Optical analog computing has recently sparked growing interest due to the appealing characteristics of low energy consumption, parallel processing, and ultrafast speed, spawning it complementary to conventional electronic computing. As the basic computing unit, optical logic operation plays a pivotal role for integrated photonics. However, the reported optical logic operations are volumetric and single-functional, which considerably hinders the practical cascadability and complex computing requirement. Here, we propose an on-chip combinational optical logic circuit using inverse design. By precisely engineering the scattering matrix of each small-footprint logic gate, all basic optical logic gates (OR, XOR, NOT, AND, XNOR, NAND, and NOR) are realized. On this foundation, we explore the assembly of these basic logic gates for general-purpose combinational logic circuits, including optical half-adder and code converter. Our work provides a path for the development of integrated, miniaturized, and cascadable photonic processor for future optical computing technologies.
1. Caulfield, H. J. and S. Dolev, "Why future supercomputing requires optics," Nat. Photon., Vol. 4, 261-263, 2010.
2. Silva, A., F. Monticone, G. Cadtaldi, V. Galdi, A. Alu, and N. Engheta, "Performing mathematical operations with metamaterials," Science, Vol. 343, 160-163, 2014.
3. Zhou, H., J. Dong, J. Cheng, W. Dong, C. Huang, Y. Shen, Q. Zhang, M. Gu, C. Qian, H. Chen, Z. Ruan, and X. Zhang, "Photonic matrix multiplication lights up photonic accelerator and beyond," Light: Sci. Appl., Vol. 11, 30, 2022.
4. Miller, D. A. B., "Are optical transistors the logical next step?," Nat. Photon., Vol. 4, 3-5, 2010.
5. Urbas, A. M., et al., "Roadmap on optical metamaterials," J. Opt., Vol. 18, 093005, 2016.
6. Qian, C., X. Lin, Y. Yang, X. Xiong, H. Wang, E. Li, I. Kaminer, B. Zhang, and H. Chen, "Experimental observation of superscattering," Phy. Rev. Lett., Vol. 122, 063901, 2019.
7. Qian, C., B. Zheng, Y. Shen, L. Jing, E. Li, L. Shen, and H. Chen, "Deep-learning-enabled self-adaptive microwave cloak without human intervention," Nat. Photon., Vol. 14, 383-390, 2020.
8. Zhen, Z., C. Qian, Y. Jia, Z. Fan, R. Hao, T. Cai, B. Zheng, H. Chen, and E. Li, "Realizing transmitted metasurface cloak by a tandem neural network," Photon. Res., Vol. 9, B229-B235, 2021.
9. Qian, C. and H. Chen, "A perspective on the next generation of invisibility cloaks --- Intelligent cloaks," Appl. Phys. Lett., Vol. 118, 180501, 2021.
10. Wang, Z., C. Qian, T. Cai, L. Tian, Z. Fan, J. Liu, Y. Shen, L. Jing, J. Jin, E. Li, B. Zheng, and H. Chen, "Demonstration of spider-eyes-like intelligent antennas for dynamically perceiving incoming waves," Adv. Intell. Syst., Vol. 3, 2100066, 2021.
11. Cai, T., S. Tang, B. Zheng, G.Wang, W. Ji, C. Qian, Z.Wang, E. Li, and H. Chen, "Ultrawideband chromatic aberration-free meta-mirrors," Adv. Photon., Vol. 3, 016001, 2021.
12. Huang, M., B. Zheng, T. Cai, X. Li, J. Liu, C. Qian, and H. Chen, "Machine-learning-enabled metasurface for direction of arrival estimation," Nanophotonics, Vol. 11, No. 9, 2022.
13. Jia, Y., C. Qian, Z. Fan, Y. Ding, Z. Wang, D. Wang, E. Li, B. Zheng, T. Cai, and H. Chen, "In-situ customized illusion enabled by global metasurface reconstruction," Adv. Funct. Mater., Vol. 2109331, 1-7, 2022.
14. Ma, W., F. Cheng, and Y. Liu, "Deep-learning-enabled on-demand design of chiral metamaterials," ACS Nano, Vol. 12, 6326-6334, 2018.
15. Malkiel, I., M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski, "Plasmonic nanostructure design and characterization via Deep Learning," Light: Sci. Appl., Vol. 7, 60, 2018.
16. Ma, W., F. Cheng, Y. Xu, Q. Wen, and Y. Liu, "Probabilistic representation and inverse design of metamaterials based on a deep generative model with semi-supervised learning strategy," Adv. Mater., Vol. 31, 1901111, 2019.
17. Liu, Z., D. Zhu, K. T. Lee, A. S. Kim, L. Raju, and W. Cai, "Compounding meta-atoms into metamolecules with hybrid artificial intelligence techniques," Adv. Mater., Vol. 32, 1904790, 2020.
18. Ma, W., Z. Liu, Z. A. Kudyshev, A. Boltasseva, W. Cai, and Y. Liu, "Deep learning for the design of photonic structures," Nat. Photon., Vol. 15, 77-90, 2021.
19. Ma, W., Y. Xu, B. Xiong, L. Deng, R. Peng, M. Wang, and Y. Liu, "Pushing the limits of functionality-multiplexing capability in metasurface design based on statistical machine learning," Adv. Mater., Vol. 34, 2110022, 2022.
20. Qiu, T., X. Shi, J. Wang, Y. Li, S. Qu, Q. Cheng, T. Cui, and S. Sui, "Deep learning: A rapid and efficient route to automatic metasurface design," Adv. Sci., Vol. 6, 1900128, 2019.
21. Zhu, R., T. Qiu, J. Wang, S. Sui, C. Hao, T. Liu, Y. Li, M. Feng, A. Zhang, C. Qiu, and S. Qu, "Phase-to-pattern inverse design paradigm for fast realization of functional metasurfaces via transfer learning," Nat. Commun., Vol. 12, 2974, 2021.
22. Tan, Q., B. Zheng, T. Cai, C. Qian, R. Zhu, X. Li, and H. Chen, "Broadband spin-locked metasurface retroreflector," Adv. Sci., Vol. 2201397, 1-7, 2022.
23. Hua, Y., C. Qian, H. Chen, and H. Wang, "Experimental topology-optimized cloak for water waves," Mater. Today Phys., Vol. 27, 100754, 2022.
24. Fan, Z., C. Qian, Y. Jia, Z. Wang, Y. Ding, D. Wang, L. Tian, E. Li, T. Cai, B. Zheng, I. Kaminer, and H. Chen, "Homeostatic neuro-metasurfaces for dynamic wireless channel management," Sci. Adv., Vol. 8, eabn7905, 2022.
25. Qian, C., Z. Wang, H. Qian, T. Cai, B. Zheng, X. Lin, Y. Shen, I. Kaminer, E. Li, and H. Chen, "Dynamic recognition and mirage using neuro-metamaterials," Nat. Commun., Vol. 13, 2694, 2022.
26. Qian, C., Y. Yang, Y. Hua, C. Wang, X. Lin, T. Cai, D. Ye, E. Li, I. Kaminer, and H. Chen, "Breaking the fundamental scattering limit with gain metasurfaces," Nat. Commun., Vol. 13, 4383, 2022.
27. Yang, Y., L. Jing, B. Zheng, R. Hao, W. Yin, E. Li, C. M. Soukoulis, and H. Chen, "Full-polarization 3D metasurface cloak with preserved amplitude and phase," Adv. Mater., Vol. 28, 6866-6871, 2016.
28. Chen, H., L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E, Vol. 70, 057605, 2004.
29. Chen, H., B. Zheng, L. Shen, H. Wang, X Zhang, N. I. Zheludev, and B. Zhang, "Ray-optics cloaking devices for large objects in incoherent natural light," Nat. Commun., Vol. 4, 1-6, 2013.
30. Camacho, M., B. Edwards, and N. Engheta, "A single inverse-designed photonic structure that performs parallel computing," Nat. Commun., Vol. 12, 1466, 2021.
31. Zhu, T., Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, "Plasmonic computing of spatial differentiation," Nat. Commun., Vol. 8, 15391, 2017.
32. Khoram, E., A. Chen, D. Liu, L. Ying, Q. Wang, M. Yuan, and Z. Yu, "Nanophotonic media for artificial neural inference," Photon. Res., Vol. 7, 823-827, 2019.
33. Zhu, Z., W. Ye, J. Ji, X. Yuan, and C. Zen, "High-contrast light-by-light switching and AND gate based on nonlinear photonic crystals," Opt. Express, Vol. 14, 1783-1788, 2006.
34. McCutcheon, M. W., G. W. Rieger, J. F. Young, D. Dalacu, P. J. Poole, and R. L. Williams, "All-optical conditional logic with a nonlinear photonic crystal nanocavity," Appl. Phys. Lett., Vol. 95, 221102, 2009.
35. Liu, Q., Z. Ouyang, C.Wu, C. Liu, and J. C.Wang, "All optical half adder based on cross structures in two-dimensional photonic crystals," Opt. Express, Vol. 16, 18992-19000, 2008.
36. Ishizaka, Y., Y. Kawaguchi, K. Saitoh, and M. Koshiba, "Design of ultra compact all-optical XOR and AND logic gates with low power consumption," Opt. Commun., Vol. 284, 3528-3533, 2011.
37. Wei, H., Z. Li, X. Tian, Z. Wang, F. Cong, N. Liu, S. Zhang, P. Nordlander, N. J. Halas, and H. Xu, "Quantum dot based local field imaging reveals plasmon-based interferometric logic in silver nanowire networks," Nano Lett., Vol. 11, 471-475, 2011.
38. Fu, Y., X. Hu, and Q. Gong, "Silicon photonic crystal all optical logic gates," Phys. Lett. A, Vol. 377, 329-333, 2013.
39. Wang, H., X. Yu, and X. Rong, "All-optical AND, XOR, and NOT logic gates based on Y-branch photonic crystal waveguide," Opt. Eng., Vol. 54, 077101, 2015.
40. Fan, R., X. Yang, X. Meng, and X. Sun, "2D photonic crystal logic gates based on self-collimated effect," J. Phys. D: Appl. Phys., Vol. 49, 325104, 2016.
41. Sang, Y., X. Wu, S. S. Raja, C. Wang, H. Li, Y. Ding, D. Liu, J. Zhou, H. Ahn, S. Gwo, and J. Shi, "Broadband multifunctional plasmonic logic gates," Adv. Opt. Mater., Vol. 6, 1701368, 2018.
42. Manjappa, M., P. Pitchappa, N. Singh, N. Wang, N. I. Zheludev, C. Lee, and R. Singh, "Reconfigurable MEMS Fano metasurfaces with multiple-input-output states for logic operations at terahertz frequencies," Nat. Commun., Vol. 9, 4056, 2018.
43. Qian, C., X. Lin, X. Lin, J. Xu, Y. Sun, E. Li, B. Zhang, and H. Chen, "Performing optical logic operations by a diffractive neural network," Light: Sci. Appl., Vol. 9, 59, 2020.
44. He, Y., P. Wang, C. Wang, J. Liu, H. Ye, X. Zhou, Y. Li, S. Chen, X. Zhang, and D. Fan, "All-optical signal processing in structured light multiplexing with dielectric meta-optics," ACS Photon., Vol. 7, 135, 2020.
45. Dang, Z., T. Chen, Z. Ding, Z. Liu, X. Zhang, X. Jiang, and Z. Zhang, "Multiport all-logic optical switch based on thermally altered light paths in a multimode waveguide," Opt. Lett., Vol. 46, 3025-3028, 2021.
46. Chao, M., B. Cheng, Q. Liu, W. Zhang, Y. Xu, and G. Song, "Novel optical XOR/OR logic gates based on topologically protected valley photonic crystals edges," J. Opt., Vol. 23, 115002, 2021.
47. Zhao, Z., Y. Wang, X. Ding, H. Li, J. Fu, K. Zhang, S. N. Burokur, and Q. Wu, "Compact logic operator utilizing a single-layer metasurface," Photon. Res., Vol. 10, 316-322, 2022.
48. Jensen, J. S. and O. Sigmund, "Topology optimization for nano-photonics," Laser Photon. Rev., Vol. 5, 308-321, 2011.
49. Rodríguez, J. A., A. I. Abdalla, B. Wang, B. Lou, S. Fan, and M. A. Cappelli, "Inverse design of plasma metamaterial devices for optical computing," Phys. Rev. Applied, Vol. 16, 014023, 2021.
50. Chung, H., J. Park, and S. V. Boriskina, "Inverse-designed waveguide-based biosensor for high-sensitivity, single-frequency detection of biomolecules," Nanophotonics, Vol. 11, 1427-1442, 2022.