Introduction
Silicon photonics has received increasing attention over the past decade for its inherent advantages, including ultra-compact size and compatibility with microelectronics fabrication processes [ 1, 2]. Moreover, the high index contrast of silicon-on-insulator (SOI) makes it possible to confine the light tightly and therefore enhance nonlinearities, enabling to exploit silicon waveguides for all-optical signal processing applications, including parametric amplification, wavelength conversion, format conversion and optical switching [ 1, 2]. In particular, wavelength conversion based on degenerate four-wave mixing (FWM) in waveguides (WGs) has been widely studied. Field enhancement in a resonant cavity, typically a microring resonator (MRR), can be applied to further increase the conversion efficiency (CE) or reduce the pump energy requirements through strengthening the nonlinear interaction between the optical waves [ 3, 4].
However, nonlinear losses in silicon due to two-photon absorption (TPA) and TPA-induced free-carrier absorption (FCA) ultimately limit the wavelength CE in both WGs and MRRs. Furthermore, MRRs are typically accessed via bus waveguides in which the FWM process also takes place, making it difficult to assess the intrinsic benefit of the field enhancement in the MRR itself. High FWM CEs were achieved in MRRs with low input pump powers in Refs. [ 3, 4]. However, a direct and quantitative comparison of CE in WGs and MRRs for a wide range of pump powers has, to the best of our knowledge, never been reported.
Recently, we have presented a theoretical comparison of FWM wavelength conversion in silicon WGs and MRRs [ 5], however, it was presented without any experimental result. In this paper, we first experimentally demonstrated enhanced CE in an MRR, and use the results to validate a numerical model. Based on the model, we quantified the relative CEs of silicon MRRs and WGs depending on the linear propagation losses.
Device fabrication
A 3.5 mm long WG and an MRR with the same bus length were fabricated on an SOI wafer with top silicon thickness of 250 nm and buried silica of 3 mm. The width and height for both straight and bend waveguides were 540 and 250 nm, respectively, which resulted in a dispersion value of -3 ps2/m for the TE mode around 1550 nm. An MRR radius of 47 mm was chosen. MRRs with smaller radii have lower power requirements due to their smaller mode volumes, which also makes the free carriers build up faster and thus results in a lower CE [ 3]. High Q-factor MRRs enable the demonstration of FWM with ultra-low pump energies, but meanwhile suffer from narrow bandwidths, which limit the data rate at which optical signal processing is achievable [ 4]. To make the MRR applicable for signal processing at a bit rate of 10 Gb/s, a field coupling coefficient around 0.6 was preferred. Therefore the coupling length and gap between the ring and the bus waveguide were designed to be 10 mm and 90 nm, respectively.
Experimental results
The experimental setup for wavelength conversion was shown in Fig. 1. Continuous wave (CW) light at 1548.19 nm was used as pump beam, while CW light at 1549.99 nm was used as the signal. Both the pump and signal lights were tuned to the resonances of the MRR and had their polarizations aligned to the TE mode of the waveguide thanks to polarization controllers (PCs). The pump light was amplified by an erbium-doped fiber amplifier (EDFA) followed by a tunable attenuator to control the pump power injected into the chip. The pump and signal lights were combined in a 3 dB coupler and launched into the MRR or WG.
Figure 2 shows the measured CE, which was defined as the ratio of the converted idler power at the device output to the signal power at its input (fixed at 0.1 mW), in both WG (triangle) and MRR (square), as a function of pump power. A CE as high as -30 dB can be achieved in the MRR with only 5 mW of pump power, which was 15 dB higher than that measured in the WG. However, the CE in the MRR quickly saturated with increasing pump power and the enhancement decreases to 5 dB when the pump power reached 50 mW.
Theoretical model
To simulate the FWM process in WGs and MRRs, a theoretical model solving a system of three coupled differential equations for the complex envelopes of the pump, signal and idler, and taking TPA and FCA into account, was used [ 6]. This model is valid as long as higher-order idlers are negligible, which is typically the case in silicon waveguides at the power levels considered in this study. The nonlinear index, TPA coefficient and effective mode area were taken equal to 6 × 10-18 m2/W, 5 × 10-12 m/W and 0.1 mm2, respectively. Due to the small wavelength separation between the interacting waves, the effect of dispersion above second order was neglected. The MRR was modeled according to Ref. [ 7]. Free carrier lifetimes of 4 ns for the MRR and 3 ns for the WG were adopted here for the devices used in the experiment. The simulated results in Fig. 2 show good agreement with the experimental characterizations.
Discussion
The CEs in WGs strongly depend on their lengths and linear losses. By optimizing the geometry of the WG, dispersion close to zero and shorter carrier lifetime can be achieved for both MRRs and WGs. The CEs of WGs were calculated as a function of pump power for different linear loss values with -0.3 ps2/m dispersion and 1 ns carrier lifetime. For each linear loss value, an optimum waveguide length that further depends on the pump power (via nonlinear absorption mechanisms) can be found, as shown in Fig. 3. The maximum CE decreases with increasing linear loss. In addition, the optimum length is reduced with increasing pump power due to TPA and FCA. In the following, three different optimum waveguide lengths are considered for the bus, depending on the linear loss (33 mm for 1 dB/cm, 11 mm for 3 dB/cm and 6 mm for 5 dB/cm), corresponding to maximized CEs.
Figure 4 shows the calculated CE of an MRR with the same radius and coupling coefficient as in the experiments. The results were also compared with those of a straight WG of same length as the bus. To evaluate the performances of the MRR and WG at higher pump powers, a maximum power of 0.3 W was used in the simulation, which was much higher than that in the experiment. At high input pump powers, the CEs of the WG and MRR were almost the same regardless of the linear loss. This is because the pump field enhancement of the MRR gives rise to higher TPA and FCA losses in the ring. However, at low pump powers, the CE of the MRR was obviously larger than that of the WG. The pump power resulting in a given CE was smaller in the MRR than in a WG of same length as the bus, and the improvement was more significant for larger loss. This is due to the fact that the enhancement of the pump power in the MRR is not high enough to induce obvious nonlinear loss.
To assess the intrinsic benefit of the field enhancement in the MRR itself, the CE of a MRR without the bus was calculated and compared with that of a straight WG of the same length as the circumference of the MRR, i.e., 0.3 mm. A maximum CE improvement of around 33–34 dB can be achieved depending on the linear losses, as shown in Fig. 5. However, the CE of the MRR begins to decrease after the pump power was over 50 mW. As a matter of fact, with the increasing of the input pump power, the CE of both MRR and WG will saturate and even drop if the TPA and FCA become dominate effects in the waveguides. Since it is more obvious for MRR due to its high Q value, the maximum CE of WG will be higher than that of MRR with a certain propagation loss and waveguide length under strong input power. And besides, the enhancement of CE for MRR with a low Q value will become non-obvious when it is compared to WG.
Conclusion
Wavelength conversion based on degenerate FWM in silicon WGs and MRRs has been experimentally and theoretically analyzed. Compared to a WG having the same length as that of the bus of the MRR, the CE in the MRR can be improved as much as 15 dB at low pump powers.