Open Access
Add to BibSonomy
Abstract
Photonic integrated spatial light receivers play a crucial role in free space optical (FSO) communication systems. In this paper, we propose a 4-channel and 6-channel spatial light receiver based on a silicon-on-insulator (SOI) using an inverse design method, respectively. The 4-channel receiver has a square receiving area of 4.4 µm × 4.4 µm, which enables receiving four Hermite-Gaussian modes (HG00, HG01, HG10, and HG02) and converting them into fundamental transverse electric (TE00) modes with insertion losses (ILs) within 1.6∼2.1 dB and mean cross talks (MCTs) less than −16 dB, at a wavelength of 1550 nm. The 3 dB bandwidths of the four HG modes range from 28 nm to 46 nm. Moreover, we explore the impact of fabrication errors, including under/over etching and oxide thickness errors, on the performance of the designed device. Simulation results show that the 4-channel receiver is robust against fabrication errors. The designed 6-channel receiver, featuring a regular hexagon receiving area, is capable of receiving six modes (HG00, HG01, HG10, HG02, HG20, and HG11) with ILs within 2.3∼4.1 dB and MCTs less than −15 dB, at a wavelength of 1550 nm. Additionally, the receiver offers a minimum optical bandwidth of 26 nm.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Free-space optical (FSO) communication has attracted extensive interest due to its advantages such as high data capacity, high directivity, and unlicensed spectrum compared to conventional microwave systems [1,2]. However, the optical wavefront of the propagating beam is severely degraded by atmospheric turbulence, which greatly reduces the coupling efficiency of FSO receivers and affects the performance of practical laser transmission systems [3,4]. To mitigate the effects of atmospheric turbulence and improve the receive performance, several methods have been reported, which can be categorized into four categories according to the types of receivers: (1) Single-mode fiber (SMF) receiver. To preserve a good coupling in a SMF receiver, an effective approach is to employ adaptive optics (AO) technology, which relies on complex algorithms and deformable mirrors to provide feedback and compensation for wavefront correction [5,6]. However, the complexity of the control algorithms limits the correction loop bandwidth in the link. (2) Multi-aperture (MA) receiver. The input wavefront is sampled by an aperture array to sum the energy from different positions of the wavefront [7–9]. However, these architectures require a coherent receiver for each aperture, which imposes strict constraints on the performance of digital signal processing and limits the scalability to a large number of apertures. (3) Multimode fiber (MMF) receiver [10–12], the light is coupled to an MMF and a spatial demultiplexer (multi-plane light converters (MPLC) or photonic lanterns (PL)) projects the coupled light onto the MMF’s modes basis, then each projection is coupled to a separate SMF and final coherently detects and combines SMFs via digital signal processing. Similarly to the MA receiver, it requires a coherent receiver for each mode which limits the scalability of the system. (4) Semi-integrated receiving system [13], which consists of two parts: a spatial light receiver and a photonic coherent combiner. Compared to digital signal processing, optical coherent combining avoids detecting the light out of each channel and subsequently adding the data signal in the electrical domain after the re-synchronization process [13–15]. Besides, the photonic coherent combiner based on Silicon on insulator (SOI) demonstrates a high degree of integration and enables the realization of numerous optical functions with an ultimate small footprint [16]. However, there is a notable optical coupling loss between the output SMFs of the current spatial light receiver and the input single-mode waveguides of the photonic coherent combiner. Therefore, researching an integrated on-chip spatial light receiver is of utmost importance due to its ability to achieve lossless integration with the photonic coherent combiner. This integration enables the realization of a fully-integrated FSO receiving system that exhibits superior performance compared to the semi-integrated receiving system. Several design methods have been proposed in the research on on-chip spatial light receivers. Traditional methods, such as grating couplers [17], and subwavelength holographic surface gratings [18], have been employed. However, these methods have limitations in terms of their ability to support multiple modes and achieve high coupling efficiency. Recently, the inverse design method has become widely applied in the design of nanophotonic devices due to its design principles being solely based on the requirements of Maxwell's theory, rather than the need for excessive theoretical analysis and expertise [19,20]. Based on this method, effective conversion of the input field (spatial light field) into the target field (waveguide mode field) can be achieved by utilizing convex optimization algorithms and high-performance computing. The inverse-designed spatial light receiver can expand the number of supported modes and allow for the selective reception of specific spatial modes. Additionally, this approach provides flexibility in terms of the shape of the receiving area, as well as the positioning and quantity of output ports. However, there has been limited research conducted on integrated spatial light receivers with multiple channels utilizing the inverse design method.
In this paper, we propose two novel types of integrated spatial light receivers based on an inverse design approach. Firstly, we design a 4-channel spatial light receiver with a receiving area of 4.4 µm × 4.4 µm. Then, we investigate the performance of the designed device through simulations, including insertion losses (ILs), mean cross talks (MCTs), and optical bandwidths. Simulation results indicate that at 1550 nm, the ILs for the HG00, HG01, HG10, and HG02 modes are 1.6 dB, 1.8 dB, 2.1 dB, and 1.9 dB, respectively. The corresponding MCTs for the four HG modes are −16 dB, −18 dB, −19 dB, and −21 dB. And the bandwidths are 44 nm, 46 nm, 28 nm, and 31 nm, all centered around 1550 ± 3 nm. Moreover, we perform a fabrication tolerance analysis that accounts for under/over-etched and oxide thickness errors. Simulation results show that the 4-channel receiver exhibits robustness against fabrication errors. At last, in order to improve the coupling efficiency between the distorted wavefront and the spatial light receiver, we designed a 6-channel receiver with a regular hexagonal receiving area, which can receive six modes (HG00, HG01, HG10, HG02, HG20, and HG11 modes) with ILs within 2.3∼4.1 dB and MCTs less than −15 dB, at a wavelength of 1550 nm. And the 6-channel receiver achieves a minimum optical bandwidth of 26 nm center at 1553 nm.
2. Modeling and inverse design
A schematic structure of a 4-channel spatial light receiver is shown in Fig. 1, which consists of a square design area and four output waveguides. The device is designed to launch a TE00 mode from port 1 when receiving HG00 mode, TE00 mode from port 2 when receiving HG10 mode, TE00 mode from port 3 when receiving HG01 mode, and TE00 mode from port 4 when receiving HG02 mode. We design the spatial light receiver consisting of three layers: the top layer is a 220 nm silicon layer (Si) with a 40 nm minimum feature size, the middle layer is clad with silicon oxide (SiO2), and the bottom layer is a metal layer made of aluminum (Al). By adding the Al reflector, we can enhance the coupling efficiency of the incoming light field. The Maxwell’s equation in the frequency domain is written as follows [21]:
Fig. 1. Schematic of the inverse design approach to generate a 4-channel spatial light receiver. We optimize a design area (denoted by the design layer) that takes HG modes as input and generates a field pattern that has a maximum overlap with the desired TE00 mode. HG00, HG10, HG01, and HG02 modes are incident vertically, and output from port1, port2, port3, and port4 respectively.
To design a high-efficiency 4-channel spatial light receiver, we optimize the structure that takes HG modes as input and generates TE00 mode out of the corresponding output waveguides whose electric field overlaps maximally with the desired TE00 mode. The figure of merit (FOM), a key parameter to characterize the process in the optimization [21], is defined as follows.
${E_i}$ is the normalized output simulated field of the TE00 mode at port1, port2, port3, and port4 corresponding to the vertical incidence of HG00, HG10, HG01, and HG02 modes respectively, and ${C_i}$ is the normalized conjugated ideal field of the TE00 mode at four output ports.
3. Photonic integrated spatial light receivers
Based on the above model and method, we design a 4-channel spatial light receiver, which has a square design area of 4.4 µm2. Four output waveguides are designed with a width of 550 nm and a thickness of 220 nm, and the buried oxide thickness is set to 510 nm. The permittivity values for SiO2 and Si are represented by 2.10 and 11.90 respectively. Based on the inverse design method reported in [22] and the open-source package Lumos provided on [23], the optimization steps are summarized in Fig. 2:
- (a) Initialization. Set a uniform permittivity distributed between 2.10 and 11.90 in the design area (as shown in Fig. 2(a));
- (b) Continuous Stage. Use the alternating directions method of multipliers (ADMM) optimization algorithm for global search (stage A) and the gradient descent optimization algorithm to find an accurate solution (stage B), and the corresponding structure pattern with continuous permittivity is shown in Fig. 2(b);
- (c) Binarization. Implement a level-set algorithm to do further optimization steps to convert the continuous permittivity of the structure into a binary one ((Fig. 2(c)). Level-set algorithm is a combination of the gradient algorithm and graph algorithm [24], which converts continuous permittivity to a binary structure with keeping the optimized physical performance. We use three high-performance computing graphics cards (A100) provided by NVIDIA on an Ubuntu system to optimize the 4-channel spatial light receiver (the final structure as shown in Fig. 2(d)) and finally use FDTD to verify our structure.
Fig. 2. Optimization steps for the 4-channel receiver in the course of (a) Initialization, (b) Continuous stage, (c) Binarization, and (d) 3D Structure.
We first characterize the transmission matrix of the 4-channel spatial light receiver by launching different $H{G_{m,n}}$ modes at a wavelength of 1550 nm. For a given $H{G_{m,n}}$ mode, we calculate the insertion losses (ILs) with $P_{m,n}^{out}/P_{m,n}^{in}$ and the mean cross talks (MCTs) with $P_{m^{\prime} \ne m,n^{\prime} \ne n}^{out}/P_{m,n}^{in}$. where $P_{m,n}^{out}$ refers to the output power of the TE00 mode when receiving the corresponding $H{G_{m,n}}$ mode and $P_{m,n}^{in}$ refers to the input power of the $H{G_{m,n}}$ mode. Figure 3 shows the transmission matrix ${P^{out}}/{P^{in}}$, and Table 1 sums up the 4-channel receiver characteristics for ILs and MCTs. The transmission matrix is quasi-diagonal and the mean cross talk is very low $( < - 16dB)$, making this architecture suitable for receiving and converting the spatial lights.
Table 1. 4-channel receiver characteristics for ${\rm H}{{\rm G}_{\textrm{mn}}}$ mode: insertion loss (IL) and mean cross talk (MCT) in dB
To explore the bandwidth performance of the 4-channel receiver, the efficiency at different wavelengths is calculated. Figure 4 illustrates the efficiency when receiving different HG modes at wavelengths ranging from 1.5 to 1.6 µm, and the top left corner of each figure depicts the corresponding optical field distribution at 1550 nm. The 3 dB bandwidths for the HG00, HG01, HG10, and HG02 modes are 44 nm, 46 nm, 28 nm, and 31 nm, respectively. All of these bandwidths are centered at a wavelength of 1550 ± 3 nm.
Fig. 4. Efficiency of HG00, HG01, HG10, and HG02 modes of the 4-channel receiver. Red dashed lines show 3 dB from each maximum. The top left corner of each figure depicts the corresponding optical field distribution at 1550 nm.
In order to ensure the robustness of the designed device against fabrication errors such as under/over-etched, a simulation analysis is performed by incrementally dilating and eroding the 4-channel spatial light receiver, ranging from 4 nm to 8 nm, with a uniform step size of 4 nm. The variations caused by these errors are shown in Fig. 5. Black lines represent the device efficiency with no error, the dashed lines represent the efficiency after being dilated by 4 nm (blue line) and 8 nm (gray line), and the solid lines represent the efficiency after being eroded by 4 nm (blue line) and 8 nm (gray line).
Fig. 5. Efficiency variations resulting from dilated/eroded errors ranging from 4 nm to 8 nm for the HG00, HG01, HG10, and HG02 modes. The symbol ‘+’ indicates over-etched, and the symbol ‘-’ represents under-etched. Black lines indicate no error. Blue solid lines represent under-etched 4 nm, and blue dashed lines represent over-etched 4 nm. Gray solid lines represent under-etched 8 nm, and gray dashed lines represent over-etched 8 nm.
As depicted in Fig. 5, under-etching primarily impacts the center wavelength corresponding to the highest efficiency. As the under-etching error increases from 4 nm to 8 nm, the center wavelength gradually shifts towards the right, while the peak coupling efficiency remains relatively constant. On the other hand, an over-etching error of 4 nm/8 nm causes a gradual leftward shift in the center wavelength, resulting in a slight reduction in peak coupling efficiency. Overall, these findings indicate that the 4-channel spatial light receiver demonstrates robustness against fabrication errors caused by under-etched and over-etched.
Then, we conduct a tolerance analysis on the oxide thickness, which refers to the distance between the Si layer and the Al layer. As shown in Fig. 6 and Table 2, the results show that when the oxide thickness falls within the range of 510${\pm} $40 nm, the fluctuations in efficiency for the HG00, HG01, HG10, and HG02 modes are below 0.26 dB, 0.18 dB, 0.25 dB, and 0.39 dB, respectively. The finding highlights the robustness of the device in dealing with oxide thickness errors during fabrication. Additionally, Fig. 6 shows that the optimal oxide thickness for both the HG01 and HG02 modes is 510 nm, while for the HG00 and HG10 modes are 520 nm and 500 nm. Taking all factors into account, the optimal thickness for the buried oxide layer is determined to be 510 nm.
Fig. 6. Efficiency variations of HG00, HG01, HG10, and HG02 modes with the oxide thickness at 510nm ± 40nm.
Table 2. Statistical analysis of the efficiency fluctuation of four HGmn modes with the oxide thickness at 510nm ± 40nm
The distorted wavefront caused by atmospheric turbulence can be considered a superposition of fundamental and higher-order modes. Increasing the number of receiver modes enhances the support for orthogonal modes, which facilitates the capture of a greater number of higher-order modes from the distorted wavefront. Therefore, we further propose a 6-channel spatial light receive, which has the capability to receive HG00, HG01, HG10, HG02, HG20, and HG11 modes and convert them into TE00 mode. Figure 7 shows a 3D schematic and a top view of the 6-channel receiver, featuring a regular hexagon design area with a side length of 2.4µm.
Fig. 7. (a) 3D structure and (b) top view of a 6-channel receiver. HG00, HG01, HG10, HG02, HG02, HG20, and HG11 modes are incident vertically, and output from port1, port2, port3, port4, port5, and port6, respectively.
Similarly, we explore the performance of the designed 6-channel receiver in terms of transmission matrix (Fig. 8), ILs and MCTs (Table 3), as well as the optical bandwidth and the corresponding optical filed distribution (Fig. 9). The bandwidth for the 6-channel receiver is 26 nm, which is mainly limited by the bandwidth when injecting HG10 mode.
Fig. 9. Efficiency of HG00, HG01, HG10, HG02 HG20, and HG11 modes of the 6-channel receiver. Red dashed lines show 3 dB from each maximum. The top left corner of each figure depicts the corresponding optical field distribution at 1550 nm.
Table 3. 6-channel receiver characteristics for ${\rm H}{\rm{G}_{\rm{mn}}}$: insertion loss (IL) and mean cross talk (MCT) in dB
4. Conclusion
In this paper, we propose a 4-channel spatial light receiver with a compact size of 4.4 µm × 4.4 µm for the HG00, HG01, HG10, and HG02 modes, and a 6-channel receiver with a regular hexagonal receiving area with each side measuring 2.4 µm, based on the inverse design method, respectively. Firstly, we perform a simulation analysis to evaluate the performance of the designed 4-channel receiver in terms of insertion losses (ILs), mean cross talks (MCTs), and optical bandwidths. Simulation results indicate that at 1550 nm, the ILs for the four HGmn modes range from 1.6∼2.1 dB, and the MCTs are less than −16 dB. The optical bandwidths of these modes range from 28 nm to 46 nm, all centered at 1550${\pm} $3 nm. In addition, Simulation results indicate that the 4-channel receiver is robust against fabrication errors. Next, we propose a 6-channel receiver, which is capable of receiving 6 HG modes (HG00, HG01, HG10, HG02, HG20, and HG11 modes) with ILs ranging from 2.3∼4.1 dB and MCTs less than −15 dB, at 1550 nm. The optical bandwidths of the six modes range from 26 nm to 51 nm, all centered at 1550 ${\pm} $3 nm. Furthermore, we will fabricate 4-channel and 6-channel spatial light receivers and evaluate their performance in receiving different HG modes. We will also assess their receiving performance under weak-to-strong turbulence in a desktop experiment.
Funding
National Natural Science Foundation of China (61935003, 62275029).
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. D. M. Boroson, B. S. Robinson, D. V. Murphy, D. A. Burianek, F. Khatri, J. M. Kovalik, Z. Sodnik, and D. M. Cornwell, “Overview and results of the Lunar Laser Communication Demonstration,” proc. SPIE 8971, 89710S (2014). [CrossRef]
2. A. Le Kernec, L. Canuet, A. Maho, M. Sotom, D. Matter, and L. Francou, “Optical feeder links for high throughput satellites and the H2020 VERTIGO project,” Communications and Observations through Atmospheric Turbulence: Characterization and Mitigation Workshop (2019).
3. Y. Dikmelik and F. M. Davidson, “Fiber-coupling efficiency for free-space optical communication through atmospheric turbulence,” Appl. Opt. 44(23), 4946–4952 (2005). [CrossRef]
4. A. N. Khan, S. Saeed, Y. Naeem, M. Zubair, Y. Massoud, and U. Younis, “Atmospheric turbulence and fog attenuation effects in controlled environment FSO communication links,” IEEE Photon. Technol. Lett. 34(24), 1341–1344 (2022). [CrossRef]
5. M. Chen, C. Liu, D. Rui, and H. Xian, “Performance verification of adaptive optics for satellite-to-ground coherent optical communications at large zenith angle,” Opt. Express 26(4), 4230–4242 (2018). [CrossRef]
6. S. Shaklan and F. Roddier, “Coupling starlight into single-mode fiber optics,” Appl. Opt. 27(11), 2334–2338 (1988). [CrossRef]
7. D. J. Geisler, T. M. Yarnall, M. L. Stevens, C. M. Schieler, B. S. Robinson, and S. A. Hamilton, “Multi-aperture digital coherent combining for free-space optical communication receivers,” Opt. Express 24(12), 12661–12671 (2016). [CrossRef]
8. C. Rao, S. Cui, Y. Tu, K. Zhou, and D. Liu, “Toward Practical Digital Phase Alignment for Coherent Beam Combining in Multi-Aperture Free Space Coherent Optical Receivers,” IEEE Access 8, 202585–202595 (2020). [CrossRef]
9. Y. Tu, S. Cui, K. Zhou, and D. Liu, “Phase Alignment With Minimum Complexity for Equal Gain Combining in Multi-Aperture Free-Space Digital Coherent Optical Communication Receivers,” IEEE Photonics J. 12(2), 1–10 (2020). [CrossRef]
10. M. Arikawa and T. Ito, “Performance of mode diversity reception of a polarization-division-multiplexed signal for free-space optical communication under atmospheric turbulence,” Opt. Express 26(22), 28263–28276 (2018). [CrossRef]
11. D. Zheng, Y. Li, H. Zhou, Y. Bian, C. Yang, W. Li, J. Qiu, H. Guo, X. Hong, Y. Zuo, I. P. Giles, W. Tong, and J. Wu, “Performance enhancement of free-space optical communications under atmospheric turbulence using modes diversity coherent receipt,” Opt. Express 26(22), 28879–28890 (2018). [CrossRef]
12. P. Cho, P. M. Pellegrino, J. Bickford, and A. Bontzos, “Investigation of turbulence-tolerant free-space optical communications via multiplane light conversion,” Opt. Eng. 61(11), 116104 (2022). [CrossRef]
13. V. Billault, J. Bourderionnet, J. P. Mazellier, L. Leviandier, P. Feneyrou, A. Maho, M. Sotom, X. Normandin, H. Lonjaret, and A. Brignon, “Free space optical communication receiver based on a spatial demultiplexer and a photonic integrated coherent combining circuit,” Opt. Express 29(21), 33134–33143 (2021). [CrossRef]
14. Y. Yang, C. Geng, F. Li, G. Huang, and X. Li, “Multi-aperture all-fiber active coherent beam combining for free-space optical communication receivers,” Opt. Express 25(22), 27519–27532 (2017). [CrossRef]
15. B. Zhang, J. Sun, C. Lao, C. H. Betters, A. Argyros, Y. Zhou, and S. G. Leon-Saval, “All-fiber photonic lantern multimode optical receiver with coherent adaptive optics beam combining,” arXiv, arXiv:2105.09516 (2021). [CrossRef]
16. C. G. Roeloffzen, L. Zhuang, C. Taddei, A. Leinse, R. G. Heideman, P. W. L. van Dijk, R. M. Oldenbeuving, D. A. Marpaung, M. Burla, and K. J. Boller, “Silicon nitride microwave photonic circuits,” Opt. Express 21(19), 22937–22961 (2013). [CrossRef]
17. M. Diab, R. Cheriton, and S. Sivanandam, “Photonic phase correctors based on grating couplers: proof of concept simulations and preliminary performance metrics,” Proc. SPIE 12185, 336–2726 (2022). [CrossRef]
18. S. Zheng, Z. Zhao, and W. Zhang, “Versatile generation and manipulation of phase-structured light beams using on-chip subwavelength holographic surface gratings,” Nanophotonics 12(1), 55–70 (2023). [CrossRef]
19. R. E. Christiansen and O. Sigmund, “Inverse design in photonics by topology optimization: tutorial,” J. Opt. Soc. Am. B 38(2), 496–509 (2021). [CrossRef]
20. J. Huang, H. Ma, D. Chen, H. Yuan, J. Zhang, Z. Li, J. Han, J. Wu, and J. Yang, “Digital nanophotonics: The highway to the integration of subwavelength-scale photonics: Ultra-compact, multi-function nanophotonic design based on computational inverse design,” Nanophotonics 10(3), 1011–1030 (2021). [CrossRef]
21. J. Lu, “Nanophotonic Computational Design,” Doctoral dissertations, Stanford University (2013), pp. 91–93.
22. A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9(6), 374–377 (2015). [CrossRef]
23. J. Lu, “Lumos,” GitHub (2013), https://github.com/JesseLu/lumos.
24. A. Y. Piggott, J. Petykiewicz, L. Su, and J. Vučković, “Fabrication-constrained nanophotonic inverse design,” Sci. Rep. 7(1), 1786 (2017). [CrossRef]
