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Abstract
We have designed three mode order converters using the sub-wavelength grating on the silicon-on-insulator substrate. The proposed mode order converters can separately realize the mode order conversion from the fundamental transverse electric mode to the first-order transverse electric mode (TE0-to-TE1), the second-order transverse electric mode (TE0-to-TE2) and the third-order transverse electric mode (TE0-to-TE3) with compact device sizes and good performances. The simulation results show that the mode order conversion efficiencies of TE0-to-TE1, TE0-to-TE2 and TE0-to-TE3 are larger than 94.4%, 95.7% and 83.7% in the wavelength ranging from 1.5 µm to 1.6 µm, the corresponding device length are 8.72 µm, 4.98 µm and 14.54 µm. In addition, the mode order converter can be fabricated with only once etching which will be advantage to the device fabrication.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photonic integrated circuits (PICs) have been considered as a candidate to replace the microelectronic circuits in order to break through the bottleneck of the information transmission rate [1]. Mode division multiplexing (MDM) technology, which can use the different spatial eigenmodes as the channels to encode the transmission data, is an important way to improve the data transmission capacity in the PICs [2,3]. The key component to realize the different spatial eigenmodes in the MDM technology is the mode order converter which can generate the multimode from the fundamental mode. Especially based on the silicon-on-insulator (SOI) platform, the mode order converter can realize the mode order conversion in the silicon waveguide with a compact size and a good performance [4,5].
According to the current reports, three methods are used to design the mode order converter, including phase matching, beam shaping and coherent scattering [6]. Up to now, many mode order converters have been demonstrated with various structures by using the methods, such as asymmetrical directional couplers [7,8], Mach-Zehnder interferometers (MZI) [9], photonic crystal waveguides [10,11], adiabatic tapers [12], dielectric metamaterials [13,14]. Among them, the mode order conversion using the asymmetrical directional coupler is achieved by the phase matching. And it can be convenient to realize the mode multiplexing and demultiplexing [7]. But the asymmetrical directional coupler is some sensitive to the wavelength and the fabrication errors. The mode order conversion using the MZI is achieved by the beam shaping which needs to split the light into different branch waveguides and then combines it in a waveguide. But the branch waveguide is usually large. Recently, dielectric metamaterials are popular for the device design due to its advantages in the freely control of the material effective refractive index and being designed inversely [15–18]. It has shown the great potential in the mode-order conversion by using the coherent scattering method. The mode-order converter based on the metamaterials can be designed with the ultra-compact footprint and it even can realize the higher order mode conversion [6,13,14,16]. But more ways still need to be explored to achieve the mode-order conversion with the excellent performances.
In this paper, we propose three sub-wavelength grating assisted mode order converters on the SOI substrate. The mode order converters can realize the mode order conversion from the fundamental transverse electric mode to the first-order transverse electric mode (TE0-to-TE1), the second-order transverse electric mode (TE0-to-TE2) and the third-order transverse electric mode (TE0-to-TE3). By optimizing, in the wavelength ranging from 1.5 µm to 1.6 µm, the mode conversion efficiencies of TE0-to-TE1, TE0-to-TE2 and TE0-to-TE3 are larger than 94.4%, 95.7% and 83.7% with the device length of 8.72 µm, 4.98 µm and 14.54 µm, respectively. The mode order converters only need one step etching process. The influence of the fabrication errors on the conversion efficiency is also analyzed.
2. Device design
The mode order converters are designed on the SOI substrate with a 220 nm thick silicon waveguide. The cross section of the waveguide is demonstrated in Fig. 1(a). The refractive indexes of Si and SiO2 are set as 3.47 and 1.44 at the wavelength of 1.55 µm. The electric field intensity distributions of the TE0 mode, TE1 mode, TE2 mode and TE3 mode in the silicon waveguide are shown in Figs . 1(b)–1(e). The sub-wavelength grating structures are entirely etching in the silicon waveguide. The role of the sub-wavelength grating is to form the perturbation so that the input fundamental mode can realize the coherent scattering and evolve into the multimodes. The period (Λ) of the sub-wavelength grating is chosen to be 0.2 µm to ensure the sub-wavelength grating working in the propagation mode [19]. The other parameters of the sub-wavelength grating are decided by optimizing in different mode order conversion.
Fig. 1. (a) The cross section of the SOI substrate with a 220 nm thick silicon waveguide. The electric field intensity distributions of the TE0 mode (b), TE1 mode (c), TE2 mode (d) and TE3 mode (e).
2.1 TE0-to-TE1
The schematic diagram of the mode order converter for TE0-to-TE1 is shown in Fig. 2. The structures of two segment gratings are the same and the interval distance is L2. Each segment grating consists of the etching strips with the uniform change ($\varDelta$h) in height. The width of the etching strip is d and the duty cycle of the grating is defined to be d/Λ. The width of the silicon waveguide is 1.2 µm. By optimizing, each segment grating includes 19 strips, h0=0.1 µm and $\varDelta$h = 0.05 µm. The duty cycle and the interval distance L2 are two important parameters to decide the mode order conversion efficiency. In Fig. 3, it demonstrates the calculated results of the transmissivity of the TE1 mode for TE0-to-TE1 by sweeping the duty cycle and the interval distance L2. Here the duty cycle and L2 are finally chosen to be 0.3 and 1.4 µm, the corresponding transmissivity of the TE1 mode is −0.09 dB. The final length of the mode order converter is 8.72 µm and the conversion efficiency for TE0-to-TE1 is up to 97.9% at the wavelength of 1.55 µm.
The electric field (Ey) distribution of the mode order converter for TE0-to-TE1 is demonstrated in Fig. 4. Obviously, the input TE0 mode is converted into the TE1 mode. The spectral response is analyzed, as shown in Fig. 5. It can be found that in the wavelength ranging from 1.5 µm to 1.6 µm, the transmissivity of the TE1 mode is larger than −0.25 dB (∼94.4% conversion efficiency) and the crosstalk is less than −15.33 dB.
2.2 TE0-to-TE2
For TE0-to-TE2, it needs to form three beams of light by the coherent scattering. And two beams of light in the both sides have the same phase which means it travels through the same optical path. The symmetric structure (along the propagation direction) can ensure the beams of light in the both sides travel through the same optical path [12,20,21]. So the mode order converter for TE0-to-TE2 is designed with a symmetric sub-wavelength grating structure alone the center of the waveguide propagation direction, as shown in Fig. 6. To better support the TE2 mode, the silicon waveguide width is set as 1.4 µm. Here each segment grating includes 11 strips, h0=0.08 µm and $\varDelta$h = 0.04 µm. By sweeping the duty cycle and the interval distance L2, the transmissivity of the TE2 mode is calculated, the results are shown in Fig. 7. Here the duty cycle and L2 are finally chosen to be 0.45 and 0.8 µm, the corresponding transmissivity of the TE1 mode is –0.06 dB. The final length of the mode order converter is 4.98 µm and the conversion efficiency for TE0-to-TE1 is up to 98.6% at the wavelength of 1.55 µm.
The electric field (Ey) distribution of the mode order conversion for TE0-to-TE2 is demonstrated in Fig. 8. It can be found that the input TE0 mode is converted into the TE2 mode. The spectral response of the mode order converter for TE0-to-TE2 is demonstrated in Fig. 9. In the wavelength ranging from 1.5 µm to 1.6 µm, the transmissivity of the TE2 mode is larger than −0.19 dB (∼95.7% conversion efficiency) and the crosstalk is less than −17.36 dB.
2.3 TE0-to-TE3
To realize the mode order conversion for TE0-to-TE3, we combine the two structures above, as shown in Fig. 10. The first segment structure (L1) is the same as the mode order converter for TE0-to-TE1. The second segment structure is similar to the mode order converter for TE0-to-TE2, but the structure parameters should be re-optimized because of the width (w2) of this segment silicon waveguide is set as 2 µm to better support the TE3 mode. In addition, to reduce the propagation losses, a taper is used to connect two segment waveguides. Finally, the taper length L5 is set as 1 µm, the second segment grating structure includes 13 strips, h0=0.1 µm and $\varDelta$h = 0.06 µm. Here the duty cycle and the interval distance L3 of the second segment structure are chosen to be 0.3 and 0.9 µm. The final length of the mode order converter is 14.54 µm and the conversion efficiency for TE0-to-TE3 is 89.8% at the wavelength of 1.55 µm.
The electric field (Ey) distribution of the mode order converter for TE0-to-TE3 is demonstrated in Fig. 11. It can be found that the TE0 mode is converted into the TE1 mode in the first segment waveguide and then converted into the TE3 mode in the second segment waveguide. It can be explained that the TE1 mode is composed of two TE0 mode with the opposite phase. Then each TE0 mode is propagated in the waveguide which is similar to the first segment structure. Each TE0 mode is converted into the TE1 mode again and the two TE1 modes form the TE3 mode. Since it doesn`t directly convert the TE0 mode to TE3 mode, the transmissivity of the TE1 mode and TE2 mode also is calculated, as shown in Fig. 12. In the wavelength ranging from 1.5 µm to 1.6 µm, the transmissivity of the TE3 mode is larger than −0.77 dB (∼83.7% conversion efficiency). It can be found the major sources of the crosstalk are the TE0 mode and TE1 mode which are less than −15.65 dB and −11.48 dB, respectively.
3. Fabrication tolerance analysis
The proposed mode order converters consists of the sub-wavelength grating structures and the sizes of the grating strip are several dozens of nanometers, which poses the great challenge to the device fabrication. So the fabrication tolerance is investigated at the wavelength of 1.55 µm by changing the width (Δd) and the height (Δhi) of the grating strip, as well as the thickness (Δt) of Si waveguide, as shown in Figs. 13(a)–13(f). Because the crosstalk in the third converter is mainly from the TE1 mode at the wavelength of 1.55 µm, it only analyses the effects of the parameter variation on the crosstalk between the TE1 mode and TE3 mode in the third converter. Within the ± 20 nm ranges, the conversion efficiencies of the three mode order converters show the large rangeability when changing the width of the grating strip. But the rangeability of the conversion efficiencies is small when changing the height of the grating strip and the thickness of Si waveguide. It also can be found that the crosstalk is more sensitive to the parameter variation for the low-order mode conversion. The results indicate that the fabrication process with the accuracy in 10 nm may be the best choice.
4. Summary
In summary, three sub-wavelength grating assisted mode order converters have been proposed to realize the mode order conversion for TE0-to-TE1, TE0-to-TE2 and TE0-to-TE3. The mode order converters can achieve the high mode order conversion efficiency over a broad wavelength range (1.5 µm ∼ 1.6 µm) with the compact device sizes. The next step is to further improve the mode order conversion efficiency for TE0-to-TE3. And the higher order mode conversions also need to be explored.
Funding
Beijing University of Posts and Telecommunications (CX2019316); National Natural Science Foundation of China (61574019, 61674020, 61874148); Natural Science Foundation of Beijing Municipality (4192043); State Key Laboratory of Information Photonics and Optical Communications (IPOC2018ZT01); 111 Project of China (B07005).
References
1. R. Helkey, A. A. M. Saleh, J. Buckwalter, and J. E. Bowers, “High-performance photonic integrated circuits on silicon,” IEEE J. Sel. Top. Quantum Electron. 25(5), 1–15 (2019). [CrossRef]
2. D. Dai, C. Li, S. Wang, H. Wu, Y. Shi, Z. Wu, S. Gao, T. Dai, H. Yu, and H. Tsang, “10-channel mode (de) multiplexer with dual polarizations,” Laser Photonics Rev. 12(1), 1700109 (2018). [CrossRef]
3. Y. He, Y. Zhang, Q. Zhu, S. An, R. Cao, X. Guo, C. Qiu, and Y. Su, “Silicon high-order mode (de) multiplexer on single polarization,” J. Lightwave Technol. 36(24), 5746–5753 (2018). [CrossRef]
4. K. Okamoto, “Progress and technical challenge for planar waveguide devices: silica and silicon waveguides,” Laser Photonics Rev. 6(1), 14–23 (2012). [CrossRef]
5. D. Dai and J. E. Bowers, “Silicon-based on-chip multiplexing technologies and devices for Peta-bit optical interconnects,” Nanophotonics 3(4-5), 283–311 (2014). [CrossRef]
6. D. Ohana and U. Levy, “Mode conversion based on dielectric metamaterial in silicon,” Opt. Express 22(22), 27617–27631 (2014). [CrossRef]
7. L. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5(1), 3069 (2014). [CrossRef]
8. Z. Chen, Y. Zhu, X. Ruan, Y. Li, Y. Li, and F. Zhang, “Bridged coupler and oval mode converter based silicon mode division (de) multiplexer and terabit WDM-MDM system demonstration,” J. Lightwave Technol. 36(13), 2757–2766 (2018). [CrossRef]
9. Y. Huang, G. Xu, and S. Ho, “An ultracompact optical mode order converter,” IEEE Photonics Technol. Lett. 18(21), 2281–2283 (2006). [CrossRef]
10. V. Liu, D. A. B. Miller, and S. Fan, “Ultra-compact photonic crystal waveguide spatial mode converter and its connection to the optical diode effect,” Opt. Express 20(27), 28388–28397 (2012). [CrossRef]
11. L. H. Frandsen, Y. Elesin, L. F. Frellsen, M. Mitrovic, Y. Ding, O. Sigmuud, and K. Yvind, “Topology optimized mode conversion in a photonic crystal waveguide fabricated in silicon-on-insulator material,” Opt. Express 22(7), 8525–8532 (2014). [CrossRef]
12. D. Chen, X. Xiao, L. Wang, Y. Yu, W. Liu, and Q. Yang, “Low-loss and fabrication tolerant silicon mode-order converters based on novel compact tapers,” Opt. Express 23(9), 11152–11159 (2015). [CrossRef]
13. H. Wang, Y. Zhang, Y. He, Q. Zhu, L. Sun, and Y. Su, “Compact silicon waveguide mode converter employing dielectric metasurface structure,” Adv. Opt. Mater. 7(4), 1801191 (2018). [CrossRef]
14. H. Jia, H. Chen, J. Yang, H. Xiao, W. Chen, and Y. Tian, “Ultra-compact dual-polarization silicon mode-order converter,” Opt. Lett. 44(17), 4179–4182 (2019). [CrossRef]
15. D. Ohana, B. Desiatov, N. Mazurski, and U. Levy, “Dielectric metasurface as a platform for spatial mode conversion in nanoscale waveguides,” Nano Lett. 16(12), 7956–7961 (2016). [CrossRef]
16. W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng, D. Liu, and M. Zhang, “Ultracompact dual-mode waveguide crossing based on subwavelength multimode-interference couplers,” Photonics Res. 6(7), 660–665 (2018). [CrossRef]
17. B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4× 2.4 µm 2 footprint,” Nat. Photonics 9(6), 378–382 (2015). [CrossRef]
18. M. Jang, Y. Horie, A. Shibukawa, J. Brake, Y. Liu, S. M. Kamali, A. Arbabi, H. Ruan, A. Faraon, and C. Yang, “Wavefront shaping with disorder-engineered metasurfaces,” Nat. Photonics 12(2), 84–90 (2018). [CrossRef]
19. R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015). [CrossRef]
20. L. Hao, R. Xiao, Y. Shi, P. Dai, Y. Zhao, S. Liu, J. Lu, and X. Chen, “Efficient TE-polarized mode-order converter based on high-index-contrast polygonal slot in a silicon-on-insulator waveguide,” IEEE Photonics J. 11(2), 1–10 (2019). [CrossRef]
21. M. Teng, K. Kojima, T. Koike-Akino, B. Wang, C. Lin, and K. Parsons, “Broadband SOI mode order converter based on topology optimization,” in Proceedings of OFC, Th2A.8, 2018.
