Inverse Design of 1×2 MMI Based on Automatic Differentiation in Silicon Photonics
Main Article Content
Abstract
Silicon photonics has experienced significant advancements in recent years, driven by the increasing demand for efficient and high-performance optical components within integrated circuits. A crucial technique in this realm is the inverse design method, which is instrumental in optimizing photonic devices. Inverse design utilizes computational algorithms to identify the optimal configuration of a device based on specific performance criteria, making it a powerful tool for enhancing silicon photonics. The integration of Automatic differentiation into the inverse design process has further revolutionized this approach by improving the precision and efficiency of optimization. This technique enhances the ability to fine-tune design parameters and achieve desired device characteristics. The 1x2 Multi-Mode Interferometer (MMI) plays a vital role in optical functions such as signal splitting, combining, and routing. Its significance in various photonic applications underscores the importance of precise design and optimization. Therefore, in this study, we focus on applying automatic differentiation (AD) to optimize the inverse design of a 1x2 MMI with a function of 3dB splitting power, aiming for minimal size to facilitate easy integration into optical systems
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.
- Creative Commons Copyright License
The journal allows readers to download and share all published articles as long as they properly cite such articles; however, they cannot change them or use them commercially. This is classified as CC BY-NC-ND for the creative commons license.
- Retention of Copyright and Publishing Rights
The journal allows the authors of the published articles to hold copyrights and publishing rights without restrictions.
References
X. Zhou, D. Yi, D. W. U Chan , and H. Ki Tsang, “Silicon photonics for high-speed communications and photonic signal processing,” npj Nanophotonics, vol. 1, no. 1, Jul. 2024.
H. Shu, L. Chang, Y. Tao, B. Shen, W. Xie, M. Jin, A. Netherton, Z. Tao, X. Zhang, R. Chen, B. Bai, J. Qin, S. Yu, X.Wang, and John E. Bowers, “Microcombdriven silicon photonic systems,” Nature, vol. 605, no. 7910, pp. 457–463, May 2022.
A. Sun, X. Deng, S. Xing, Z. Li, J. Jia, G. Li, A. Yan, P. Luo, Y. Li, Z. Luo, J. Shi, Z. Li, C. Shen, B. Hong, W. Chu, X. Xiao, N. Chi, and J.n Zhang, “Inverse design of an ultra-compact dualband wavelength demultiplexing power splitter with detailed analysis
of hyperparameters,” Optics Express, vol. 31, no. 16, pp. 25415–25415, Jun. 2023.
Z. Li, Z. Zhou, C. Qiu, Y. Chen, B. Liang, Y. Wang, L. Liang, Y. Lei, Y. Song, P. Jia, Y. Zeng, L. Qin, Y. Ning, and Lijun Wang, “The Intelligent Design of Silicon Photonic Devices,” Advanced Optical Materials, vol. 12, no. 7, Feb. 2024.
Y. Shi, Y. Zhang, Y. Wan, Y. Yu, Y. Zhang, X. Hu, X. Xiao, H. Xu, L. Zhang, and B. Pan, “Silicon photonics for high-capacity data communications,” Photonics Research, vol. 10, no. 9, p. A106-A134, Aug. 2022.
S. Shekhar, W. Bogaerts, L. Chrostowski, J. E. Bowers, M. Hochberg, R. Soref, and B. J. Shastri, “Roadmapping the next generation of silicon photonics,” Nature Communications, vol. 15, no. 1, p. 751, Jan. 2024.
H. Zhang, M. Gu, X. D. Jiang, J. Thompson, H. Cai, S. Paesani, R. Santagati, A. Laing, Y. Zhang, M. H. Yung, Y. Z. Shi, F. K. Muhammad, G. Q. Lo, X. S. Luo, B. Dong, D. L. Kwong, L. C.
Kwek, and A. Q. Liu, “An optical neural chip for implementing complex-valued neural network,” Nature Communications, vol. 12, no. 1, p. 457, Jan. 2021.
T. Zhou, X. Lin, J. Wu, Y. Chen, H. Xie, Y. Li, J. Fan, H. Wu, L. Fang, and Q. Dai, “Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit,” Nature Photonics, vol. 15, no. 5, pp. 367–373, Apr. 2021.
R. Chen, H. Shu, B. Shen, L. Chang, W. Xie, W. Liao, Z. Tao, J. E. Bowers, and X.Wang, “Breaking the temporal and frequency congestion of Li- DAR by parallel chaos,” Nature photonics, vol. 17, no. 4, pp. 306–314, Mar. 2023.
L. Feng, M. Zhang, J. Wang, X. Zhou, X. Qiang, G. Guo, and X. Ren, “Silicon photonic devicesfor scalable quantum information applications,” Photonics Research, vol. 10, no. 10, pp. A135–A153,
Aug. 2022.
S. Zhao, W. Liu, J. Chen, Z. Ding, and Y. Shi, “Broadband Arbitrary Ratio Power Splitters Based on Directional Couplers With Subwavelength Structure,” IEEE Photonics Technology Letters, vol. 33, no. 10, pp. 479–482, May 2021.
Z. Lin and W. Shi, “Broadband, low-loss silicon photonic Y-junction with an arbitrary power splitting ratio,” Optics Express, vol. 27, no. 10, p. 14338, May 2019.
B. Wu, C. Sun, Y. Yu, and X. Zhang, “Integrated Optical Coupler With an Arbitrary Splitting Ratio Based on a Mode Converter,” IEEE Photonics Technology Letters, vol. 32, no. 1, pp. 15–18, Nov. 2019.
J. Zhu, Q. Chao, H. Huang, Y. Zhao, Y. Li, L. Tao, X. She, H. Liao, R. Huang, Z. Zhu, X. Liu, Z. Sheng, and F. Gan, “Compact, broadband, and lowloss silicon photonic arbitrary ratio power splitter using adiabatic taper,” Applied Optics, vol. 60, no. 2, p. 413-416, Jan. 2021.
S. Hong, J. Yoon, J. Kim, J. Kim, B. Neseli, H. Yoon, H.n Park, and H. Kurt, “Design of MMI-based 1x4 power splitters with optimized parabolic input and output ports on SOI platform,” Silicon Photonics XVIII, vol. 12426, pp. 11, Mar. 2023.
S. Kroker, S. Lanteri, O. Miller, Jens Niegemann,and L. Ramunno, “Inverse design in photonics: introduction,” Journal of the Optical Society of America B, vol. 41, no. 2, p. IDP1-IDP2, Jan. 2024.
Z. Lin, C. Roques-Carmes, Raphaël Pestourie, M. Soljačić, A. Majumdar, and S. G. Johnson, “Endto-end nanophotonic inverse design for imaging and polarimetry,” Nanophotonics, vol. 10, no. 3, pp.1177–1187, Dec. 2020.
W. Hadibrata, H. Wei, S. Krishnaswamy, and K. Aydin, “Inverse Design and 3D Printing of a Metalens on an Optical Fiber Tip for Direct Laser Lithography,” Nano Letters, vol. 21, no. 6, pp. 2422– 2428, Mar. 2021.
G. König, C. Fu, J. Stollenwerk, C. Holly, and P. Loosen, “Automated lens design for optical systems consisting of stock lenses,” Optics Express, vol. 29, no. 24, pp. 39027–39041, Oct. 2021.
B. MacLellan, P. Roztocki, J. Belleville, L. RomeroCortés, K. Ruscitti, B. Fischer, J. Azaña, and R. Morandotti, “Inverse Design of Photonic Systems,” Laser and Photonics Review, vol. 18, no. 5, Feb. 2024.
M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons , “Deep Neural Network Inverse Design of Integrated Photonic Power Splitters,” Scientific Reports, vol. 9, no. 1, p. 1368, Feb. 2019.
X. Xu, Y. Li, and W. Huang, “Inverse design of the MMI power splitter by asynchronous double deep Q-learning,” Optics Express, vol. 29, no. 22, pp.35951–35964, Oct. 2021.
Y. Kim and S.-H. Hong, “Inverse design of compact silicon photonic waveguide reflectors and their application for Fabry–Perot resonators,” Nanophotonics, vol. 13, no. 15, pp. 2829–2837, Apr. 2024.
M. F. Langer, J. T. Frank, and F. Knoop, “Stress and heat flux via automatic differentiation,” The Journal of Chemical Physics, vol. 159, no. 17, Nov. 2023.
C. Chen, Y. Yang, Y. Xiang, and W. Hao, “Automatic
Differentiation is Essential in Training Neural Networks for Solving Differential Equations,” arXiv (Cornell University), May 2024.
A. Luce, R. Alaee, F. Knorr, and F. Marquardt, “Merging automatic differentiation and the adjoint method for photonic inverse design,” Machine Learning: Science and Technology, vol. 5, no. 2, p. 025076, Jun. 2024.
S. Hooten, P. Sun, L. Gantz, M. Fiorentino, R. G. Beausoleil, and V. Vaerenbergh, “Automatic differentiation accelerated shape optimization approaches to photonic inverse design on rectilinear simulation grids,” arXiv (Cornell University), Jan.
T. W. Hughes, I. A. D. Williamson, M. Minkov, and S. Fan, “Forward-Mode Differentiation of Maxwell’s Equations,” ACS Photonics, vol. 6, no. 11, pp. 3010–3016, Oct. 2019.
M. Minkov, I. A. D. Williamson, L. C. Andreani, D. Gerace, B. Lou, A. Song, T. W. Hughes, and S. Fan, “Inverse Design of Photonic Crystals through Automatic Differentiation,” ACS Photonics, vol. 7, no. 7, pp. 1729–1741, Jun. 2020.
“HIPS/autograd,” GitHub, Jun. 04, 2021.https://github.com/HIPS/autograd.
A. Paszke et al., “Automatic differentiation in PyTorch,”, 2017, Available:https://openreview.net/pdf?id=BJJsrmfCZ
A. Agrawal, A.h Modi, A. Passos, A.n Lavoie, A. Agarwal, A. Shankar, I. Ganichev, J. Levenberg, M. Hong, R. Monga, and S. Cai, “TensorFlow Eager: A Multi-Stage, Python-Embedded DSL for Machine Learning,” arXiv (Cornell University), Jan. 2019.
J. Bradbury, ”JAX: composable transformations of Python+ NumPy programs.” (2018).
A. G. Baydin, B. A. Pearlmutter, A. A. Radul, and J. M. Siskind, “Automatic differentiation in machine learning: a survey,” arXiv.org, Feb. 05, 2018.
C. Pflaum and Z. Rahimi, “A finite difference frequency domain (FDFD) method for materials with negative permittivity,” International Conference on Electromagnetics in Advanced Applications, pp. 799–802, Sep. 2009.
D. Van, T. Schrijvers, J. McKinna, and A. Vandenbroucke, “Forward- or reverse-mode automatic differentiation: What’s the difference?,” Science of Computer Programming, vol. 231, p. 103010, Jan. 2024.
P. A. Besse, M. Bachmann, H. Melchior, L. B. Soldano, and M. K. Smit, “Optical bandwidth and fabrication tolerances of multimode interference couplers,” Journal of Lightwave Technology, vol. 12, no. 6, pp. 1004–1009, Jun. 1994.
M. Bachmann, P. A. Besse, and H. Melchior, “Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting,” Applied Optics, vol. 34, no. 30, p. 6898-6910, Oct. 1995.