Spontaneous and stimulated Raman scattering in silica-cladded silicon photonic crystal waveguides

The transmittance spectrum of the devices for TE-like polarization is shown in Fig. 2. We redrew the outline of the PhC patterns based on the SEM images [Fig. 1(b)] and calculated the corresponding photonic band diagram, which is also shown in Fig. 2. The measured transmittance is low around the wavelength range from 1400 to 1460 nm because the WG modes are above the light-line, which means the losses in the out-of-plane direction is increased. In addition, this region also overlapped with the slab modes, which is indicated by the grey-colored region in the band diagram in Fig. 2. The observed stop-band around 1550 nm agrees well with the calculated mode-gap. This clear opening of mode gap indicates the difference of the measured structure from the simple wire waveguide. The group index (n_g) of 10.5 was estimated at 1560 nm, near the band edge, from the band structure in Fig. 2. For comparison, we calculated n_g of ∼4 at the same wavelength for a wire WG with a width of 320 nm, which corresponds to the average width of the undulated central wire of the PhC WG. This also differentiates the PhC WG from such a simple wire WG. The high transmittance regions around wavelengths of 1470 to 1540 nm and 1575 to 1630 nm correspond to the PhC WG guiding modes. These guiding modes have symmetric field distribution as discussed in Ref. 27. We intended to use the bandedge regions of these modes for pump and Stokes waves because large enhancement of Raman scattering is expected due to the simultaneous slowdown of the group velocities both for pump and Stokes waves. Due to the imperfection in the fabrication [see Fig. 1(b)], the wavelength difference of the two bandedges cannot match the Raman shift in silicon in the real device. Therefore, the pump wavelength must be operated at around 1460 nm so that the Stokes wavelength operated at low group velocity region (around 1580 nm). At 1460 nm, the waveguide modes are located at around or even above the light-line not close to a bandedge, where large reduction of group velocity occurs. Thus, strong slow light effect as those in the designed structure is not likely to be observed. However, the Stokes wavelengths can be located in the low group velocity regions of a guiding mode. Thus, the slow-light effect for the Stokes wave is still expected to be observed. In this study, we investigated Raman scattering whose Stokes wavelengths located at around the bandedge of the first guiding mode corresponding to the high transmission region ranging from 1575 to 1630 nm.

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We first measured the Stokes signal generated by Raman scattering from the CW pump beam. Figure 3 summarizes the results of wavelength dependences of Stokes power. For illustrating the spectral region investigated here, in Fig. 3(a), we again plotted the transmittance spectra around the operation wavelength regions of pump (1430–1520 nm) and Stokes waves (1544.9–1650.5 nm) simultaneously. A vertical line connecting the top and bottom axes gives us a pair of pump and Stokes wavelengths, whose difference matches the Raman shift of silicon (Δω_R = 2π × 15.6 THz). In the spectrum for Stokes wave (brown curve), clear interference fringes are observed. The interference fringes were originated from the mode mismatch between access wire WGs and the PhC WG.

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Figure 3(b) plots the Stokes powers measured at various pump powers of 3, 5, and 10 mW as a function of the Stokes wavelength. In these measurements, we carefully chose the pump wavelengths so that the corresponding Stokes wavelengths located at the interference peaks in the linear transmittance spectrum. For all three pump powers, Stokes power is increased when the wavelength approaches to the bandegde of the guiding mode for the Stokes wave although the transmittance of the mode for the pump becomes low (see the shadowed region in Fig. 3). At the pump power of 3 mW, the Stokes power measured at 1579.5 nm was about 5 times stronger than that at 1624.9 nm. At this pump power, only spontaneous Raman scattering is likely to occur (see also Fig. 4 and related discussions). The large difference in the transmittance of the pump waves over the measured spectral range makes it difficult to compare Raman scattering efficiencies at these two wavelengths directly from the experiment. However, slow-light effect for the Stokes wave can be considered as one of the origins for the enhancement of spontaneous Raman scattering in this range. In the present experiment, due to the limitation of the emission wavelength of our pump laser, we could measure the Stokes signal longer than 1579.5 nm. A larger enhancement of spontaneous Raman scattering is also expected in the Stokes wavelengths from 1568 to 1579 nm, where the group velocity for the Stokes wave becomes smaller.

The enhancement of Raman scattering in the lower group velocity region of the Stokes wave (i.e., at around 1580 nm) is much pronounced for higher pump powers, particularly at 10 mW. This result suggests that stimulated Raman scattering can take place at higher pump powers. For detailed investigations, we measured the Stokes signal power at different wavelengths as a function of pump power. The results are shown in Fig. 4. The pump wavelengths were chosen as 1459.6, 1461.8, and 1473.7 nm. The corresponding Stokes wavelengths are λ₁ (1579.5 nm), λ₂ (1582.1 nm), and λ₃ (1596.0 nm), which are located at a transmittance peak and valley wavelengths in the lower group velocity region, and a transmittance peak wavelength in a higher group velocity region, respectively, as shown in the inset of Fig. 4. As expected, the Stokes signal power in the λ₁ case increased superlinearly when the pump power increased above ∼4 mW. This indicates the onset of stimulated Raman scattering. On the other hand at lower pump powers, only spontaneous Raman scattering occurs and the Stokes intensity increased linearly as shown in the eye guide (broken line). In contrast, in the λ₃ case, even with higher transmission of the pump compared with the λ₁ case, the Stokes power only increased linearly since the Raman scattering efficiency in the λ₃ case is lower than that in the λ₁ case as shown in Fig. 3(b). No nonlinear increase was observed also in the λ₂ case although the wavelength is located very close to λ₁. This can be attributed to the weaker confinement of Stokes photons because λ₂ located at a valley point in the interference.

Utilizing the stimulated Raman scattering, it is possible to achieve amplification of a signal beam, which is simultaneously coupled to a silicon waveguide with the pump beam.^3,4) In this experiment we used a coupler to combine the pump beam with the signal beam at the corresponding Stokes wavelength as shown in Fig. 5(a). In order to clearly understand the experiment conditions, here, we define three observed powers as P_s-off,p-on, P_s-on,p-off, and P_s-on,p-on. The measured integrated power over the Stokes line when only the pump beam is on is defined as P_s-off,p-on. This contains the Stokes signals created only by the pump beam. On the other hand, P_s-on,p-off is defined as the measured integrated power when only the signal beam is on. Thus, P_s-on,p-off is the transmitted power of the signal beam through the WG. Finally, P_s-on,p-on denotes the measured integrated power when both signal and pump beams are on. This contains the contributions from Raman scattering induced not only by pump but also by simultaneous existence of pump and signal. Thus, if the Raman gain occurs, P_s-on,p-on should be larger than P_s-off,p-on + P_s-on,p-off. Here, we define Raman on–off gain as

$$\begin{equation} G_{\text{on--off}} = 10\log \frac{P_{\text{s-on,p-on}} - P_{\text{s-off,p-on}}}{P_{\text{s-on,p-off}}}. \end{equation} \tag{ 1 }$$

To clearly see the signal amplification effect, this on–off gain excludes the contribution of Raman scattering signal created solely by the pump beam (see the numerator).

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In Fig. 5(b), the G_on–off as a function of pump power at different operation wavelengths were plotted. The pump and signal laser of the amplification experiments were both operated under CW condition. The input signal power was kept at 15 pW. Within the pump power range used in the present experiments, the maximum G_on–off as high as 1.5 dB was obtained in the λ₃ case. On the other hand, in the λ₁ case, the maximum G_on–off reached up to 2.6 dB even with the lower transmittance of the pump than in the λ₃ case. This difference in G_on–off reflects the difference of slow-light effect in part. Devices, where the pump waves below the light line are available, would enable to investigate the slow light effect on G_on–off in more detail. This would be our one of future works.