal processing applications .
In this paper, we present a full time-resolved characterization of XPM induced via the large Kerr nonlinearity in a a-Si:H core optical fiber. Although XPM has been widely investigated in c-Si waveguides, with its use being demonstrated for ultrafast all-optical switching , gating , and 3R regeneration , only limited studies have been made in a-Si:H . The experiments are conducted using a pump-probe set-up where a strong pump pulse induces a nonlinear phase shift on a weak probe at a different wavelength. Numerical simulations based on a set of coupled nonlinear propagation equations are used to analyze the influence of the probe pulse and waveguide parameters on the spectral modulation. We will show that strong modulation can be observed on both picosecond and femtosecond probe pulses during propagation through a 5.7μm diameter a-Si:H core fiber. The large red-shift of 10nm recorded for the femtosecond pulses, sufficient to yield a modulation extinction ratio of 12dB, is comparable to what has been observed in c-Si waveguides with nanoscale dimensions, further demonstrating the potential use of these fibers for nonlinear optical control.
2. Theory20], which is not unreasonable given that our fiber lengths are typically much shorter than the dispersion length. The complex nonlinear parameters are defined as γj,l = k0jn2/Aeff + iβTPAj,l/2Aeff, where the values of the Kerr nonlinearity n2 ∼ 1.5 × 10−13 cm2/W and the effective area of the fundamental mode in the 5.7μm fiber core Aeff ∼ 14μm2 are assumed to be constant over the closely spaced wavelength range , whilst the degenerate and non-degenerate TPA parameters for the pump and probe are βTPAp,p ∼ 0.8cm/GW, βTPAs,s ∼ 0.5cm/GW, and βTPAp,s ≈ βTPAs,p ∼ 0.5cm/GW . We note that the values of the nonlinear parameters yield a FOMNL ∼ 1.2 for this fiber, which although being larger than that of c-Si, is slightly lower than our previous report of 1.5 in Ref. . The remaining terms denote the linear loss α ∼ 3dB/cm, also assumed to be the same for both wavelengths, and the free-carrier contribution σfj = σj(1 + iμj)N, where σj ∼ 1 × 10−16cm2 and the dimensionless free-carrier dispersion (FCD) parameters μj are μp ∼ 1.102 and μs ∼ 1.07, as described in . Finally, the free-carrier density N(z,t) is determined by the rate equation (3), where νj are the respective photon frequencies and the carrier lifetime is τ ∼ 87ns, as determined by pump-probe measurements in the micron sized a-Si:H core fiber .
3.1. XPM characterization
In order to characterize the XPM process we used the pump-probe set-up shown in Fig. 1(a). The a-Si:H fiber had a length of only 8mm, which was much shorter than the pump-probe walk-off lengths for the pulses considered in our measurements (LW ∼ 9cm and LW ∼ 2cm for the picosecond and femtosecond pulses, respectively). This allowed for the temporal separation of the pulses to be controlled by an optical delay line (ODL), as illustrated. For each experiment, the transform limited pump pulses were taken directly from the output of a fiber laser operating at 1540nm with a duration of 700fs (FWHM) and repetition rate of 40MHz. To generate the probe pulses at a different wavelength, part of the pump beam was picked-off and directed through a highly nonlinear fiber (HNLF), with the parameters: β2 = 0.96ps2/km, γ = 20W−1km−1, α = 3.45dB/km, and L = 500m (at λ = 1550nm), which produced a flat, broadband spectrum that could be filtered to the desired wavelength. For the initial measurements a narrow, 1nm band-pass filter (BPF) centered at 1590nm was used to produce pulses with a duration of 3ps (FWHM). The resulting probe pulses were then amplified using a dispersion compensated erbium doped fiber amplifier (EDFA) and characterized using a frequency resolved optical gating (FROG) pulse analyzer (Southern Photonics HR150), which confirmed that the low dispersion HNLF had not introduced any significant frequency chirp. The pump and probe beams were combined at a non-polarizing 50/50 beam splitter and the temporal overlap between the pulses was monitored using an autocorrelator (AC) before free-space coupling into the fiber using a 0.4NA/60x objective. Coupled peak powers of the pump and probe pulses were ∼ 300W and 1W, respectively. Significantly, at this low probe power, no nonlinear modulation of the signal was observed in the absence of the pump. The output from the a-Si:H fiber was captured using a second 0.4NA/60x objective and recorded on an optical spectrum analyzer (OSA) in which the sweep function was synchronized to the ODL.
Figure 1(b) plots a spectrogram of the probe pulse intensity as a function of temporal delay. In our experiments, a negative time delay corresponds to the probe pulses trailing behind the pump, and a positive time delay when the probe leads the pump. Modulation of the spectral envelope is evident over a large range of delay times, with new spectral components being generated symmetrically about the central probe wavelength. To illustrate this in more detail, Fig. 2 shows the measured spectral profiles (red curves) for selected delay times compared to the solutions obtained by solving Eqs. (1)–(3) (blue curves). The good agreement between the simulations and experiments, with only modest differences in the low power wings (around the −6dB level), verifies the use of these coupled GNLSEs for analyzing XPM effects in the a-Si:H fibers. Both sets of analysis reveal that for these picosecond probe durations the spectral conversion is modest, with little reduction of the central lobe, so that there is no significant wavelength shifting of the signal beam. In addition to this, we note that the depletion of the probe energy between the delay times 0–2ps seen in Fig. 1(b) is largely due to cross-absorption modulation (XAM) , and that the slight reduction of the probe peak power at Δt = −6ps compared to 6ps can be attributed to FCA induced by the leading pump.
3.2. XPM-induced frequency shifting
Previous investigations of XPM in c-Si waveguides conducted for a range of pulse durations revealed that the strong Kerr nonlinear index change resulting from shorter (femtosecond) pulses can dominate over the free-carrier effects to produce larger wavelength shifts . Thus, in an effort to observe wavelength shifting in the a-Si:H fiber, the original BPF in Fig. 1(a) was replaced with a wider 15nm filter centered at 1587nm which produced probe pulses with a duration of 800fs (FWHM). Although the HNLF did broaden these pulses slightly with respect to the pump, the FROG measurements confirmed that the induced chirp was still negligible. Using the same set-up and input pulse peak powers (Pp ∼ 300W and Ps ∼ 1W) as for Fig. 1, Fig. 3(a) plots the corresponding spectrogram for the femtosecond probe. Comparing these results with those for the picosecond pulses, it can be seen that there has been a much stronger depletion of the central probe wavelength close to the zero delay point, this time clearly associated with XPM induced wavelength conversion, with new spectral components appearing around ∼ 1597nm, though we still expect some power reduction to be due to XAM. The extent of the wavelength shifting can be seen more clearly by plotting a trace of the peak spectral components as a function of delay in Fig. 3(b) (red curve) which reveals that an initial modest blue-shift of ∼ 4nm is followed by a large red-shift of ∼ 10nm. This red-shift is comparable to the largest shifts that have been observed in nanoscale c-Si waveguides (∼ 15nm in Ref. ), making it quite remarkable for a waveguide of these micron sized dimensions. Moreover, the probe’s central wavelength transitions from blue to red-shifted on a time scale of only ∼ 100fs, indicating truly ultrafast wavelength conversion. The measured shifts and transition times are in reasonable qualitative agreement with the solutions of Eqs. (1)–(3) (blue curve), with the simulations similarly predicting an asymmetric shifting with a strong red-shift of ∼ 15nm when the probe leads the pump.
The discrepancies between the shape of the experimental and numerical data curves, such as the oscillations on the blue shifting side and the mismatch in the size of the peak wavelength shifts, are similar to what have previously been observed for wavelength shifting of femtosecond pulses in c-Si waveguides. In Ref.  these differences were attributed to uncertainties in the waveguide dispersion, while in Ref.  they were ascribed to the asymmetric input spectral profile of the probe. In our measurements it is likely that both of these aspects play a role as there are uncertainties in the fiber dispersion parameters due to the c-Si approximation, and the filtered probe spectrum is also asymmetric with a small pedestal at ∼ 1595nm, as evident from the profile displayed in Fig. 4(a). (Note: the small oscillations across the spectrum are due to the transmission profile of the Fabry-Perot bandpass filter). Detailed simulations with various waveguide and pulse parameters indicate that the precise shape of the wavelength shifting curve is due to a complex interplay between the dispersion, nonlinearity and the loss terms. As these effects are more pronounced for the shorter pulses, any uncertainties in the fiber parameters given in Section 2 will alter the femtosecond pulse propagation more profoundly, making a direct comparison with the experiments more difficult. Nevertheless, these simulations suggest that a further decrease in the probe duration to around 600fs should result in symmetric up/down conversions on the order of 17nm, some of the largest shifts predicted to date.
Finally, Fig. 4(b) shows the measured spectral profiles taken for the delays corresponding to the largest blue and red-shifts. These large Kerr induced shifts are obtained in the vicinity of the zero delay point as this is where the pump-probe interaction is strongest. The observation of the blue-shift being closer to the zero delay is similar to what has been reported in Refs. [15, 18], and at the time of the largest blue-shift there is already some growth in the red-shifted peak. Additional simulations suggest that the modest nature of the blue-shift is due to the increased nonlinear absorption (TPA and FCA) experienced by the trailing probe as more symmetric shifting can be obtained when the effects of TPA are neglected in our numerical analysis. Using this spectral data, we can calculate the on-off conversion extinction defined as the ratio of the spectral peak at the largest wavelength shift to the value at the original 1587nm carrier. The 10nm red-shift at 1597nm yields a spectral extinction of ∼ 12dB while the smaller blue-shift at 1583nm yields a reduced extinction of ∼ 3dB. It is worth noting that by moving to even shorter probe pulses where the simulations predict a more symmetric conversion, the large wavelength shifts associated with the high n2 of the a-Si:H material should still yield sizable on-off extinction ratios. Furthermore, although the large shifts shown in Fig. 3(b) are obtained with high pump peak powers, by scaling the fiber core size down towards the nanoscale dimensions used on-chip , similarly large shifts should be attainable using milliwatt power levels for low power optical switching .
We have characterized the effects of XPM on short pulse propagation in a hydrogenated amorphous silicon core fiber. The experimental results are in good agreement with simulations of the coupled GNLSEs, with the large wavelength shifts of up to 10nm attributed to the high Kerr nonlinear index of the material. This wavelength conversion is sufficient to yield extinction ratios of the order of 12dB, even for relatively broadband sub-picosecond probe pulses. Thus these results provide further motivation for the use of a-Si:H waveguides in nonlinear optical applications at telecoms wavelengths. With further optimization of the waveguide dimensions it should be possible to design a-Si:H fibers and waveguides for low power optical switching on a femtosecond time-scale.
The authors acknowledge EPSRC ( EP/G051755/1 and EP/I035307/1), NSF ( DMR-1107894) and the Penn State Materials Research Science and Engineering Center ( NSF DMR-0820404) for financial support.
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