Non-reciprocal frequency transition with harmonic order doubling in spacetime crystals
-
摘要:
针对传统磁性非互易器件体积庞大、成本高昂且损耗严重的问题，本文提出了一种基于基片集成波导（Substrate Integrated Waveguide, SIW）的时空晶体超表面天线，可实现紧凑、高效的无磁非互易辐射与波束调控。利用现场可编程门阵列（Field Programmable Gate Array, FPGA）控制PIN二极管阵列在SIW表面实现等效动态行波调制，并基于Floquet-Bloch理论构建色散模型，阐明了时变系统中的动态色散及谐波模式选择机制。实验结果表明：在波导端口激励下，实现了频率-动量映射的多波束辐射；而在自由空间入射条件下，则观测到了确定性的非互易频谱跃迁现象，信号遵循谐波阶数倍增的规律发生频率上转换。实验在一阶及高阶谐波通道中均证实了时间反演对称性破缺，并实现了高达17.9dB的非互易隔离度。该研究验证了SIW时空编码技术在构建无磁非互易器件方面的有效性，为在下一代智能无线通信系统中实现频率转换、单向传输、伪多普勒效应提供了一种有效的技术途径。
Abstract:Our work presents a spacetime crystal metasurface antenna based on substrate integrated waveguide (SIW). It addresses the limitations of traditional magnetic non-reciprocal devices, such as large volume, high cost, and significant losses. The proposed antenna enables compact, efficient, magnetless non-reciprocal radiation and beam manipulation. An FPGA (Field Programmable Gate Array)-controlled PIN diode array is employed to implement equivalent dynamic traveling-wave modulation on the SIW surface. A dispersion model, combining Floquet-Bloch theory and the transfer matrix method, elucidates the dynamic dispersion characteristics and the harmonic mode selection mechanism in the time-varying system. Experimental results demonstrate that, under waveguide port excitation, the system generates multi-beam radiation governed by frequency-momentum mapping. In contrast, under free-space incidence conditions, a deterministic non-reciprocal spectral transition is observed, where the signals undergo frequency up-conversion according to a harmonic order-doubling rule. The device achieves a maximum non-reciprocal isolation of 17.9 dB, confirming the breaking of time-reversal symmetry in both the first- and higher-order harmonic channels. This work validates the effectiveness of SIW-based spacetime coding technology for constructing magnetless non-reciprocal devices, providing a promising technological approach for frequency conversion, unidirectional transmission, and pseudo-Doppler effects in next-generation intelligent wireless communication systems.
-
图 1 时空晶体的色散关系和辐射模式分析。(a) 均匀调制的时空晶体在纯空间截断下的示意图。(b) 基于能带结构的Floquet-Bloch模式激发机理分析。
Figure 1. Dispersion relation and radiation mode analysis of the spacetime crystal. (a) Schematic of a uniformly modulated spacetime crystal subject to purely spatial truncation. (b) Analysis of the Floquet-Bloch mode excitation mechanism based on the band structure.
图 2 时空晶体天线的结构与实验系统示意图。(a) 所提出的SIW时空晶体天线的三维分解结构图,该周期性阵列由82个单元组成。(b)元原子的局部放大图，PIN二极管用于实现单元的可编程开关。(c) 实验系统示意图
Figure 2. Schematic of the spacetime crystal antenna structure and experimental system. (a) Exploded 3D view of the proposed SIW spacetime crystal antenna, whose periodic array consists of 82 unit cells. (b) Enlarged view of a single meta-atom, where PIN diodes enable programmable switching of the unit. (c) Schematic of the experimental system.
图 3 时空晶体天线的散射模式与实验结果分析。(a) 时空晶体天线的实验装置示意图。(b) 波导端口激励下不同阶次模式（m=1,2,3）的极坐标辐射图。(c) 时空晶体的色散关系图。(d) 色散关系的局部放大图。(e) 基于色散关系的角度-频率映射图。
Figure 3. Scattering modes and experimental characterization of the spacetime crystal antenna. (a) Experimental setup of the spacetime crystal antenna. (b) Polar radiation patterns of different-order modes (m=1, 2, 3) under waveguide-port excitation. (c) Dispersion relation of the spacetime crystal. (d) Enlarged view of the dispersion relation. (e) Angle-frequency mapping derived from the dispersion relation.
图 4 时空晶体天线的非互易性散射模式与频谱响应实验结果。(a) 端口2激发信号ω1=ω0+Ω，入射角θ1≈40°时的实验示意图。(b) 对应的时空晶体色散关系图。(c) θ1≈40°时接收信号在ω2=ω0+2Ω处的频谱响应。(d) 端口3激发信号ω2=ω0+2Ω，入射角θ2≈0°时的实验示意图。(e) 对应的时空晶体色散关系图。(f) θ2≈0°时接收信号在ω4=ω0+4Ω处的频谱响应。(g) 端口4激发信号ω3=ω0+3Ω，入射角θ3≈-38°时的实验示意图。(h) 对应的时空晶体色散关系图。(i) θ3≈-38°时接收信号在ω6=ω0+6Ω处的频谱响应。
Figure 4. Experimental characterization of non-reciprocal scattering modes and spectral responses in the spacetime crystal antenna. (a) Experimental setup for Port-2 excitation at ω1=ω0+Ω with an incident angle of θ1≈40°. (b) Corresponding dispersion relation of the spacetime crystal. (c) Spectral response of the received signal at ω2=ω0+2Ω for θ1≈40°. (d) Experimental setup for Port-3 excitation at ω2=ω0+2Ω with an incident angle of θ2≈0°. (e) Corresponding dispersion relation of the spacetime crystal. (f) Spectral response of the received signal at ω4=ω0+4Ω for θ2≈0°. (g) Experimental setup for Port-4 excitation at ω3=ω0+3Ω with an incident angle of θ3≈-38°. (h) Corresponding dispersion diagram of the spacetime crystal. (i) Spectral response of the received signal at ω6=ω0+6Ω for θ3≈-38°.
-
[1] CALOZ C, ALÙ A, TRETYAKOV S, et al. Electromagnetic nonreciprocity[J]. Physical Review Applied, 2018, 10(4): 047001. doi: 10.1103/PhysRevApplied.10.047001 [2] GUO X X, DING Y M, DUAN Y, et al. Nonreciprocal metasurface with space–time phase modulation[J]. Light: Science & Applications, 2019, 8(1): 123. [3] JIA R D, TAN T C, MISHRA S S, et al. On-chip active non-reciprocal topological photonics[J]. Advanced Materials, 2025, 37(26): 2501711. [4] WANG ZH B, ZHANG Y L, HU X X, et al. Self-induced optical non-reciprocity[J]. Light: Science & Applications, 2025, 14(1): 23. [5] FENG W B, FAN X Y, YANG H S, et al. Suppressing polarization non-reciprocity and backscattering noise in dual-polarization modulation and sensing interferometric fiber optic gyroscope[J]. Journal of Lightwave Technology, 2025, 43(20): 9724-9732. doi: 10.1109/JLT.2025.3605360 [6] PEDERGNANA T, FAURE-BEAULIEU A, FLEURY R, et al. Loss-compensated non-reciprocal scattering based on synchronization[J]. Nature Communications, 2024, 15(1): 7436. doi: 10.1038/s41467-024-51373-y [7] CHAO K, YAM V, VIVIEN L, et al. Critical nonreciprocity in gyrotropic coupled-waveguide system for TE-mode optical isolator and circulator[J]. arXiv preprint arXiv: 2502.10075, 2025. (查阅网上资料, 不确定本条文献类型及格式是否正确, 请确认). [8] REGEV D, REGEV S, SHILO S, et al. Non-magnetic four-port electronic circulators based on 90∘ non-reciprocal phase-shifters[J]. Scientific Reports, 2024, 14(1): 4022. doi: 10.1038/s41598-024-54468-0 [9] GUO CH, ASADCHY V S, ZHAO B, et al. Light control with Weyl semimetals[J]. eLight, 2023, 3(1): 2. doi: 10.1186/s43593-022-00036-w [10] LI H Y, CLERCKX B. Non-reciprocal beyond diagonal RIS: multiport network models and performance benefits in full-duplex systems[J]. IEEE Transactions on Communications, 2025, 73(11): 12221-12234. doi: 10.1109/TCOMM.2025.3568222 [11] FANG X Y, LI M M, LAI Z Y, et al. Multifunctional space–time-modulated metasurface for direction of arrival estimation and RCS manipulation in a single system[J]. IEEE Transactions on Microwave Theory and Techniques, 2024, 72(6): 3797-3808. doi: 10.1109/TMTT.2023.3330898 [12] TAKAHAGI K, TENNANT A. Fundamental study on electrically controllable broadband and thin non-reciprocal metasurface[C]. 2023 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (USNC-URSI), IEEE, 2023: 1421-1422. [13] ADAM J D, DAVIS L E, DIONNE G F, et al. Ferrite devices and materials[J]. IEEE Transactions on Microwave Theory and Techniques, 2002, 50(3): 721-737. doi: 10.1109/22.989957 [14] SRAVYA K S S, CHEDURUPALLI S, RAJU K C J. Magnet-less circulator with bulk acoustic wave filter delay elements[C]. 2023 IEEE Microwaves, Antennas, and Propagation Conference (MAPCON), IEEE, 2023: 1-4. [15] ZARIF A, JAMSHIDI K. Non-reciprocity in a silicon photonic ring resonator with time-modulated regions[J]. Optics Express, 2024, 32(15): 26938-26953. doi: 10.1364/OE.521475 [16] KORD A, ALÙ A. Magnetless circulators based on synthetic angular-momentum bias: recent advances and applications[J]. IEEE Antennas and Propagation Magazine, 2021, 63(6): 51-61. doi: 10.1109/MAP.2020.3043437 [17] SHI Y, YU Z F, FAN SH H. Limitations of nonlinear optical isolators due to dynamic reciprocity[J]. Nature Photonics, 2015, 9(6): 388-392. doi: 10.1038/nphoton.2015.79 [18] SHALTOUT A, KILDISHEV A, SHALAEV V. Time-varying metasurfaces and Lorentz non-reciprocity[J]. Optical Materials Express, 2015, 5(11): 2459-2467. doi: 10.1364/OME.5.002459 [19] HAGAG M F, JONES T R, SEDDIK K, et al. Nonreciprocal signal growth in space-time modulated transmission lines[J]. Scientific Reports, 2025, 15(1): 18992. doi: 10.1038/s41598-025-03006-7 [20] TARAVATI S. Giant linear nonreciprocity, zero reflection, and zero band gap in equilibrated space-time-varying media[J]. Physical Review Applied, 2018, 9(6): 064012. doi: 10.1103/PhysRevApplied.9.064012 [21] TOUBOUL M, LOMBARD B, ASSIER R C, et al. High-order homogenization of the time-modulated wave equation: non-reciprocity for a single varying parameter[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2024, 480(2289): 20230776. doi: 10.1098/rspa.2023.0776 [22] 何真, 卓立强, 李志, 等. 石墨烯等离激元时间晶体中的慢光[J]. 中国光学(中英文), 2022, 15(4): 845-861.HE ZH, ZHUO L Q, LI ZH, et al. Slow light in graphene plasmonic time crystals[J]. Chinese Optics, 2022, 15(4): 845-861. (in Chinese). [23] SOUNAS D L, ALÙ A. Non-reciprocal photonics based on time modulation[J]. Nature Photonics, 2017, 11(12): 774-783. doi: 10.1038/s41566-017-0051-x [24] CHEN X Q, ZHANG L, ZHENG Y N, et al. Integrated sensing and communication based on space-time-coding metasurfaces[J]. Nature Communications, 2025, 16(1): 1836. doi: 10.1038/s41467-025-57137-6 [25] HU Y, CHEN SH N, SHI Y, et al. Space-time coding metasurface for multifunctional holographic imaging[J]. Advanced Materials Technologies, 2024, 9(12): 2302164. doi: 10.1002/admt.202302164 [26] 张磊, 崔铁军. 时空编码数字超材料和超表面研究进展[J]. 中国科学基金, 2021, 35(5): 694-700. doi: 10.16262/j.cnki.1000-8217.2021.05.004ZHANG L, CUI T J. Recent progress of space-time-coding digital metamaterials and metasurfaces[J]. Bulletin of National Natural Science Foundation of China, 2021, 35(5): 694-700. (in Chinese). doi: 10.16262/j.cnki.1000-8217.2021.05.004 [27] JIANG ZH Y, WU ZH Q, ZHANG CH, et al. Angle-resolved multimode engineering in spacetime crystals[J]. Science China Physics, Mechanics & Astronomy, 2026, 69(4): 244212. [28] ZHAO H Q, SMALYUKH I I. Space-time crystals from particle-like topological solitons[J]. Nature Materials, 2025, 24(11): 1802-1811. doi: 10.1038/s41563-025-02344-1 [29] RASKATLA V, LIU T, LI J, et al. Continuous space-time crystal state driven by nonreciprocal optical forces[J]. Physical Review Letters, 2024, 133(13): 136202. doi: 10.1103/PhysRevLett.133.136202 [30] JIANG ZH Y, WU ZH Q, MA Q CH, et al. Multicolor space-time engineering to steer a frequency comb[J]. Physical Review Applied, 2025, 24(4): 044004. doi: 10.1103/xmg5-cbl2 [31] HE J H, ZHUANG J K, MA Q CH, et al. Nonlinear refractive index compensation enables accurate spectral shifting in varactor-driven plasmonic waveguides[J]. Applied Physics Letters, 2026, 128(11): 111104. doi: 10.1063/5.0316546 [32] TARAVATI S, ELEFTHERIADES G V. Full-duplex nonreciprocal beam steering by time-modulated phase-gradient metasurfaces[J]. Physical Review Applied, 2020, 14(1): 014027. doi: 10.1103/PhysRevApplied.14.014027 [33] TARAVATI S. Nonreciprocal entanglement of frequency-distinct qubits[J]. Advanced Quantum Technologies, 2025, 8(10): e2500171. [34] ZHANG CH, WU ZH Q, JIANG ZH Y, et al. Spacetime crystals engineering sideband-free radiation for high-rate transmission[J]. Communications Physics, 2025, 8(1): 490. doi: 10.1038/s42005-025-02395-5 [35] ZHUANG J K, MA Q CH, JIANG ZH Y, et al. Temporal pulse engineering of spectral evolution in a synthetic frequency lattice[J]. Chinese Physics Letters, 2025, 42(10): 100404. doi: 10.1088/0256-307X/42/10/100404 [36] YU Z F, FAN SH H. Complete optical isolation created by indirect interband photonic transitions[J]. Nature Photonics, 2009, 3(2): 91-94. doi: 10.1038/nphoton.2008.273 [37] LIRA H, YU Z F, FAN SH H, et al. Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip[J]. Physical Review Letters, 2012, 109(3): 033901. doi: 10.1103/PhysRevLett.109.033901 [38] PAKNIYAT S, GOMEZ-DIAZ J S. Magnet-free electromagnetic nonreciprocity in two-dimensional materials[J]. Journal of Applied Physics, 2024, 136(4): 041101. doi: 10.1063/5.0207377 -
下载:
计量
- 文章访问数: 34
- HTML全文浏览量: 20
- PDF下载量: 1
- 被引次数: 0
