Open Access
Add to BibSonomy
Abstract
A tapered bus-waveguide is demonstrated to enhance the waveguide-to-cavity coupling by mass-productive, cost-effective i-line UV lithography. Through enlarging the overlap between the evanescent wave and waveguide resonator, we experimentally show that the coupling strength of silicon nitride waveguides can be 7 times stronger than the conventional coupling of a uniform, straight bus-waveguide. For the first time, strong over-coupling is identified at a 400 nm gap and quality factor ≈ 105 without elongating the coupling length. This design relieves the fabrication limits and provides the flexibility for coupling control, especially in the strongly over-coupled regime with i-line UV lithography.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent decades, microresonators have been widely used in integrated photonic circuits, ranging from modulators, filters, detectors [1–3], and nonlinear applications [4–7], such as second harmonic generation [5] and optical micro-comb generation [6,7]. By the aid of metal-oxide-semiconductor (CMOS) fabrication technique, integrated planar waveguides show high quality (Q) factor (>106) in different photonic platforms, including silicon nitride (Si3N4) [7–10], high-index doped silica (Hydex) [7,8], lithium niobate (LN) [11], gallium nitride (GaN) [12], and aluminum gallium arsenide (AlGaAs) [13]. Among all of these works, the ideality of coupling from the source waveguide to the resonator is of critical importance in integrated photonics. For linear photonics, critical coupling, in which the rate of energy decay in the resonator equals the rate of energy transfer between the resonator and waveguide, is preferred to offer strong extinction ratio and high sensitivity in optical communication [1,2] and sensors [14]. Intuitively, a strong coupling coefficient can be achieved by reducing the coupling gap between the straight bus-waveguide and resonators. In the meantime, by improving the fabrication process, a high-Q resonator yields low cavity loss and relaxes the requirement for a narrow gap. However, for the most popular optical modulators based on refractive-index modulation, a high-Q resonator has longer photon life time, which limits the modulation bandwidth of an optical modulator [15]. The typical Q factor is < 106 for high-speed optical communication [15,16]. Therefore, to achieve high extinction ratio, decent coupling strength of a high confinement waveguide is still needed; for instance, the gap size is set < 200 nm for significant coupling in air-cladded silicon resonators [17], III-nitride disks [18], and silicon nitride resonators [19]. In contrast to the well-established linear applications, ideality of coupling is also essential for applications in nonlinear and quantum systems. It has been shown both experimentally and theoretically that the over-coupled resonators offer higher conversion efficiency for optical frequency comb generation [20,21], while in quantum squeezing, over-coupling provides better efficiency of squeezing [22]. This implies again a narrow gap down to a few hundred nanometers is needed to achieve strong modal overlap. Nevertheless, as limited by fabrication processes, a gap size < 400 nm requires the time-consuming electron beam lithography (EBL) or costly deep UV (DUV) lithography; besides, for a gap < 300 nm, air void may be found in-between the resonator and bus waveguide for a subtractive process, resulting in scattering loss or a uniformity issue [10,19]. To solve this restriction, early approaches aim to elongate the effective coupling regime by geometrically designing pulley [18,23,24], tapered gap [25,26], or racetrack waveguides [26]. However, although these simple structures help to tailor the coupling into critical or even over-coupling, it requires larger coupling regime and therefore complicates the circuit design. Recently, a tapered bus-waveguide is theoretically introduced to enhance waveguide coupling by enlarging the mode-field diameters of the waveguide [27], but this work is only limited to numerical analysis. Meanwhile, a pulley structure with adiabatic / tapered resonators is utilized for strong over-coupling but a small gap (100 nm) by EBL is still needed [28].
In this study, we experimentally show the enhancement of waveguide-to-cavity coupling with the aid of a tapered bus-waveguide by i-line UV lithography. Traditionally, mass-productive, cost-effective i-line UV lithography provides the potentials for high-Q microresonator fabrication [29–31]; however, these studies only show conditions in critical-coupling with a racetrack configuration [29] or with Q > 106 [30] or in under-coupling [31]. Our work results in several new findings. First, for the first time, we demonstrate strong coupling in Si3N4 waveguide resonators without geometrically changing the coupling length. This provides a simpler layout configuration for applications in microresonators. In addition, without the need of a narrow gap (< 400 nm), standard lithography creates potentials in large-scale manufacturing of both linear and nonlinear photonics. Second, in comparing to the traditional straight bus-waveguide, the coupling strength is 7 times stronger and the coupling is tailored from under-coupled to over-coupled regimes, showing the flexibility in coupling ideality. In addition, we show the enhanced coupling can be stronger than that of a conventional waveguide with a small gap (≈ 300 nm) fabricated by the costly, time-consuming EBL. Last, over-coupling can be achieved with a 400 nm gap and moderate Q factors ≈ 105, providing accessibility in fabricating low-cost, high-speed photonic modulators and phase shifters. This also alleviates the burden for achieving critical coupling in a short wavelength due to the limited Q factors from the scattering loss [18].
2. Waveguide and resonator design
For the design of the bus-waveguide, we study the waveguide with a single-side taper. The schematic diagram is shown in Figs. 1, where g is the gap size between the bus- and resonator-waveguides, wt is the minimal taper width in the center of the coupling regime, Lt is the taper length, and R is the radius of resonators [27].
For the single-side taper, the bus-waveguide is linearly tapered down on one side of the waveguide whereas the minimal gap between the bus- and resonator-waveguide is kept no less than 400 nm. This design results in a feasible fabrication window for i-line lithography; also, there is no fabrication process of narrow pitches needed at the coupling regime. Previously, we have realized this design theoretically in bus-to-resonator coupling of planar waveguides [27]. Here, we demonstrate this idea on a mature, integrated Si3N4 platform to optimize the waveguide-to-resonator coupling. To adapt this taper design with i-line lithography, the mask layout is set at g = 400 nm, wt = 0.4 µm or 1 µm, and Lt = 10 or 30 µm. These parameters, which are feasible for i-line lithography, are set to have both negligible transmission loss at the tapered waveguide and efficient coupling enhancement based on the numerical model in Ref. [27].
3. Device fabrication
In fabrication, a 4 µm thick silicon oxide (SiO2) layer was thermally grown on 4-inch silicon wafers in a diffusion furnace. A 500 nm Si3N4 film was then deposited by low-pressure chemical vapor deposition (LPCVD) at 800 ℃ as the core layer, assuring no cracks formed under the chamber condition. Next, the waveguides and microresonators are patterned using i-line stepper (365 nm) lithography (FPA-3000 i5+) with ≈ 750 nm positive-tone resist (PFI38) at dosage 1307 J/m2. We transfer the pattern to the Si3N4 film using SF6-based etchants in a high-density plasma etching tool (HDP, Unaxis / Nextral 860L). In order to compare the taper effect and the coupling enhancement, we also fabricate a resonator by EBL (Elionix ELS-7500EX), which is coupled with a straight bus-waveguide at a 300 nm gap. Figures 2(a)-(b) show the microscope and SEM images of the fabricated Si3N4 waveguides for both E-beam and i-line lithography. Finally, a 1 µm SiO2 cladding layer is deposited upon the Si3N4 resonators with plasma-enhanced chemical vapor deposition (SAMCO PD-220N). The corresponding focused ion beam (FIB) image at coupling is shown in Fig. 2(c). We can clearly see that the height of the narrow taper is in consistent with that of the (wide) resonator waveguide.
Fig. 2. Microscope and SEM images of fabricated Si3N4 waveguides (a) without taper by EBL and (b) with a 1 µm taper width by i-line lithography. (c) FIB image of the coupling regime.
4. Coupling characterization
To characterize the coupling, we study the through-port response from the bus-waveguide. The response function of power transmission in relative to wavelength λ can be written as [32]:
4.1 Taper effect for air-cladded waveguides
We first study the waveguide coupling before cladding the oxide layer. The width of bus- and resonator-waveguides are set at 2 µm and 3 µm, respectively. High refractive index contrast between Si3N4 and air provides strong confinement and minimizes the bending loss. However, strong confinement also limits the coupling strength between waveguides and a low coupling coefficient is obtained. Figures 3 show the transmission response of the waveguides fabricated by i-line lithography without and with a nano-taper. For the analyzed resonances, the mode family with highest intrinsic Q is adopted as the fundamental resonant mode, and the exemplary peaks are shown away from other mode families in order to avoid unwanted mode coupling [33]. The fitting results for the resonances investigated are shown in Table 1. For the waveguide without the taper, the coupling is at the under-coupled regime with $\frac{{\kappa _e^2}}{{\kappa _p^2}} = 0.34$; as for the one with taper width wt = 1 µm, the coupling coefficient is 6.1 times stronger than that without a taper. This pushes the resonator into over-coupling with $\frac{{\kappa _e^2}}{{\kappa _p^2}} = 2.31$. The enhancement can be further enhanced to 7.1 times stronger by shrinking the taper width (wt) down to 0.4 µm, resulting in deep over-coupling with $\frac{{\kappa _e^2}}{{\kappa _p^2}} = 3$. For all the fitted resonances, similar quality factors are obtained on the order of 105, showing no impact on the intrinsic loss of resonators.
Fig. 3. Transmission response of i-line lithography fabricated Si3N4 waveguide resonators (a) without a taper, (b) with 1 µm taper width, and (c) with 0.4 µm taper width.
Table 1. Resonance characterization and coupling coefficients without and with tapers for air-cladded resonators
As for the effect on taper length, shorter taper length at 10 µm shows slightly lower enhancement (≈ 6.5 times) comparing to that at 30 µm. It can be explained by that the coupling length seemed by the resonators effectively increases for the 30 µm taper length, similar to that in a pulley waveguide. However, here we introduce a relatively simple layout design and the need of fabricating a long, uniformly narrow gap is not necessary.
4.2 Taper effect for oxide-cladded waveguides
Next, we study the coupling for the oxide-cladded waveguides. Most waveguides are cladded with an oxide layer, providing better fiber-to-waveguide coupling, lower transmitted loss, protection from dusts and integrated electrical wires. In addition, oxide-cladding helps to reduce the high contrast between Si3N4 and air, reducing unwanted support-guided modes in the resonators [34]. Figures 4 show the transmission response of the waveguides after cladding a 1 µm SiO2 layer. The corresponding fitting results for the resonances investigated are shown in Table 2. In comparison with the air-cladded waveguide, oxide-cladded waveguides show less confinement and thus slightly larger coupling coefficients ($\kappa _e^2$=0.017) are obtained for waveguides without the taper. As for the tapered one, enhancement of coupling can be found but only 2∼3 times stronger. Our works here show that the taper design may be more favorable for waveguide coupling with high index contrast.
Fig. 4. Transmission response of i-line lithography fabricated Si3N4 waveguide resonators after cladding 1 µm SiO2 layer (a) without a taper, (b) with 0.4 µm taper width, and (c) with 0.4 µm taper width and a drop-port.
Table 2. Resonance characterization and coupling coefficients without and with tapers for oxide-cladded resonators
We should also note here that since $\kappa _e^2$ and $\kappa _p^2$ are replaceable in Eq. (1). The coupling condition cannot be determined by merely fitting the transmission response at the bus-waveguide. To uniquely verify the coupling, a drop-port geometry is also designed for a resonator with the taper wt = 0.4 µm and Lt = 30 µm. The response function can be written as [32,35]:
4.3 Comparison with EBL-fabricated waveguides
Last, we focus our findings on the coupling strength and compare to that with the conventional EBL-fabricated resonators. For resonators by EBL, the gap is set at g = 300 nm, as shown in Fig. 2(a). This gap size is accessible due to the higher available resolution of EBL. The resonances are characterized with air-cladding in which the taper offers significant enhancement on coupling for the resonators by i-line lithography as previously identified. Figures 5 show the transmission response and the corresponding fitting results are shown in Table 3. By comparing the transmission spectra with that of the i-line fabricated resonators, EBL provides more vertical sidewalls and therefore helps to realize a single-mode waveguide [19]. We can clearly observe that, although the coupling coefficient $\kappa _e^2$ = 0.032 is stronger than that by i-line lithography without a taper, the coupling is still in the under-coupled regime even with a smaller gap. This suggests that the proposed taper design provides a more efficient way for coupling enhancement.
Fig. 5. Transmission response of an EBL-fabricated waveguide resonator at g = 300 nm without tapers.
Table 3. Resonance characterization and coupling coefficients for an EBL-fabricated resonator
These results exhibit a significant finding. With the taper design by the mass-productive i-line lithography, stronger coupling can be achieved than that of conventional resonators fabricated by EBL with a narrower gap. This relieves the fabrication (resolution) requirements on the gap size.
5. Discussion
In this section, we further explore the designed nano-taper in more details and compare the figure of merit of the fabricated waveguide resonators. First, we look at the gap effect on the coupling strength. As mentioned earlier, reducing the gap size intuitively enhances the coupling strength but this process is limited by the fabrication restriction, especially on lithography. We show the coupling coefficient versus the gap size in Fig. 6. For the resonators without a taper, the coupling coefficient can be adjusted from 0.008 to 0.032 by reducing the gap size (g) from 0.5 µm to 0.3 µm, showing around 4 times enhancement. For the one with a taper, the enhancement can be up to 7 times. This taper design provides stronger coupling strength than gap optimization.
Considering that Si3N4 waveguide resonators are heavily studies due to it compatibility both in linear and nonlinear photonics, we compare the coupling performance of Si3N4 integrated resonators reported previously and summarize in Table 4. Traditionally, by the aid of EBL, Si3N4-based resonators have reached Q factor more than 107. However, as mentioned earlier, this high-Q resonator is not suitable for high-speed communication, such as optical modulators or phase shifters. Therefore, a moderate Q ≈ 105 may be more preferable for these applications. For the first time, our work here demonstrates strong over-coupling ($\frac{{\kappa _e^2}}{{\kappa _p^2}} = 3$) at 400 nm gap and Q ≈ 105 without elongating the coupling length by a complicated pulley or racetrack structure. We should mention here that the Q factor can be further improved by high-temperature thermal annealing [10,19]. However, even with a higher Q ≈ 107, coupling design is still needed for i-line lithography to achieve over-coupling due to its limited resolution. Moreover, by comparing with the mature Si3N4 platform, most emerging candidates of microresonators, such as GaN [12], AlGaAs [13], AlN [30], and lithium niobate [5,11], exhibit Q less than 5 × 106. The taper design provides an alternative pathway to optimize the coupling in critical- or over-coupled regimes for these platforms.
Table 4. Comparison of coupling schemes for Si3N4 waveguide resonators
6. Conclusions
To conclude, we experimentally show the enhancement of waveguide-to-resonator coupling by designing a tapered bus-waveguide at the coupling regime. Utilizing the conventional i-line lithography, strongly over-coupling can be realized in Si3N4 waveguide resonators with moderate Q factor ≈ 105 and a 400 nm gap. In comparison with the traditional waveguide coupling without a taper, the coupling strength can be enhanced 7 times by tapering down the waveguide from 2 µm to 0.4 µm. This work provides a flexible way to optimize the waveguide coupling for novel photonics designs, especially in the strong over-coupled regime.
Funding
National Science and Technology Council NSTC (109-2221-E-008-091-MY2, 111-2221-E-008 -026).
Acknowledgment
P.-H. W. acknowledges the research financial support from the National Science and Technology Council (NSTC), Taiwan under grant numbers 109-2221-E-008-091-MY2 and 111-2221-E-008-026. The authors would like to acknowledge chip fabrication support provided by Taiwan Semiconductor Research Institute (TSRI), Taiwan, for i-line lithography and the Nano Facility Center (NFC) of National Yang Ming Chiao Tung University (YMCT), Taiwan, for LPCVD and FIB processes.
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.
References
1. S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photonics Rev. 6(2), 145–177 (2012). [CrossRef]
2. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997). [CrossRef]
3. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010). [CrossRef]
4. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010). [CrossRef]
5. R. Luo, H. Jiang, S. Rogers, H. Liang, Y. He, and Q. Lin, “On-chip second-harmonic generation and broadband parametric down-conversion in a lithium niobate microresonator,” Opt. Express 25(20), 24531–24539 (2017). [CrossRef]
6. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010). [CrossRef]
7. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011). [CrossRef]
8. D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7(8), 597–607 (2013). [CrossRef]
9. A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17(14), 11366–11370 (2009). [CrossRef]
10. Y. Xuan, Y. Liu, L. T. Varghese, A. J. Metcalf, X. Xue, P.-H. Wang, K. Han, J. A. Jaramillo-Villegas, A. A. Noman, C. Wang, S. Kim, M. Teng, Y. J. Lee, B. Niu, L. Fan, J. Wang, D. E. Leaird, A. M. Weiner, and M. Qi, “High-Q silicon nitride microresonators exhibiting low-power frequency comb initiation,” Optica 3(11), 1171–1180 (2016). [CrossRef]
11. C. Wang, M. Zhang, R. Zhu, H. Hu, and M. Lončar, “Monolithic lithium niobate photonic circuits for Kerr frequency comb generation and modulation,” Nat. Commun. 10(1), 978 (2019). [CrossRef]
12. E. Stassen, M. Pu, E. Semenova, E. Zavarin, W. Lundin, and K. Yvind, “High-confinement gallium nitride-on-sapphire waveguides for integrated nonlinear photonics,” Opt. Lett. 44(5), 1064–1067 (2019). [CrossRef]
13. W. Xie, L. Chang, H. Shu, J. C. Norman, J. D. Peters, X. Wang, and J. E. Bowers, “Ultrahigh-Q AlGaAs-on-insulator microresonators for integrated nonlinear photonics,” Opt. Express 28(22), 32894–32906 (2020). [CrossRef]
14. N. Jokerst, M. Royal, S. Palit, L. Luan, S. Dhar, and T. Tyler, “Chip scale integrated microresonator sensing systems,” J. Biophotonics 2(4), 212–226 (2009). [CrossRef]
15. Y. Hu, X. Xiao, H. Xu, X. Li, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “High-speed silicon modulator based on cascaded microring resonators,” Opt. Express 20(14), 15079–15085 (2012). [CrossRef]
16. Q. Xu, B. Schmidt, J. Shakya, and M. Lipson, “Cascaded silicon micro-ring modulators for WDM optical interconnection,” Opt. Express 14(20), 9431–9435 (2006). [CrossRef]
17. M. Soltani, S. Yegnanarayanan, L. Qing, and A. Adibi, “Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: theory and experiment,” IEEE J. Quantum Electron. 46(8), 1158–1169 (2010). [CrossRef]
18. F. Tabataba-Vakili, L. Doyennette, C. Brimont, T. Guillet, S. Rennesson, B. Damilano, E. Frayssinet, J. Duboz, X. Checoury, S. Sauvage, M. E. Kurdi, F. Semond, B. Gayral, and P. Boucaud, “Demonstration of critical coupling in an active III-nitride microdisk photonic circuit on silicon,” Sci. Rep. 9(1), 18095 (2019). [CrossRef]
19. M. H. P. Pfeiffer, C. Herkommer, J. Liu, T. Morais, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Photonic Damascene process for low-loss, high-confinement silicon nitride waveguides,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–11 (2018). [CrossRef]
20. X. Xue, P. Wang, Y. Xuan, M. Qi, and A. M. Weiner, “Microresonator Kerr frequency combs with high conversion efficiency,” Laser Photonics Rev. 11(1), 1600276 (2017). [CrossRef]
21. P.-H. Wang, K.-L. Chiang, and Z.-R. Yang, “Study of microcomb threshold power with coupling scaling,” Sci. Rep. 11(1), 1–10 (2021). [CrossRef]
22. Y. K. Chembo, “Quantum dynamics of Kerr optical frequency combs below and above threshold: Spontaneous four-wave mixing, entanglement, and squeezed states of light,” Phys. Rev. A 93(3), 033820 (2016). [CrossRef]
23. M. H. P. Pfeiffer, J. Liu, M. Geiselmann, and T. J. Kippenberg, “Coupling ideality of integrated planar high-Q microresonators,” Phys. Rev. Appl. 7(2), 024026 (2017). [CrossRef]
24. E. S. Hosseini, S. Yegnanarayanan, A. H. Atabaki, M. Soltani, and A. Adibi, “Systematic design and fabrication of high-Q single-mode pulley-coupled planar silicon nitride microdisk resonators at visible wavelengths,” Opt. Express 18(3), 2127–2136 (2010). [CrossRef]
25. D. T. Spencer, J. F. Bauters, M. J. R. Heck, and J. E. Bowers, “Integrated waveguide coupled Si3N4 resonators in the ultrahigh-Q regime,” Optica 1(3), 153–157 (2014). [CrossRef]
26. D. Dai, B. Yang, L. Yang, Z. Sheng, and S. He, “Compact microracetrack resonator devices based on small SU-8 polymer strip waveguides,” IEEE Photonics Technol. Lett. 21(4), 254–256 (2009). [CrossRef]
27. P.-H. Wang, Y.-X. Zhong, and S.-A. Huang, “Numerical analysis of nanotapered waveguides for cavity coupling optimization,” J. Nanophotonics 15(4), 046006 (2021). [CrossRef]
28. G. Liang, H. Huang, A. Mohanty, M. C. Shin, X. Ji, M. Carter, S. Shrestha, M. Lipson, and N. Yu, “Robust, efficient, micrometre-scale phase modulators at visible wavelengths,” Nat. Photonics 15(12), 908–913 (2021). [CrossRef]
29. R. Sun, J. Cheng, J. Michel, and L. Kimerling, “Transparent amorphous silicon channel waveguides and high-Q resonators using a Damascene process,” Opt. Lett. 34(15), 2378–2380 (2009). [CrossRef]
30. J. Liu, H. Weng, A. A. Afridi, J. Li, J. Dai, X. Ma, H. Long, Y. Zhang, Q. Lu, J. F. Donegan, and W. Guo, “Photolithography allows high-Q AlN microresonators for near octave-spanning frequency comb and harmonic generation,” Opt. Express 28(13), 19270–19280 (2020). [CrossRef]
31. K. Wu and A. W. Poon, “Stress-released Si3N4 fabrication process for dispersion-engineered integrated silicon photonics,” Opt. Express 28(12), 17708–17722 (2020). [CrossRef]
32. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Modeling and measurement of losses in silicon-on-insulator resonators and bends,” Opt. Express 15(17), 10553–10561 (2007). [CrossRef]
33. X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Laser Photonics Rev. 9(4), L23–L28 (2015). [CrossRef]
34. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]
35. P. H. Wang, Y. Xuan, L. Fan, L. T. Varghese, J. Wang, Y. Liu, X. Xue, D. E. Leaird, M. Qi, and A. M. Weiner, “Drop-port study of microresonator frequency combs: power transfer, spectra and time-domain characterization,” Opt. Express 21(19), 22441–22452 (2013). [CrossRef]
36. J. Liu, E. Lucas, A. S. Raja, J. He, J. Riemensberger, R. N. Wang, M. Karpov, H. Guo, R. Bouchand, and T. J. Kippenberg, “Photonic microwave generation in the X-and K-band using integrated soliton microcombs,” Nat. Photonics 14(8), 486–491 (2020). [CrossRef]
