Vol. 186
Latest Volume
All Volumes
PIER 186 PIER 185 PIER 184 PIER 183 PIER 182 PIER 181 PIER 180 PIER 179 PIER 178 PIER 177 PIER 176 PIER 175 PIER 174 PIER 173 PIER 172 PIER 171 PIER 170 PIER 169 PIER 168 PIER 167 PIER 166 PIER 165 PIER 164 PIER 163 PIER 162 PIER 161 PIER 160 PIER 159 PIER 158 PIER 157 PIER 156 PIER 155 PIER 154 PIER 153 PIER 152 PIER 151 PIER 150 PIER 149 PIER 148 PIER 147 PIER 146 PIER 145 PIER 144 PIER 143 PIER 142 PIER 141 PIER 140 PIER 139 PIER 138 PIER 137 PIER 136 PIER 135 PIER 134 PIER 133 PIER 132 PIER 131 PIER 130 PIER 129 PIER 128 PIER 127 PIER 126 PIER 125 PIER 124 PIER 123 PIER 122 PIER 121 PIER 120 PIER 119 PIER 118 PIER 117 PIER 116 PIER 115 PIER 114 PIER 113 PIER 112 PIER 111 PIER 110 PIER 109 PIER 108 PIER 107 PIER 106 PIER 105 PIER 104 PIER 103 PIER 102 PIER 101 PIER 100 PIER 99 PIER 98 PIER 97 PIER 96 PIER 95 PIER 94 PIER 93 PIER 92 PIER 91 PIER 90 PIER 89 PIER 88 PIER 87 PIER 86 PIER 85 PIER 84 PIER 83 PIER 82 PIER 81 PIER 80 PIER 79 PIER 78 PIER 77 PIER 76 PIER 75 PIER 74 PIER 73 PIER 72 PIER 71 PIER 70 PIER 69 PIER 68 PIER 67 PIER 66 PIER 65 PIER 64 PIER 63 PIER 62 PIER 61 PIER 60 PIER 59 PIER 58 PIER 57 PIER 56 PIER 55 PIER 54 PIER 53 PIER 52 PIER 51 PIER 50 PIER 49 PIER 48 PIER 47 PIER 46 PIER 45 PIER 44 PIER 43 PIER 42 PIER 41 PIER 40 PIER 39 PIER 38 PIER 37 PIER 36 PIER 35 PIER 34 PIER 33 PIER 32 PIER 31 PIER 30 PIER 29 PIER 28 PIER 27 PIER 26 PIER 25 PIER 24 PIER 23 PIER 22 PIER 21 PIER 20 PIER 19 PIER 18 PIER 17 PIER 16 PIER 15 PIER 14 PIER 13 PIER 12 PIER 11 PIER 10 PIER 09 PIER 08 PIER 07 PIER 06 PIER 05 PIER 04 PIER 4 PIER 03 PIER 02 PIER 01
2026-10-03
Freeform Direct-Written Nonreciprocal Metasurfaces on Ferrite Film for Terahertz Bidirectional Beam Modulation
By
Progress In Electromagnetics Research, Vol. 186, 64-71, 2026
Abstract
Bidirectional wavefront control requires metasurfaces that encode distinct responses in opposite propagation directions. Ferrite films possessing nonreciprocity at terahertz frequencies are crucial for bidirectional control; however, they are difficult to pattern. We address this materials-fabrication mismatch by one-step, resist-free femtosecond direct laser writing (DLW), which directly transforms continuous low-loss lanthanum-doped yttrium iron garnet (La:YIG) films into freeform nonreciprocal metasurfaces. This approach sculpts complete nonreciprocal metasurfaces (NRMs) with meta-atoms in a wide variety of prism geometries, including hexagonal, oval, rectangular, and pentagonal forms, directly in the film. By reconfiguring gyrotropic resonances of each element, we demonstrate precise nonreciprocal control of THz beams through unidirectional transmission, bidirectional beam focusing, and holographic imaging. This streamlined fabrication strategy dramatically lowers the barrier to NRM research and broadens its applicability across several scientific fields.
Supplementary Information
Citation
Qindong Xie, Weihao Yang, Zechuan Bin, Xiaowei Wang, Xiuli Yue, Tang Fu, Lei Bi, Baile Zhang, and Peiheng Zhou, "Freeform Direct-Written Nonreciprocal Metasurfaces on Ferrite Film for Terahertz Bidirectional Beam Modulation," Progress In Electromagnetics Research, Vol. 186, 64-71, 2026.
doi:10.2528/PIER26072705
References

1. Zhang, Xi-Cheng and Jingzhou Xu, Introduction to THz Wave Photonics, Springer, 2010.
doi:10.1007/978-1-4419-0978-7

2. Ferguson, Bradley and Xi-Cheng Zhang, "Materials for terahertz science and technology," Nature Materials, Vol. 1, 26-33, September 2002.
doi:10.1038/nmat708        Google Scholar

3. Zhang, X.-C., "Terahertz wave imaging: Horizons and hurdles," Physics in Medicine and Biology, Vol. 47, No. 21, 3667-3677, October 2002.
doi:10.1088/0031-9155/47/21/301        Google Scholar

4. Lyu, Nanfang, Jian Zuo, Yuanmeng Zhao, and Cunlin Zhang, "Terahertz synthetic aperture imaging with a light field imaging system," Electronics, Vol. 9, No. 5, 830, 2020.
doi:10.3390/electronics9050830        Google Scholar

5. Liu, Bingwei, Yan Peng, Yufan Hao, Yiming Zhu, Shengjiang Chang, and Songlin Zhuang, "Ultra-wideband terahertz fingerprint enhancement sensing and inversion model supported by single-pixel reconfigurable graphene metasurface," PhotoniX, Vol. 5, 435-465, April 2024.
doi:10.1186/s43074-024-00129-4        Google Scholar

6. Cai, Bin, Lingling Yang, Ling Wu, Yongzhi Cheng, and Xiangcheng Li, "Dual-narrowband terahertz metamaterial absorber based on all-metal vertical ring array for enhanced sensing application," Physica Scripta, Vol. 99, No. 9, 095503, August 2024.
doi:10.1088/1402-4896/ad65c3        Google Scholar

7. Yang, Yihao, Yuichiro Yamagami, Xiongbin Yu, Prakash Pitchappa, Julian Webber, Baile Zhang, Masayuki Fujita, Tadao Nagatsuma, and Ranjan Singh, "Terahertz topological photonics for on-chip communication," Nature Photonics, Vol. 14, No. 7, 446-451, April 2020.
doi:10.1038/s41566-020-0618-9        Google Scholar

8. Wang, Wenhao, Yi Ji Tan, Thomas CaiWei Tan, Abhishek Kumar, Prakash Pitchappa, Pascal Szriftgiser, Guillaume Ducournau, and Ranjan Singh, "On-chip topological beamformer for multi-link terahertz 6G to XG wireless," Nature, Vol. 632, No. 8025, 522-527, August 2024.
doi:10.1038/s41586-024-07759-5        Google Scholar

9. Zhao, Dan, Fei Fan, Jiayue Liu, Zhiyu Tan, Hao Wang, Qinghui Yang, Qiye Wen, and Shengjiang Chang, "Terahertz magneto-optical metadevice for active spin-selective beam steering and energy distribution with nonreciprocal isolation," Optica, Vol. 10, No. 10, 1295-1301, September 2023.
doi:10.1364/optica.499425        Google Scholar

10. Zhao, Dan, Fei Fan, Qiang Xue, Hao Wang, Yunyun Ji, Qinghui Yang, Qiye Wen, and Shengjiang Chang, "Terahertz magnetic moiré grating for enhanced chirality manipulation and nonreciprocal spin isolation," Advanced Functional Materials, Vol. 34, No. 42, 2404881, April 2024.
doi:10.1002/adfm.202404881        Google Scholar

11. Caloz, Christophe, Andrea Alù, Sergei Tretyakov, Dimitrios Sounas, Karim Achouri, and Zoé-Lise Deck-Léger, "Electromagnetic nonreciprocity," Physical Review Applied, Vol. 10, 047001, 2018.
doi:10.1103/physrevapplied.10.047001        Google Scholar

12. Yu, Zongfu and Shanhui Fan, "Complete optical isolation created by indirect interband photonic transitions," Nature Photonics, Vol. 3, 91-94, 2009.
doi:10.1038/nphoton.2008.273        Google Scholar

13. Yu, Letian and Baile Zhang, "Energy variation in stochastically driven light walks [Invited]," Optical Materials Express, Vol. 15, No. 3, 555, February 2025.
doi:10.1364/ome.546407        Google Scholar

14. Long, Yang, Linyang Zou, Letian Yu, Hao Hu, Jiang Xiong, and Baile Zhang, "Inverse design of topological photonic time crystals via deep learning," Optical Materials Express, Vol. 14, No. 8, 2032, July 2024.
doi:10.1364/ome.525396        Google Scholar

15. Tripathi, Aditya, Chibuzor Fabian Ugwu, Viktar S. Asadchy, Ihar Faniayeu, Ivan Kravchenko, Shanhui Fan, Yuri Kivshar, Jason Valentine, and Sergey S. Kruk, "Nanoscale optical nonreciprocity with nonlinear metasurfaces," Nature Communications, Vol. 15, No. 1, 5077, June 2024.
doi:10.1038/s41467-024-49436-1        Google Scholar

16. Cotrufo, Michele, Andrea Cordaro, Dimitrios L. Sounas, Albert Polman, and Andrea Alù, "Passive bias-free non-reciprocal metasurfaces based on thermally nonlinear quasi-bound states in the continuum," Nature Photonics, Vol. 18, No. 1, 81-90, November 2023.
doi:10.1038/s41566-023-01333-7        Google Scholar

17. Yang, Weihao, Jun Qin, Jiawei Long, Wei Yan, Yucong Yang, Chaoyang Li, En Li, Juejun Hu, Longjiang Deng, Qingyang Du, and Lei Bi, "A self-biased non-reciprocal magnetic metasurface for bidirectional phase modulation," Nature Electronics, Vol. 6, No. 3, 225-234, March 2023.
doi:10.1038/s41928-023-00936-w        Google Scholar

18. Liu, Gui-Geng, Subhaskar Mandal, Xiang Xi, Qiang Wang, Chiara Devescovi, Antonio Morales-Pérez, Ziyao Wang, Linyun Yang, Rimi Banerjee, Yang Long, Yan Meng, Peiheng Zhou, Zhen Gao, Yidong Chong, Aitzol García-Etxarri, Maia G. Vergniory, and Baile Zhang, "Photonic axion insulator," Science, Vol. 387, No. 6730, 162-166, January 2025.
doi:10.1126/science.adr5234        Google Scholar

19. Li, Yi-Lei, Teng-Fei Li, Qi-Ye Wen, Fei Fan, Qing-Hui Yang, and Sheng-Jiang Chang, "Terahertz magneto-optical effect of wafer-scale La: Yttrium iron garnet single-crystal film with low loss and high permittivity," Optics Express, Vol. 28, No. 14, 21062, July 2020.
doi:10.1364/oe.395668        Google Scholar

20. Li, Yi-Lei, Ding Zhang, Min Luo, Qing-Hui Yang, Fei Fan, Sheng-Jiang Chang, and Qi-Ye Wen, "Terahertz magneto-optical response of bismuth-gadolinium-substituted rare-earth garnet film," Optics Express, Vol. 29, No. 15, 23540, July 2021.
doi:10.1364/oe.431234        Google Scholar

21. Zhang, Xilai, Dan Zhao, Ding Zhang, Qiang Xue, Fei Fan, Yulong Liao, Qinghui Yang, and Qiye Wen, "Wafer-level substrate-free YIG single crystal film for a broadband tunable terahertz isolator," Photonics Research, Vol. 12, No. 3, 505, March 2024.
doi:10.1364/prj.509876        Google Scholar

22. Li, Zhen-Ze, Hua Fan, Lei Wang, Xu Zhang, Xin-Jing Zhao, Yan-Hao Yu, Yi-Shi Xu, Yi Wang, Xiao-Jie Wang, Saulius Juodkazis, Qi-Dai Chen, and Hong-Bo Sun, "Super-stealth dicing of transparent solids with nanometric precision," Nature Photonics, Vol. 18, No. 8, 799-808, May 2024.
doi:10.1038/s41566-024-01437-8        Google Scholar

23. Jiang, Lan, An-Dong Wang, Bo Li, Tian-Hong Cui, and Yong-Feng Lu, "Electrons dynamics control by shaping femtosecond laser pulses in micro/nanofabrication: Modeling, method, measurement and application," Light: Science & Applications, Vol. 7, No. 2, 17134, August 2017.
doi:10.1038/lsa.2017.134        Google Scholar

24. Meza, Lucas R., Satyajit Das, and Julia R. Greer, "Strong, lightweight, and recoverable three-dimensional ceramic nanolattices," Science, Vol. 345, No. 6202, 1322-1326, September 2014.
doi:10.1126/science.1255908        Google Scholar

25. Yuan, Shixing, Liao Chen, Ziwei Wang, Wentao Deng, Zhibo Hou, Chi Zhang, Yu Yu, Xiaojun Wu, and Xinliang Zhang, "On-chip terahertz isolator with ultrahigh isolation ratios," Nature Communications, Vol. 12, No. 1, 5570, September 2021.
doi:10.1038/s41467-021-25881-0        Google Scholar

26. Tamagnone, Michele, Clara Moldovan, Jean-Marie Poumirol, Alexey B. Kuzmenko, Adrian M. Ionescu, Juan R. Mosig, and Julien Perruisseau-Carrier, "Near optimal graphene terahertz non-reciprocal isolator," Nature Communications, Vol. 7, No. 1, 11216, April 2016.
doi:10.1038/ncomms11216        Google Scholar

27. Mu, Qianyi, Fei Fan, Sai Chen, Shitong Xu, Chuanzhong Xiong, Xin Zhang, Xianghui Wang, and Shengjiang Chang, "Tunable magneto-optical polarization device for terahertz waves based on InSb and its plasmonic structure," Photonics Research, Vol. 7, No. 3, 325-331, February 2019.
doi:10.1364/prj.7.000325        Google Scholar

28. Jia, Ridong, Thomas Caiwei Tan, Sobhan Subhra Mishra, Wenhao Wang, Yi Ji Tan, and Ranjan Singh, "On-chip active non-reciprocal topological photonics," Advanced Materials, Vol. 37, No. 26, 2501711, April 2025.
doi:10.1002/adma.202501711        Google Scholar

29. Lin, Shuai, Sinhara Silva, Jiangfeng Zhou, and Diyar Talbayev, "A one-way mirror: High-performance terahertz optical isolator based on magnetoplasmonics," Advanced Optical Materials, Vol. 6, No. 19, 1800572, July 2018.
doi:10.1002/adom.201800572        Google Scholar

30. Zhao, Dan, Fei Fan, Zhiyu Tan, Hao Wang, and Shengjiang Chang, "Tunable on-chip terahertz isolator based on nonreciprocal transverse edge spin state of asymmetric magneto-plasmonic waveguide," Laser & Photonics Reviews, Vol. 17, No. 2, 2200509, November 2022.
doi:10.1002/lpor.202200509        Google Scholar

31. Zhang, Jing Cheng, Geng-Bo Wu, Mu Ku Chen, Xiaoyu Che, Yao Liang, Din Ping Tsai, and Chi Hou Chan, "Electromagnetic wave tailoring: From one dimension to multiple dimensions," Electromagnetic Science, Vol. 1, No. 3, 1-21, September 2023.
doi:10.23919/emsci.2023.0013        Google Scholar

32. Liu, Changhao, Fan Yang, Shenheng Xu, and Maokun Li, "Reconfigurable metasurface: A systematic categorization and recent advances," Electromagnetic Science, Vol. 1, No. 4, 1-23, December 2023.
doi:10.23919/emsci.2023.0002        Google Scholar

33. Shalaginov, Mikhail Y., Sensong An, Yifei Zhang, Fan Yang, Peter Su, Vladimir Liberman, Jeffrey B. Chou, Christopher M. Roberts, Myungkoo Kang, Carlos Rios, Qingyang Du, Clayton Fowler, Anuradha Agarwal, Kathleen A. Richardson, Clara Rivero-Baleine, Hualiang Zhang, Juejun Hu, and Tian Gu, "Reconfigurable all-dielectric metalens with diffraction-limited performance," Nature Communications, Vol. 12, No. 1, 1225, February 2021.
doi:10.1038/s41467-021-21440-9        Google Scholar

34. Shalaginov, Mikhail Y., Sawyer D. Campbell, Sensong An, Yifei Zhang, Carlos Ríos, Eric B. Whiting, Yuhao Wu, Lei Kang, Bowen Zheng, Clayton Fowler, Hualiang Zhang, Douglas H. Werner, Juejun Hu, and Tian Gu, "Design for quality: Reconfigurable flat optics based on active metasurfaces," Nanophotonics, Vol. 9, No. 11, 3505-3534, June 2018.
doi:10.1515/nanoph-2020-0033        Google Scholar

35. Pi, Dapu, Juan Liu, and Yongtian Wang, "Review of computer-generated hologram algorithms for color dynamic holographic three-dimensional display," Light: Science & Applications, Vol. 11, No. 1, 231, July 2022.
doi:10.1038/s41377-022-00916-3        Google Scholar

36. Wu, Jiachen, Kexuan Liu, Xiaomeng Sui, and Liangcai Cao, "High-speed computer-generated holography using an autoencoder-based deep neural network," Optics Letters, Vol. 46, No. 12, 2908-2911, June 2021.
doi:10.1364/ol.425485        Google Scholar

37. Georgi, Philip, Qunshuo Wei, Basudeb Sain, Christian Schlickriede, Yongtian Wang, Lingling Huang, and Thomas Zentgraf, "Optical secret sharing with cascaded metasurface holography," Science Advances, Vol. 7, No. 16, eabf9718, April 2021.
doi:10.1126/sciadv.abf9718        Google Scholar

38. Shi, Liang, Beichen Li, Changil Kim, Petr Kellnhofer, and Wojciech Matusik, "Towards real-time photorealistic 3D holography with deep neural networks," Nature, Vol. 591, No. 7849, 234-239, March 2021.
doi:10.1038/s41586-020-03152-0        Google Scholar

39. Ni, Xingjie, Alexander V. Kildishev, and Vladimir M. Shalaev, "Metasurface holograms for visible light," Nature Communications, Vol. 4, 2807, 2013.
doi:10.1038/ncomms3807        Google Scholar

40. Wang, Lei, S. Kruk, Hanzhi Tang, T. Li, Ivan Kravchenko, Dragomir N. Neshev, and Y. Kivshar, "Grayscale transparent metasurface holograms," Optica, Vol. 3, No. 12, 1504-1505, 2016.
doi:10.1364/optica.3.001504        Google Scholar

41. Wu, Jun Wei, Zheng Xing Wang, Lei Zhang, Qiang Cheng, Shuo Liu, Shuang Zhang, Ji Ming Song, and Tie Jun Cui, "Anisotropic metasurface holography in 3-D space with high resolution and efficiency," IEEE Transactions on Antennas and Propagation, Vol. 69, No. 1, 302-316, January 2021.
doi:10.1109/tap.2020.3008659        Google Scholar

42. Nath, Uddipan, Sagnik Banerjee, Carlo Santini, Rocco Citroni, Fabio Mangini, and Fabrizio Frezza, "Simple and cost-effective design of a THz-metamaterial-based hybrid sensor on a single substrate," Sensors, Vol. 25, No. 12, 3660, 2025.
doi:10.3390/s25123660        Google Scholar