1. Introduction

The silicon-on-insulator (SOI) platform stimulates increasing interest in waveguide based nonlinear optics. During the last decade, effects such as four-wave mixing (FWM) [1–11], Raman scattering [12–15], self phase modulation (SPM) [2,4] and cross phase modulation (XPM) [2,4] were studied by various groups. After 2006 however, only few experiments on SOI waveguides using high intensity CW light in the telecom window were reported [5,6,8]. Instead, most of studies took up mid-infrared light [7,10,16], pulsed light [4,7,16] or low intensities [11,17]. Until today the question remains whether we can deploy SOI nonlinear optics in the telecom window for CW applications such as parametric amplifiers. In this paper we shall present our recent experimental results of four-wave mixing based wavelength conversion in nano-rib waveguides with p-i-n diode structures. The reason for using a p-i-n diode along the waveguide structure is to remove the free carriers induced by two photon absorption (TPA). Free carriers cause additional absorption that is highly detrimental for nonlinear effects like Raman scattering (SRS) or FWM. In this paper, we show that efficient removal of free carriers from nano-waveguides can be achieved using p-i-n waveguide diodes. The thus available higher intensities on a smaller waveguide cross section allow for considerably improved parametric scattering efficiencies, opening the perspective for telecom CW parametric amplifiers.

Some groups already demonstrated CW nonlinear optical effects in SOI rib waveguides with reverse biased p-i-n diode such as Raman lasing [14,15], and wavelength conversion [3]. However, these works analyzed larger waveguides of 1.5µm x 1.55µm (width x height). In another work, reverse biased p-i-n diodes on nano-waveguides proved to be an efficient free carrier removal scheme [18], reducing free carrier lifetimes down to ps. However, this work did not experimentally investigate nonlinear optical effects. Most of the work on wavelength conversion and parametric gain was done for silicon nano-waveguides without active carrier removal [1,2,4–11]. These experiments therefore suffered from free carrier absorption or used a pulsed pump in order to strongly reduce free carrier absorption in the waveguide [4]. In the Table 1 . at the end of the paper we compare experimental results achieved by other groups to the results of this work.

Table 1. Summary of CW Four-wave Mixing Results in Literature and This Work

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2. Simulation method

In previous publications concerning four-wave mixing wavelength conversion in silicon waveguides two different definitions of conversion efficiency η have been used. One approach defines efficiency as ratio η_0L = P_signal(0)/P_idler(L) [1,11]. The other definition is η_LL = P_signal(L)/P_idler(L) [3,6,9]. In the following we shall focus on the latter definition because of ease of comparison with the experimental results of other groups that performed CW four-wave mixing experiments. The definition is illustrated in Fig. 1 . The theoretical limit for this efficiency is 1, i.e. η_LL = 0 dB.

 

Fig. 1 Parametric conversion efficiency as presented by Ophir et al. [9]

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In order to have a first understanding of the four-wave mixing process in our nano-waveguides, we conducted a numerical analysis. We studied 500-nm wide, 220-nm high SOI rib waveguides with 50-nm slab height. The effective area was estimated to be ~0.1 µm², dispersion D = −1000 ps/(nm∙ km), linear loss coefficient was 2 dB/cm, two photon absorption (TPA) coefficient was 0.9 cm/GW and the nonlinear coefficient gamma 200 W⁻¹m⁻¹ [1]. The simulations made use of Fourier split-step algorithm for the calculation of accumulated conversion gain and losses. The model considered TPA, but neglected free-carrier absorption, which we consider strongly reduced by the reverse biased p-i-n structure. This corresponds to neglecting carrier diffusion in the waveguides, which has been a major concern in previous publications [5,6,8]. We took this approach because of a preceding numerical analysis [19], which had shown that free-carrier lifetime can be reduced by several orders of magnitude compared to waveguides without reverse biased p-i-n junction. This approach remains valid until carrier screening reduces the drift field across the waveguide. Therefore, introducing p-i-n structures also significantly eases the theoretical analysis.

Results of the simulations are shown in Fig. 2 . The depicted spectrum exemplifies signal and pump at the input, while signal, pump, and idler are present at the output. In the waveguide, linear loss and TPA will decrease the pump and the signal, while parametric scattering along the waveguide creates idler photons as well as signal photons. The dynamics of the process is better visible if we plot conversion gain as a function of waveguide length. The conversion efficiency saturates at η_LL = 0dB, if sufficient power is present in the waveguide. About 26-dBm pump power are required to achieve saturation on a length scale of 10 cm. Shorter devices are possible if more pump power can be injected into the waveguide.

 

Fig. 2 (a) Typical simulated spectrum at the input and at the output of the waveguide (L = 4cm). In our experiment, the idler is only present at the output. (b) Conversion efficiency plotted vs. waveguide length for a set of pump powers.

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3. Device fabrication and measurement setup

For our experiments we fabricated SOI nano-rib waveguides. The in- and out-coupling was realized by standard 1D-grating couplers. The samples were fabricated in a BiCMOS line with 248-nm lithography. Doped regions were created by implantation of B and As with 10¹⁸ cm⁻³ concentration to create p- and n-regions, respectively. Separation between doping regions was designed to be 1.2 µm. Higher doped contact regions were placed further away from the waveguide and contacted by metal electrodes. Figure 3 shows the waveguide cross-section made with a scanning electron microscope (SEM). The waveguides were covered with 100 nm silicon oxide and 90 nm silicon nitride. On top of the latter 1 µm of silicon oxide were deposited to separate the waveguides and the metal electrodes.

 

Fig. 3 SEM cross-section of rib-waveguide as used for the nonlinear experiments in this paper. The waveguide height was H = 220nm, slab height s = 50nm, the rib width w = 500nm.

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The four-wave mixing experiment was performed using the setup shown in Fig. 4 . For pumping we deployed a tunable CW laser source followed by erbium-doped fiber amplifier (EDFA) with a maximum power of 5 W and a polarization controller. The CW pump was injected into the low-loss input of the 10-dB fiber optical coupler. Here, the pump (attenuated by 1 dB) was combined with the CW signal (attenuated by 11 dB) and the combined pump-signal-beam was delivered to the input grating coupler. Photodiode 1 (PD1) was dedicated to measuring pump power when the signal was turned off to determine background and pump peak. A cleaved fiber was used to couple light to the input of the device under test (DUT) and couple it out at the output of the DUT. On the output side, before reaching the optical spectrum analyzer (OSA), the light was attenuated by about 13 dB. Photodiode 2 (PD2) was used for the optimization of coupling. All the presented experiments were performed for TE polarization. During the measurements the temperature of the device under test (DUT) was stabilized at 35 °C and the applied voltage was controlled using probes placed on contact pads of the measured sample.

 

Fig. 4 Scheme of the measurement setup to characterize four-wave mixing in the waveguides.

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4. Results

In our experiment we used waveguides with and without p-i-n diode. On the realized structures we measured 2 dB/cm linear propagation loss by the cut-back method. We did not observe significant increase of loss for high pump power with bias applied. More detailed information about propagation loss in waveguides used for our experiment can be found in the recently accepted paper [20]. In- and out-coupling loss was 5 dB, respectively. In Fig. 5 we show the measured conversion efficiency as a function of the in-coupled pump power for waveguides without p-i-n diode. The waveguides had a length of 1 and 4 cm, the 4cm waveguide had about 4x as many turns as the 1cm waveguide. We observe at small pump powers a rapid increase of the idler signal, however, soon followed by a saturation of efficiency around −24 dB, as the pump power keeps increasing. Such low conversion efficiencies are not surprising, since the parametric scattering will suffer from free-carrier absorption (nonlinear loss). The carriers are created by two-photon absorption, with typical free-carrier lifetimes around 1 ns [1].

 

Fig. 5 Parametric conversion efficiency vs. pump power for two nano-waveguides (1 cm and 4 cm). The waveguides were fabricated without p-i-n, and show clear saturation behavior.

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Measurements on waveguides with p-i-n diode are shown in the next graphs. The first graph in Fig. 6 shows a typical measured spectrum at the output of the waveguides. The conversion efficiency as defined above is directly accessible from such spectra. The right hand graph in Fig. 6 shows the conversion efficiency as determined from the 4-cm long waveguides with a p-i-n diode. Plotted are the conversion efficiencies for a set of reverse bias voltages as a function of in-coupled pump power. Even for zero applied bias we observe a considerable increase of the straight part of the conversion efficiency characteristic compared to Fig. 5, which we attribute to the build-in field of the p-i-n junction and the carrier removal when a power supply is connected. However, at about 20-dBm pump power we also observe saturation, which can again be attributed to free carriers in the waveguide. In case of the reverse biased waveguides we observe an increase of the conversion efficiency following higher pump powers. No saturation is visible up to the power levels available in our setup.

 

Fig. 6 (a) Degenerate FWM spectrum, as observed after 4 cm nano-waveguide with a p-i-n diode. The power was attenuated to record the spectrum. (b) Conversion efficiency vs. in-coupled power, for a set of reverse bias voltages up to −20V.

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To determine peak conversion efficiency and bandwidth of the process we conducted a wavelength dependent measurement. The signal wavelength was detuned from the pump wavelength, and the conversion efficiency was determined from a 4-cm long waveguide. The experimental results are plotted in Fig. 7 .

 

Fig. 7 Conversion efficiency vs. detuning of signal-pump, for three different pump wavelengths. Pump power in the waveguide was 26 dBm.

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We did not observe a broadband high efficiency spectrum as reported in previous work [3]. Instead, our efficiency starts to decrease at about 6-nm detuning. We attribute the narrower bandwidth in our experiment to the fact that waveguides with shallow slab (in our case 50 nm) have a non-ideal dispersion, which is a known bandwidth limiting factor. The trend of the measured characteristic can be reproduced by our four-wave mixing model assuming a dispersion of −1000 ps/(nm∙km), as indicated by the fitting line in Fig. 7. The best conversion efficiency we achieved for pump wavelength of 1542 nm with a detuning of 3 nm. Peak efficiency was better than −1 dB. Referring to the continuous wave FWM results obtained by Mathlouthi et al. [6] in the shallow etched nano-rib waveguides without p-i-n diode we observed improvement of more than 4.5 dB. Compared to the state-of-the-art p-i-n diode assisted waveguides [3] we observe an improvement of more than 7 dB, which is a considerable advance for CW parametric wavelength conversion in silicon waveguides around 1550 nm.

Considering such high conversion efficiencies, the question arises whether it will be possible to achieve conversion gain using silicon nano-waveguides with integrated p-i-n diodes. We believe that this is possible if grating efficiency can be increased and if the linear waveguide loss can be further decreased. Increase of grating efficiency has been demonstrated, e.g. by means of silicon overgrowth [21]. Lower loss waveguides have been demonstrated as well for shallow etched geometries, with loss reaching as low as 0.3 dB/cm [22].

We estimated the conversion gain using our numerical model. We compared two waveguide geometries. Figure 8 shows conversion efficiency versus waveguide length of the nano-waveguides with p-i-n junctions with 0.5 dB/cm loss and of the 1.5-µm p-i-n assisted waveguides with 0.4 dB/cm loss, which correspond to the waveguides used in [3,6]. Our model indeed predicts parametric conversion gain for CW operation around 1550 nm if linear loss can be reduced to 0.5 dB/cm. We also observe that parametric gain is not achievable with the micrometer waveguides. Since there is a potential for reducing linear loss in nano-rib-waveguides below 0.3 dB/cm [21], an even higher parametric gain may be possible.

 

Fig. 8 Conversion efficiency comparing signal input with idler output as predicted from our simple model. Only nano-waveguides allow for net- conversion gain.

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5. Conclusions

In this work we show that reverse biased p-i-n diodes integrated with silicon nano-waveguides allow for a considerable increase of four-wave mixing efficiency in CW mode at 1550 nm compared to previously published results. To put our experimental findings into perspective, we compared them in Table 1 with the CW state-of-the-art work at 1550 nm. By reducing linear loss and by increasing grating coupler efficiency, we expect parametric gain from silicon waveguide based structures for 1550nm light in CW mode.