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Abstract
Low-loss optical waveguides are highly desired for nonlinear photonics such as four-wave mixing (FWM), optical parametric amplification, and pulse shaping. In this work, low-loss silicon photonic spiral waveguides beyond the single-mode regime are proposed and demonstrated for realizing an enhanced FWM process. In particular, the designed 2-µm-wide silicon photonic waveguides are fabricated with standard foundry processes and have a propagation loss as low as ∼0.28 dB/cm due to the reduced light-matter interaction at the waveguide sidewalls. In the experiments, strong FWM effect is achieved with a high conversion efficiency of −8.52 dB in a 2-µm-wide and 20-cm-long silicon photonic waveguide spiral, and eight new wavelengths are generated with the pump power of ∼80 mW (corresponding to a low power density of ∼195 mW/µm2). In contrast, the FWM efficiency for the 0.45-µm-wide waveguide spiral is around −15.4 dB, which is much lower than that for the 2-µm-wide waveguide spiral. It can be seen that silicon photonics beyond the singlemode regime opens a new avenue for on-chip nonlinear photonics and will bring new opportunities for nonlinear photonic applications.
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1. Introduction
Silicon photonics is seen as a key enabling technology for next-generation ultra-dense on-chip integration of photonic and electronic circuits because it has great advantages in foundry-fabrication-process compatibility and ultra-high refractive-index contrast. Developments of silicon photonics in these years have revolutionized numerous applications from optical communications and optical computing to optical sensing/imaging and autonomous vehicles [1]. Silicon itself has a large intrinsic Kerr nonlinearity (n2 = 6.5 × 10−18m2/W at telecom-band) [2,3], which is about ∼240 times higher than that of silica [4], and ∼27 times higher than that of silicon nitride [5]. Moreover, silicon nanophotonic waveguides with effective mode areas as small as ∼0.1 µm2 can effectively realize light confinement, which even boosts the nonlinear response further. As one of the most representative nonlinear photonic effects, Kerr-effect-induced four-wave mixing (FWM), has been attracting intensive attention for many years. It usually involves the coherent interaction of two pump photons that generates two new photons at different frequencies [6–10]. As it is well known, FWM has many potential applications, such as all-optical signal regeneration [11], optical parametric amplification [12], optical comb generation [13], optical oscilloscopes [14], waveform compression [15], and spontaneous FWM for on-chip quantum entanglement [16].
Although silicon nanophotonic waveguides have unrivaled nonlinearities, the strong two-photon absorption (TPA) of silicon at infrared band (C-band) and TPA-induced free carrier absorption (FCA) pose a fundamental limitation to the performance of nonlinear photonic devices [17,18]. Under steady-state illumination, the carrier density can be as high as ∼1018 cm-3, which causes significant optical losses for existing and new generated signals. The losses from nonlinear photonic absorption and linear propagation scattering limit the maximum power levels Pp that can operate in waveguide, and also greatly reduce effective nonlinear interaction length Leff [19,20], which are critical to a FWM process. To reduce nonlinear absorption effects, many attempts took up high pulsed pump [21], mid-infrared light [22,23], or low intensities using resonating structures [24]. On the other hand, Continuous-wave (CW) pumped FWM is highly desired in most practical applications such as on-chip optical parametric amplifiers [12]. One of the promising solutions is to sweep the free carriers by using a p-i-n junction, in which way FCA can be reduced significantly [25] and consequently strong FWM was observed [26,27]. However, it requires complex fabrication processes that brings high cost for the fabrication. Other architectures without p-i-n junctions have also been demonstrated, such as tailoring the waveguide dispersion or optimizing the pump power and the waveguide length [28]. But very few remarkable experimental results have been shown. In contrast, in the past year great progresses have been made with CMOS-compatible silicon nitride (Si3N4) waveguides [29], which do not have high Kerr nonlinearity but has low TPA and low propagation losses [30], enabling Kerr nonlinearity-based frequency combs and solitons [31], spectral translation [32], and low-threshold optical parametric oscillation (OPO) [33].
Therefore, it is still much desired to realize efficient FWM effect with silicon photonic waveguides if the TPA and the propagation loss can be reduced greatly. From the perspective of losses origin, one can see that the linear propagation loss is also critical to an FWM process. However, it is quite difficult to realize low-loss propagation in a regular 450-nm-wide singlemode silicon photonic waveguide, because it usually has a propagation loss of several dB/cm due to roughness-induced scattering losses under existing fabrication level. One solution is to smoothen the waveguide sidewalls by developing improved fabrication processes, which however is usually incompatible with multi-project wafers (MPW) foundry for silicon photonics. Another one is to decrease the interaction strength of the optical field with the sidewalls by e.g. using structures like shallowly-etched ridge or decreasing core thickness [34,35]. But this is usually unfriendly for further photonic integration due to the non-compact footprints, and furthermore it is also not compatible with the popular 220-nm-thick silicon-on-insulator (SOI) platform [36]. Recently, the concept of multimode photonics has demonstrated great potential because of the potential to significantly reduce the waveguide propagation loss [37,38], which is very attractive for the applications of nonlinear photonics [39,40]. For example, a high-Q silicon microring resonator using the combination of singlemode bending ridge waveguides and multimode straight ridge waveguides has been realized with efficient degenerate FWM [39]. However, so far CW-pumped FWM in 220-nm-thick multimode silicon photonic strip waveguide spiral has not been reported yet.
In this work, we propose silicon photonic waveguides beyond the singlemode regime and demonstrate enhanced CW-pumped FWM with standard 220-nm SOI photonic waveguides. In particular, the present silicon photonic waveguides designed with a core region broadened to 2 µm have a propagation loss as low as ∼0.28 dB/cm even when fabricated with standard foundry processes. Meanwhile, a tapered Euler-curve S-bend is introduced to ensure the structure compactness, ultra-low-loss propagation for the fundamental mode, and ultra-low excitation ratio of higher-order modes. Owing to the ability of low-loss propagation, the effective length Leff can be as long as a few centimeters or more, which helps greatly enhance the on-chip nonlinear photonic effect (e.g., FWM). As an example, strong nonlinear wavelength conversion process is achieved in a 2-µm-wide and 20-cm-long waveguide spiral, evidenced by the FWM conversion efficiency as high as −8.52 dB and eight new wavelengths generated by cascaded FWM processes under a pump power of ∼80 mW. Correspondingly the pump power density is about 195 mW/µm2 only, which is much smaller than the level of 571 mW/µm2 used in the experiments for a singlemode silicon photonic waveguide. As a result, silicon photonics beyond the singlemode regime opens a new avenue for on-chip nonlinear photonics and will bring new opportunities for nonlinear photonic applications.
2. Theory
2.1 Ultra-low-loss multimode photonic waveguide spiral
Figure 1(a) illustrates the present multimode silicon photonic waveguide spiral for FWM processes. In particular, multimode Archimedean spiral waveguides and a tapered Euler-curve S-bend are introduced in the present design. Figure 1(b) shows the calculated transmission loss for the cases with different waveguide widths from 0.45 µm to 3.2 µm by using a three-dimensional volume current method [41]. Here, the sidewall roughness σsidewall and the top/bottom-surface roughness σtop/bottom are reasonably assumed as 4.6 nm and 0.42 nm, respectively, according to the previous results given in [42]. When the core width wco increases from 0.45 µm to 2 µm or more, the mode is much more confined in the core region which has less interaction with the sidewalls, as shown by the field mode profiles simulated using Finite-Difference Eigenmode (FDE) solver (MODE solutions, Lumerical). The insets of Fig. 1(b) clearly show that the scattering loss at the sidewalls (red curve), which is usually the dominant loss source, show an exponential decrease with increasing widths. While, the top/bottom surface induced scattering loss (black curve) is small, and only needs to be considered when the waveguide width is large enough. Therefore, it is expected to reduce the total scattering loss (blue curve) to be very low by broadening the core width wco to e.g. > 2 µm. In the present case, when the core width increases from 0.45 µm to 2 µm, the total scattering loss is reduced from 5.6 dB/cm to 0.26 dB/cm in simulation. Even though it is possible to further lower the scattering loss by further broadening the core region, one should make some balance in design by considering the difficulty for achieving compact bending radii and sufficiently power density for nonlinear photonics. Therefore, here we choose wco = 2 µm. Accordingly, the gap width is chosen as wgap = 1.5 µm for Archimedean spiral whose bending radius is gradually varied, in order to avoid any non-negligible evanescent coupling [43]. For such an Archimedean spiral, the bending radius can be reduced to be small without obvious higher-order mode excitation. For the tapered Euler-curve S-bend at the middle of the Archimedean spiral, the curvature radii (Rmax, Rmin) and core width Ws need to be optimized to ensure low excess losses and low inter-mode crosstalk at the junction, as well as compact design [42,44]. We give an analysis for the dependence of the excess loss on the radius Rmax and the core width Ws, showing that the excess loss is as low as 0.001 dB when choosing Ws < 0.6 µm and Rmax > 20 µm. Here we choose Ws = 0.6 µm and Rmax = 25 µm for the present design. Finally, the minimal radius of Rmin = 10 µm is chosen here to make the effective diameter Deff of the curve equal to Rmax. As a result, the designed tapered Euler-curve S-bend exhibits low-loss and low-crosstalk for the fundamental mode light propagation even in a small footprint, which is critical for nonlinear photonics applications.
Fig. 1. (a) Schematic illustration of a silicon photonic waveguide spiral with wco = 2 µm and h = 220 nm; (b) Calculated total propagation loss as the core width wco varies. The insets show the TE0 modal field profiles for the cases of wco= 0.45, 1, 1.5, 2, 3 µm, respectively.
2.2 Four-wave mixing (FWM) in silicon photonic waveguides
To determine the optimal width and length of the optical waveguide for nonlinear optical experiments, here we give an analysis for the FWM process in a silicon photonic waveguide. The linear loss and nonlinear losses including the TPA- and FCA-induced nonlinear losses and the self-phase modulation (SPM) are considered. The coupled equations for the FWM process in silicon waveguide under the CW operation are given as [28]
Figure 2(a) shows the simulated signal net gain of a silicon photonic waveguide spiral for the cases with different core widths and varied waveguide lengths under the same pump power of 0.1 W. It is observed that the signal gain increases quickly and then becomes saturated as the waveguide core widths increases. The certain core width wsat corresponding to the saturated net gain increases as the length increases. For example, for a 1-cm-long spiral waveguide, the saturation core width wsat is about 0.7 µm and the saturation net gain is about −0.40 dB. In contrast, for a 100-cm-long spiral waveguide, the saturation core width wsat increases to ∼2.5 µm and the saturation net gain is about −7.75 dB. Furthermore, the saturation net gain increases from −0.40 dB to 7.86 dB as the length increases from 1 cm to 20 cm and then decreases to −7.75 dB as the length increases further to 100 cm. In order to be clarified, Fig. 2(b) shows the calculated net gain for the silicon photonic waveguides with different core widths of wco = 0.45, 1, 2 and 3 µm as the wavelength length increases. It can be seen that there is an optimal waveguide length Lopt for achieving the maximal net gain Gmax for any given waveguide core width. This can be explained as follows. Initially the FWM effect is accumulated and thus increases as the waveguide length increases from zero. On the other hand, the pump power decreases and the accumulated linear propagation loss for the new wavelength increases as the waveguide length increases. As a result, the net gain might be lowered when the waveguide is very long. Definitely, it is possible to achieve a high net gain for a widened silicon photonic waveguide because of the lowered propagation loss. For example, for the case of wco = 2 µm, the maximal net gain Gmax is as high as 13 dB. On the other hand, when the core width increases further, the maximal net gain might be lower because the power density and the FWM efficiency become lower. And it notes that widened silicon photonic waveguide have advantages in signal gain over the singlemode one with wco = 0.45 µm when longer waveguide lengths and more pump power are provided, which is depicted in Fig. 2(c). When it is still desired to enhance the FWM effect, one should increase the pump power, as shown in Fig. 2(d). From this figure, it can be seen that the net gain can be increased further to 9.8 dB for the case of wco = 2 µm by increasing the pump power to 0.2 W. In contrast, the maximal net gain for the silicon photonic waveguides with wco = 0.45 µm is only 0.36 dB. As a summary, it can be seen that the FWM effect can be enhanced strongly by using the present low-loss silicon photonic waveguide with a broadened core.
Fig. 2. (a) Calculated net gain versus the waveguide width when the waveguide length L = 1, 5, 10, 20, 50 and 100 cm, respectively; (b) Calculated net gain versus the waveguide length when the waveguide width Wco = 0.45, 1, 2 µm and 3 µm, respectively; (c) Calculated net gain versus the waveguide width when waveguide length L = 1 cm and L = 20 cm, respectively; (d) Calculated net gain versus coupled pump power for the cases with different widths of Wco = 0.45 and 2 µm and different lengths of L = 1, 5, 10, 20 and 50 cm.
In order to give a quick evaluation and straightforward understanding for the Kerr nonlinear optical performance of the fundamental mode in a multimode silicon photonic waveguide, here we define a figure of merit (FOM) by ignoring the nonlinear losses as follows [49,50]
Figure 3 shows the calculated FOM for a silicon photonic waveguide as the core width wco varies from 0.45 µm to 3 µm. For the silicon photonic waveguides with hco = 220 nm considered in this paper, the propagation loss decreases quickly as the core width increases from 0.45 µm while the slope becomes less for a wider core, and the propagation loss finally becomes insensitive to the core width when wco > 2 µm, as shown in Fig. 1(b). Meanwhile, the effective mode area increases linearly from 0.12 µm2 to 0.41 µm2 as the core width increases from 0.45 µm to 2 µm. As a result, the FOM has a maximum of ∼25 µm/W around wopt = 1.73 µm, as shown in Fig. 4. The FOM maximum is improved by ∼5 times compared to the case of wco = 0.45 µm. As mentioned above, the FOM shown in Fig. 3 is overestimated because there are some nonlinear losses (like TPA and FCA) in practice. Since a narrow waveguide has higher power density and higher nonlinear losses than a wide waveguide when the injected pump power is the same, the FOM for the narrow waveguide is more overestimated than that for the wide waveguide. As a result, in the following part, we choose the design of a silicon photonic waveguide with wco = 2 µm (which is slightly wider than the optimal core width wopt) and L = 20 cm. Meanwhile, a 0.45-µm-wide and 1-cm-long silicon photonic waveguide spiral is also fabricated to give a comparison.
Fig. 4. Microscope images of the fabricated device. (a) the 2-µm-wide and 20-cm-long waveguide spiral; (b) enlarged tapered Euler-curve S-bend; (c) grating coupler; (d) Scanning electron microscope (SEM) of the broadened silicon photonic waveguide; (e) Measured transmissions of the 2-µm-wide waveguide spirals with different lengths L = 5, 10, 20, 50, and 100 cm on the same chip.
3. Experiments
The designed multimode silicon photonic waveguide spirals devices were taped out in CMOS-compatible MPW silicon photonics foundry (Institute of Microelectronics of the Chinese Academy of Sciences) with the standard processes. Here, experimentally, we prepared five waveguide spirals with different lengths (e.g., L = 5, 10, 20, 50 and 100 cm) for the same core width Wm = 2 µm. Figure 4(a) shows the microscope image of the fabricated 20-cm-long waveguide spiral for which the maximal bending radius is about 480 µm. The enlarged view of the tapered Euler-curve S-bend is shown in Fig. 4(b). Here grating couplers shown in Fig. 4(c) were used for efficient chip-fiber coupling, and the measured coupling loss is about 4.2 dB. From the scanning electron microscope (SEM) picture shown in Fig. 4(d), it can be seen that the widened silicon photonic waveguide shows smooth sidewalls/surfaces, which is critical for realizing a low propagation loss. The propagation loss of the waveguide spirals was measured by using the setup combining an amplified spontaneous emission (ASE) and an optical spectrum analyzer (OSA). These measured transmissions in the wavelength-band from 1530 nm to 1580 nm are shown in Fig. 4(e). By fitting the data of measured losses for different lengths of spirals, the linear propagation loss for the fabricated 2-µm-wide waveguide was estimated as ∼0.28 dB/cm. For comparison and correlation, the waveguide spirals with other core widths of Wm = 0.45, and 1.6 µm were also prepared and the measured losses are 5.6 dB/cm and 0.38 dB/cm, respectively. These measurement results for the propagation losses are consistent with the numerical simulation.
The FWM experiment was performed by using the setup shown in Fig. 5(a). A CW pump light with a fixed wavelength of 1550.15 nm and another tunable CW pump light are followed by the corresponding polarization controller. These two pump lights are combined through a 3-dB coupler, and was then amplified by an erbium-doped fiber amplifier (EDFA). Then the amplified pump lights were coupled to the chip through the on-chip grating coupler. A powermeter was used to monitoring the signal out from the chip through a 99/1 fiber-optic splitter. The signal from the chip was then received by an OSA passing through a variable optical attenuator (VOA), which was inserted to protect the OSA. Here, all the experiments were performed for TE polarization. In the FWM experiment, the 450-nm-wide and 2-µm-wide waveguide spirals fabricated on the same chip were used. Figures 5(b) and 5(c) show the measured transmission spectra for the 2-µm-wide waveguide spiral with a length of 20 cm and the 0.45-µm-wide waveguide with a length of 1 cm, respectively. Here the maximum pump power is about 80 mW, and the measured spectra clearly indicate that the 2-µm-wide waveguide spiral enables much stronger FWM process than the 0.45-µm-wide one. More importantly, for the 2-µm-wide waveguide spiral, eight new wavelengths are generated and thus a comb-like output spectrum is observed. Meanwhile, the measured conversion efficiency (red arrow) for idler #1 (i1) and idler #2 (i2) is −13.18 dB for the 2-µm-wide waveguide spirals, which is the strongest cascaded FWM in a non-resonant 220-nm-thick silicon strip waveguide without any free-carrier depletion. In contrast, for 0.45-µm-wide waveguide spirals, the measured conversion efficiency for idler #1 (i1) and idler #2 (i2) is −27.64 dB only. It is worth mentioning that the maximum power density in the 2-µm-wide waveguide spiral is only 195 mW/µm2, which is much smaller than the level of 571 mW/µm2 in the 0.45-µm-wide waveguide spiral. Therefore, the strongest FWM effect obtained in this experiment is owing to the lowered propagation loss and alleviated two photon absorption in the widened silicon photonic waveguide spiral.
Fig. 5. (a) Experimental setup for the FWM measurement. Pump #1 and Pump #2 are two tunable lasers. PC: polarization controller; EDFA: erbium-doped fiber amplifier; VOA: variable optical attenuator; OSA: optical spectrum analyzer; PM: power meter; Chip: low-loss waveguide spirals; Measured results for the FWM effect in the 2-µm -wide waveguide spiral with a length of 20-cm (b) and in the 0.45-µm-wide waveguide spiral with a length of 1 cm (c). Here the pump power is ∼80 mW and the spectra are normalized for comparison.
The typical FWM conversion efficiency (CE) measurement was also conducted by launching a signal-pump pair into the waveguide in a degenerate pump configuration. Here, CE is defined as the ratio of the generated idler power over the output signal power when input pump power is much stronger than that of signal [24,53], which is different from the case shown in Fig. 5. Here the 2-µm-wide/20-cm-long and 0.45-µm-wide/1-cm-long silicon photonic waveguide spirals were used. Pump was amplified, and then combined with signal in a 90/10 fiber-optic coupler before launching into the chip. A small detuning bandwidth of 0.5 nm between the signal and the pump was chosen in the power-dependent CE test. And the pump power was gradually increased while the signal power remained constant. Figure 6(a) shows the measured FWM CE as a function of the coupled pump power to the 2-µm-wide and 0.45-µm-wide waveguides. From this figure, it can be visible that the generated idler signal increases quickly at first and then it becomes saturated for both cases as the pump power further increases. For the 2-µm-wide waveguide spiral, the highest FWM CE is around −8.52 dB when the pump power reaches to 80 mW (which is the maximum available in the lab). In contrast, the FWM CE for the 0.45-µm-wide waveguide spiral is around −15.4 dB, which is much lower compared to that for the 2-µm-wide waveguide spiral. As shown in Fig. 6(a), the efficiency of −5 dB can be achieved for the 2-µm-wide waveguide spiral when increasing the pump power to 0.4 W according to the theoretical model. Unfortunately, the pump power is limited by the relatively low chip-fiber coupling efficiency and the damage threshold power of the grating coupler. Alternatively, low-loss edge couplers can be possibly used for achieving better coupling efficiency and higher pump power before damaged, which makes it possible to achieve a higher FWM efficiency. To further study the bandwidth of the FWM process, the wavelength-dependence was measured, as shown in Fig. 6(b). Here the pump wavelength was fixed at 1550.15 nm and the signal wavelength was detuned around 1550 nm with a range of ±10 nm. As it can be seen from Fig. 6(b), there is some efficiency degradation from –8.52 dB to –15 dB as the detuning is more than ±10 nm for the 2-µm-wide waveguide, which is similar to the result for the 0.45-µm-wide waveguide. Figure 6(c) shows experimentally how the efficiency is influenced by the waveguide length in the cases with a 2-µm- or 0.45-µm-wide waveguide spiral. For the 2-µm-wide one, it can be seen that the conversion efficiency increases from –14.3 dB to the maximum of –8.52 dB as the waveguide length increases from 5 cm to 20 cm, and then decreases greatly to –22.46 dB when the length increases further to 100 cm. There is an optimal value for the waveguide length around Lopt ≈ 20 cm to achieve the maximal conversion efficiency, which is in a good agreement with the simulation results in Figs. 2(a) and 2(b). In contrast, for the 0.45-µm-wide one, the efficiency decreases rapidly when waveguide lengths increase from 1 cm to 3 cm because the loss increases significantly.
Fig. 6. (a) Measured FWM efficiency in the 2-µm-wide and 0.45-µm-wide waveguide spirals as the pump powers varies; (b) Measured FWM efficiency as the signal wavelength detunes from the pump wavelength. The pump power is ∼80 mW, and the spectra are normalized for comparison. (c) Measured FWM efficiency as the waveguide length increases for the cases with a 2-µm- or 0.45-µm-wide waveguide spiral.
Table 1 gives a summary for the reported CW-pumped FWM effects in silicon photonic waveguides. Particularly, here we only consider the non-resonant structures without carrier sweeping (which usually needs a PN structure fabricated with a complicated and expensive processes). As demonstrated in [9], the propagation loss of regular singlemode strip waveguide is usually >1 dB/cm, which is an obstacle for the enhancement of FWM effects. As a result, high power density is usually required [9]. When using rib waveguides, the propagation loss can be reduced to less than 1 dB/cm. However, it suffers weak mode confinement and large bending radii are generally required. In contrast, the proposed broadened silicon photonic waveguide spiral is fully compatible with standard MPW foundry processes and has a propagation as low as 0.28 dB/cm. Furthermore, the minimal bending radius is compact as 10-µm by introducing the design of tapered Euler-curve S-bends. Meanwhile, it is not necessary to introduce high power density for achieving high FWM efficiency, which is significant to realize efficient nonlinear photonic devices integrated with an on-chip laser diode pump in the future.
Table 1. Comparison of CW pumped FWM results in SOI without p-i-n junction (C-band)
4. Conclusions
In this paper, we have proposed and demonstrated the enhancement of the FWM effect in silicon photonic waveguides beyond the singlemode regime. It has been shown that the propagation loss of silicon photonic waveguides is reduced significantly from 5.6 dB/cm to 0.28 dB/cm when widening the core width from 0.45 µm to 2.0 µm. The theoretical model has shown that there is an optimal core width around 1.73 µm for achieving the maximal FWM efficiency according to the defined FOM, and the FOM maximum is improved by ∼5 times compared to the case of wco = 0.45 µm. Here we have developed 2-µm-wide and 20-cm-long silicon photonic waveguide spirals with a tapered Euler-curve S-bend to ensure structure compactness, ultra-low-loss propagation for the fundamental mode, and ultra-low excitation of higher-order modes. With the 2-µm-wide and 20-cm-long silicon photonic waveguide spiral, in our experiment eight new wavelengths have been generated by injecting a pump light of 80 mW (corresponding to a very low power density of 195 mW/µm2), and the measured FWM conversion efficiency is as high as −8.52 dB. In contrast, the FWM efficiency for the 0.45-µm-wide waveguide spiral is around −15.4 dB, which is much lower compared to that for the 2-µm-wide waveguide spiral. It has shown that the multimode silicon photonic waveguide enables much stronger FWM effect than a traditional 0.45-µm-wide singlemode waveguide because of the lower propagation loss and lower nonlinear loss with low power density. Regarding that the pump power density is not very high, it is possible to achieve efficient on-chip FWM effect even without carrier sweeping, and the fabrication becomes very simple and low-cost. Furthermore, using a low pump power makes it also possible to realize efficient nonlinear photonic chip integrated with an on-chip laser diode pump in the future. As a summary, the present widened silicon photonic waveguide spiral opens a new avenue for realizing on-chip nonlinear photonics, which is very attractive for many applications such as on-chip parametric amplification, signal processing, and quantum photon source.
Funding
National Major Research and Development Program (2018YFB2200200, 2018YFB2200201); National Science Fund for Distinguished Young Scholars (61725503); National Natural Science Foundation of China (61961146003, 62111530147, 91950205); Natural Science Foundation of Zhejiang Province (LD19F050001); Zhejiang Provincial Major Research and Development Program (No. 2021C01199); Fundamental Research Funds for the Central Universities.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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