We observe for the first time net optical gain in a low loss silicon waveguide in silicon-on-insulator (SOI) based on stimulated Raman scattering with a pulsed pump laser at 1.545 μm. We show that pulsed pumping with a pulse width narrower than the carrier recombination lifetime in SOI significantly reduces the free carrier generation rate due to two-photon absorption (TPA) in silicon. For a 4.8 cm long waveguide with an effective core area of ~1.57 μm2, we obtained a net gain of 2 dB with a pump pulse width of ~17 ns and a peak pump power of ~470 mW inside the waveguide.
©2004 Optical Society of America
Stimulated Raman scattering (SRS) in silicon waveguide in optical communication wavelengths around 1.55 μm has recently attracted a great deal of attention [1–4], because it offers an opportunity for optical amplification, wavelength conversion, switching, and lasing in silicon. Although silicon possesses a large Raman scattering coefficient which is several orders of magnitude higher than that for silica commonly used for fiber Raman amplifiers , to date there has been no observation of net optical gain in silicon. One of the reasons is that in the telecom wavelength range of 1.3-1.6 μm silicon exhibits notable two-photon absorption (TPA) [6, 7], though linear optical absorption is negligibly small  because the one-photon energy is smaller than the energy band gap. Owing to the long carrier recombination lifetime in silicon, the relatively weak TPA [2, 6, 7] could generate a noticeable amount of free carriers under high power pumping conditions and the resulting free carrier absorption (FCA) can largely offset and even surpass the Raman gain [3, 4]. Therefore, suppression of the free carrier generation due to the TPA seems to be one of the keys to achieve net optical gain in silicon.
In this paper, we model the SRS in a silicon waveguide with pulsed pumping. We show that the TPA-induced FCA can be significantly reduced with a pump pulse width narrower than the carrier lifetime. We experimentally measured the SRS of a low-loss silicon waveguide by use of pulse pump-probe techniques. For a waveguide of 4.8 cm long and with an effective core area of 1.57 μm2, we observed a net gain of 2 dB with a peak pump power of ~470 mW inside the waveguide.
2. Device fabrication and characterization
In order to achieve net optical gain in a silicon waveguide via the SRS, one has to minimize the optical loss while maximizing the Raman gain. To this end, we designed and produced a low-loss silicon waveguide with a small cross section. The silicon rib waveguide used in our experiment is fabricated on (100) surface of a lightly p-doped (doping concentration <2×1015 cm-3) silicon-on-insulator (SOI) substrate using standard photolithographic patterning and reactive ion etching techniques. The rib waveguide width is 1.52 μm, the rib height is 1.45 μm, and the etch depth is 0.63 μm, as shown in Fig. 1. The effective core area of the waveguide is calculated to be ~1.57 μm2 for TE mode and ~1.41 μm2 for TM mode at a wavelength of 1.55 μm. The small cross section of the waveguide reduces the required optical power to achieve a larger Raman gain since it is the optical intensity that determines the Raman scattering intensity . To increase the pump-probe beam interaction length (in turn larger Raman gain), the waveguide was formed in an S-shaped curve with a total length of 4.8 cm with a bend radius of 400 μm. The straight sections of the waveguide are oriented along the  direction.
We characterized the linear optical transmission loss of the silicon waveguide by using a Fabry-Perot (FP) resonance technique at low input light power . To form a FP cavity, the waveguide facets were polished but uncoated. From the measured FP fringes generated using a tunable laser around the wavelength of 1.55 μm and modeled waveguide/air interface reflection coefficient based on 3-dimension finite difference time domain (FDTD) method , we obtained a linear loss of ~0.22 dB/cm for the 4.8 cm long silicon waveguide including the bend loss (TE and TM modes have a similar transmission loss). The uncertainty in the waveguide loss measurement is estimated to be within 0.1dB/cm. For the SRS gain measurement using pump-probe technique, the waveguide facets were polished and an anti-reflection coating was applied to both facets to minimize Fresnel reflection losses.
3. Modeling of pulsed pump and CW probe wave interaction
As has been shown previously [3, 4], in the continuous wave (CW) excitation the TPA in silicon induces a significant amount of free carriers because of the relatively long carrier recombination lifetime. These photo-generated free carriers induce additional optical loss due to the free carrier plasma dispersion effect . To reduce such an effect, we propose to use a pulsed pump laser instead of CW laser. As will be shown below, the peak free carrier density generated by the TPA can be significantly reduced when the pump pulse width is small relative to the carrier lifetime in the silicon waveguide.
When a silicon waveguide is excited by a laser pulse with an intensity profile of I(t, z) (we assume that light propagates along the z direction), the TPA induced free carrier density [N(t, z)] is described by 
In Eq. (1), β is the TPA coefficient, hv is the one-photon energy, and τ is the carrier recombination lifetime. In our experiment, the input pump pulse intensity profile can be described by a Gaussian shape of
where I0 is the peak intensity and T0 is the full width at half maximum (FWHM) of the pulse. Taking into account the TPA and TPA induced FCA, we may describe the pump intensity evolution along the waveguide by the following equation [12, 13]:
where α is the linear absorption coefficient and σ is the free carrier absorption cross section. At the wavelength of 1.55 μm, σ=1.45×10-17 cm2 for silicon . Note that we neglected the pump depletion effect in Eq. (3) because the Raman conversion efficiency in our experiment is small. We also ignored the pump pulse broadening effect due to waveguide dispersion in our analysis since the pulse width used in our experiment is relatively large (~17 ns) and the waveguide length is much shorter than the dispersion length . The SRS signal [Is(t, z)] in the waveguide may be described by 
where gr is the Raman gain coefficient. At the waveguide input, the probe beam is CW, i.e. Is(t,0)=constant. However, inside the waveguide the probe signal is time dependent because of the pulsed pump and pump induced free carrier density. By solving coupled Eqs. (1), (3), and (4) with the input pulse shape described in Eq.(2), one can obtain the pump and probe beam propagation properties as well as the time and position dependent free carrier density generated by the TPA in the silicon waveguide.
To understand the pump pulse propagation and the pump pulse induced carrier density along a silicon waveguide, we solved coupled Eqs. (1) and (3) numerically. The boundary condition used for the free carrier density is N(t=-∞,z)=0 since the pulse repetition rate used in our experiment is very low (10 kHz). Figure 2 shows the calculated pump pulse evolution along a 4.8 cm long waveguide. In the modeling, we used a peak pump intensity of I0=50 MW/cm2, pulse width of T0=17 ns, and a carrier lifetime of τ=25 ns (the carrier lifetime of the silicon waveguide in our experiment was previously determined ). We note that there are some variations (typically <5 ns) in the carrier lifetime for different waveguides within the same wafer. However, our modeling suggests that such a small change in the carrier lifetime only slightly affects the final results on the Raman intensity since the pump pulse width used in our experiment is shorter than the carrier lifetime. The TPA coefficient is β=0.5 cm/GW . We see from Fig. 2 that both the peak intensity and pulse shape changes as the pump pulse propagates in the waveguide. The optical attenuation is due to both linear and nonlinear optical absorption. The asymmetry in the pump pulse shape is due to the photo-generated free carrier absorption effect. This can be more clearly seen from the modeled free carrier density profile, since the FCA is proportional to the carrier density [cf. Eq. (3)]. Figure 3 shows the simulated carrier density profile at three different positions along the waveguide with the same pumping conditions in Fig. 2. It appears from Fig. 3 that the time dependence of the carrier density is asymmetric and the peak density decreases as the pump beam propagates along the waveguide. The peak carrier density occurs slightly after the pump intensity reaches the maximum value. This results from the competition between the carrier generation and decay processes.
Figure 4 shows the simulated carrier density profile at the waveguide input (z=0) with peak pump intensity of I0=50 MW/cm2 for different pulse widths. Figure 4 indicates that the peak carrier density is strongly dependent on the pulse width for the same peak pump intensity. The narrower the optical pulse, the smaller the resulting carrier density. Thus, one would expect that the TPA induced FCA is smaller for a narrower pulse as compared to the CW excitation. This would help achieving net Raman gain in a silicon waveguide.
4. Experimental results and analysis
We measured the SRS of the silicon waveguide by use of pump-probe techniques. In the experiment, a pulsed pump beam and a CW probe beam are combined with a wavelength multiplexer and coupled into the waveguide under investigation through free space mode-matching optics consisting of a pair of microscope objective lenses mounted on precision alignment stages. The output beam of the waveguide is collimated by another objective lens, and an optical filter is used to separate the pump and probe beams. The probe beam passes through the filter and is detected with a broadband photo-detector while the pump beam is blocked by the filter. Fiber polarization controllers are used to set the polarization states of the pump and probe beams. The coupling efficiency into the waveguide is estimated to be ~12% by measuring the input and output power of the waveguide and taking the waveguide loss into account.
For the Raman gain measurements, the pump laser is a pulsed laser operating at 1545 nm with a pulse width of T0=17 ns, and the probe laser is a CW external cavity tunable diode laser with a line width of <1 MHz. The probe laser power is 2 mW and its polarization is aligned with the TM mode of the waveguide. We measured the time dependent probe signal both on and off the Raman wavelength for a given input pump power and pulse width.
Figure 5(a) shows the measured probe signals through a 4.8 cm silicon waveguide in the presence of a pump pulse with a peak pump power of 470 mW inside the waveguide. When the probe is set to the Stokes wavelength of 1680 nm (on Raman wavelength), we observe an increase in the probe signal due to the SRS. The on-off gain is ~3 dB. When the probe is detuned from the Stokes wavelength by ~2 nm (off Raman wavelength), we observe a probe beam loss because of the pump pulse generated free carriers (see Fig. 3). The on-off loss is ~2.85 dB. The FWHM of the SRS gain spectrum was previously measured to be 75 GHz (or 0.6 nm) . Therefore, when the probe wavelength is detuned away from the Stokes wavelength by 3 times of the SRS gain spectrum width, the Raman gain coefficient is practically equal to zero. As indicated in Fig. 5(a), we define the on-off gain (loss) as the probe signal changes between the pump pulse on and off when the probe wavelength is on (off) Raman wavelength. Taking into account the linear waveguide loss of 0.22 dB/cm, we obtained a net gain of G=2 dB for the waveguide. The net gain G of a waveguide is defined as
where Iin and Iout are the input probe intensity and peak output probe intensity inside the waveguide at the Raman wavelength. Thus the waveguide length dependence of the Raman gain is implicitly included in Eq. (5). Figure 5(b) shows the modeled probe signal for a 4.8 cm long waveguide with T0=17 ns, I0=30 MW/cm2, and τ=25 ns. By comparing Fig. 5(a) and (b), we see that the measured and modeled on-off gain and loss as well as the probe signal profiles are in excellent agreement.
Figure 6 shows the modeled and measured net Raman gain as a function of the pump intensity. The solid symbols represent the experimental results and solid curve is the modeling result. With a Raman gain coefficient of gr=10.5 cm/GW, the modelled net gain is in good agreement with measurements. Comparable Raman gain coefficients of 20 cm/GW  and 37 cm/GW  have been reported previously. Discrepancies between these values require further investigation both theoretical and experimental. The net gain in Fig. 6 was directly determined from the measured on-off gain minus the linear optical loss of the waveguide, and is therefore not influenced by the Raman gain coefficient used in the modeling. We also notice that four-wave mixing (FWM) could influence the SRS, which depends on the phase matching condition [5, 16]. However, our modeling shows that the phase matching condition in the silicon waveguide used in our experiment is not satisfied so that the FWM should have negligible effect on the gain coefficient.
In conclusion, we have modeled and observed net optical gain in a silicon waveguide excited by a pulsed pump laser. We have shown that the pulsed excitation reduces the TPA induced FCA so that the Raman gain exceeds the nonlinear optical loss. The pump pulse induced carrier density peak and the pump pulse peak inside the waveguide are temporarily shifted. As a result, the peak Raman signal is less influenced by the FCA in the pulse pumping as compared to CW excitation. We measured the SRS by using pulse pump-probe techniques. For a waveguide of 4.8 cm, we obtained a net gain of 2 dB with a peak pump power of 470 mW and a pulse width of ~17 ns. The modeled probe signal profile is also in good agreement with measurements. The achievement of net optical gain in silicon is an important step in being able to produce active devices in silicon.
The authors thank R. Nicolaescu for his contribution in the early stages of this work; A. Alduino, D. Tran, and J. Johnson for assistance in device fabrication and sample preparation; R. Jones and H. Liu for helpful discussions; S. Koehl for data collection software development.
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