Open Access
Add to BibSonomy
Abstract
On-chip micro-ring resonators (MRRs) with low loss and large free spectral ranges (FSRs) are important for photonic devices. So far, ultra-low-loss silicon-nitride (Si3N4) waveguides are primarily fabricated in laboratories, as they often demand special processes to reduce transmission losses. While, Si3N4 waveguides fabricated by the standard multi-project wafer (MPW)-based processes often suffer from significant sidewall scattering, resulting in high scattering losses. Here, we present an innovative approach to photonics by introducing a compact and multi-mode structure. This approach significantly reduces the contact between the optical field and the rough sidewalls in the high-confinement Si3N4 waveguide. By incorporating modified Euler bends, and a weakly tapered gap directional coupler, adiabatic transmission with simultaneous ultra-low loss and compact size is achieved even in 7-µm wide waveguide. Results show that the intrinsic quality factor Qi of MRR is (6.8 ± 0.4) × 106 at the wavelength of 1550 nm, which is approximately four times higher than the previously reported by the same fabrication process. An ultra-low loss of 0.051 ± 0.003 dB/cm is achieved based on the standard LIGENTEC-AN800 technology. This accomplishment addresses a critical challenge in high-confinement waveguides. Our work provides new insights into the low propagation loss in Si3N4 waveguides and provides a broader prospect for integrated photonics in the ultra-high-Q regime.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the past decades, integrated photonic technology has been successfully translated from laboratory research to industrial applications, and has impacted today's optical communication networks [1]. On-chip micro-ring resonators (MRRs) with low propagation loss have the promise of revolutionizing numerous fields, including microwave photonic filters (MPFs) [2], sensors [3], lasers [4], nonlinear optics [5], and quantum optics [6]. Recently, Zhang et al. fabricated a compact MRR based on silicon (Si) with a record high intrinsic quality factor (Qi) of 1.02 × 107 [7]. However, the Q-factor has almost reached its limit due to the two-photon absorption at the telecommunication wavelength [8]. Silicon nitride (Si3N4) has emerged as a leading material in the second revolution due to its wide transparency range, excellent optical nonlinearity for photonic integrated circuits (PICs), compatibility with large-scale semiconductor manufacturing [9–12], and ultralow-loss [13].
High-Q Si3N4 MRR was fabricated on extremely thin (40 nm) Si3N4 films based on subtractive processing as early as 2014 [14]. This is because the low-confinement waveguide is less sensitive to sidewall roughness. In 2021, a record high Qi MRR of 422 million was fabricated based on the low-confinement Si3N4 waveguide [15]. However, it relies on a large mode volume, weak constraints, and millimeter-scale bending radii. For compact photonic routing or nonlinear applications requiring dispersion engineering, high confinement waveguides with low propagation loss are significantly desired. Many sophisticated fabrication processes have been developed to minimize the scattering points at the interfaces of the high confinement waveguide. Based on the traditional subtractive process [16], optical propagation loss of 1∼3 dB/m are achieved base on high confinement Si3N4 waveguides [17–19]. However, they are achieved by introducing extra fabrication processes, such as multi-pass electron beam lithography (EBL) [18,20], or annealing at 1200 °C in special ambient to drive out the residual N-H bonds [18,19] to provide ultra-smooth interfaces and reduce the absorption loss. Alternatively, the photonic Damascene process [21] can also be used to fabricate high confinement Si3N4 waveguides with low propagation loss, which enables the use of substrate topography for stress control and thin film crack prevention. However, the ultra-low propagation loss achieved in these literatures relies on improving fabrication process, such as preforming reflow (substrate should be annealed at 1250 °C over 18 hours long) to reduce the sidewall roughness of waveguide preforms [21–24] and the substrate is also thermally annealed at 1200 °C to drive out the residual hydrogen impurities in the Si3N4 film [24]. Both the high stress of the films and the high temperature make it really challenging to fabricate these devices in standard foundry. Up to now, it is still very challenging to develop an optimized manufacturing process for different material platforms to achieve ultra-smooth interfaces. Moreover, in ultralow-loss PICs, mode mixing due to non-adiabatic transition can be the dominant cause for spatial mode interaction and may also lead to the increase of threshold for nonlinear processes [25]. Therefore, MRRs with ultralow-loss, compact and spatial-mode-interaction-free are very crucial in nonlinear photonic integrated circuits. However, based on the standard LIGENTEC-AN800 technology in the MPW foundry, the lowest propagation loss reported to date is as high as 0.2 dB/cm at 1550 nm [26].
In this work, we overcome the above challenges and demonstrate an ultralow-loss MRR by optimizing the waveguide structure. This novel design leverages multi-mode structures to minimize scattering loss, marking a significant advancement in the field of integrated photonics. At the same time, the MRR suppresses spatial mode interaction and effectively operates highly multi-mode waveguides in the single-mode regime. The MRR consists of two multimode waveguide bends (MWBs) based on modified Euler bends, four linear adiabatic tapers (LATs) and two multimode straight waveguides (MSWs). A directional coupler with weakly tapered gap is used to achieve the fundamental mode coupling and reduce excess coupling loss. By shaping the mode using a highly multimode structure to reduce the overlap with the waveguide interfaces, only the fundamental mode is excited and propagates in the multimode waveguide with ultralow-loss. The racetrack resonator is fabricated with 800-nm-Si3N4 MPW foundry processes. With the help of Euler MWBs and the LATs, we show that the MRR has an intrinsic quality factor of (6.8 ± 0.4) × 106 at the wavelength of 1550 nm, and a compact footprint of 0.17 × 1.76 mm2. It indicates that the waveguide propagation loss is only 0.051 ± 0.003 dB/cm, which is approximate one-fourth of the reported under the same MPW foundry process. Therefore, for high-confinement Si3N4 waveguides, a broadened core region helps to solve the issue of high propagation loss. More importantly, the method can be applied to different material platforms, thus greatly relaxing the fabrication processing requirements.
2. Design and simulation
For an MRR, there are several sources of optical loss, which seriously reduce the quality factor. Theoretically, the intrinsic quality factor Qi can be expressed as [27]
where Qext, Qrad, Qmat and Qsca are quality factors determined by external conditions, Ref. [28] shows that during the wavelength of about 1.52 µm and 1.55-1.57 µm, the bulk absorption loss is mainly attributed to N-H and Si-H impurities in Si3N4 waveguides. The material-limited quality factor can be simply given as [27]: where αmat is the material absorption coefficient with contributions from both bulk absorption and Rayleigh scattering. The high-temperature annealing steps of the waveguide core and cladding can reduce the residual hydrogen content, thus further reducing the Si3N4 material loss [21]. In general, the bending loss can be negligible when the bending radius is large enough. While, the scattering loss is the main source of propagation loss. It is caused by surface roughness and occurs at the interface between the core and cladding, which is sensitive to the lithography and etching process [22]. Previously, complex fabrication processes are used to minimize the scattering points at the interfaces [18–24]. However, they are non-standard and incompatible with the standard MPW foundries. Qsca can be simply given by [27]:In this paper, adiabatic transmission of the fundamental mode is achieved by using adiabatic coupling and adiabatic bending. Low propagation loss is also achieved by using multimode structure to reduce the contact between the light field and the rough sidewall. Figure 1 is the schematic diagram of the proposed compact ultra-high-Q MRR. Figure 1(a) shows the three-dimensional (3D) view of the designed ultra-high-Q MRR. Figure 1(b) shows the top view of the designed ultra-high-Q racetrack MRR. It is mainly composed of two multimode straight waveguides (MSWs), two 180° modified Euler multimode waveguide bends (MWBs) and four LATs, which are used to connect the MSWs and MWBs. The parameters of the MRR are designed to be: the width of the bus waveguide, MWBs and MSWs are 1.0 µm, 1.5 µm and 7.0 µm, respectively. The gap between the bus waveguide and the MWBs are 0.9 µm and the length of LATs (Lt) and MSWs (Ls) are 150 and 1000 µm, respectively.
The cross-sectional view of the coupling is shown in Fig. 2(a). The MRR in this paper is fabricated by the MPW foundry (LIGENTEC, Switzerland) with the standard LIGENTEC-AN800 technology. A 3.3-µm-thick silica thin film was deposited on the top as the upper cladding, and the wafer is with an 800-nm thick Si3N4 layer and a 4-µm-thick buried-oxide layer. The coupling region is designed based on weakly tapered gap coupling. By reasonably designing the gap and the bending radii of the bus and racetrack waveguide, we can decrease the phase-mismatching and obtain a more adiabatic coupling region than symmetric couplers and straight couplers [14]. Figure 2(b) shows the simulated TE0 mode propagation in the coupling region by using the full 3D finite-difference time-domain (FDTD) simulations (Lumerical FDTD). This design not only increases the coupling efficiency of the TE0 (TE = transverse electric) mode but also has a lower excess loss for the coupler.
Fig. 2. Design of the compact ultra-high-Q MRR. (a) Cross-section of the coupling region; (b) FDTD simulations of TE0 mode propagation in the coupling region; (c) Simulated TE0 mode propagation in the designed 180° Euler MWBs; (d) Calculated MERs of the higher-order TE modes excited by TE0 mode, in the waveguide consisting of an input MSW, a 180° Euler MWB, and an output MSW, when Rmin = 63 µm, Rmax = 4000 µm; (e) Relationship between the scattering loss and waveguide width for TE0 mode based on n-w model (Lc = 50 nm, σ = 1.0, 2.5 and 4 nm respectively); (f) Simulated mode profile when the waveguide width is 7 µm.
Notably, both defects and surface roughness can induce spatial mode interaction in multimode waveguides, especially when a waveguide curvature experiences a non-adiabatic transition due to bending-induced mode mismatch. Euler bend is an effective adiabatic structure that has a curvature varying linearly with its path length. It can not only achieve adiabatic transmission of fundamental mode, but also can achieve a more compact footprint. Notably, the maximum radius Rmax and the minimum radius Rmin of the Euler bend should be accurately designed. Rmax should ensure that only the fundamental mode is excited between MSWs and MWBs, while Rmin should ensure that only the fundamental mode is excited in the coupling region with a small effective bending radius (Reff). When Rmin = 63 µm and Rmax = 4000 µm, the simulated TE0 mode propagation in the designed 180° Euler MWBs is shown in Fig. 2(c) by using the Lumerical FDTD Solutions. It can be seen that almost no multimode interference can be observed, which indicates the designed Euler MWBs work very well. By using the Lumerical FDTD Solutions we also simulate and calculate the mode excitation ratios (MERs) of the higher-order TE modes excited by TE0 mode when Rmin = 63 µm and Rmax = 4000 µm. As shown in Fig. 2(d), the calculated MERs, such as TE1 and TE2 are all below –30 dB in the broadband wavelength from 1500 to 1600 nm. Therefore, the crosstalk of the higher-order modes in the Euler MWBs can be ignored.
To predict the scattering loss of straight waveguide caused by sidewall roughness, we use the n-w model in simulation [29]. It is indicated that the dependence of scattering loss on the waveguide width (w) is only related to the derivative of the effective refractive index (neff) concerning the w. The n-w model, which is suitable for 3D laterally confined waveguides, enables an accurate description of realistic optical waveguides and provides simple design rules for optimizing the waveguide geometry to reduce the scattering loss generated by sidewall roughness [29].
Figure 2(e) shows the relationship between the scattering loss and the waveguide width w for TE0 mode based on n-w model when the correlation length (Lc) of the roughness is 50 nm and the standard deviation of the roughness (σ) is 1.0, 2.5 and 4.0 nm, respectively. The estimated scattering loss of the waveguide (σ = 2.5 nm and Lc = 50 nm) are 0.18, 0.03 and 0.015 dB/cm when the waveguide widths are 1, 3 and 7 µm, respectively. Therefore, wider waveguides can achieve lower scattering loss and relax complex fabrication process requirements. Additionally, LATs are used to connect MWBs and MSWs, and extend the w to 7 µm adiabatically. Figure 2(f) shows the simulated mode profile when the waveguide width w is 7 µm. The interaction between the TE0 mode and the rough sidewalls is significantly weakened, thus significantly reducing the scattering loss.
3. Device fabrication and experimental test results
The device is manufactured on an 800-nm thick Si3N4 platform with a 4-µm-thick buried oxide layer and a 3.3-µm-thick top cladding oxide layer by LIGENTEC. It has a footprint of only 0.17 × 1.76 mm2. Figure 3 shows the false color images of the fabricated ultra-high-Q MRR. Figure 3(a) shows the global view of the fabricated device. The microscopic images of the coupling region, the linear adiabatic taper and the modified Euler bends are shown in Fig. 3(b), (c), and (d), respectively.
Fig. 3. False color images of the fabricated ultra-high-Q MRR. (a) The global view of the fabricated device; (b) Coupling region; (c) Adiabatic taper; (d) The modified Euler bends.
Figure 4(a) shows the experimental setup for characterizing the Q factor of the fabricated ultra-high-Q MRR. It can also be used to realize a microwave photonic notch filter (MPNF) with an ultra-narrow bandwidth. Since the spectral measurement is restricted by the resolution (2.5 GHz @ 1550 nm) of the optical spectrum analyzer (OSA, Yokogawa AQ6370C). We use a microwave photonic link, as shown in Fig. 4(a) to measure the ultrahigh-Q resonator transmission through vector network analyzer (VNA). At first, a phase modulator (PM, Covega Mach 40) is driven by a radio frequency generator emitted from a vector network analyzer (VNA, Anritsu MS4647B). Here, an optical carrier as the input signal is emitted by a tunable laser source (TLS, NKT Basik E15), and the signal after the PM via a polarization controller (PC1) is phase modulated with two sidebands. Then the phase-modulated light is launched into an optical bandpass filter (OBPF). One of the first-order sidebands is eliminated and a single sideband (SSB) signal is achieved correspondingly. Then the light is amplified by an erbium-doped fiber amplifier (EDFA), and coupled into and out of the device under test (DUT) via a pair of tapered optical fibers (OMT-APC-TJ-1 M), which are fixed by the flip-top fiber optic clamps (OMFG06, OMTOOLs). This optical signal is then collected by a high-speed photodetector (PD, SHF AG-Berlin), which converts the signal from the optical domain to the electrical domain. At last, a MPNF is obtained and precisely measured by VNA, which can generate a sweep electrical signal for PM. In this case, the microwave signal can well reflect the MRR response and thus one can precisely measure the Q factor.
Fig. 4. (a) Experimental setup for characterizing the Q factor of the compact ultra-high-Q MRR based on VNA. (b) Measured transmission spectrum of the MRR when both TE and TM mode resonances exist. (c) The zoomed-in view of the major resonance of TE0 mode shown in (b). TLS: tunable laser source; PC: polarization controller; PM: phase modulator; OBPF: optical bandpass filter; EDFA: erbium-doped fiber amplifier; DUT: device under test; PD: photodetector; VNA: vector network analyzer.
The measured transmission spectrum of the MRR is shown in Fig. 4(b). We can see that both TE0 and fundamental transverse magnetic (TM0) modes resonances exist. This is because the Si3N4 waveguide is thick enough to support TM0 mode transmission. The free spectral ranges (FSRs) of the TE0 and TM0 mode are respective 39.99 GHz and 39.30 GHz, which agree well with the simulated values of respective 0.320 nm and 0.314 nm. No higher-order mode resonance is observed within two FSRs, indicating that adiabatic transmission of the fundamental mode is guaranteed. It also agrees well with the simulation results. In Fig. 4(c), we show one example of measured normalized TE0 mode transmission spectra of MRR. The loaded Q factor (Ql) of the TE0 mode can be fitted well by Lorentz-shape curves (see the black curve). The spectral interval corresponding to the middle between the maximal value and the minimal value of the transmission magnitude is denoted as the linewidth of the resonant notch [17]. During the experiment, the scanning span and point of VNA are set as 200 MHz and 4001, respectively. Therefore, the corresponding scanning resolution is 50 kHz. The measured Ql of MRR is 6.5× 106 at the wavelength of 1550 nm, and the intrinsic Q factor of the TE0 mode for MRR is calculated to be 6.8 × 106 by the equation Qi = 2 × Ql / (1 + sqrt(TF)), where TF is the minimum on-resonance normalized transmission between 0 and 1 [30]. We conducted multiple measurements of the Ql for MRRs designed with the same structure and fabricated on the same wafer. The statistically determined Ql value is (6.5 ± 0.3) × 106, and the corresponding calculated intrinsic Qi is (6.8 ± 0.4) × 106. The calculated effective index neff of the TE0 mode is 1.85, and the calculated waveguide propagation loss α0 is 0.051 ± 0.003 dB/cm by the equation α0 = 10 × (2 × π × neff / (Qi × λ)) × lg(e) around 1550 nm [31]. The standard deviations include random errors from the measurement setup and analysis noise in the data. The whole length of ultra-high-Q MRR is 3720 µm and has a compact footprint of 0.17 × 1.76 mm2 with the help of modified Euler MWBs. Compared with previously reported MRR based on the same fabrication process [26], the intrinsic Q factor is boosted to approximate four times magnitude higher, which indicates the effectiveness of our proposed approach.
Table 1 presents a recent comparison of ultra-high-Q Si3N4 resonators. Notably, high-Q MRRs on ultra-thin (40 nm) Si3N4 films have been achieved, but they faced limitations due to their large mode volume, weak constraints, and substantial bending radii. Regarding high-confinement waveguides like the photonic Damascene process, they did reduce propagation loss but necessitated complex fabrication steps. These included “preform reflow” to minimize scattering points and high-temperature annealing to achieve low material absorption losses, both of which posed fabrication challenges. Our proposed high-Q Si3N4 resonator is manufactured using the standard LIGENTEC-AN800 technology in the MPW foundry. Under identical process conditions, the MRR's Q factor has surged roughly four-fold, resulting in a substantial enhancement of the MRR's performance. With its ample FSR and compact footprint, it finds versatile applications in generating soliton micro-combs or electro-optic combs with microwave repetition rates.
Table 1. Comparison of ultra-high-Q Si3N4 resonators reported.
4. Conclusion
In summary, we have demonstrated a high-Q MRR based on high-confinement Si3N4, without the extra need for surface-smoothing process improvements. Its advantages include low scattering loss, high intrinsic Q-factor, standard manufacturing processes, large FSR, cross-platform compatibility, and practicality for foundry fabrication. Experimental results around 1550 nm wavelength confirm an intrinsic Q-factor of (6.8 ± 0.4) × 106, with waveguide propagation loss of only 0.051 ± 0.003 dB/cm, approximately one-fourth of what was previously reported using the same MPW process. With further exploration and refinement, the proposed universal multi-mode waveguide design approach holds the potential to revolutionize high-confinement waveguides, achieving ultra-low loss with high device density and integration, thus significantly relaxing manufacturing process requirements. This advancement promises broad applications across various industries. This research signifies progress and innovation in the field of integrated photonics.
Funding
National Key Research and Development Program of China (NO. 2018YFA0704403); National Natural Science Foundation of China (61975249); Program for HUST Academic Frontier Youth Team (NO. 2018QYTD08); Independent Innovation Foundation of HUST (5003187117); Project of Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing University of Aeronautics and Astronautics), Ministry of Education (NJ20230001).
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. E. Agrell, M. Karlsson, A. R. Chraplyvy, et al., “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016). [CrossRef]
2. D. Marpaung, J. Yao, and J. Capmany, “Integrated microwave photonics,” Nat. Photonics 13(2), 80–90 (2019). [CrossRef]
3. Y. Yu, S. Cui, G. J. Yang, et al., “ANN-Assisted High-Resolution and Large Dynamic Range Temperature Sensor Based on Simultaneous Microwave Photonic and Optical Measurements,” IEEE Sens. J. 23(2), 1105–1114 (2023). [CrossRef]
4. S. Gundavarapu, G. M. Brodnik, M. Puckett, et al., “Sub-hertz fundamental linewidth photonic integrated Brillouin laser,” Nat. Photonics 13(1), 60–67 (2019). [CrossRef]
5. M. H. P. Pfeiffer, A. Kordts, V. Brasch, et al., “Photonic Damascene process for integrated high-Q microresonator based nonlinear photonics,” Optica 3(1), 20–25 (2016). [CrossRef]
6. X. Lu, Q. Li, D. A. Westly, et al., “Chip-integrated visible-telecom photon pair sources for quantum communication,” Nat. Phys. 15(4), 373–381 (2019). [CrossRef]
7. L. Zhang, S. Hong, Y. Wang, et al., “Ultralow-Loss Silicon Photonics beyond the Singlemode Regime,” Laser Photonics Rev. 16(4), 2100292 (2022). [CrossRef]
8. C. Wang and C. P. Search, “Enhanced rotation sensing by nonlinear interactions in silicon microresonators,” Opt. Lett. 39(15), 4376–4379 (2014). [CrossRef]
9. D. J. Moss, R. Morandotti, A. L. Gaeta, et al., “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7(8), 597–607 (2013). [CrossRef]
10. Q. Wilmart, H. El Dirani, N. Tyler, et al., “A Versatile Silicon-Silicon Nitride Photonics Platform for Enhanced Functionalities and Applications,” Appl. Sci. 9(2), 255 (2019). [CrossRef]
11. A. Frigg, A. Boes, G. Ren, et al., “Low loss CMOS-compatible silicon nitride photonics utilizing reactive sputtered thin films,” Opt. Express 27(26), 37795–37805 (2019). [CrossRef]
12. H. El Dirani, L. Youssef, C. Petit-Etienne, et al., “Ultralow-loss tightly confining Si3N4 waveguides and high-Q microresonators,” Opt. Express 27(21), 30726–30740 (2019). [CrossRef]
13. J. F. Bauters, M. J. R. Heck, D. John, et al., “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19(4), 3163–3174 (2011). [CrossRef]
14. D. T. Spencer, J. F. Bauters, M. J. R. Heck, et al., “Integrated waveguide coupled Si3N4 resonators in the ultrahigh-Q regime,” Optica 1(3), 153–157 (2014). [CrossRef]
15. M. W. Puckett, K. Liu, N. Chauhan, et al., “422 Million intrinsic quality factor planar integrated all-waveguide resonator with sub-MHz linewidth,” Nat. Commun. 12(1), 934 (2021). [CrossRef]
16. Z. Ye, K. Twayana, P. A. Andrekson, et al., “High-Q Si3N4 microresonators based on a subtractive processing for Kerr nonlinear optics,” Opt. Express 27(24), 35719–35727 (2019). [CrossRef]
17. X. Ji, J. K. Jang, U. D. Dave, et al., “Exploiting Ultralow Loss Multimode Waveguides for Broadband Frequency Combs,” Laser Photonics Rev. 15(1), 2000353 (2021). [CrossRef]
18. Z. Ye, F. Lei, K. Twayana, et al., “Integrated, Ultra-Compact High-Q Silicon Nitride Microresonators for Low-Repetition-Rate Soliton Microcombs,” Laser Photonics Rev. 16(3), 2100147 (2022). [CrossRef]
19. Z. Ye, H. Jia, Z. Huang, et al., “Foundry manufacturing of tight-confinement, dispersion-engineered, ultralow-loss silicon nitride photonic integrated circuits,” Photonics Res. 11(4), 558 (2023). [CrossRef]
20. X. Ji, F. A. S. Barbosa, S. P. Roberts, et al., “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4(6), 619–624 (2017). [CrossRef]
21. M. H. P. Pfeiffer, J. Q. Liu, A. S. Raja, et al., “Ultra-smooth silicon nitride waveguides based on the Damascene reflow process: fabrication and loss origins,” Optica 5(7), 884–892 (2018). [CrossRef]
22. X. Ji, J. Liu, J. He, et al., “Compact, spatial-mode-interaction-free, ultralow-loss, nonlinear photonic integrated circuits,” Commun. Phys. 5(1), 84 (2022). [CrossRef]
23. J. Liu, E. Lucas, A. S. Raja, et al., “Photonic microwave generation in the X- and K-band using integrated soliton microcombs,” Nat. Photonics 14(8), 486–491 (2020). [CrossRef]
24. J. Liu, G. Huang, R. N. Wang, et al., “High-yield, wafer-scale fabrication of ultralow-loss, dispersion-engineered silicon nitride photonic circuits,” Nat. Commun. 12(1), 2236 (2021). [CrossRef]
25. T. Herr, V. Brasch, J. D. Jost, et al., “Mode Spectrum and Temporal Soliton Formation in Optical Microresonators,” Phys. Rev. Lett. 113(12), 123901 (2014). [CrossRef]
26. D. Chatzitheocharis, D. Ketzaki, G. Patsamanis, et al., “Design of Vernier-ring reflectors in thick Si3N4 platform,” Proc. SPIE 11689, 64 (2021). [CrossRef]
27. A. Schliesser, “Cavity optomechanics and optical frequency comb generation with silica whispering-gallery-mode microresonators,” in Handbook of Ph.D. thesis, A. Schliesser, ed. (Academic, 2009).
28. J. F. Bauters, M. J. Heck, D. D. John, et al., “Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding,” Opt. Express 19(24), 24090–24101 (2011). [CrossRef]
29. D. Melati, F. Morichetti, and A. Melloni, “A unified approach for radiative losses and backscattering in optical waveguides,” J. Opt. 16(5), 055502 (2014). [CrossRef]
30. S. Roberts, X. Ji, J. Cardenas, et al., “Measurements and Modeling of Atomic-Scale Sidewall Roughness and Losses in Integrated Photonic Devices,” Adv. Opt. Mater. 10(18), 2102073 (2022). [CrossRef]
31. R. Gao, N. Yao, J. Guan, et al., “Lithium niobate microring with ultra-high Q factor above 108,” Chin. Opt. Lett. 20(1), 011902 (2022). [CrossRef]
