Abstract
1. Introduction
Highly nonlinear integrated waveguides play a key role in ultra-fast all-optical signal processing. A large number of nonlinear optics phenomena and applications have been demonstrated, in a variety of complementary metal–oxide–semiconductor (CMOS) compatible nonlinear integrated waveguides[
One platform that has drawn the attention of researchers in the field of nonlinear optics over the past decade involves the use of high-index doped silica glass[
In this paper, a series of 49 GHz Si-nc embedded micro-ring resonators (MRRs) are fabricated and their nonlinear properties characterized. The waveguide structure of the MRR consists of a thin layer of Si-nc, embedded in a high-index doped silica glass core. The main advantages of using Si-nc are its CMOS-compatiblility, relatively high nonlinearity, and negligible two-photon absorption (TPA)[
2. Waveguide fabrication
Other than the deposition of a thin layer of Si-nc film in the middle of the core, the devices were fabricated using CMOS-compatible processes similar to those described in Refs. [14, 15, 21]. Plasma-enhanced chemical vapor deposition (PECVD) was employed in the deposition of the Si-nc embedded core waveguide films, beginning with a 1 μm n = 1.60 high-index doped silica layer on the SiO2 lower cladding, followed by a ~ 50 nm thick amorphous silicon (a-Si) and finally another 1 μm n = 1.60 high-index doped silica layer to complete the deposition process. The deposited core film was then patterned, etched and clad with SiO2 to form the waveguide. It is important to note that in addition to nonlinearity enhancement, the inclusion of an a-Si film will also increase the propagation and potentially TPA losses if its thickness is too great. On the basis of existing research into the dependency of the Si-nc layer location on waveguide nonlinearity and dispersion[
As the FWM conversion efficiency depends strongly on the Q-factor of the ring resonator, MRRs with different Q-factors are compared, so as to identify the maximum conversion efficiency of the Si-nc embedded waveguide structure. The Q-factor of the ring resonator can be varied by adjusting the gap separation between the bus waveguide and the ring. In our experiment, there are eight MRRs on one chip within a footprint of ~ 1 × 1 cm2. In addition, MRRs with different dimensions are compared. For waveguides with a width of 2 μm, gap separations vary from 1.2 to 1.6 μm with a step of 0.1 μm, while for waveguides with a width of 3 μm, gap separations vary from 0.8 to 1.2 μm with a step of 0.2 μm. Further details of these parameters are listed in Table 2. Generally, larger waveguide cross-sections result in weaker mode distribution confinement, while propagation loss would be lower.
Transmission electron microscope (TEM) images of the annealed a-Si thin films reveal the Si-nc grain sizes and distributions throughout the whole wafer, and are shown in Fig. 1(a). From the TEM images we can conclude that after annealing under an N2 atmosphere, Si-nc grains with a diameter of about 3 nm are obtained and the nanocrystal grains distribute uniformly across the wafer.
Figure 1.(Color online) (a) TEM image of the Si-nc layer prior to deposition of the upper high-index doped silica layer. The sample was polished to an approximate 5 nm thickness for TEM characterization. (b) Computed dispersion of 1.75 × 1.75
The designed cross-section geometries for Si-nc embedded waveguide are 2 × 2 μm2 and 3 × 2 μm2 with 50 nm Si-nc sandwiched in the core center. However, the cross-sectional dimensions of the as-deposited waveguides shrank by 13%−15% after the annealing process, as shown in the SEM images in Figs. 1(c) and 1(e). The actual dimensions of the two sets of waveguides are 1.75 × 1.75 μm2 (w/20 nm Si-nc - D1) and 2.55 × 1.75 μm2 (w/20 nm Si-nc - D6), respectively, with the thickness of the Si-nc layer being ~ 20 nm.
The mode profiles shown in Figs. 1(d) and 1(f) reveal that the electric field is tightly confined in the high-index doped silica core region. The zero-dispersion wavelengths of the transverse electric (TE) modes for the four waveguides are 1590 nm (w/o Si-nc - D6), 1520 nm (w/20 nm Si-nc - D6), 1520 nm (w/o Si-nc - D1), and 1340 nm (w/20 nm Si-nc - D1), respectively. With the exception of the waveguide with a cross-section of 2.55 × 1.75 μm2 and without the Si-nc layer (w/o Si-nc - D6), all waveguides exhibit normal dispersion in the telecommunication window, due to the shrinkage of the cross-section, which shifted the dispersion towards the shorter wavelength direction. Normal dispersion will decrease the FWM conversion efficiency, but as our goal is to enhance the nonlinearity by introducing the Si-nc thin film, we can still compare our results among these waveguides. Moreover, for waveguides with marginally smaller normal dispersion, we demonstrate their applications in all-optical analog-to-digital conversion[
3. Intensity enhancement simulation
Optical intensity in the micro-ring is much higher than in the bus waveguide if the round-trip gain is larger than the loss. In an MRR with a configuration as shown in Fig. 2(a), the intensity enhancement factor B on resonance (with loss α < 1) is given by
Figure 2.(Color online) (a) Model of a basic add–drop single MRR[
where κ and t are the coupling parameters of MRR. The * represents the conjugated complex value of κ and t. α denotes the loss coefficient in the micro-ring (α = 1 for zero loss).
The intensity enhancement factor B as a function of coupling coefficient κ was simulated for different propagation losses and various ring radii, results of which are presented in Figs. 2(b) and 2(c), respectively. Intensity enhancement in the ring is a function of round-trip loss and coupling coefficient. At a given round-trip loss, there is an optimal coupling coefficient located on the under coupled side of the critical coupling point, where the intensity enhancement is at its maximum. For a lossless resonator, intensity enhancement factor B is equal to the inverse of the power coupling coefficient. As a function of radius, enhancement increases with decreased radius. This is due mainly to the reduction of the mode volume and round-trip loss. Enhancement B can increase Kerr nonlinearity, which is beneficial in nonlinear processes, such as FWM.
4. Waveguide characterization
The linear properties of the fabricated ring resonators with the conventional waveguide structure are shown in Table 3 and for the MRRs with the Si-nc waveguide in Table 4. It can be seen that the loaded Q-factors for both the conventional and the Si-nc embedded MRRs increase as a function of gap separation from 1.2 to 1.6 μm for the 1.75 × 1.75 μm2 MRRs and from 0.8 to 1.2 μm for the 2.55 × 1.75 μm2 MRRs, indicating that the MRRs are not loss limited. With the field enhancement factor in the resonator proportional to its finesse, the amount of stored power in the resonator is higher for resonators with a higher Q value, for a given input power. However, as the gap separation increases, the Q value will saturate once the intrinsic loss is larger than the coupling between the resonator and the bus waveguide. At that point, the power in the resonator decreases and the efficiency will subsequently decrease. With increasing gap separation, Q increases, while κ and B decrease. With increasing waveguide width, Q value increases, while κ, α and B decrease. Intensity enhancement factor B is obtained by fitting the curve of the through port and the drop port. As the thickness of the Si-nc film is more than an order of magnitude smaller than the wavelength, it has almost no effect on the effective index of the MRRs so that the FSRs of the MRRs with and without the Si-nc layers are similar.
The coupling coefficients κ1, κ2, and the propagation loss in the ring α in Tables 3 and 4 are extracted from the measured responses by fitting the measured responses with the analytical formulas[
The fiber to waveguide coupling loss for the MRRs devices is around 5 dB/facet. Figs. 3(a)–3(d) show the measured responses from through port and drop port across the C-band for TE mode of the 49 GHz FSR. The 3 dB bandwidth for the four waveguides from Fig. 3(e) to Fig. 3(h) is 269, 288, 367, and 379 MHz, respectively.
Figure 3.(Color online) Optical response of TE mode from the through port and drop port of 49 GHz MRRs with (a, e) cross-section of 1.75 × 1.75
5. Results and discussions
The nonlinear parameter γ was measured for the 49 GHz MRRs, based on the conversion efficiency η of the FWM process, with the field enhancement from the micro-ring also taken into consideration, in accordance with[
where R denotes the radius of the MRR. Here, FEp, FEs and FEi represent the field enhancement at the pump, signal and idler wavelengths, respectively. The product
When a laser with high pump power is launched into the waveguide, the generated heat will shift the resonances. Thermal shift rate of the high-index doped silica glass is approximately 17 pm/°C at 1550 nm[
Figure 4.(Color online) (a) Experimental setup for FWM process. (b–e) Recorded spectra from OSA of MRRs with cross-section of 1.75 × 1.75
The generated first and second idler signals from the FWM process in the MRRs are shown in Figs. 4(b)–4(e). When aligning the pump and signal wavelengths with the resonances, idler peaks can be recorded on both sides with the frequencies satisfying the energy conservation
We note that while both the 1.75 × 1.75 μm2 and 2.55 × 1.75 μm2 MRRs have similar Q-factors, but the 1.75 × 1.75 μm2 MRR has a higher FWM converson efficiency due to the higher power density, shown in Fig. 5(a). The measured nonlinear parameter γ extracted from the FWM measurement for the MRRs is shown in Table 5. It can be seen that γ increased from 0.144 to 0.366 W−1m−1 for the 1.75 × 1.75 μm2 MRR and from 0.120 to 0.212 W−1m−1 for the 2.55 × 1.75 μm2 MRR with the addition of the Si-nc film. The increase of the nonlinear parameter γ by adding the Si-nc film is with the tradeoff of additional propagation loss, resulting in a lower Q-factor and intensity enhancement of the MRRs, which results in the low FWM conversion efficiency. Fig. 5(b) plots the linear relationship of the idler power versus the square of the pump power and reveals a quadratic dependence, demonstrating that the Si-nc film exhibits no TPA and 3PA absorption under input pump powers up to 15 mW, and which is limited by the available CW pump source. Moreover, using long path length spiral waveguides with the same embedded Si-nc thin film, we observed that the TPA is negligible, derived from measured reciprocal transmission as a function of the coupled peak power[
Figure 5.(Color online) (a) Conversion efficiency versus incident pump power for FWM in the 49 GHz MRRs for with and without Si-nc thin film cases. (b) Idler power dependence of the square of the pump power for FWM in the MRRs for with and without Si-nc thin film cases.
Table Infomation Is Not Enable6. Conclusions
In conclusion, we have fabricated a series of 49 GHz MRRs with embedded Si-nc layers and measured their FWM efficiency. The Si-nc film is formed by the deposition of a thin layer of a-Si film in the middle of the core waveguide, and subsequently crystallized at a high temperature. We found that the addition of the Si-nc film increased the propagation loss by approximately 0.11 to 0.15 dB/cm and reduced the Q-factor of the MRRs by one half, however the Si-nc film doubles the nonlinear parameter γ. By adding a thin layer of Si-nc film, it is possible to enhance the nonlinearity of the waveguide and to improve these waveguide circuits for all optical signal processing applications.
Acknowledgments
This work is supported by the Research Grants Council, University Grants Committee (GRF 11213618), and the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB24030300).
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