Open Access
Add to BibSonomy
Abstract
A design method for ultrahigh-Q microring resonators (MRRs) based on Bezier free-form curves was proposed and demonstrated. An MRR consisting of a specially designed 180° waveguide bend, a directional coupler, and two low-loss multi-mode strip waveguides was designed. The free-form curves were used to increase the degree of freedom in the design, shaping the waveguide bend with a gradient width and curvature. This design effectively reduced the propagation loss caused by the roughness of waveguide sidewalls and the mode mismatch loss caused by the excitation of high order modes. The small effective radius of only 20µm enabled the MRR to have a large free spectral range (FSR) and a compact and flexible structure. The MRR was manufactured using a standard process provided by foundry and measured to have an ultrahigh loaded Q factor of 1.86 × 106 and a FSR of about 1 nm.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent several years, photonic integrated circuits (PICs) technology has developed greatly and has become a hot research area. As an essential component of PICs, microring resonators (MRRs) are widely used in many fields, including optical sensors [1–3], microwave filters [4–7], frequency combs [8], external cavity lasers [9,10], optical modulators [11,12] and so on. In these fields, the high quality factor (Q), compact size and large free spectral range (FSR) of MRRs are usually required to achieve higher accuracy, lower crosstalk and higher integration degree. Meanwhile, silicon photonics has considerably impacted the development of PICs due to its superior compatibility with complementary metal-oxide semiconductor (CMOS) processing technology. This compatibility with CMOS technology also makes silicon photonics one of the most promising platforms for PICs to realize high integration density. As discussed, MRRs based on silicon photonics with high Q, large FSR and small size is an promising development direction.
Many approaches have been explored to improve the Q factor and reduce the size of silicon MRRs. Suspended MRRs [13–15] are a type of the MRRs with high-Q and a compact size. Researchers demonstrated a silicon MRR suspended in the air with an intrinsic Q factor of 9.2 × 105 and a radius of 9µm [13]. A suspended silicon microdisk resonator was also achieved which has an intrinsic Q factor as high as 1.94 × 108 and a diameter of 1 mm [14]. Despite the ultra-high Q factors of suspended MRRs can be obtained, the processing techniques needed for their fabrication are usually sophisticated. The etchless process [16,17] is another method to obtain high Q resonators which fabricates waveguides using the thermal oxidation of the silicon instead of conventional etching processes. The roughness of waveguide sidewalls caused by etching can be avoided and thus the Q factors of the resonators manufactured can also be improved consequently by using etchless processes. The Q factors of 5.1 × 105 [16] and 7.6 × 105 [17] have been reported respectively. However, the thermal oxidation process of silicon is not a universal process and is not provided by multi-project wafer (MPW) foundries at present. Some studies have been dedicated to optimizing the materials of the cladding and the core to reduce the losses of waveguides and further improve the Q factor of MRRs [18,19]. Waveguides with different doped SiO2 core and cladding were utilized to design a MRR and a Q of 1.83 × 106 was achieved. However, its radius is as large as 1600µm [18]. A MRR that is composed of the ridge silicon waveguides buried by TeO2 deposited cladding was demonstrated with a Q of 1.5 × 106 [19]. Significant progress in reducing the waveguide surface roughness has been achieved recently by optimizing processing technologies including dry etching, chemical mechanical polishing and lithography. Depending on the relevant reports, a Si3N4 MRR with a Q of 3.7× 107 and a radius of 115 µm was achieved [20]. The studies mentioned above both focus on improving the Q factors of MRRs by using special processes or optimized materials. However, these methods cannot be achieved by the standard processes provided by foundries, which limits their applications and increases costs. There have been some studies that have achieved high Q factors based on standard CMOS-compatible processes [21–23]. Numerous studies have demonstrated the method of replacing single-mode waveguides used in MRRs with low-loss multi-mode waveguides to reduce the sidewall scattering loss and further achieve ultrahigh-Q factors. A MRR fabricated using standard SOI fabrication techniques was measured with a Q factor of approximately 2 × 106 at critical coupling [21]. This research effectively reduced the loss of the MRR by using multi-mode rib waveguides (MMRWs) for light transmission, however, it is a large-area ring resonator with a small FSR. Another study also demonstrated a racetrack MRR with an ultra-high Q factor of 1.1 × 106, which is composed of straight MMRWs and single-mode rib waveguide (SMRW) bends. The MRR has a bend radius as small as 20µm, however its FSR is as small as 0.208 nm [22]. A novel MRR with multi-mode strip waveguide (MMSW) bends based on modified Euler curves were designed and a loaded Q factor of about 1.3 × 106 was achieved [23]. The reported MRR has a compact structure as the effective radius of the bend is just 29µm. However, it has an inflexible coupler which may limit its practical applications.
As mentioned above, it is essential to design the MRRs with high Q, large FSR and compact and flexible structure based on standard silicon photonics manufacturing processes. In this paper, we proposed and demonstrated a method based on free-form curves to design the geometry of MRRs. This design could effectively suppress the propagation loss and mode mismatch loss to obtain the ultrahigh-Q, large FSR and compact and flexible structure of MRRs.
2. Design and structure
An MRR adapted to the standard CMOS-compatible process of wafer foundries was designed. The base material is a standard silicon-on-insulator (SOI) wafer with a 2 µm SiO2 buried-oxide (BOX) layer and a 220 nm top silicon layer. The strip waveguide structure was chosen for the design of the MRR due to its better light confinement properties, compared to ridge waveguide. The MRR was designed to work with the fundamental transverse electric (TE) mode, which is appropriate for most applications.
The Q factor of MRRs is mainly limited by the propagation loss of the waveguides which compose the MRRs. There are two kinds of dominating losses including the scattering loss caused by the rough waveguide sidewalls and the mode mismatch loss caused by the bent waveguides. It has been demonstrated that the scattering loss can be effectively suppressed by increasing the width of waveguide [23–28], as this can weaken the interaction between the lightwave and the rough waveguide sidewalls. However, when the waveguide is widened, the mode mismatch loss will significantly increase, as high-order modes can be more easily excited in wider waveguide bends.
In order to reduce the scattering loss of MRRs and suppress the excitation of high-order modes, we proposed a method based on free-form curves for the design of MRRs. The notion of the method derives from the free-form surface used in optical lens design, which can enable lenses with unusual properties. Bezier curves, initially used by French engineer Pierre Bezier for the design of car bodies, can be used to draw arbitrarily contour lines and are widely used in industrial design now due to their flexibility. In this sense, Bezier curves can be regarded as a type of free-form curves. The three-dimensional (3D) view and the top view of the designed MRR are shown in Fig. 1(a) and Fig. 1(b), respectively. The MRR was designed in a racetrack shape and consists of three parts, including a directional coupler (the blue part), a 180° waveguide bend (the red part) and two wide MMSWs (the green part). Here, the 180° waveguide bend and the directional coupler are two parts that need to be specially optimized because the mode mismatch loss is mainly generated in these bent and coupling parts. In this study, Bezier curves were utilized to optimize the geometry of the 180° waveguide bend and the directional coupler.
Fig. 1. The (a) 3D and (b) top view of the designed MRR. The inset shows the cross section of the waveguides at the light coupling position.
Bezier curves are now widely used for curve fitting, which can replace a discrete case with a more continuous structure. This way, a path can be well defined by providing sufficient control points. The path defined by a Bezier curve is given as:
In this study, it was found that quintic Bezier curves can provide sufficient degrees of freedom for designing the MRR. The 180° waveguide bend of the MRR has a symmetric structure, so in order to simplify the design, only half of the bend needs to be determined. As shown in Fig. 2, the contour line of the half bend was divided into an inner line (red) and an outer line (blue). The two lines were defined by two different Bezier curves, each with six control points. The coordinates of the 12 control points were set as:
The values of r1 and r2 are determined by the required size of the MRR. Upon evaluation, it was found that a 1:2 length-width ratio for the half bend was better for maintaining the propagation of the fundamental TE mode. However, it should be noted that the length-width ratio is not limited to 1:2 and can be adjusted as needed. In this study, r1 and r2 were set to 12.5µm and 25µm, respectively. The parameters b1, b2, b3 and b4 were used to adjust the coordinates of corresponding control points to optimize the geometry of the half bend. The propagation of the fundamental TE mode is simulated using the three-dimensional finite difference time domain (3D-FDTD) method provided by the commercial software Lumeical, and the propagation loss and excitation of higher-order modes are evaluated in real time. After optimization, the parameters b1, b2, b3 and b4 were determined to be 0.5, 0.8, 0.22 and 0.95, respectively. The directional coupler simply consists of the 180° bend and an adjacent single-mode straight waveguide (SMSW). The power coupling ratio of the fundamental TE mode can be adjusted by changing the width of the gap (wgap) between the bend and the SMSW to achieve the best coupling condition for the MRR. Here, wgap was set to 410 nm, resulting in a coupling ratio of approximately 0.00136, which allowed the MRR to operate under a critical coupling condition.
The propagation and field distribution of the fundamental TE mode in the designed bend and directional coupler were calculated and simulated within the band of 1530 nm to 1570 nm, as shown in Fig. 3(a)-(b). Figure 3(c) shows the transmission of the fundamental TE mode and the excitation of high order modes. The mode excitation caused by the light coupling of the designed directional coupler is depicted in Fig. 3(d), obtained by calculating the proportion of each mode to the total coupled light. It is evident that the propagation of the fundamental TE mode was maintained well and the excitation of high order modes was limited to lower than or close to -40 dB. The simulation results show that the fundamental TE mode can propagate in the designed bend and directional coupler with ultra-low loss, which means that the Q factor of the MRR composed of them will be significantly enhanced.
Fig. 3. The propagation and field distribution of the fundamental TE mode in (a) the designed bend and (b) the directional coupler. (c) The calculated transmission of the fundamental TE mode and the excitation of high order modes as the light wave propagates through the designed waveguide bend. (d) The mode excitation when the light wave is coupled from the bus waveguide to the waveguide bend.
3. Fabrication and measurement
The designed MRR was fabricated using the 180 nm silicon photonics platform provided by Chongqing United Microelectronics Center (CUMEC, China). This platform provides MPW services based on standard SOI with 2µm BOX and 220 nm top silicon. Its silicon photonics chip manufacturing processes are compatible with standard CMOS processes, including deep UV lithography and inductively coupled plasma dry etching. This platform provides three etching depths for waveguide fabrication: shallow etching (70 nm), deep etching (150 nm) and full etching (220 nm). Only full etching is needed for the fabrication of the designed MRR, as it is all composed of stripe waueguides. The vertical grating coupler in the device library provided by the platform was used for the light coupling input and output of the designed MRR.
In order to measure the Q factor of the manufactured MRRs, a C-band tunable laser (Thorlabs TLX1) was used as the source and an optical power meter (Newport 918D) was used to monitor the light transmissions. The light transmissions between the chip and the laser source, as well as the power meter, were completed using polarization-maintaining fibers. The microscope image of one of the MRRs and the chip-fiber light coupling was shown in Fig. 4.
Figure 5 shows the measured results. The spectral responses around 1560 nm are shown in Fig. 5(a) and it can be seen the FSR of the MRR is as high as about 1 nm. Additionally, no resonance peaks of high-order modes were observed, indicating that the designed structure can suppress them well. Figure 5(b) shows the measured data of a resonance peak and its fitted Lorentzian curve. In order to obtain the full width at half maximum (FWHM) of the resonance peak, Lorentzian curve fitting is used and the result shows that the FWHM is about 0.838pm. The loaded Q factor of the MRR can be calculated as Qload = λ / Δλ = 1.86 × 106. Mode splitting is a phenomenon caused by the waveguide surface roughness and fabrication imperfection, which can only be observed when the Q of the resonant cavity is high enough [23]. Figure 5(b) shows the observed mode splitting phenomenon in the measurement, further demonstrating the ultra-high Q of the MRR.
Fig. 5. (a) The measured spectral responses of the designed MRR. (b) The measured resonance peak and its fitted Lorentzian curve. (c) The measured mode splitting.
This work was compared to previously reported all-pass type silicon MRRs with a Q-factor higher than 106, as shown in Table 1. [23,29–32]. To facilitate comparison, we adopted the definition of effective radius (Reff) consistent with Ref. [23]. The Reff of a 180° waveguide bend is defined as the radius of a regular 180° arc bend with the same perimeter. Using this definition, the perimeter of the present 180° waveguide bend is approximately 63µm, resulting in an effective radius of 20µm. Through data fitting analysis [18,32], the loss of the present MRR was estimated to be 0.24 dB/cm. In comparison to the MRRs listed in Table 1, the present MRR has the smallest Reff and highest FSR.
Table 1. Comparison of all-pass type silicon MRRs
4. Conclusion
In this paper, we proposed and demonstrated a design method of MRRs and realized an ultrahigh-Q silicon racetrack MRR. The designed MRR consists of a specially designed 180° waveguide bend, a directional coupler and two low-loss MMSWs. Based on quintic Bezier free-form curves, the geometry of the 180° waveguide bend was designed with a gradient curvature and width, which progressively increases from 0.45um in the center to 1.6µm at both ends, with an effective radius of only 20µm. This design ensures that only the fundamental mode can propagate in the waveguide bend with low loss, and no high order modes can be excited. Meanwhile, the 0.45µm width in the center of the bend waveguide allows for a compact directional coupler consisting of the waveguide bend and an adjacent 0.45µm-wide SMSW, because the fundamental mode can be easily coupled by a symmetrical structure. With a width of 1.6µm, the two wide MMSWs can significantly decrease the propagation losses of the fundamental mode caused by the waveguide sidewall's roughness. The MRR, which was designed using the proposed method, was fabricated using only a standard full etching process provided by the MPW foundry. The loaded Q factor of 1.86 × 106 and FSR of approximately 1 nm were measured. The compact and flexible structure, large FSR, and ultra-high Q factor of the MRRs will significantly improve their applications in several fields. The proposed method successfully increases the degree of freedom for the design of MRRs and can be extended to the design of more photonic devices, which will provide more possibilities for their optimization.
Funding
International Partnership Program of the CAS (174GJHZ2022016GC); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2020121); National Natural Science Foundation of China (12074405).
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. B. Su, C. Wang, Q. Kan, et al., “Compact Silicon-on-Insulator Dual-Microring Resonator Optimized for Sensing,” J. Lightwave Technol. 29(10), 1535–1541 (2011). [CrossRef]
2. M. A. Guillén-Torres, E. Cretu, N. A. Jaeger, et al., “Ring Resonator Optical Gyroscopes—Parameter Optimization and Robustness Analysis,” J. Lightwave Technol. 30(12), 1802–1817 (2012). [CrossRef]
3. D. Dai and S. He, “Highly sensitive sensor based on an ultra-high-Q Mach-Zehnder interferometer-coupled microring,” J. Opt. Soc. Am. B 26(3), 511–516 (2009). [CrossRef]
4. M. Rasras, K. Tu, D. Gill, et al., “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Lightwave Technol. 27(12), 2105–2110 (2009). [CrossRef]
5. D. Liu, H. Xu, Y. Tan, et al., “Silicon photonic filters,” Microw Opt. Technol. Lett. 63(9), 2252–2268 (2021). [CrossRef]
6. Y. Xie, Y. Shi, L. Liu, et al., “Thermally-Reconfigurable Silicon Photonic Devices and Circuits,” IEEE J. Select. Topics Quantum Electron. 26(5), 1–20 (2020). [CrossRef]
7. H. Yang, J. Li, G. Hu, et al., “Hundred megahertz microwave photonic filter based on a high Q silicon nitride multimode microring resonator,” OSA Continuum 3(6), 1445–1455 (2020). [CrossRef]
8. 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]
9. C. Xiang, W. Jin, J. Guo, et al., “Effects of nonlinear loss in high-Q Si ring resonators for narrow-linewidth III-V/Si heterogeneously integrated tunable lasers,” Opt. Express 28(14), 19926–19936 (2020). [CrossRef]
10. T. Aihara, T. Hiraki, T. Fujii, et al., “Heterogeneously integrated widely tunable laser using lattice filter and ring resonator on Si photonics platform,” Opt. Express 30(10), 15820–15829 (2022). [CrossRef]
11. T. Baba, S. Akiyama, M. Imai, et al., “50-Gb/s ring-resonator-based silicon modulator,” Opt. Express 21(10), 11869–11876 (2013). [CrossRef]
12. D. Zheng, C. Qiu, H. Zhang, et al., “Demonstration of a Push-Pull Silicon Dual-Ring Modulator With Enhanced Optical Modulation Amplitude,” J. Lightwave Technol. 38(14), 3694–3700 (2020). [CrossRef]
13. W. Jiang, J. Zhang, and Q. Lin, “Compact suspended silicon microring resonators with ultrahigh quality,” Opt. Express 22(1), 1187–1192 (2014). [CrossRef]
14. J. Gu, J. Liu, Z. Bai, et al., “Dry-etched ultrahigh-Q silica microdisk resonators on a silicon chip,” Photonics Res. 9(5), 722–725 (2021). [CrossRef]
15. S. Liu, W. Sun, Y. Wang, et al., “End-fire injection of light into high-Q silicon microdisks,” Optica 5(5), 612–616 (2018). [CrossRef]
16. L. W. Luo, G. S. Wiederhecker, J. Cardenas, et al., “High quality factor etchless silicon photonic ring resonators,” Opt. Express 19(7), 6284–6289 (2011). [CrossRef]
17. A. Griffith, J. Cardenas, C. B. Poitras, et al., “High quality factor and high confinement silicon resonators using etchless process,” Opt. Express 20(19), 21341–21345 (2012). [CrossRef]
18. Y. Yin, X. Yin, X. Zhang, et al., “High-Q-Factor Silica-Based Racetrack Microring Resonators,” Photonics 8(2), 43 (2021). [CrossRef]
19. K. Miarabbas Kiani, D. B. Bonneville, A. P. Knights, et al., “High-Q TeO2–Si Hybrid Microring Resonators,” Appl. Sci. 12(3), 1363 (2022). [CrossRef]
20. X. Ji, F. A. 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. Guillén-Torres, K. Murray, H. Yun, et al., “Effects of backscattering in high-Q, large-area silicon-on-insulator ring resonators,” Opt. Lett. 41(7), 1538–1541 (2016). [CrossRef]
22. Y. Zhang, X. Hu, D. Chen, et al., “Design and demonstration of ultra-high-Q silicon microring resonator based on a multi-mode ridge waveguide,” Opt. Lett. 43(7), 1586–1589 (2018). [CrossRef]
23. L. Zhang, L. Jie, M. Zhang, et al., “Ultrahigh-Q silicon racetrack resonators,” Photonics Res. 8(5), 684–689 (2020). [CrossRef]
24. K. Yap, A. Delâge, J. Lapointe, et al., “Correlation of Scattering Loss, Sidewall Roughness and Waveguide Width in Silicon-on-Insulator (SOI) Ridge Waveguides,” J. Lightwave Technol. 27(18), 3999–4008 (2009). [CrossRef]
25. K. K. Lee, D. R. Lim, H. Luan, et al., “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77(11), 1617–1619 (2000). [CrossRef]
26. H. Shang, D. Sun, P. Yu, et al., “Investigation for Sidewall Roughness Caused Optical Scattering Loss of Silicon-on-Insulator Waveguides with Confocal Laser Scanning Microscopy,” Coatings 10(3), 236 (2020). [CrossRef]
27. D. E. Hagan and A. P. Knights, “Mechanisms for optical loss in SOI waveguides for mid-infrared wavelengths around 2µm,” J. Opt. 19(2), 025801 (2017). [CrossRef]
28. J. Bauters, M. Heck, D. John, et al., “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19(4), 3163–3174 (2011). [CrossRef]
29. A. Biberman, M. J. Shaw, E. Timurdogan, et al., “Ultralow-loss silicon ring resonators,” Opt. Lett. 37(20), 4236–4238 (2012). [CrossRef]
30. M. A. Guillén-Torres, M. Caverley, E. Cretu, et al., “Large-area, high-Q SOI ring resonators,” in Photonics Conference (IEEE, 2014), pp. 336–337.
31. M. Burla, B. Crockett, L. Chrostowski, et al., “Ultra-high Q multimode waveguide ring resonators for microwave photonics signal processing,” in International Topical Meeting on Microwave Photonics (IEEE, 2015), pp. 1–4.
32. L. Zhang, S. Hong, Y. Wang, et al., “Ultralow-loss silicon photonics beyond the singlemode regime,” Laser Photonics Rev. 16, 2100292 (2022). [CrossRef]
