Open Access
Add to BibSonomy
Abstract
A polarization beam-splitting multimode filter using pixelated waveguides has been presented and experimentally demonstrated in this paper. Finite difference time domain method and direct binary search optimization algorithm are employed to optimize pixelated waveguides to realize compact size, broad bandwidth, large extinction ratio, low insertion loss, and good polarization extinction ratio. Measurement results show that, in a wavelength range from 1520 to 1560 nm, for the fabricated device working at transverse-electric polarization, the measured insertion loss is less than 1.23 dB and extinction ratio is larger than 15.14 dB, while for transverse-magnetic polarization, the corresponding insertion loss lower than 0.74 dB and extinction ratio greater than 15.50 dB are realized. The measured polarization extinction ratio larger than 15.02 dB is achieved. The device’s length is only 15.4 µm.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Due to excellent CMOS compatibility, high speed, and broad bandwidth, silicon photonics technology has been seen as a highly competitive solution of satisfying the rapidly growing demand for transmission capacity [1,2]. To expand the transmission capacity, diverse technologies, such as polarization division multiplexing, wavelength division multiplexing, and mode division multiplexing (MDM) have been investigated. Among them, each mode of the MDM system can be regarded as a separate data channel, and the corresponding transmission capacity is significantly improved by increasing the number of supported guided modes [3,4]. Up to now, various photonic devices used in on-chip integrated MDM systems have been extensively studied, including mode converters [5,6], polarization beam splitters [7,8], mode multiplexers [9,10], multimode waveguide bend [11,12] etc.
Mode filters are one of basic components in on-chip integrated MDM systems, which can reduce modal crosstalk significantly and improve system stability by removing unwanted modes or achieve modal routing by passing the desired modes [13]. In recent years, multimode optical filters have been demonstrated by utilizing different structures, for instance, Mach-Zender interferometer [14,15], multimode interference coupler [16], one-dimensional photonic crystal waveguide [17], subwavelength grating [18], asymmetric directional coupler [19]. Nevertheless, most of the reported multimode optical filters only support single polarization state operation. Although a polarization-insensitive mode filter using the asymmetric directional coupler can handle the first six modes, it still encounters the drawback of large footprint [19]. Therefore, a polarization-insensitive multimode optical filter with compact size is highly desired. Meanwhile, separating the different polarization states after mode filtering onto different links requires a cascade of the polarization beam splitter, which occupies a larger size. To the best of our knowledge, a polarization beam-splitting multimode filter (PBSMF) combining polarization beam splitting with mode filtering functions has not been discussed before.
In this paper, we present and experimentally demonstrate a PBSMF using pixelated waveguides. The pixelated waveguides are optimized by using finite difference time domain (FDTD) method and direct binary search (DBS) optimization algorithm to achieve broad bandwidth (BW), large extinction ratio (ER), low insertion loss (IL), good polarization extinction ratio (PER), and compact size. Experimental results reveal that, for the fabricated PBSMF working at transverse-electric (TE) polarization, the measured IL < 1.23 dB and ER > 15.14 dB are obtained in a wavelength range from 1520 to 1560 nm, while for transverse-magnetic (TM) polarization, the corresponding IL < 0.74 dB and ER > 15.50 dB are achieved. The measured PER > 15.02 dB is realized. In addition, the length of the fabricated PBSMF is only 15.4 µm.
2. Design and analysis
Figure 1(a) depicts the structure of the presented PBSMF, which contains an asymmetric directional coupler using the pixelated waveguide and a mode filter utilizing a pixelated region. By altering the pixels’ materials, the corresponding effective refractive index is adjusted, thereby controlling the behavior of the optical field. Since the input optical field and the expected output optical field are pre-known, the relevant refractive index distribution requires to be gradually optimized to decrease the deviation between the expected output optical field and the actual one, and consequently the predetermined function could be realized. A cross-sectional view of the coupling region in the asymmetric directional coupler is described in Fig. 1(b). Figure 1(c) shows the effective refractive indexes of the first seven modes in a silicon strip waveguide with a thickness of Hs = 220 nm changing with the waveguide width. Due to the phase matching, the input TM1 mode can be coupled into the pixelated waveguide, and then comes out from the output O1, while other modes perform the forward propagation and enter the mentioned mode filter using a pixelated region. Figure 1(d) illustrates the detail diagram of the pixelated unit. The shape for each pixel is a square of 200 × 200 nm2 with a central circular hole, in which the logical state is ‘‘1’’ or ‘‘0’’, standing for the hole filled with SiO2 or Si. The diameter Dt is 100 nm and the spacing width G2 is also 100 nm. After passing through the pixelated region, the input TE0, TE2, TM0, and TM2 modes are blocked and the input TE1 mode exits from the output port O2. To effectively separate the TM1 mode from other modes and pick out the TE1 mode from the remaining modes, structural parameters of the proposed PBSMF ought to be carefully designed.
Fig. 1. (a) Schematic diagram of the proposed polarization beam-splitting multimode filter (b) Cross-sectional view of the coupling region in the asymmetric directional coupler along the dotted line X-X ‘ (c) Effective refractive indexes of the first seven modes in a silicon strip waveguide with a thickness of Hs = 220 nm as a function of the waveguide width (d) Detail diagram of the pixelated unit.
The widths W1 and W2 are chosen as W1 = 1.30 µm and W2 = 1.48 µm to support TE0, TE1, TE2, TM0, TM1, and TM2 modes and ensure efficient coupling of TM1 mode. The spacing width G1 is 100 nm. The coupling length L1 is selected to be 10 µm. The pixelated region in the mode filter comprises three pixelated rectangle waveguides. The corresponding lengths and widths are chosen as L2 = 4.40 µm, L3 = 5.40 µm, L4 = 4.30 µm, W3 = 1.20 µm, and W4 = 0.40 µm. In order to improve the coupling efficiency in a short coupling length and enhance the passing rate of the desired mode in a compact length, the FDTD method and DBS optimization algorithm [20,21] are adopted to optimize the corresponding logical states of pixels in the pixelated waveguide and pixelated region. The definition of the optimization figure of merit (FoM) for the asymmetric directional coupler or mode filter is written as:
- (1) Initialize all pixels in the pixelated waveguide (the pixelated region), the logical states of all pixels are set to be “0”, and the variables p and q are set as p = 1 and q = 1.
- (2) Carry out FDTD simulation and calculate the FoM1 (FoM2).
- (3) Randomly select a pixel, change its logical state, carry out FDTD simulation, and recalculate the FoM1 (FoM2). If the FoM1 (FoM2) is improved, the logical state will be saved. Otherwise, the logical state is flipped.
- (4) The variables p and q will set to be p = 1 and q = q + 1, if p > 343 (305) is satisfied. Otherwise, renew the variable p to be p = p + 1, and return to step 3.
- (5) Terminate the optimization when q > 10 or FoM1 (FoM2) > 0.99 is satisfied. Otherwise, return to step 3.
FoM1 and FoM2 changing with the number of iterations are described in Fig. 2. When the number of iterations reaches 8, the values of FoM1 and FoM2 are beginning to stabilize. The weight coefficients are set as α1=α2 = 1 in the simulation.
Figure 3 depicts the simulated light propagation of the optimized PBSMF. As shown in Figs. 3(a)–3(f), when TE1, TE0, TE2, TM1, TM0, and TM2 modes are input into the port I1, the TE0, TE2, TM0, and TM2 modes are blocked, while the TE1 mode passes through the pixelated region and comes out from the port O2, and the TM1 mode is coupled into the pixelated waveguide and exits from the port O1. In other words, for the designed PBSMF, the device’s function can be well executed.
Fig. 3. At 1550 nm, the simulated light propagation in the optimized PBSMF with the input (a) TE1, (b) TE0, (c) TE2, (d) TM1, (e) TM0, or (f) TM2 mode.
Figures 4(a)–4(d) depict the simulated ER, IL, and PER of the designed PBSMF changing with the wavelength. For the designed PBSMF, the simulated ERTM1-TM0 > 20.57 dB, ERTM1-TM2 > 20.26 dB, ERTM1-TE0 > 18.22 dB, ERTM1-TE2 > 17.10 dB, ERTM1-TE1 > 17.72 dB, ILTM1 < 0.21 dB, and PERTM1 > 16.98 dB are obtained from 1500 to 1560 nm. Meanwhile, the simulated ERTE1-TE0 > 23.94 dB, ERTE1-TE2 > 19.12 dB, ERTE1-TM0 > 20.50 dB, ERTE1-TM1 >16.43 dB, ERTE1-TM2 > 26.00 dB, ILTE1 < 0.76 dB and PERTE1 > 17.21 dB are achieved from 1500 to 1560 nm. At 1550 nm, the simulated ERTM1-TM0, ERTM1-TM2, ERTM1-TE0, ERTM1-TE1, ERTM1-TE2, ILTM1, and PERTM1 are 21.23 dB, 21.00 dB, 18.65 dB, 18.89 dB, 18.21 dB, 0.126 dB and 20.11 dB. The simulated ERTE1-TE0, ERTE1-TE2, ERTE1-TM0, ERTE1-TM1, ERTE1-TM2, ILTE1, and PERTE1 are 23.99 dB, 28.53 dB, 20.86 dB, 19.95 dB, 29.52 dB, 0.29 dB, and 18.73 dB. The IL, ER and PER involved above are defined as:
Fig. 4. Simulated (a), (b) ER, (c) IL, and (d) PER of the designed PBSMF changing with the wavelength.
Figure 5 depicts the impact of the diameter variation ΔD and the waveguide width variation ΔW on the simulated IL, PER and ER of the designed PBSMF. As seen in Fig. 5, different values of ΔD and ΔW have a significant impact on the simulated IL, ER and PER. When ΔW increases from -20 to 20 nm and the corresponding ΔD decreases from 20 to -20 nm, within a bandwidth from 1500 to 1560 nm, IL < 1.18 dB, PER > 12.52 dB, and ER > 12.34 dB are realized in TM polarization, while in TE polarization, the calculated IL < 1.50 dB, PER > 11.94 dB, ER > 10.94 dB are achieved.
Fig. 5. Simulated (a)-(j) ER, (k),(l) IL and (m),(n) PER of the designed PBSMF changing with ΔW and ΔD.
3. Fabrication and characterization
The designed PBSMF is realized on an SOI wafer. The device pattern was first determined by adopting electron beam lithography. And then, by utilizing two-step inductively coupled plasma dry etching process, the silicon layer was etched. Finally, by employing plasma enhanced chemical vapor deposition, the SiO2 upper-cladding layer was deposited. The microscope image of the fabricated PBSMFs cascaded with three-mode (de)multiplexers working at TE and TM polarizations and two pairs of the corresponding three-mode (de)multiplexers is described in Fig. 6. Cascaded particle-swarm-optimized counter-tapered couplers [22] are adopted to construct the above-mentioned three-mode (de)multiplexers.
A broadband light source, a polarization controller, and an optical spectrum analyzer were employed to characterize the fabricated PBSMFs and the related three-mode (de)multiplexers. TM-polarized or TE-polarized light beam was coupled into and out of the fabricated devices by employing the focusing grating couplers or the photonic crystal structure. The two pairs of three-mode (de)multiplexers were characterized first. After that, the fabricated silicon PBSMFs cascaded with the corresponding three-mode (de)multiplexers were measured. The measured transmission of any one mode in the silicon PBSMF was normalized by subtracting the transmission of the corresponding mode in a pair of three-mode (de)multiplexers. The measured ER, IL, and PER of the fabricated PBSMF are shown in Fig. 7. It can be found that, the measured ERTM1-TM0 > 18.76 dB, ERTM1-TM2 > 18.32 dB, ERTM1-TE0 > 16.39 dB, ERTM1-TE1 > 15.5 dB, ERTM1-TE2 > 16.05 dB, ILTM1 < 0.74 dB and PERTM1 > 15.02 dB are obtained from 1520 to 1560 nm. The measured ERTE1-TE0 > 20.49 dB, ERTE1-TE2 > 16.63 dB, ERTE1-TM0 > 16.88 dB, ERTE1-TM1 > 15.14 dB, ERTE1-TM2 > 23.89 dB, ILTE1 < 1.23 dB and PERTE1 > 15.04 dB are realized from 1520 to 1560 nm. At 1550 nm, the measured ERTM1-TM0, ERTM1-TM2, ERTM1-TE0, ERTM1-TE1, ERTM1-TE2, ILTM1 and PERTM1 are 19.18 dB, 19.27 dB, 16.81 dB, 15.85 dB, 16.65 dB, 0.63 dB and 16.61 dB, respectively. The ERTE1-TE0, ERTE1-TE2, ERTE1-TM0, ERTE1-TM1, ERTE1-TM2, ILTE1 and PERTE1 are measured to be 21.47 dB, 23.65 dB, 17.4 dB, 16.53 dB, 24.83 dB, 0.71 dB and 15.77 dB. The main reason for the slightly worse experimental results compared to the simulation results is as follows. Due to process deviations, the actual waveguide width and aperture deviates from the optimal value in varying degrees, resulting in decreased ER, increased IL, and narrowed BW. Note that in Figs. 5 and 7, it is observed that, the measured IL, PER, and ER are basically consistent with the simulated ones in the case of ΔW=+15 nm and ΔD = -15 nm. Furthermore, owing to the bandwidth limitation of the laser source, the measured BW is narrower than the simulated one. Table 1 lists the experimental performance comparison between our proposed PBSMF and other reported polarization-insensitive mode filter handling the first six modes. From Table 1, it can be found that, the proposed PBSMF in this work has a smaller IL, a wider BW, a more compact size, a good ER, and the polarization-dependent beam splitting capability. To further improve the performance of the presented PBSMF, more high-quality and high-precision fabrication processes and smaller minimum feature size can be used in the future.
Fig. 7. Measured ER in the case of (a) TM or (b) TE polarization, (c) IL, and (d) PER of the fabricated PBSMF
Table 1. Experimental performance comparison between our proposed PBSMF and other reported polarization-insensitive mode filter handling the first six modes.
4. Conclusion
In summary, a PBSMF using pixelated waveguides has been proposed, designed, and experimentally demonstrated. To realize broad BW, low IL, large ER, good PER, and compact size, FDTD method and DBS optimization algorithm are used for performing the optimization of the pixelated waveguides. The optimized PBSMF was fabricated on the SOI platform to verify the feasibility of the device design, and then the fabricated devices were characterized experimentally. The measurement results show that, within a BW from 1520 to1560 nm, for the filter working at TM polarization, the IL < 0.74 dB and ER > 15.50 dB are obtained, while for the filter working at TE polarization, the IL < 1.23 dB and ER > 15.14 dB are realized. The PER of the fabricated PBSMF is measured to be larger than 15.02 dB. Besides, the device’s length is only 15.4 µm. With these functionalities and properties, our proposed PBSMF can provide an attractive option for the construction of large-scale photonic integrated circuits and the implementation of MDM technology.
Funding
National Natural Science Foundation of China (62275134, 62234008, 61875098); Natural Science Foundation of Zhejiang Province (LY20F050003, LY20F050001); Youth Science and Technology Innovation Leading Talent Project of Ningbo (2023QL003); Natural Science Foundation of Ningbo (2022J099); The K. C. Wong Magna Fund in Ningbo University.
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. H. Atabaki, S. Moazeni, F. Pavanello, et al., “Integrating photonics with silicon nanoelectronics for the next generation of systems on a chip,” Nature 556(7701), 349–354 (2018). [CrossRef]
2. A. Rahim, T. Spuesens, R. Baets, et al., “Open-Access Silicon Photonics: Current Status and Emerging Initiatives,” Proc. IEEE 106(12), 2313–2330 (2018). [CrossRef]
3. K. Zou, K. Pang, H. Song, et al., “High-capacity free-space optical communications using wavelength- and mode-division-multiplexing in the mid-infrared region,” Nat. Commun. 13(1), 7662 (2022). [CrossRef]
4. 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]
5. Z. Yuan, Y. Wang, H. Fan, et al., “Silicon Subwavelength Gratings Assisted Ultra-Broadband Dual-Polarization Mode-Order Converter,” J. Lightwave Technol. 41(9), 1–11 (2023). [CrossRef]
6. H. Jia, H. Chen, T. Wang, et al., “Multi-Channel Parallel Silicon Mode-Order Converter for Multimode On-Chip Optical Switching,” IEEE J. Select. Topics Quantum Electron. 26(2), 8302106 (2020). [CrossRef]
7. H. Xu, Y. Qin, G. Hu, et al., “Meta-Structured Silicon Nanophotonic Polarization Beam Splitter with an Optical Bandwidth of 415 nm,” Laser Photonics Rev. 17(4), 2200550 (2023). [CrossRef]
8. W. Chen, B. Zhang, P. Wang, et al., “Ultra-compact and low-loss silicon polarization beam splitter using a particle-swarm-optimized counter-tapered coupler,” Opt. Express 28(21), 30701–30709 (2020). [CrossRef]
9. S. Mao, L. Cheng, C. Zhao, et al., “Compact hybrid five-mode multiplexer based on asymmetric directional couplers with constant bus waveguide width,” Opt. Lett. 48(10), 2607–2610 (2023). [CrossRef]
10. W. Chen, P. Wang, T. Yang, et al., “Silicon three-mode (de)multiplexer based on cascaded asymmetric Y junctions,” Opt. Lett. 41(12), 2851–2854 (2016). [CrossRef]
11. S. Sun, Z. Yang, J. Wang, et al., “Ultra-sharp silicon multimode waveguide bends based on double free-form curves,” Photonics Res. 10(6), 1484–1490 (2022). [CrossRef]
12. L. H. Gabrielli, D. Liu, S. G. Johnson, et al., “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3(1), 1217 (2012). [CrossRef]
13. L. Zhang, Z. Guo, X. Gu, et al., “Highly scalable and flexible on-chip all-silicon mode filter using backward mode conversion gratings,” Opt. Express 30(24), 43439–43452 (2022). [CrossRef]
14. K. T. Ahmmed, H. P. Chan, and B. Li, “Broadband high-order mode pass filter based on mode conversion,” Opt. Lett. 42(18), 3686–3689 (2017). [CrossRef]
15. C. Sun, W. Wu, Y. Yu, et al., “Integrated tunable mode filter for a mode-division multiplexing system,” Opt. Lett. 43(15), 3658–3661 (2018). [CrossRef]
16. M. Teng, Y. J. Lee, A. Al Noman, et al., “Phase insensitive high order mode pass filter with low reflection for two-mode division multiplexing,” in Optical Fiber Communication Conference (OFC) 2019 (OSA, 2019), p. Th2A.5.
17. X. Guan, Y. Ding, and L. H. Frandsen, “Ultra-compact broadband higher order-mode pass filter fabricated in a silicon waveguide for multimode photonics,” Opt. Lett. 40(16), 3893–3896 (2015). [CrossRef]
18. Y. He, Y. Zhang, H. Wang, et al., “On-chip silicon mode blocking filter employing subwavelength-grating based contra-directional coupler,” Opt. Express 26(25), 33005–33012 (2018). [CrossRef]
19. K. T. Ahmmed, H. P. Chan, and B. Li, “Scalable selective high order mode pass filter architecture with asymmetric directional couplers,” Opt. Express 28(19), 28465–28478 (2020). [CrossRef]
20. B. Shen, P. Wang, R. Polson, et al., “An integrated-nanophotonics polarization beamsplitter with 2.4× 2.4 µm2 footprint,” Nat. Photonics 9(6), 378–382 (2015). [CrossRef]
21. T. Muratsubaki, T. Fujisawa, Y. Sawada, et al., “Direct-binary-search algorithm for fabrication-tolerant photonic-crystal-like subwavelength structures and its application to a four-mode waveguide crossing in 2 µm waveband,” Jpn. J. Appl. Phys. 61(4), 042003 (2022). [CrossRef]
22. W. Chen, H. Li, B. Zhang, et al., “Silicon mode (de) multiplexer based on cascaded particle-swarm-optimized counter-tapered couplers,” IEEE Photonics J. 13(1), 6600210 (2021). [CrossRef]
