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磁共振无线电能传输(wireless power transfer, WPT)技术是近年来近场调控的研究重点之一, 其在移动电话、植入式医疗设备以及电动汽车等诸多方面都具有重要的应用价值. 对于复杂传能通道需求(例如机械臂等), 通常需要引入中继线圈构造多米诺耦合阵列. 然而, 传统的多米诺耦合阵列存在明显的局限性: 近场耦合导致的多重频率劈裂, 使得系统无法保持固定的工作频率; 耦合阵列易受到构造误差及参数扰动影响; 目前研究多数集中在单负载传输, 多负载传输系统仍然亟待开发; 能量传输方向难以灵活控制. 近年来, 光子人工微结构为拓扑物理提供了良好的研究平台, 使得拓扑特性得到了广泛的研究. 拓扑结构的最显著特征是具有非零的拓扑不变量以及由体边对应确定的鲁棒性边界态, 这一天然特性能够免疫制造缺陷和无序扰动. 不仅如此, 通过调整拓扑态的波函数分布能够使能量精准局域, 从而实现定向的WPT. 因此, 将拓扑模式用于耦合阵列WPT具有重要的科学意义. 本文主要阐明了基于宇称-时间(parity-time, PT)对称的通用型双线圈和三线圈WPT的基本原理, 并且介绍了不同拓扑构型下的多米诺线圈阵列能够实现鲁棒的WPT, 包括一维周期性模型(SSH链组成的有效二阶PT对称和有效三阶PT对称系统)、一维非周期性模型(拓扑缺陷态、类SSH链、准周期Harper链)以及高阶拓扑模型, 最后对拓扑模式在WPT的应用方向进行了展望.
Magnetic resonance wireless power transfer (WPT) has gradually become a popular research topic of near-field regulation in recent years, with wide applications in the fields of mobile phones, implantable medical devices, electric vehicles, and many other fields. However, several challenges remain to be addressed: near-field coupling, which induces multiple frequency splits and prevents the system from maintaining a fixed operating frequency; coupled arrays, which are susceptible to structural errors and parameter perturbations; current research, which primarily focuses on single-load transmission and has resulted in undeveloped multi-load transmission systems; the direction of transmission, which is difficult to control flexibly. In recent years, photonic artificial microstructures have provided a flexible platform for studying topological physics, arousing significant research interest in their fundamental topological characteristics. The most prominent features of topological structures are their nonzero topological invariant and the robust edge states determined by the bulk-edge correspondence: these features can overcome disturbances caused by defects and disorders. Moreover, by modulating the wave function distribution of topological states, energy can be precisely localized, enabling directional WPT. Therefore, implementing topological modes in WPT systems are of significant scientific importance. This review summarizes recent researches on topological models for robust WPT, which are divided into three main parts. The first part introduces one-dimensional periodic topological structures, focusing primarily on the significant improvements in transmission efficiency and robustness achieved by utilizing topological edge states in the Su-Schrieffer-Heeger (SSH) model for WPT. Moreover, a composite chain formed by two SSH chains is constructed to realize a higher-order parity-time (PT) symmetric topological model. This approach solves the frequency splitting caused by coupled edge states and exhibits lower power losses in standby mode. The second part discusses several types of aperiodic one-dimensional topological chains. By introducing topological defect states at the interface between two different dimer chains, robust multi-load WPT is achieved. Furthermore, based on the integration of artificial intelligence algorithms, the SSH-like topological model enables more efficient and robust WPT than traditional SSH model. The asymmetric edge states in quasi-periodic Harper chain provide a solution for directional transmission in WPT applications. By introducing nonlinear circuits, this model enables active control of the transfer direction. The third part presents the application of high-order topological corner states in multi-load robust WPT, demonstrating the selective excitation of both symmetric and asymmetric corner modes. Finally, the application prospects of topological modes in WPT systems are discussed. With the development of new physics, the integration of non-Hermitian physics and topological physics holds great promise for achieving simultaneous energy-information transfer, and is expected to achieve compatible WPT, wireless communication, and wireless sensing within a single system. Such a fusion technology will provide breakthroughs in efficiency, robustness, and multifunctionality for next-generation wireless systems. 
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Keywords:
- topological photonics /
- parity-time symmetry /
- wireless power transfer
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图 1 (a)—(c) 二阶PT对称系统原理图、本征值谱、效率; (d)—(f) 三阶PT对称系统原理图、本征值谱、效率
Fig. 1. (a)–(c) Schematic diagram, eigenvalue spectrum, and transfer efficiency of a second-order PT-symmetric system; (d)–(f) similar to panels (a)–(c), but for third-order PT-symmetric system.
图 2 基于磁共振线圈的多米诺无线传能技术 (a) 多米诺无线传能原理图, 包括源线圈、谐振线圈阵列和负载线圈; (b) 多米诺无线传能应用场景, 从左到右分别为机械臂、绝缘子串和智能桌面
Fig. 2. Domino WPT composed of the composite coil resonators: (a) Domino WPT schematic diagram, including source coil, resonant coil array, and load coil; (b) application of Domino WPT, from left to right are robotic arm, insulator string, and smart desk, respectively.
图 3 TWPT系统的实验演示[56] (a) 拓扑SSH链示意图, 每个原胞(黑色虚线框)由两个绕向相反的线圈组成(以红色和蓝色箭头标示); (b) 由同向/反向绕圈原胞构成的系统的能带结构; (c) 实测效率随频率与$ w/v $的变化关系, 白色虚线表示$ w/v=1 $, 用于区分拓扑平庸与非平庸相[56]; (d) 固定工作频率下实测效率随$ w/v $的变化曲线; (e)—(h) 相同条件下测得的传输特性, 其中无序强度d = 1.5 cm/ 2.5 cm, 其中(e), (g)为TWPT系统, (f), (h)为传统多米诺形式WPT系统
Fig. 3. Experimental demonstration of the TWPT system[56]: (a) Schematic of the TWPT chain, each unit cell (black dashed box) is composed of two coils with opposite winding directions (marked with red and blue arrows); (b) band structure of unit cells composed of same/opposite winding directions; (c) measured efficiency versus both frequency and $ w/v $, the white dashed line indicates $ w/v=1 $, separating the topologically trivial and nontrivial phase; (d) measured efficiency versus $ w/v $ at a fixed working frequency; (e)—(h) measured transmission for the same situation with the disorder strength d = 1.5 cm/2.5 cm in TWPT system (e), (g) and conventional domino-form WPT system (f), (h).
图 4 二聚体链中拓扑边界态和界面态构建有效三阶PT对称系统实现高效鲁棒性WPT[65] (a) 基于谐振线圈构造含拓扑缺陷的二聚体链用于长程WPT的模型示意图; (b) 含拓扑缺陷二聚体拓扑链的本征值谱; (c) 3个耦合拓扑态的LDOS; (d) 有效三阶PT对称的非厄米系统的相图; (e) 具有有效三阶PT对称的拓扑二聚体链在待机和工作状态下反射谱; (f), (g) 有效三阶系统工作状态和待机状态的LED演示实验
Fig. 4. Topological edge mode and topological interface mode of the dimer chains to realize the effective third-order PT-symmetric system and then realize robust WPT[65]: (a) Schematic diagram of the model for using a dimer chain with topological defects constructed by resonant coils for long-range WPT; (b) eigenvalues spectra of the dimer chains with topological defects; (c) LDOS of three coupled topological modes; (d) eigenfrequencies of topological WPT system with effective third-order PT symmetry; (e) measured reflection spectrum of the topological dimer chain with effective third-order PT symmetry under working and standby states; (f), (g) experimental demonstration by using LED lamps of WPT system with effective third-order PT symmetry at working state and standby state.
图 5 基于大面积拓扑缺陷态的WPT系统[71] (a)大面积拓扑缺陷态的耦合分布; (b)拓扑缺陷态扩展大面积拓扑缺陷态的示意图; (c)本征值谱的实部, 箭头标示零能模式对应的大面积拓扑缺陷态; (d)理论计算的大面积拓扑缺陷态的LDOS; (e)实验测量的大面积拓扑缺陷态的LDOS; (f)不同耦合强度比下的LDOS和IPR; (g)基于LED灯照明的WPT实验演示图
Fig. 5. WPT system based on large-area topological defect states[71]: (a) Coupling distribution of large-area topological defect states; (b) schematic diagram of topological defect states expanding into large-area topological defect states; (c) real part of the eigenvalues spectra, with arrows indicating the zero-energy modes corresponding to large-area topological defect states; (d) theoretically calculated LDOS for large-area topological defect states; (e) experimentally measured LDOS for large-area topological defect states; (f) LDOS and IPR under different coupling strength ratios; (g) experimental demonstration of WPT by using LED lamps.
图 6 GDOA算法在耦合链拓扑WPT中的应用[75] (a) GDOA与长程WPT结合概念图; (b)训练步数为20, 2000和200000时效率和耦合分布的变化; (c)基于机器学习的GDOA流程; (d)不同振子单位数量下的梯度优化结果; (e)不同目标频率下的梯度优化结果; (f)谐振线圈位置对应的耦合强度分布, 红色柱状图表示梯度优化链, 蓝色柱状图表示SSH链; (g)优化链和SSH链波函数$\varPhi $的分布; (h) 3种链的传输率随无序干扰强度的变化趋势图, 小球代表实验结果
Fig. 6. Application of GDOA in topological WPT realized by coupled chain[75]: (a) Conceptual diagram illustrating the integration of the GDOA with long-range WPT; (b) evolution of transmission efficiency and coupling distribution after 20, 2000, and 200000 training steps; (c) flowchart of machine learning based GDOA; (d) gradient optimization results for different numbers of resonator units; (e) gradient optimization results for different target frequencies. (f) distribution of coupling strength with respect to the position of resonant coils, with red bars representing the gradient optimized chain and blue bars representing the SSH chain; (g) distribution of wave functions; (h) transmission of the three chains varies with the intensity of disorder disturbance, the measured results are marked by the dots.
图 7 拓扑Harper链和非对称边界态[52] (a)由16个谐振单元构成的Harper链示意图; (b)有限尺寸Harper链的投影能带结构随拓扑参数ϕ的变化关系, 不同颜色线条表示不同链长, 两个带隙中均存在边界态, 每个带隙中实线表示与链长无关的边缘态, 并标注了各带隙的绕数; (c)图(b)中Harper链的本征值谱; (d)—(g) E1—E4的归一化场分布
Fig. 7. Topological Harper model and the asymmetric edge states[52]: (a) Schematic of a Harper chain with 16 resonators; (b) projected band structure of the finite-size Harper chain as a function of the topological parameter ϕ, different color lines indicate different chain lengths, the edge states exist in the two bandgaps, in each bandgap, the solid line represents the edge state independent of the chain lengths, the winding number for each bandgap is indicated; (c) the eigenvalues spectra of the Harper chain in panel (a); (d)–(g) normalized intensity distributions of different edge states (E1–E4).
图 8 Harper拓扑链中非对称边界态用于鲁棒性定向WPT[80] (a)基于谐振线圈构造的Harper链用于定向WPT的耦合强度分布; (b) Harper拓扑链的DOS; (c) Harper拓扑链非对称边界态的LDOS; (d)定向传输的效率增强系数; (e), (f)左边界态和右边界态的LED灯演示实验
Fig. 8. Asymmetric topological edge state in topological Harper chain for robust directional WPT[80]: (a) Coupling strength distribution of a Harper chain for directional WPT constructed by resonant coils; (b) DOS spectrum of the topological Harper chain; (c) LDOS spectrum of asymmetric edge states in the topological Harper chain; (d) efficiency enhancement ratio for directional transmission; (e), (f) experimental demonstration of LED lamps using the left edge state and right edge state.
图 9 鲁棒性定向WPT的主动控制[80] (a)基于VCD的共振线圈样品图; (b)主动控制谐振线圈的有效电路图; (c)外加电压和间距分别调控谐振频率和耦合强度; (d)Harper链非对称边界态实现定向WPT的实验测试图; (e)外加电压调控长程定向WPT
Fig. 9. Active control of robust directional WPT[80]: (a) Photograph of a resonant coil sample utilizing a VCD; (b) equivalent circuit diagram of the actively controlled resonant coil; (c) modulation of resonant frequency and coupling strength achieved through external voltage application and adjustment of inter-coil spacing; (d) experimental setup demonstrating directional WPT using asymmetric edge states in a Harper chain; (e) modulation of long-range directional WPT using external voltage.
图 10 高阶拓扑角态的鲁棒性多负载WPT系统[88] (a)—(c)二维光子SSH模型的两层晶格示意图, 其中位于顶层(底层)的原子由橙色(靛蓝色)表示, 在一个原胞(灰色虚线方块)中, 原子被标记为A, B, C和D, 红色、蓝色和靛蓝色线分别表示胞内耦合p和胞间耦合q, 以及次近邻耦合μ; 其中(a)为平庸相; (b)为临界相; (c)为拓扑相; (d)能带结构; (e)有限结构不同模式的IPR; (f)实验示意图; (g)对称型拓扑角态实验观测; (h)对称型拓扑角态的鲁棒性验证; (i)非对称型拓扑角态实验观测
Fig. 10. High-order topological corner states in a robust multi-load WPT system[88]: (a)–(c) Schematic of a two-layer lattice of 2D photonic SSH model, in which the atoms located on the top (bottom) layer are represented by orange (indigo), in a unit cell (gray dashed square), the atoms are labelled as A, B, C, and D, red, blue and indigo lines represent intracell coupling p and intercell coupling q, and next-nearest-neighbor coupling μ, respectively. Among them, (a) trivial phase; (b) critical phase; (c) topological phase; (d) band structure; (e) IPR of different modes in a finite structure; (f) schematic diagram of the experimental setup; (g) experimental observation of symmetric topological corner states; (h) robustness verification of symmetric topological corner states; (i) experimental observation of asymmetric topological corner states.
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