Vol. 175
Latest Volume
All Volumes
PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2022-10-15
Solving Multivariable Equations with Tandem Metamaterial Kernels
By
Progress In Electromagnetics Research, Vol. 175, 139-147, 2022
Abstract
A fundamental building block in characterizing and tackling scientific and industrial questions boils down to the ability of quickly solving mathematical equations. However, with the ever-growing volume of information and unsustainable integration growth in electronic processors, a radically new modality for solving equations is highly imminent. Here, we introduce an electromagnetic counterpart to solve multivariable complex equations, where two metamaterialkernels are connected in series to form a closed-loop electromagnetic system. Complex-valued information is carried by electromagnetic fields, and the equation solution for arbitrary input signals can be recursively attained after a number of feedbacks. As an illustration, we present the capability of such system in solving eight complex equations, and inversely design two 4 × 4 metamaterialkernels by topology optimization, whose average element error is reduced to smaller than 10-4. Having accomplished all unknown coefficients with high fidelity, our work represents a conspicuous apparatus for a myriad of enticing applications in ultra-compact signal processing and neuromorphic computing.
Citation
Qingze Tan, Chao Qian, Tong Cai, Bin Zheng, and Hongsheng Chen, "Solving Multivariable Equations with Tandem Metamaterial Kernels," Progress In Electromagnetics Research, Vol. 175, 139-147, 2022.
doi:10.2528/PIER22060601
References

1. Waldrop, M. M., "The chips are down for Moore's law," Nature, Vol. 530, 144-147, 2016.
doi:10.1038/530144a

2. Solli, D. R. and B. Jalali, "Analog optical computing," Nat. Photon., Vol. 9, 704-706, 2015.
doi:10.1038/nphoton.2015.208

3. Lee, S. H., "Optical analog solutions of partial differential and integral equations," Opt. Eng., Vol. 24, 240141, 1985.
doi:

4. Ferrera, M., Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azana, "On-chip CMOS-compatible all-optical integrator," Nat. Commun., Vol. 1, 1-5, 2010.
doi:10.1038/ncomms1028

5. Rajbenbach, H., Y. Fainman, and S. H. Lee, "Optical implementation of an iterative algorithm for matrix inversion," Appl. Opt., Vol. 26, 1024-1031, 1987.
doi:10.1364/AO.26.001024

6. Wu, K., C. Soci, P. P. Shum, and N. I. Zheludev, "Computing matrix inversion with optical networks," Opt. Express, Vol. 22, 295-304, 2014.
doi:10.1364/OE.22.000295

7. Cederquist, J., "Integral-equation solution using coherent optical feedback," J. Opt. Soc. Am., Vol. 71, 651-655, 1981.
doi:10.1364/JOSA.71.000651

8. Cederquist, J. and S. H. Lee, "Coherent optical feedback for the analog solution of partial differential equations," J. Opt. Soc. Am., Vol. 70, 944-953, 1980.
doi:10.1364/JOSA.70.000944

9. Leger, J. R. and S. H. Lee, "Coherent optical implementation of generalized two-dimensional transforms," Opt. Eng., Vol. 18, 185518, 1979.
doi:10.1117/12.7972422

10. 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.
doi:10.1038/s41566-020-0604-2

11. Gong, D., T. Ma, J. Evans, and S. He, "Deep neural networks for image super-resolution in optical microscopy by using modified hybrid task cascade U-net," Progress In Electromagnetics Research, Vol. 171, 185-199, 2021.
doi:10.2528/PIER21110904

12. Chen, X., Z. Wei, M. Li, and P. Rocca, "A review of deep learning approaches for inverse scattering problems," Progress In Electromagnetics Research, Vol. 167, 67-81, 2020.
doi:10.2528/PIER20030705

13. 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.
doi:10.1364/PRJ.418445

14. Qian, C. and H. Chen, "A perspective on the next generation of invisibility cloaks --- Intelligent cloaks," Appl. Phys. Lett., Vol. 118, 180501, 2021.
doi:10.1063/5.0049748

15. Hua, Y., C. Qian, H. Chen, and H. Wang, "Experimental topology-optimized cloak for water waves," Mater. Today Phys., Vol. 27, 100754, 2022.
doi:10.1016/j.mtphys.2022.100754

16. 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.
doi:10.1126/sciadv.abn7905

17. 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.

18. 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.
doi:10.1038/s41467-022-30377-6

19. 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.
doi:10.1117/1.AP.3.3.036003

20. 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.
doi:10.1038/s41467-022-32067-9

21. Zhang, J., C. Qian, Z. Fan, J. Chen, E. Li, J. Jin, and H. Chen, "Heterogeneous transfer-learning-enabled diverse metasurface design," Adv. Opt. Mater., Vol. 2200748, 1-9, 2022.

22. 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. 32, 2109331, 2022.
doi:10.1002/adfm.202109331

23. Hu, Z., N. He, Y. Sun, Y. Jin, and S. He, "Wideband high-re ection chiral dielectric metasurface," Progress In Electromagnetics Research, Vol. 172, 51-60, 2021.
doi:10.2528/PIER21121903

24. Wu, N., Y. Zhang, H. Ma, H. Chen, and H. Qian, "Tunable high-Q plasmonic metasurface with multiple surface lattice resonances," Progress In Electromagnetics Research, Vol. 172, 23-32, 2021.
doi:10.2528/PIER21112006

25. 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.
doi:10.1364/PRJ.7.000823

26. 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.
doi:10.1002/aisy.202100066

27. 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.
doi:10.1038/s41377-020-0303-2

28. Zhou, Y., H. Zheng, I. I. Kravchenko, and J. Valentine, "Flat optics for image differentiation," Nat. Photon, Vol. 14, 316-323, 2020.
doi:10.1038/s41566-020-0591-3

29. Kwon, H., D. Sounas, A. Cordaro, A. Polman, and A. Alu, "Nonlocal metasurfaces for optical signal processing," Phys. Rev. Lett., Vol. 121, 173004, 2018.
doi:10.1103/PhysRevLett.121.173004

30. Cordaro, A., H. Kwon, D. Sounas, A. F. Koenderink, A. Alu, and A. Polman, "High-index dielectric metasurfaces performing mathematical operations," Nano Lett., Vol. 19, 8418-8423, 2019.
doi:10.1021/acs.nanolett.9b02477

31. Silva, A., F. Monticone, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, "Performing mathematical operations with metamaterials," Science, Vol. 343, 160-163, 2014.
doi:10.1126/science.1242818

32. Su, L., A. Y. Piggott, N. V. Sapra, J. Petykiewicz, and J. Vuckovic, "Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer," ACS Photon., Vol. 5, 301-305, 2017.
doi:10.1021/acsphotonics.7b00987

33. Jensen, J. S. and O. Sigmund, "Topology optimization for nano-photonics," Laser Photonics Rev., Vol. 5, 308-321, 2011.
doi:10.1002/lpor.201000014

34. Qu, Y., H. Zhu, Y. Shen, J. Zhang, C. Tao, P. Ghosh, and M. Qiu, "Inverse design of an integrated-nanophotonics optical neural network," Sci. Bull., Vol. 65, 1177-1183, 2020.
doi:10.1016/j.scib.2020.03.042

35. Hughes, T. W., I. A. D. Williamson, M. Minkov, and S. Fan, "Wave physics as analog recurrent neural network," Sci. Adv., Vol. 5, eaay6946, 2019.
doi:10.1126/sciadv.aay6946

36. Harris, N. C., J. Carolan, D. Bunandar, M. Prabhu, M. Hochberg, T. Baehr-Jones, M. L. Fanto, A. M. Smith, C. C. Tison, P. M. Alsing, and D. Englund, "Linear programmable nanophotonic processors," Optica, Vol. 5, 1623, 2018.
doi:10.1364/OPTICA.5.001623

37. Estakhri, N. M., B. Edwards, and N. Engheta, "Inverse-designed metastructures that solve equations," Science, Vol. 363, 1333-1338, 2019.
doi:10.1126/science.aaw2498

38. Camacho, M., B. Edwards, and N. Engheta, "A single inverse-designed photonic structure that performs parallel computing," Nat. Commun., Vol. 12, 1466, 2021.
doi:10.1038/s41467-021-21664-9

39. Hughes, T. W., M. Minkov, Y. Shi, and S. Fan, "Training of photonic neural networks through in situ backpropagation and gradient measurement," Optica, Vol. 5, 864-871, 2018.
doi:10.1364/OPTICA.5.000864

40. Beneck, R. J., A. Das, G. Mackertich-Sengerdy, R. J. Chaky, Y. Wu, S. Soltani, and D. Werner, "Reconfigurable antennas: A review of recent progress and future prospects for next generation," Progress In Electromagnetics Research, Vol. 171, 89-121, 2021.
doi:10.2528/PIER21081109

41. 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, No. 2, 158-178, 2022.