1. Introduction

Supercontinuum (SC) generation is a large spectral broadening that arises during propagation of a light pulse in a transparent nonlinear material. With appropriate dispersion of the nonlinear medium, strongly broadened spectra have been observed in a variety of media (solids, liquids and gases) [1]. However, the very high pump power required to observe supercontinuum generation in these bulk devices limits their application potential. With the advent of microstructured fibers [2], which allow increasing the effective nonlinearity and provide control over the group velocity dispersion, bright supercontinuum sources can be obtained with low pump pulse energies. This transformed SC generation into a mature field, with several commercial applications such as wavelength division multiplexing (WDM) communication [3], optical frequency metrology [4] and biophotonics [5].

Today, the integration of SC sources is a hot topic, with promising results obtained in compact devices [6–8]. On-chip SC generation has the potential of providing integrated components with small footprints that can be fabricated at low cost and in high volumes. Silicon-on-insulator (SOI) waveguides, thanks to their CMOS compatibility and high nonlinearity, are one of the most promising ultra-compact nonlinear devices for SC generation.

In 2007 Yin et al. [9] reported the first numerical simulations of SC generation in a 1.2 cm long crystalline silicon waveguide extending over 400 nm, when a 50 fs pulse at 1.55 µm propagates as a third-order soliton. Promptly after, Hsieh et al. published the experimental demonstration in a 4.7 mm long crystalline silicon waveguide [10], using a 100 fs pulse. A spectral broadening of approximately 300 nm was obtained at 1.55µm. In both cases two photons absorption (TPA) clamps the maximum power in the chip, thereby limiting the maximum achievable spectral broadening.

In both studies, the waveguides were engineered to exhibit anomalous group velocity dispersion. Contrary to the normal dispersion regime where due to poor phase-matching the main nonlinear process is self phase modulation (SPM) [11, 12], the anomalous dispersion regime allows in addition to SPM many other nonlinear effects such as, modulation instability, soliton shift and soliton fission [2]. The combination of some or all these effects allows maximum spectral broadening of the SC. In crystalline silicon nanowires using femtosecond pulses, SPM and soliton fission were the main nonlinear processes reported in [9, 10].

Using picosecond pulsed pump lasers represents another interesting regime in which cascaded four-wave mixing (FWM), modulation instability (MI), SPM and Raman scattering are the most important nonlinear processes involved in SC generation in anomalous dispersion waveguides. Recently, the combination of all these effects was reported to be responsible for the demonstration of SC generation in a 2 cm crystalline silicon waveguide spanning three-quarters of an octave from 1535 to 2525 nm [13]. This broad bandwidth was achieved by using a 2.14 µm wavelength picosecond pump laser. At this pump photon energy, which lies close to the half-bandgap energy of crystalline silicon, the effects of TPA and free carriers absorption are strongly reduced, thereby allowing stronger nonlinear effects.

Recently, attention has focused on hydrogenated amorphous silicon (a-Si-H) waveguides [14–21]. This material is characterized by a larger band-gap than crystalline silicon (1.6 eV versus 1.12 eV, see [18]), resulting in a lower TPA absorption and a significantly higher figure of merit ($FOM={\gamma }_{real}/4\pi {\gamma }_{im}$, where${\gamma }_{real}$ and ${\gamma }_{im}$ are the real and the imaginary parts of the nonlinear parameter$\gamma$, respectively) at telecom wavelengths [16, 17]. Several nonlinear functions such as parametric amplification [18], frequency conversion [19] and all-optical signal processing [21] were demonstrated.

The major drawback of this material at telecommunication wavelength is optical degradation which has been reported in some experiments when injecting high pump power into the waveguides [21]. However a-Si-H waveguides that do not exhibit optical degradation have also been reported, when short pump pulses are used (1ps <FWHM< 1.8ps) [16, 17].

In this work, we demonstrate, by exploiting its high FOM, SC generation in a-Si-H waveguides at telecommunication wavelengths using picosecond pulses. We investigate the SC in waveguides of different widths ranging from 500 nm to 800 nm (nominally 220 nm thickness), which changes the dispersion of the waveguide. Correspondingly we observe large changes in the bandwidth of the SC. In the wider waveguides that produce the broadest SC, the output spectra show good stability even after several hours of continuous exposure to the high peak power pulse train.

2. Experiment and results

The a-Si-H waveguides are fabricated in a 220 nm-thick hydrogenated amorphous silicon layer deposited on top of a silicon dioxide layer using a low temperature Plasma Enhanced Chemical Vapor Deposition (PECVD) process. The a-Si-H film was formed by plasma decomposition of silane (SiH₄) gas combined with Helium (He) for dilution. Waveguides of varying lengths L (1 to 7cm) and cross section (500 × 220 nm², 700 × 220 nm², 750 × 220 nm² and 800 × 220 nm²) were fabricated using 193 nm optical lithography and dry etching.

As a first step, at low power, we estimated the propagation losses for TE polarization of waveguides of different width, see Table 1. (For the 500nm wide waveguide the linear losses were measured to high precision using waveguides of different length. For the 700, 750 and 800nm wide waveguides we only had waveguides of 1 cm length. The linear losses were estimated by adjusting the measured SPM spectra to numerical simulations. Hence the estimated error is much larger).

Table 1. Linear and nonlinear losses as a function of waveguides width

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Then, to obtain the nonlinear absorption for each waveguide we measured the transmission T as a function of peak power using 1.6ps pulses generated by a picosecond laser source. Using the equation:

The high index contrast between silicon and the surrounding media (air or SiO₂), which gives rise to strong optical confinement, results in a high effective nonlinearity parameter ${\gamma }_{real}$ of the a-Si-H waveguides. Consequently, and due to the comparatively low nonlinear absorption, the nonlinear FOM ($FOM={\gamma }_{real}/4\pi \times {\gamma }_{im}$) was found to be greater than 2 at telecommunication wavelengths [16–18], thereby paving the way to efficient nonlinear photonic applications.

The high optical confinement contributes also to a waveguide geometry induced anomalous dispersion at telecommunication wavelengths. This anomalous dispersion provides the phase matching conditions necessary for the appearance of the nonlinear effects responsible for the SC generation.

For the experimental demonstration of SC generation, a telecommunication wavelength picosecond pulse train (0.8 ps < FWHM < 1.6 ps depending on the center wavelength, and with a repetition rate of 10 MHz) generated by a tunable optical fiber cavity is used as the pump. In a first experiment, we used the waveguide with a 500 × 220 nm² cross section and 1 cm length. In waveguides with similar cross section, SPM and MI in the picosecond regime were already reported [18, 21]. The coupling losses between the lensed fibers and the tapered waveguide are estimated to be 6-7 dB. The output beam is sent into a mid-IR optical spectrum analyzer (OSA) at a 1 nm resolution for analysis.

Figure 1 shows the dependence of the output spectrum as a function of on chip peak pump power at a pump center wavelength of λ_pump = 1560 nm (FWHM≈1 ps). At low pump power, the spectral width varies only slightly. However, above a threshold pump power many peaks appear and the spectral width increases sharply until at the highest on chip peak power of 15.1W, the spectral width has increased to reach a value more than 300 nm at −30 dB from the pump peak.

 

Fig. 1 SC generation in a 1cm long 500 × 220 nm² a-Si-H waveguide: output spectrum as function of on chip peak pump power. The spectra are vertically offset by multiples of 40 dB for clarity.

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To obtain some insight into the nonlinear processes involved in this widening, we discuss the evolution of the spectrum as a function of the power. We observe even at the lowest input power, the pump spectrum is broadened by SPM. When the on chip pump peak power reaches 2.4 W the spectrum is further broadened by SPM and two MI sidebands due to the amplification of background noise at wavelengths for which the phase matching condition is satisfied, detuned by approximately 24 nm from the pump wavelength, as shown in Fig. 1. Peaks due to higher order sidebands that are created when the first order sidebands become strong are also observed [22].

However, an unexpected peak is seen at 2.4 W peak pump power shifted by 19.4 THz from the pump. We discuss briefly the possible origin of this peak. The detuning of the peak changes approximately by 7 THz when changing the pump wavelength from 1560 nm to 1530 nm. This rules out a Raman shift, which would occur at fixed detuning. In addition, the Raman shift in amorphous silicon was measured to be around 14.5 THz [23]. The value of the dispersion (β₂ = −2 ps²/m) of the waveguide has been estimated at telecommunication wavelengths in [18] from a four-wave-mixing based conversion efficiency spectrum at low power. From this we deduce that the peak could not be generated by soliton fission, as the estimated nonlinear length and soliton fission length [2], of L_NL = 476 μm and L_SF = 1.2 cm (P = 3W) respectively, do not allow for this process in a 1 cm long waveguide.

Having eliminated these two possibilities, the only known process that could produce this peak is dispersive wave generation, often referred to as Cherenkov radiation [24]. Note that a similar frequency shifted radiation peak has been predicted and observed in the femtosecond regime in crystalline silicon waveguides [25, 26].

In the long pulse regime such a radiation has been attribute to the formation of pre-solitonic breathers along the pump pulse when modulation instability is the main nonlinear effect behind the supercontinuum generation [27, 28]. To confirm these interpretations would require a measurement of the dispersion of the waveguide and detailed numerical simulations. Unfortunately measurements of the dispersion are not available at present.

At the highest peak power, both parts are joined and the SC is flattened, probably due to cascaded four wave mixing.

Concerning stability, we observed a decrease of SC bandwidth as a function of time due to optical degradation of the waveguide [Fig. 2(a)]. This process is faster during the first hour. It then reaches a kind of steady state regime where the degradation becomes very slow. Figure 2(b) depicts a comparison between SC spectra generated using a 1530 nm (FWHM≈1.6 ps, P_peak = 6 W) pump wavelength at t = 0 minutes and after 15 hours of illumination.

 

Fig. 2 (a) Evolution of the SC bandwidth as a function of time at −30 dBm from the pump peak. (b) Comparison between SC bandwidth at the beginning of the experiment (blue curve, t = 0 minutes), and after degradation (red curve, t = 15 hours). The dashed line represent the level at which the SC bandwidth evolution was calculated for panel (a).

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As discussed in [18, 21], the degradation probably originates from the Staebler-Wronski effect [29, 30]. We have measured that the optical degradation can be attributed to an increase of the linear and nonlinear losses, resulting in a decrease over time of the nonlinear efficiency. We have also observed that in a-Si-H waveguides the rate of degradation depends on pulse duration: it is much lower when shorter pulses are used. Annealing the samples at 200 °C for 5 minutes, reverses the degradation and restores all the optical properties of the a-Si-H waveguides [21].

To study the role of the waveguide geometry on the SC bandwidth and stability, we performed other experiments in waveguides of 700 nm, 750 nm and 800 nm width and 1cm length (thickness 220 nm). In these experiments both waveguides facets are cleaved, and the lensed fiber to chip coupling losses at each facet are measured to be in the range [9dB-12dB]. The output spectra for the three waveguides are depicted in Fig. 3. For each waveguide width, pump wavelength and pump power were optimized to obtain the broadest spectrum. The best results are obtained for the 800nm wide waveguide for which a spectral broadening greater than 550 nm is observed with an on chip peak power as low as 4 W.

 

Fig. 3 SCs generation in 1 cm long a-Si-H waveguides with a cross-section of 700 × 220 nm² (a), 750 × 220 nm² (b), and 800 × 220 nm² (c) observed on a mid-IR OSA. In panel (a) the pump wavelength is 1560nm (FWHM ≈1 ps), while it is 1530 nm (FWHM ≈1.6 ps) in panel (b) and (c). The on chip peak power is estimated to be 12 W, 9 W and 4 W respectively.

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The evolution of the spectra with optical power is similar to that observed in the 500nm wide waveguide see Fig. 1. Therefore we expect that the processes responsible for the SC generation are the same in all waveguides, namely SPM, MI, dispersive wave generation and cascaded four-wave mixing.

Changing the waveguide width affects dispersion, which affects the nonlinear processes that give rise to the SC. This explains why the spectra observed in Fig. 3 differ. In particular it is interesting to compare the detuning $\Omega$ of the modulation instability sideband between the waveguides of 500 nm and 700 nm width, see Figs. 4(a) and 4(b). Larger detuning, due to an anomalous dispersion β₂ near to zero, is observed in the 700 nm wide waveguide, as predicted by the relation$\Omega =\sqrt{2{\gamma }_{real}P/{\beta }_2}$ [31]. This combined with the detuning of the dispersive wave, explains the greater spectral width of the SC in the wider waveguides.

 

Fig. 4 Output spectra of MI process in 1cm long waveguides of cross section of 500 × 220 nm² (a) and 700 × 220 nm² (b) respectively. A 3.8 ps pulsed laser (power on chip = 8 W) was used for the waveguide of 500 nm of width, and a 1.6 ps pulsed laser (power on chip = 3.3 W) for the waveguide of 700 nm of width.

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In Table 2 we report the estimated values of the nonlinear coefficient ${\gamma }_{real}$ and the nonlinear FOM. The nonlinear coefficient ${\gamma }_{real}$ was estimated by fitting the observed SPM spectra of each waveguide with numerical simulations.

Table 2. Nonlinear coefficient and FOM as a function of waveguides width

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We were surprised to observe good stability of the SC over time in the wider waveguides, see Fig. 5 where the bandwidth is shown not to have changed after 1 hour of illumination in a 750 nm wide waveguide.

 

Fig. 5 Stability of the SC generated in a waveguide of 750 nm of width (blue curve (t = 0 minutes), red curve (t = 60 minutes)): after 1 hour the spectrum has not changed (compare with Fig. 3(b)).

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The same stability was observed in the 700 nm and 800 nm wide waveguides. In work that will be reported in detail elsewhere, we observed also high SC stability in waveguides of width 700 nm, 750 nm and 800 nm when femtosecond pulses were used at telecommunication wavelength.

This stability can originate from the lower degradation in the broad waveguides that can be partially attributed to the lower TPA, short pulse width and lower light intensity. However this observation also indicates that the optical degradation is a highly nonlinear phenomenon, since small changes of the propagation conditions completely change whether or not degradation occurs. This could be due to the number or energy of the free carriers required for the Staebler-Wronski effect.

3. Conclusion

We have demonstrated SC generation in 1 cm long CMOS compatible hydrogenated amorphous silicon waveguides. Using wide waveguides (up to 800 nm width) that provide very low dispersion, we demonstrated a spectral broadening greater than 550 nm around telecommunication wavelengths with a low on chip peak power of 4 W. Quite unexpectedly, we did not observe any optical degradation in the wider waveguides. These results highlight the potential of a-Si-H for integrated, on chip, non linear optics.