Open Access
Add to BibSonomy
Abstract
Using cascaded Mach-Zehnder interferometers (CMZIs) provides an attractive option for realizing coarse wavelength-division (de)multiplexing (CWDM) filters with low losses, low crosstalk, flat tops, and high scalability. However, they usually have large footprints and insufficient fabrication tolerances, due to the inferior performance of conventional directional couplers (DCs) used for MZIs. Here, a four-channel CMZI wavelength-division (de)multiplexer based on novel Bezier-shape DCs with compact footprints, broad bandwidths and decent fabrication tolerances. For the fabricated (de)multiplexer with 20-nm channel spacing, the excess loss is less than 0.5 dB and the crosstalk is lower than −19.5 dB in the 1-dB bandwidth of 12.8 nm. For the case with a core-width deviation of ±20 nm, the device still performs very well with low losses and low crosstalk. Compared to the state-of-the-art MZI-based CWDM filters, the present device has slightly high performances and a footprint of 0.012 mm2 shrunk greatly by ∼3-folds. This work can be extended for more channels and other material platforms.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
On-chip optical filters [1] have already gained significant interests for various applications, including optical interconnects [2], on-chip spectroscopy [3,4], optical computing [5,6], etc. For example, optical filters are playing a very important role in coarse wavelength-division multiplexing (CWDM) systems, which has large channel spacing to be immune from random wavelength shifts. Currently, various on-chip WDM filters have been demonstrated based on arrayed-waveguide gratings (AWGs) [7], planar concave gratings (PCGs) [8], multimode interferometers (MMIs) [9], Bragg gratings [10–12], micro-ring resonators (MRRs) [4,13] as well as Mach-Zehnder interferometers (MZIs) [14–17,23,24]. Among them, AWGs [7] and PCGs [8] are suitable for realizing the (de)multiplexers with narrow channel-spacing and numerous channels, and have been popular for dense WDM (DWDM) systems [7,8]. MMIs usually have relatively large fabrication tolerances and relatively high excess losses (ELs) of ∼2 dB as well as limited bandwidths of 8.5 nm [9]. In contrast, MRRs [4] are popular for realizing compact WDM filters with low losses. However, it is usually difficult to achieve the central wavelengths aligned critically due to the random fabrication errors. As an alternative, Bragg gratings provide a possible solution for realizing CWDM filters because it is very flexible to design the bandwidths and the central wavelengths as desired. Particularly, multimode waveguide gratings were introduced to be circulator-free and currently high-performance multi-channel CWDM filters have been realized with box-like responses, which have low losses and low crosstalks [10–12]. In general, the device with fine periodic structures, e.g., subwavelength gratings (SWG) [19], Bragg gratings [10–12], etc., may have great challenges for the fabrications.
In contrast, using cascaded MZIs (CMZIs) provides an attractive option for realizing CWDM filters. Usually a CMZI-based CWDM filter consists of n directional couplers (DCs) and (n−1) pairs of interference arms. To construct a CWDM filter with 2 l channels, one needs l stages of MZIs in cascade, including (20 + 21+…+2l−1) CMZIs in total, in which case many DCs are used [14,15]. Apparently, the footprint, the performance, the fabrication tolerance of a multi-channel MZI-based CWDM filter highly depends on the DCs used [14]. As demonstrated, MZI-based CWDM filters [14–17] can achieve flat-top responses with low ELs. However, they often suffer from low fabrication tolerances and relatively large footprints, especially when multiple channels are needed. As demonstrated in [14], the MZI-based CWDM filter with straight DCs was realized with a large footprint of ∼0.11 mm2 and narrow bandwidths. Arc-bent DCs with broad bandwidths and improved fabrication tolerances were used and a four-channel MZI-based CWDM filter was realized with high performance [17]. However, the arc-bent DCs usually have large footprints, preventing the footprint shrinking.
In this work, we propose and demonstrate a flat-top four-channel MZI CWDM filter by using Bezier-shape DCs [18] with compact footprints, large bandwidths, low ELs, decent fabrication tolerances. For the fabricated CWDM filter with a channel spacing of ∼20 nm, the measured 0.5-dB, 1-dB, 3-dB bandwidths are as large as ∼15 nm, 16.5 nm, 20 nm for all four channels. Furthermore, the footprint of the device is as small as ∼0.012 mm2, which is shrunk greatly by ∼3-folds compared to the previously state-of-the-art work [17], owing to the Bezier-shape DCs developed by our semi-inverse design method [18,19].
2. Structure and design
In this work, we demonstrate a four-channel CWDM filter, which is based on the silicon-on-insulator (SOI) wafer with a 220-nm-thick Si core layer and a 2-µm-thick BOX layer and a silicon dioxide upper-cladding. As shown in Fig.(a), the device is designed with multiple stages in cascade. For example, consider the case with four wavelength-channels of 1523, 1543, 1563 and 1583 nm. These four channels are first interleaved into two streams by Filter #1, i.e., the odd channels and the even channels. The two channels of 1523-nm and 1563-nm are then separated by Filter #2, while the two channels of 1543-nm and 1583-nm are then separated by Filter #3, as shown in Fig. 1. Figure 1(b) shows the configuration of each stage of filter consisting of three pairs of 500-nm-wide interference-arms and four DCs. The coupling ratios of DCs #1-#4 are optimized to be 0.5, 0.2, 0.2 and 0.04, respectively [17]. To align the center wavelengths, the length differences between the two arms of each phase shifter are chosen in the Table 1. As shown in the Fig. 1(c), each DC is designed by using Bezier curves with uniform waveguide widths of w = 500 nm. Such a DC consists of two flexibly adjustable shaped bending sections (green part) and two transition sections (yellow part) connecting the bending section and the input/output sections (blue part) [18]. And points Pnup/down (n = 1, 2, 3…) on the Bezier-curves are used to define the shape of the waveguides [18].
Fig. 1. Design of the four-channel CWDM filter based on CMZIs. (a) Schematic of the proposed CWDM filter consisting of multi-stages of CMZIs in cascade. (b) Configuration of each stage of filters with CMZIs. (c) Configuration of the Bezier-shape DC.
Table 1. The length differences between the interference-arm pairs in Filters #1, #2, and #3.
Figures 2(a)-(c) show the optimization process of Bezier-shape DCs with three different coupling ratios of 0.5, 0.2, 0.04. The decrease in figure of merit (FOM) becomes difficult as the coupling ratio of the DCs increases, and the total optimized simulation time is ∼18 h, ∼9.5 h, and ∼4 h for coupling ratios of 0.5, 0.2, and 0.04, respectively. The FOM for the wavelength λi is given by [18],
Fig. 2. Design of the Bezier-curve-shape DCs. (a)-(c) The figure of merit (FOM) of the designed directional couplers with the coupling ratio of 0.04 (a), 0.2 (b), 0.5 (c). (d)-(f) The simulated coupling ratio spectra for the Bezier-curve-shape DCs with waveguide width deviation δw = −20, −10, 0, 10, 20 nm for the coupling ratio of 0.04 (d), 0.2 (e), 0.5 (f). (g)-(i) The simulated light propagation fields at the wavelengths of 1490/1550/1610 nm with the coupling ratio of 0.04 (g), 0.2 (h), 0.5 (i).
Figure 2(a) illustrates the optimization process for Bezier-shape DCs with a coupling ratio of 0.5. When the optimization of step 1 is slow, the optimization of step 2 is performed by manually changing the shape or adding optimization points, i.e., increasing the order of the Bezier curves. A FOM is obtained as 0.125 after optimized with step 1 to step 4. Similarly, the FOM is optimized to 0.145 and 0.035 for the coupling ratios of 0.2 and 0.04, respectively, as shown in Fig. 2(b) and Fig. 2(c). The simulation time is acceptable regarding that a regular personal computer (CPU i5 11400F, only 4 cores used, and 32 Gb RAM with no GPU used) was used. As discussed in our previous work [18,19], the present method has the advantage of handling complex design problems with relatively large device footprints with acceptable time cost. The wavelength dependence of the coupling ratio for the Bezier-shape DCs is calculated by using the 3D Finite Difference Time Domain (FDTD) method, as shown in Figs. 2(d)-(f). When δw = 0, the Bezier-shape DC with a target coupling ratio of 0.5 has a large bandwidth of ∼125 nm for the coupling ratio between 0.45-0.55. Similarly, the Bezier-shape DC with the target coupling ratios of 0.2/0.04 exhibits a large bandwidth of ∼110 nm for the coupling ratios between 0.15/0.03 and 0.25/0.05, respectively. When the width deviations of +/−20 nm are induced, the Bezier-shape DCs with target coupling ratios of 0.5, 0.2, 0.04 respectively have bandwidths of ∼125/105, ∼95/70, ∼120/80 nm, showing competitive performance. In the Supplement 1, we also give an analysis for the dependence of the coupling ration on the core height variation. Figures 2(g)-(i) show the simulated light propagation in the Bezier-shape DCs designed with coupling ratios of 0.5, 0.2, and 0.04 (at the central wavelength) when operating at three wavelengths of 1490, 1550, and 1610 nm, respectively, which directly verifies the ability of broadband operation for the present Bezier-shape DCs. It should be noted that the demonstration given above for the C band can be also extended to the other bands such as O band, L band, etc. We give a comparison for straight DCs, arc-bent DCs, and the present Bezier-shape DCs with different target coupling ratios (see Supplement 1). Arc-bent DCs are defined by bending radii R, arc angles θ and waveguide width w [20]. All three types of DCs are designed with the same waveguide widths of w = 500 nm. Their gaps are set to 150-160 nm, which are compatible to the 130-nm silicon photonics commercial foundry process technologies and the electron-beam lithography technology. The comparison leads to the conclusion that the present Bezier-shaped DCs offer considerably higher performance compared to regular arc-bent DCs, and due to the more degrees of freedom the footprint is considerably shrunken by ∼2-folds. As a result, it is expected to realize high-performance MZI filters with compact footprints and decent fabrication tolerances by introducing Bezier-shape DCs.
Figure 3 shows the simulated transmission spectra of the designed MZI CWDM filters based on Bezier-shape DCs by utilizing the transfer matrix method. The transmission spectra of the CMZI based on straight DCs, bent DCs, are also shown in Supplement 1. As expected, the CWDM filter based on Bezier-shape DCs shows a broader operation bandwidth than the devices with straight DCs and bent DCs, due to the bandwidth difference between the DCs. Figure 3(b) shows that the CTs are −24.8, −22.6, −23.5, and −19.8 dB at four center wavelengths, respectively. Furthermore, the CT is less than ∼−19.5 dB over a ∼12.8-nm bandwidth for each channel. The 0.5-dB, 1-dB and 3-dB bandwidths are calculated to be ∼15, 16.5 and 20 nm for all the four channels.
Fig. 3. Simulated transmission spectra. (a) Filter #1 based on Bezier-shape DCs, (b) Four-channel CWDM filter based on Bezier-shape DCs. Here the mode numbers in S parameters correspond to the port numbers given in Fig. 1(b).
3. Fabrication and measurement
In Fig. 4, the designed four-channel CWDM filter was fabricated on a silicon-on-insulator (SOI) wafer with a 220 nm-thick top-silicon layer and a 2-µm-thick buried dioxide layer. The silicon photonic waveguides were fabricated by electron-beam lithography and inductively-coupled plasma (ICP) dry-etching. Then the cladding layer is a 2.2-µm-thick silicon dioxide deposited by chemical vapor deposition. Figure 4(a) shows the microscope images of the fabricated CWDM filter, whose total size is as small as ∼ 210 × 58 µm2. Figure 4(b) shows the SEM images of the Filter #1 and Filters #2, #3. Furthermore, Fig. 4(c) shows the SEM images of Bezier-shape DCs with coupling ratios of 0.5, 0.2, 0.04.
Fig. 4. Fabricated devices. (a) The microscope image of the fabricated 4-channel CWDM filter on silicon. (b) SEM images of the three cascaded MZIs. (c) SEM image of the Bezier-curve-shape DCs.
Figure 5 shows the measured transmission spectra for the fabricated CWDM filter when the width deviations δw varies from −20 nm to 20 nm. As shown in Fig. 5(a), when there is no width deviation (δw = 0), the ELs at the center wavelengths for the four channels are <0.5 dB, while the 0.5 dB/1 dB/3 dB-bandwidths are respectively ∼15/16.5/20 nm. Meanwhile, the CTs at the center wavelengths for the four channels are −23.8/−23.5/−25.7/−24.1 dB, respectively. Besides, all four channels are flat-top and have broad bandwidths of 12.8 nm, within which the CT is < −19.5 dB. The adjacent channel isolation and non-adjacent channel isolation are characterized to be >17 dB and >18 dB, which illustrates that broadband Bezier-shaped DCs contribute to the MZI performance. It can be seen that the measured results are close to the simulated ones shown in Fig. 3(f). In the future, we will further optimize the interference arm waveguide width to reduce the random phase fluctuations, which is conducive to increasing the tolerance.
Fig. 5. Measured transmission spectra of the fabricated CWMD filter with some waveguide width deviation δw. (a) δw = 0, (b) δw = −20 nm, (c) δw = −10 nm, (d) δw = 10, (e) δw = 20 nm. The mode numbers in S parameters are consistent with the port numbers in Fig. 1(a).
When there are some width deviations of +/−20 nm and +/−10 nm, as shown in Figs. 5(b)-(e), the EL does not increase almost, while the CT sightly increases. Specifically, when δw=+/−10 nm, the CT is less than −18.5/19.5 dB over a 12.8-nm bandwidth for all channels (see Fig. 5(c) and 5(d)). When δw=+/−20 nm, the CT is less than −15.5 dB over a 12.8-nm pass band for all channels (see Fig. 5(b) and 5(e)). As shown in Fig. 5, the center wavelengths have red-shifts as the width deviation δw increases, owing to the increases of the phase differences of MZIs. Such an issue can be alleviated by introducing broaden arm waveguides for the MZIs, as suggested in Refs. [21,22,25].
Table 2 gives a comparison of the state-of-the-art CWDM (de)multiplexers reported in recent years. AWGs and PCGs are suitable for DWDM applications due to their limited bandwidths. For example, the demonstrated AWGs [7] and PCGs [8] with 20 nm channel spacing have a 1-dB bandwidth of 5 nm. Meanwhile, they have much larger ELs than MZI-based CWDM filters due to the mode mismatch when light propagates forward in AWGs and PCGs. Similarly, AMMI filters have large ELs (∼2 dB) and limited bandwidths (8.5 nm) as shown in [9]. In contrast, Bragg gratings [10–12] can realize high-performance filters with low ELs, low CT, and broad bandwidths. On the other hand, Bragg gratings usually require fine fabrication regarding their tiny feature sizes. As a comparison, CMZI-based CWDM filters do not have any tiny structures and no special fabrication is needed. Among the CMDM filters realized by CMZIs with straight DC [14], MMI [16], and bent DC [17], the CMZI with bent DCs [17] achieves low CT of −20 dB and low ELs of ∼ 1 dB as well as a footprint of ∼0.03 mm2, while the fabrication tolerance is also decent. Note that this CWDM filter in [17] is developed for the O-band. Thus, the device footprint would be even larger when designed for the C band (which has longer wavelengths and is considered in this paper). Finally, it can be seen that our device working in the C-band achieves high performance with low CT of < −19.5 dB, low ELs of ∼ 0.4 dB and broad 0.5-dB-bandwidths of 15 nm, which is comparable to the state-of-the-art work [17], while the CWDM filter has a footprint of ∼0.012 mm2 (which is shrunk by ∼3-folds than the device with bent DCs). As a summary, the present CWDM filter based on CMZIs with Bezier-shape DCs has shown advantages of low ELs, flat tops, high scalability, footprint compactness and fabrication ease.
Table 2. Comparison of the reported four-channel CWDM (de)multiplexers on silicon.
4. Conclusion
In summary, we have designed and demonstrated four-channel CMZI-based wavelength (de)multiplexers by using Bezier-shape directional couplers. The Bezier-shape DCs developed by an efficient inverse design method. The low search-space-dimension and high design degree of freedom guarantee the Bezier-shape DCs to have a low loss (< 0.1 dB) and a large bandwidth (>100 nm) within a compact area. The Bezier-shape DCs which work well with broad bandwidth can have excellent fabrication tolerances. The three designed Bezier-shape DCs with the coupling ratios of 0.5:0.5, 0.2:0.8 and 0.04:0.96 have slightly better performance and much shorter lengths in contrast to bent DCs. Based on these Bezier-shape DCs, three MZIs in cascade have been developed and act as two-stages of interleavers to form a four-channel wavelength demultiplexer. The fabricated wavelength (de)multiplexer with 20-nm channel-spacing has box-like spectral responses with low CT < −19.5 dB and low ELs < 0.5 dB. The measured 0.5-dB, 1-dB, 3-dB wavelength bands are ∼15 nm, 16.5 nm, 20 nm for all the 4 channels. In addition, the waveguide width deviation of ±20 nm causes slight performance degradation only in loss, crosstalk, and bandwidth for the wavelength (de)multiplexer. Importantly, the present Bezier-DC-based CMZI wavelength demultiplexer has comparable performance and a compact footprint shrunk by ∼3-folds compared to the state-of-the-art bent-DC based CMZI wavelength demultiplexer. Because the phase errors due to fabrication non-uniformity are the key metric that dominates fabrication variability, we will optimize the phase error afterwards. The present concept can be extended to more channel applications and other material waveguide platforms. Since the present wavelength (de)multiplexer exhibits high compactness and fabrication ease as well as performance excellence (such as low crosstalk, low losses, high scalability), it shows great potential for applications such as CWDM optical communications.
Funding
National Major Science and Technology Projects of China (2018YFB2200200/2018YFB2200201); The Leading Innovative and Entrepreneur Team Introduction Program of Zhejiang (2021R01001); Fundamental Research Funds for the Central Universities (2021QNA5002); Natural Science Foundation of Zhejiang Province (LD19F050001, LD22F040004, LQ21F050006, LZ18F050001); National Natural Science Foundation of China (61961146003, 62205292, 91950205, 92150302); National Science Fund for Distinguished Young Scholars (61725503).
Acknowledgments
The authors thank the Applied Nanotools (ANT) for help processing device for this work.
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.
Supplemental document
See Supplement 1 for supporting content.
References
1. D. Liu, H. Xu, Y. Tan, et al., “Silicon photonic filters,” Microw Opt Technol Lett 63(9), 2252–2268 (2021). [CrossRef]
2. L.-W. Luo, N. Ophir, C.P. Chen, et al., “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014). [CrossRef]
3. D. Pohl, M. Reig Escalé, M. Madi, et al., “An integrated broadband spectrometer on thin-film lithium niobate,” Nat. Photonics 14(1), 24–29 (2020). [CrossRef]
4. L. Zhang, M. Zhang, T. Chen, et al., “Ultrahigh-resolution on-chip spectrometer with silicon photonic resonators,” Opto-Electron. Adv. 5(7), 210100 (2022). [CrossRef]
5. Y. Shen, N.C. Harris, S. Skirlo, et al., “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11(7), 441–446 (2017). [CrossRef]
6. I.A.D. Williamson, T.W. Hughes, M. Minkov, et al., “Reprogrammable Electro-Optic Nonlinear Activation Functions for Optical Neural Networks,” IEEE J. Select. Topics Quantum Electron. 26(1), 1–12 (2020). [CrossRef]
7. P. Pan, J. An, Y. Wang, et al., “Compact 4-channel AWGs for CWDM and LAN WDM in data center monolithic applications,” Opt. Laser Technol. 75, 177–181 (2015). [CrossRef]
8. S. Pathak, P. Dumon, D. Van Thourhout, et al., “Comparison of AWGs and Echelle Gratings for Wavelength Division Multiplexing on Silicon-on-Insulator,” IEEE Photonics J. 6(5), 1–9 (2014). [CrossRef]
9. Y. Hu, R.M. Jenkins, F.Y. Gardes, et al., “Wavelength division (de)multiplexing based on dispersive self-imaging,” Opt. Lett. 36(23), 4488 (2011). [CrossRef]
10. M. Hammood, A. Mistry, H. Yun, et al., in Optical Fiber Communication Conference (OFC) 2020 (Optica Publishing Group, San Diego, California, 2020), p. M3F.5.
11. D. Liu, M. Zhang, Y. Shi, et al., “Four-Channel CWDM (de)Multiplexers Using Cascaded Multimode Waveguide Gratings,” IEEE Photonics Technol. Lett. 32(4), 192–195 (2020). [CrossRef]
12. J. He, D. Liu, B. Pan, et al., “High-performance lithium-niobate-on-insulator optical filter based on multimode waveguide gratings,” Opt. Express 30(19), 34140 (2022). [CrossRef]
13. D. Liu, J. He, Y. Xiang, et al., “High-performance silicon photonic filters based on all-passive tenth-order adiabatic elliptical-microrings,” APL Photonics 7(5), 051303 (2022). [CrossRef]
14. S.-H. Jeong, D. Shimura, T. Simoyama, et al., “Si-nanowire-based multistage delayed Mach–Zehnder interferometer optical MUX/DeMUX fabricated by an ArF-immersion lithography process on a 300 mm SOI wafer,” Opt. Lett. 39(13), 3702 (2014). [CrossRef]
15. F. Horst, W.M.J. Green, S. Assefa, et al., “Cascaded Mach-Zehnder wavelength filters in silicon photonics for low loss and flat pass-band WDM (de-)multiplexing,” Opt. Express 21(10), 11652 (2013). [CrossRef]
16. Z. Zhao, Z. Li, J. Niu, et al., “Eight-Channel LAN WDM (De)Multiplexer Based on Cascaded Mach–Zehnder Interferometer on SOI for 400GbE,” Photonics 9(4), 252 (2022). [CrossRef]
17. H. Xu and Y. Shi, “Flat-Top CWDM (De)Multiplexer Based on MZI With Bent Directional Couplers,” IEEE Photonics Technol. Lett. 30(2), 169–172 (2018). [CrossRef]
18. L. Yu, J. Guo, H. Xiang, et al., “High-performance 2×2 bent directional couplers designed with an efficient semi-inverse design method,” J. Lightwave Technol. 1, 1 (2023).
19. J. Guo, L. Yu, H. Xiang, et al., “Realization of advanced passive silicon photonic devices with subwavelength grating structures developed by efficient inverse design,” Adv. Photon. Nexus 2(02), 1 (2023). [CrossRef]
20. S. Chen, Y. Shi, S. He, et al., “Low-loss and broadband 2 × 2 silicon thermo-optic Mach–Zehnder switch with bent directional couplers,” Opt. Lett. 41(4), 836 (2016). [CrossRef]
21. L. Song, W. Liu, Y. Peng, et al., “Low-Loss Calibration-Free 2 × 2 Mach-Zehnder Switches with Varied-Width Multimode-Interference Couplers,” J. Lightwave Technol. 40(15), 5254–5259 (2022). [CrossRef]
22. L. Song, T. Chen, W. Liu, et al., “Towards calibration-free Mach–Zehnder switches for next-generation silicon photonics,” Photonics Res. 10(3), 793 (2022). [CrossRef]
23. H. Xu, L. Liu, and Y. Shi, “Polarization-insensitive four-channel coarse wavelength-division (de)multiplexer based on Mach–Zehnder interferometers with bent directional couplers and polarization rotators,” Opt. Lett. 43(7), 1483–1486 (2018). [CrossRef]
24. H. Xu, D. Dai, and Y. Shi, “Low-crosstalk and fabrication-tolerant four-channel CWDM filter based on dispersion-engineered Mach-Zehnder interferometers,” Opt. Express 29(13), 20617–20631 (2021). [CrossRef]
25. L. Song, H. Li, and D. Dai, “Mach-Zehnder silicon photonic switch with low random phase errors,” Opt. Lett. 46(1), 78–81 (2021). [CrossRef]
