Open Access
Add to BibSonomy
Abstract
We fabricate three-dimensional wavelength-division multiplexing (3D-WDM) interconnects comprising three SixNy layers using a CMOS-compatible process. In these interconnects, the optical signals are coupled directly to a SixNy grating coupler in the middle SixNy layer and demultiplexed by a 1 × 4 SixNy array waveguide grating (AWG). The demultiplexed optical signals are interconnected from the middle SixNy layer to the bottom and top SixNy layers by four SiOxNy interlayer couplers. A low insertion loss and low crosstalk are achieved in the AWG. The coupling losses of the SiOxNy interlayer couplers and SixNy grating coupler are ∼1.52 dB and ∼4.2 dB, respectively.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High-density integrations with compact photonic devices based on silicon, silicon nitride (SixNy), InP, and LiNbO3 photonics have attracted considerable attention for applications in 5G/6G, quantum optics, and neuromorphic photonics [1–9]. Recently, the number of photonic components in complex photonic integrated circuit (PIC) systems has been rapidly increasing. However, this high-density integration of the PIC is limited by the relatively large size of the photonic components and the minimum distance between optical waveguides (WGs) required to suppress crosstalk [10]. It has become increasingly difficult to integrate all the necessary photonic components into a two-dimensional (2D) structure. Thus, the three-dimensional PIC (3D-PIC) is an excellent candidate for solving the above limitations associated with integration in the 2D-PIC. Moreover, various studies have demonstrated the increase in integration density in a 3D-PIC structure [10–16]. On the other hand, wavelength division multiplexing (WDM) is a key technology that can enlarge the data transmission capacity. Various WDM devices fabricated on a 2D plane such as Si, SixNy, InP, and SU8 based AWGs have been reported [17–24]. Furthermore, the incorporation of WDM devices into 3D structures increases the data capacity and offers a high integration density in the 3D-PIC, while maintaining a compact size. Several WDM devices embedded in 3D structures have been reported, but there are no optical interconnections between vertical layers within 3D structures or only simulation results [25–26].
This paper reports a 3D-WDM interconnect based on three SixNy layers, which includes a four-channel SixNy AWG, a SixNy grating coupler, and four SiOxNy interlayer couplers. In the fabricated 3D-WDM interconnect device, the input multiplexed optical signal is vertically coupled to the middle layer by the SixNy grating coupler and is then demultiplexed by the SixNy AWG. The demultiplexed signals travel from the middle SixNy layer to the lower and upper SixNy layers through a SiOxNy interlayer coupler. A low insertion loss for the embedded SixNy AWG is achieved in the 3D-WDM interconnects by incorporating the SixNy grating coupler and SiOxNy interlayer couplers. The fabricated 3D-WDM interconnects show that the SixNy AWG can play a role in the 3D structure with low loss.
2. Design and fabrication
Figure 1 shows a schematic of the 3D-WDM interconnects consisting of three SixNy layers, which includes a grating coupler, a 1 × 4 SixNy AWG, and four SiOxNy interlayers couplers positioned between the SixNy layers. First, a multiplexed optical signal is coupled into a SixNy grating coupler in the SixNy layer 2 and demultiplexed by a 1 × 4 SixNy AWG. By using the SiOxNy interlayer couplers, the two output signals of the SixNy AWG are interconnected to the WGs (D1 and D2) in the SixNy layer 1, and the other two signals are interconnected to the WGs (U1, U2) in the SixNy layer 3.
Fig. 1. Schematic illustration of 3D-WDM interconnects consisting of three SixNy layers, which includes a grating coupler, four-channel SixNy AWG, and four SiOxNy interlayer couplers positioned between SixNy layers.
The single-mode conditions in the SixNy WG are calculated as a function of the cross-sectional area (W × T), and the height of the SixNy WG is set to 0.5 µm for the single-mode operation of the 3D-WDM interconnect device, as shown in Fig. 2(a). Figure 2(b) illustrates the schematics of the SixNy grating coupler. To achieve a high coupling efficiency for the SixNy grating coupler, simulations are performed with various grating periods (P), etch depths (D), and incident angles of a single-mode fiber (θ) using Lumerical FDTD [27] under the condition of applying index-matching oil. For a fixed thickness (Tg) of 0.5 µm, Figs. 2(c) and 2(d) show the coupling efficiency as a function of P and D, respectively. Optimal design parameters, P = 960 nm, D = 360 nm, and θ = 3.68°, are obtained with a coupling efficiency of 55.6% using a parametric sweep.
Fig. 2. (a) Calculated single-mode conditions in the SixNy WG as a function of cross-sectional area (W × T). (b) Schematic diagram of the SixNy grating coupler used in the simulation. Coupling efficiency of the SixNy grating coupler as a function of (c) P and (d) D.
In 3D photonic interconnects using vertically stacked SixNy layers, crosstalk between SixNy layers needs to be as small as possible to achieve the best performance for each photonic component within the 3D-PIC. An interlayer coupler connecting two SixNy WGs with a large spacing layer is required to achieve a low-crosstalk condition. Simulations for the interlayer coupler are performed via Lumerical eigenmode analysis [27]. The SiOxNy material, which has a lower refractive index compared to SixNy WGs, was chosen for the fabrication of the interlayer coupler because the optical modes that propagate the lower refractive index WG can easily recombine into an optical WG with a higher refractive index. In addition, since the mode size increases in the interlayer coupler having a low refractive index, the spacing between the SixNy layers can be made larger and noise generated between the SixNy layers can be minimized. Figure 3 shows a schematic illustration and the calculated coupling efficiency of the SiOxNy interlayer coupler. The SixNy WG with a cross-sectional area of 0.5 × 0.5 µm2 in layer 1 is positively tapered and overlaps with a SiOxNy bidirectional taper structure whose cross-sectional area (WSiON × TSiON) is tapered in both directions for length Lt. In addition, the SiOxNy bidirectional taper structure overlaps with the inversely tapered SixNy WG of layer 2. The SixNy and SiOxNy structures have a tapered tip width of 0.2 µm. The refractive index of SiOxNy is 1.862 at λ = 1.55 µm. The efficiency of coupling between the SixNy WGs, located in layers 1 and 2, by the SiOxNy interlayer coupler with a fixed WSiON of 1 µm and various TSiON is calculated as a function of Lt. For TSiON of 1 µm, 1.5 µm, and 3 µm, coupling efficiencies of more than 95% are obtained when Lt is above 20 µm, 40 µm, and 130 µm, respectively.
Fig. 3. Schematic illustration and calculated coupling efficiency as a function of Lt of the SiOxNy interlayer coupler.
Light scattering at the star coupler boundary in the AWG causes an increase in the insertion losses and crosstalk. A SixNy AWG is designed using a double-etched structure that combines a shallowly etched inverse-tapered WG and a deeply etched channel WG to suppress scattering at the star coupler boundary, as shown in Fig. 4(a). The adiabatic mode conversion from a slab WG to an arrayed WG is simulated with optimal design parameters such as slab WG thickness (0.5 µm), inverse taper length (dt = 5 µm), distance (r = 9 µm) from slab WG to channel arrayed WG, shallow etch depth (0.3 µm), and arrayed WG thickness (0.8 µm). Figure 4(b) shows the optical mode field profiles and cross-sectional images at positions ①–⑤ in Fig. 4(a). A simulation of the optical mode field profiles is performed using the Lumerical eigenmode analysis [27]. The simulation results indicate that the slab mode was converted adiabatically to the fundamental mode of the arrayed WG. The designed SixNy AWG consists of 1 × 4 channels with a 5-nm-channel spacing, and a wide free spectral range of 40 nm is applied to improve the uniformity of the insertion loss. A compact device with a size of 500 × 650 µm2 is achieved with a star coupler focal length of 85.93 µm and a length difference of 27.19 µm between adjacent arrayed WGs.
Fig. 4. (a) Schematic diagram of SixNy AWG and star coupler boundary and (b) optical mode fields at each point in the star coupler boundary.
Based on the aforementioned simulation results, the 3D-WDM interconnects including the SixNy grating coupler, SixNy AWG, and SiOxNy interlayer couplers were fabricated. Figure 5 shows the fabrication process of the 3D-WDM interconnect device. Layer 1, layer 2, and layer 3 of the SixNy, with thicknesses of 0.5 µm, 0.8 µm, and 0.5 µm, respectively, were deposited via plasma-enhanced chemical vapor deposition (PECVD) and etched to fabricate the grating coupler, AWG, and vertically interconnected WGs. Before layers 2 and 3 were deposited, the SiO2 spacing layer was covered and flattened via chemical–mechanical polishing (CMP). To fabricate the interlayer coupler, SiO2 was etched into a vessel with a bidirectional tapered structure. Subsequently, the SiOxNy was filled into the vessel structure, and the SiOxNy layer was planarized via CMP. The SiO2 etch rate is carefully controlled to protect the SixNy waveguide from over etching.
Figure 6 shows microscopic images and an SEM image of the fabricated 3D-WDM interconnect device. The top view of the microscopic image in Fig. 6(a) shows the 3D-WDM interconnect device consisting of a SixNy grating coupler, a 1 × 4 SixNy AWG, and SiOxNy interlayer couplers. The reference WG consists only of a SixNy grating coupler and a single-mode SixNy WG. The cross-sectional microscopic image in Fig. 6(b) shows the output waveguides (D1, D2, U1, and U2) and the reference WG of the fabricated 3D-WDM interconnect device. The SEM image in Fig. 6(c) shows the cross-section of the monitoring pattern of the 3D structure in Fig. 6(a) consisting of a SixNy grating coupler, three SixNy layers, and two SiOxNy interlayer couplers. The SixNy grating coupler was fabricated with a period of 960 nm, a SixNy thickness of 491 nm, and an etch depth of 373 nm. In the interlayer coupler, the SiOxNy thickness was 0.5 µm. The measured refractive indices of the SixNy and SiOxNy layers at λ = 1.55 µm were 2.11 and 1.862, respectively. To improve the roughness of the surface after the CMP, wet etching using a buffered oxide etch (BOE) (30:1) was performed for 5 seconds. The wafer was annealed at 600°C for 30 min to improve the adhesion between the vertically stacked layers. A CMOS-compatible process using I-line photolithography was used to fabricate the devices.
Fig. 6. Microscopic images ((a) Top view, (b) side view) and (c) cross-sectional SEM images of the fabricated 3D-WDM interconnect device.
3. Experiments and discussions
The output facet of the fabricated 3D-WDM interconnect device was polished to couple the output optical signal to the cleaved single-mode fiber. The optical spectra of the fabricated 3D-WDM interconnect devices were measured using an optical spectrum analyzer (Agilent 86143 B) and a broadband light source (EDFA). The measured optical spectra of the fabricated 3D-WDM interconnect devices were normalized using a reference WG. The propagation loss was measured by the cutback method, and the measured propagation loss of the SixNy WG using the CMP process was 0.2 dB/mm.
Figure 7 shows the calculated and measured coupling efficiencies of the SixNy grating coupler fabricated in the 3D-WDM interconnect device. The dimensions of the grating coupler were obtained, and the void (air gap) was determined via the SEM image. The period of the grating couplers was 960 nm. The SixNy thickness, etch depth, and duty cycle measured on the grating coupler were 491 nm, 373 nm, and 0.42, respectively. To measure the coupling loss, the measured transmission spectrum of the grating coupler was normalized by the spectrum of the input light. The measured coupling loss was 4.2 dB with a 1-dB bandwidth of ∼62 nm. The simulations of the fabricated grating coupler structure with the void (GC_w_void) and without void (GC_wo_void) were performed using the Lumerical FDTD [27]. The calculated coupling losses for the GC_w_void and GC_wo_voids were 3.2 dB and 3.0 dB, and the 1 dB bandwidths were 57 nm and 58 nm, respectively. Calculations indicate that the void does not significantly affect the coupling loss and 1 dB bandwidth. Therefore, the measured loss is relatively large compared to the calculation result due to the surface reflection between the air and the SiO2 upper cladding of the grating coupler, sidewall roughness, and the imperfections of the measurement such as the fiber angle and polarization. In addition, the SixNy grating coupler was fabricated in a 2D structure, and a coupling loss of 3.7 dB was measured with a 1 dB bandwidth of ∼70 nm. The performance degradation in the grating coupler in the 3D interconnect device compared to that in the 2D structure may result from the different cladding thickness.
Fig. 7. Calculated and measured coupling efficiency of the SixNy grating coupler fabricated in the 3D-WDM interconnect device. The inset shows the SEM image and schematic diagram of the fabricated grating coupler.
Figure 8 shows the measured and calculated coupling losses of the fabricated SiOxNy interlayer coupler with a thickness (TSiON) of 0.55 µm and a width (WSiON) of 1 µm. Figure 8(b) shows the calculated coupling loss of the proposed SiOxNy interlayer coupler, as shown in Fig. 8(a). Figures 8(d)–(f) show the measured coupling loss of the fabricated SiOxNy interlayer coupler and the calculated coupling loss for the SiOxNy interlayer coupler including the voids, as shown in Fig. 8(c). In order to measure the coupling loss of the SiOxNy interlayer coupler, the measured transmission spectrum for 10 period SiOxNy interlayer couplers as shown in the illustration of Fig. 8(d) were normalized by the transmission spectrum of the straight waveguide. A simulation of the SiOxNy interlayer coupler, including the voids, was performed using the Lumerical eigenmode analysis [27]. Simulations were performed for various void dimensions and compared with experimental results. When fabricating the SiOxNy interlayer couplers, a SiOxNy layer was deposited via the PECVD on a pre-etched SiO2 vessel structure with a bidirectional tapered pattern. At this time, it was difficult to fill the SiOxNy into a narrow taper structure, and voids were produced during this process. The measured coupling losses were within the range of 0.8–1.7 dB for the interlayer coupler with an inverse taper length (Lt) of 20, 100, and 200 µm. The experimental and calculated results were mutually consistent implying that the measurement loss increases as a result of the mode mismatch between the SixNy WG, and SiOxNy interlayer couplers caused by the voids generated in the interlayer coupler. This problem can be solved by correcting the fabrication process of the interlayer coupler or using other methods, as reported in [15].
Fig. 8. (a) Schematic of the proposed SiOxNy interlayer coupler. (b) Calculated coupling efficiency of the SiOxNy interlayer coupler in Fig. (a). (c) Schematic of the SiOxNy interlayer coupler including voids. (d)-(f) Measured coupling loss of the fabricated SiOxNy interlayer coupler, and the calculated coupling loss for the SiOxNy interlayer coupler including the voids in Fig. 8(c). Illustration in Fig. 8(d): schematic diagram of 10 period SiOxNy interlayer couplers.
For a spectral measurement of the fabricated 3D-WDM interconnect device, the optical signal was combined with a SixNy grating coupler in the SixNy layer 2. Then the demultiplexed spectra of the 1 × 4 SixNy AWG were measured at the outputs of the SixNy layer 1 (D1 and D2) and outputs of the SixNy layer 2 (U1 and U2). Figure 9(a) shows the measured insertion loss in more than ten 3D-WDM interconnect devices. The average insertion loss was 3.03 dB, which includes the losses of the SixNy AWG and SiOxNy interlayer couplers. The standard deviation of the insertion loss was 0.401 dB. By correcting the average loss of the interlayer coupler, 1.52 dB, from the average loss of the 3D interconnect devices, a low average loss of 1.51 dB was obtained for a SixNy AWG with a loss non-uniformity of 1.19 dB. In addition, the standard deviation of the peak position was approximately 1.625 nm, owing to the sidewall roughness and the non-uniformity of the thickness of the SixNy WG based on the CMP process. Figure 9(b) shows the measured normalized transmission spectra of the best device among the fabricated 3D-WDM interconnect devices. The measured insertion losses of the 3D-WDM interconnect devices were within 2.54–3.67 dB with a crosstalk within the range of −22.61 to −25.06 dB. The insertion loss of the SixNy AWG with a loss correction using the transmission spectrum of the SiOxNy interlayer coupler was within 1.08–2.01 dB. The reported low-insertion losses of the SixNy AWGs fabricated with 2D structures operating at C-band were 0.9 dB [21], and 1.5–2.7 dB [28], respectively. The results indicated that the low-loss operation of the SixNy AWG was possible in 3D structures, even though the CMP process increased the propagation loss and non-uniformity. The insertion loss and uniformity of the 3D-WDM interconnect device could be improved by optimizing the conditions of the fabrication process and the design parameters.
Fig. 9. (a) Average insertion loss measured on more than ten 3D-WDM interconnect devices. (b) Measured normalized transmission spectra of the best device among the fabricated 3D-WDM interconnect devices.
4. Conclusions
In this study, 3D-WDM interconnects consisting of three SixNy layers with a SixNy grating coupler, a 1 × 4 SixNy AWG, and SiOxNy interlayer couplers were fabricated. The optical signal coupled with a SixNy grating coupler at the SixNy layer 2 was demultiplexed by a 1 × 4 SixNy AWG and then interconnected to the output SixNy WGs at the SixNy layer 1 and SixNy layer 3 by the SiOxNy interlayer couplers. In the fabricated 1 × 4 channel SixNy AWG within the 3D structure, a low insertion loss within 1.08–2.01 dB was achieved with a low crosstalk within −22.61 to −25.06 dB. The coupling loss of the SiOxNy interlayer couplers was ∼1.52 dB and that of the SixNy grating coupler was ∼4.2 dB. The results show that the SixNy AWG embedded in the 3D structure performed accurately with low insertion loss. Moreover, the 3D-WDM interconnects can be improved to the application level by improving the performance of the SixNy AWG and SiOxNy interlayer couplers and optimizing the design parameters and fabrication process. The 3D WDM interconnect device can be applied to complex integrated photonics systems that require large-capacity data transmission such as data center, 5G/6G, and high-performance computing. By assigning different wavelengths to each of the vertically stacked layers and giving them various functions, complex photonics systems can be systematically and compactly integrated.
Funding
Ministry of Science and ICT, South Korea (2020-0-01268); National Research Council of Science and Technology (CAP-15-05-ETRI).
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. Dang, O. Amin, B. Shihada, and M.-S. Alouini, “What should 6G be?” Nat. Electron. 3(1), 20–29 (2020). [CrossRef]
2. R. Sabella, “Silicon photonics for 5G and future networks,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–11 (2020). [CrossRef]
3. B. Zong, C. Fan, X. Wang, X. Duan, B. Wang, and J. Wang, “6G technologies,” IEEE Vehicular Technology Magazine (2019).
4. G. Serafino, F. Amato, C. Porzi, B. Hussain, V. Toccafondo, M. Chiesa, F. Scotti, A. Bogoni, and P. Ghelfi, “Photonic integrated circuits for beamforming in 5G wireless communications,” The International Photonics and Optoelectronics Meeting, OT3A.2 (2019).
5. J. Wang, F. Sciarrino, A. Laing, and M. G. Thompson, “Integrated photonic quantum technologies,” Nat. Photonics 14(5), 273–284 (2020). [CrossRef]
6. D. M. Lukin, C. Dory, M. A. Guidry, K. Y. Yang, S. D. Mishra, R. Trivedi, M. Radulaski, S. Sun, D. Vercruysse, G. H. Ahn, and J. Vučković, “4H-silicon-carbide-on-insulator for integrated quantum and nonlinear photonics,” Nat. Photonics 14(5), 330–334 (2020). [CrossRef]
7. A. W. Elshaari, W. Pernice, K. Srinivasan, O. Benson, and V. Zwiller, “Hybrid integrated quantum photonic circuits,” Nat. Photonics 14(5), 285–298 (2020). [CrossRef]
8. B. J. Shastri, A. N. Tait, T. F. de Lima, M. A. Nahmias, H.-T. Peng, and P. R. Prucnal, “Principles of neuromorphic photonics,” in Encyclopedia of Complexity and Systems Science (Springer, 2018), pp. 1−37.
9. M. A. Nahmias, B. J. Shastri, A. N. Tait, T. Ferreira de Lima, and P. R. Prucnal, “Neuromorphic photonics,” Opt. Photonics News 29(1), 34–41 (2018). [CrossRef]
10. J. Chiles, S. M. Buckley, S. W. Nam, R. P. Mirin, and J. M. Shainline, “Design, fabrication, and metrology of 10100 multi-planar integrated photonic routing manifolds for neural networks,” APL Photonics 3(10), 106101 (2018). [CrossRef]
11. J. Chiles, S. Buckley, N. Nader, S. W. Nam, R. P. Mirin, and J. M. Shainline, “Multi-planar amorphous silicon photonics with compact interplanar couplers, cross talk mitigation, and low crossing loss,” APL Photonics 2(11), 116101 (2017). [CrossRef]
12. Y. Zhang, A. Samanta, K. Shang, and S. J. B. Yoo, “Scalable 3D silicon photonic electronic integrated circuits and their applications,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–10 (2020). [CrossRef]
13. S. J. B. Yoo, B. Guan, and R. P. Scott, “Heterogeneous 2D/3D photonic integrated microsystems,” Microsyst. Nanoeng. 2(1), 16030 (2016). [CrossRef]
14. K. Shang, S. Pathak, B. Guan, G. Liu, and S. J. B. Yoo, “Low-loss compact multilayer silicon nitride platform for 3D photonic integrated circuits,” Opt. Express 23(16), 21334–21342 (2015). [CrossRef]
15. K. Shang, S. Pathak, G. Liu, S. Feng, S. Li, W. Lai, and S. J. B. Yoo, “Silicon nitride tri-layer vertical Y-junction and 3D couplers with arbitrary splitting ratio for photonic integrated circuits,” Opt. Express 25(9), 10474–10483 (2017). [CrossRef]
16. W. D. Sacher, J. C. Mikkelsen, P. Dumais, J. Jiang, D. Goodwill, X. Luo, Y. Huang, Y. Yang, A. Bois, P. G.-Q. Lo, E. Bernier, and J. K. S. Poon, “Tri-layer silicon nitride-on-silicon photonic platform for ultra-low-loss crossings and interlayer transitions,” Opt. Express 25(25), 30862–30875 (2017). [CrossRef]
17. S. Tondini, C. Castellan, M. Mancinelli, C. Kopp, and L. Pavesi, “Methods for low crosstalk and wavelength tunability in arrayed-waveguide grating for on-silicon optical network,” J. Lightwave Technol. 35(23), 5134–5141 (2017). [CrossRef]
18. U. Khana, M. Fiersb, Y. Xinga, and W. Bogaertsa, “Experimental phase-error extraction and modelling in silicon photonic arrayed waveguide gratings,” Proc. SPIE 11285, 1128510 (2020). [CrossRef]
19. S. S. Cheung and M. R. T. Tan, “Silicon nitride (Si3N4) (De-) multiplexers for 1-µm CWDM optical interconnects,” J. Lightwave Technol. 38(13), 3404–3413 (2020). [CrossRef]
20. J. Park, M. Kwack, J. Joo, and G. Kim, “Low-loss single mode operation in silicon multi-mode arrayed waveguide grating with a double-etched inverse taper structure,” J. Opt. 19(8), 085801 (2017). [CrossRef]
21. J. F. Bauters, J. R. Adleman, M. J. R. Heck, and J. E. Bowers, “Design and characterization of arrayed waveguide gratings using ultra-low loss Si3N4 waveguides,” Appl. Phys. A 116(2), 427–432 (2014). [CrossRef]
22. B. Yang, Y. Zhu, Y. Jiao, L. Yang, Z. Sheng, S. He, and D. Dai, “Compact arrayed waveguide grating devices based on small SU-8 strip waveguides,” J. Lightwave Technol. 29(13), 2009–2014 (2011). [CrossRef]
23. Y. Barbarin, X. J. M. Leijtens, E. A. J. M. Bente, C. M. Louzao, J. R. Kooiman, and M. K. Smit, “Extremely small AWG demultiplexer fabricated on InP by using a double-etch process,” IEEE Photonics Technol. Lett. 16(11), 2478–2480 (2004). [CrossRef]
24. J. Park, J. Joo, G. Kim, S.-W. Yoo, and S. Kim, “Low-crosstalk silicon nitride arrayed waveguide grating for the 800-nm band,” IEEE Photonics Technol. Lett. 31(14), 1183–1186 (2019). [CrossRef]
25. X. Jiang, Z. Yang, Z. Liu, Z. Q. Dang, Z. Ding, Q. Chang, and Z. Zhang, “3D integrated wavelength demultiplexer based on a square-core fiber and dual-layer arrayed waveguide gratings,” Opt. Express 29(2), 2090–2098 (2021). [CrossRef]
26. X. Zhu, W. Hong, N. Bai, and X. Sun, “Theoretical investigation of compact high-resolution interleaved arrayed waveguide gratings with multi-layer structures,” OSA Continuum 3(12), 3332–3342 (2020). [CrossRef]
27. FDTD, MODE, Lumerical, https://www.lumerical.com/
28. K. Shang, S. Pathak, C. Qin, and S. J. B. Yoo, “Low-loss compact silicon nitride arrayed waveguide gratings for photonic integrated circuits,” IEEE Photonics J. 9(5), 1–5 (2017). [CrossRef]
