Unidirectional bound states in the continuum in Weyl semimetal nanostructures
Fig. 1(a), the usual setup with symmetric radiation of leaky mode. (b), the unidirectional leaky wave enabled by unidirectional BIC in antiparallel-magnetism configuration. (c), the reflection map with incident wave. Here, kx is the x component of incident wave vector. (d), the quality factor of leaky mode in forward directions and at Γ point. Here, quality factor is defined as the ratio of real and imaginary part of eigenvector
Bound states in the continuum (BICs) enable perfect wave localization and significantly enhance light–matter interactions although systems are optically open. Those trapped modes without the leaky-wave radiation in an open continuum are important in numerous applications, including optical nonlinearity, light emitters, and nano-sensors.
BICs in common reciprocal media are bounded by the time-reversal symmetry, rendering difficulties to manipulate the freedom related to leaky directions. For example, an emitter in dielectric cores must radiate symmetrically in both forward and backward directions, due to the open channels coupled to the radiation continuum (Fig. 1a). Thus, asymmetric leaky mode and light harvesting are not available in those configurations. Breaking the reciprocity and developing the unidirectional BICs would be of great significance to allow more exotic light-matter interactions.
To address this problem, the research group led by Prof. Yong-Zhe Zhang from the Beijing University of Technology, cooperating with Prof. Cheng-Wei Qiu from the National University of Singapore, proposed an approach to use the emerging low-dimensional quantum materials of magnetic Weyl semimetal (MWS), which is naturally endowed with a magneto-optical plasmonic response. By covering the dielectric core by paired MWS with antiparallel magnetism, the unidirectional and nonreciprocal BIC could be formed, where the radiation of leaky modes from a dielectric core could only be supported in one direction.
The relevant research results are published in Photonics Research, Volume. 10, Issue 8, 2022 (Chen Zhao, Guangwei Hu, Yang Chen, Qing Zhang, Yongzhe Zhang and Cheng-Wei Qiu. Unidirectional bound states in the continuum in Weyl semimetal nanostructures[J]. Photonics Research, 2022, 10 (8): 1828-1838).
Those results are theoretically developed, suggesting that the interference of the Fabry-Perot modes in the system and magnetic epsilon-near-zero (ENZ) resonance of MWS would close the leaky channel despite it is within the radiation continuum, i.e. Re (β/k0) ≤ 1. Such important result depends deeply on infrared magneto-plasmonic response of MWS, as, for example, perfect destructive interference only holds true for forward leaky mode at ~3 μm but not valid for backward ones.
Therefore, a perfect unidirectional BIC could exist (Fig. 1c) with diverging quality factor (Fig. 1d). Moreover, a symmetry-protected BIC at Γ point in such nonreciprocal system is achieved as the system is under (rotation of π about y axis followed by time reversal) and symmetry (up–down mirror symmetry of the x–z plane), as shown in Fig. 1b.
Due to the flexibility of magneto-optical properties of MWSs via varying the Fermi level, the propagation constant and resonant frequency of unidirectional BICs can be dynamically tuned, offering a pathway of tunable BICs for practical applications, spanning a broad frequency range, such as leaky wave antenna, efficient energy delivering and nonreciprocal energy harvesting. This technology could largely impact the infrared technologies as it allows both new fundamental optical physics for wave control and the extreme light-matter interactions.
Future work can further study the evolution and topological nature of BIC in nonreciprocal system. It may also be possible to design the asymmetric structures to further leverage the symmetry breaking for more exotic nonreciprocal devices.
磁性外尔半金属：新兴量子材料实现单向连续域中束缚态
图1（a）一般结构泄露模式的对称辐射示意图;（b）反平行磁化结构中单向BIC模式的单向辐射示意图;（c）结构反射谱;（d）两种BIC模式的品质因子和单向BIC的辐射比
图2（a）-（d）不同自发磁化强度和方向时结构反射谱;（e）不同费米能级下MWS介电常数角频率色散关系;（f）等离子体共振频率与费米能级关系图
在开放系统中，连续域中束缚态（BICs）可实现光场的完美局域并显著增强光与物质的相互作用。此类完全压制向外辐射的泄露模式在很多领域都具有重要应用，例如光学非线性，光发射器和纳米传感器等。
然而，BICs通常产生于满足时间反演对称性的互易媒介中，表明结构内的光发射器总会在正反两个方向上有对称的辐射能量，其会限制结构对泄露模式辐射方向的调控，因而无法实现非对称辐射模式和单向的光场局域功能。因此，通过打破洛伦兹互易定理产生单向传输的BICs对于实现特殊的光与物质相互作用具有重要意义。
实现非互易的常用方式为外加磁场，而磁场设备往往比较庞大，不利于光子器件的小型化设计，而磁性外尔半金属（MWS）由于具有新颖的电子结构而受到研究者广泛关注。MWS的电子色散关系存在手性相反的外尔点，相当于相空间一对正负磁荷，因此这种自身存在的内禀磁性使之成为构建非互易系统的理想媒介。
为解决以上问题并实现此特殊光学态，北京工业大学张永哲教授课题组和新加坡国立大学仇成伟教授课题组合作，利用新兴的量子材料——磁性外尔半金属（MWS）构建具有反平行磁化的波导结构，从而形成单向透射的非互易BICs，实现泄露模式的单向辐射。相关研究成果发表于Photonics Research 2022年第8期（Chen Zhao, Guangwei Hu, Yang Chen, Qing Zhang, Yongzhe Zhang and Cheng-Wei Qiu. Unidirectional bound states in the continuum in Weyl semimetal nanostructures[J]. Photonics Research, 2022, 10 (8): 1828-1838）。
依靠MWS自身天然存在的磁光等离子体响应，该团队利用近红外波段（~ 3μm）其介电常数接近于零的特性，使等离子体共振模式和系统内法布里-珀罗共振模式耦合发生相干相消，可以有效地关闭辐射通道。
通过理论推导计算得到，尽管耦合模式处于辐射连续域中（模式传播常数的实部小于真空自由传播光的波矢），耦合模式仍然可以被单向地束缚在结构内，从而表现出极高的品质因子。此外，由于系统满足 （时间反演和面内180° 旋转）和 （x-z平面镜面翻转）对称性，在该非互易系统中还可以在Γ点产生一个对称性保护的BIC，如图1所示。
由于MWS的磁光特性可以通过费米能级或自发磁化强度进行调谐，因此可以改变这些单向传输BICs的传播常数和共振频率，使其在宽频域范围实现动态调控，如图2所示。这一结果所揭示的基础光物理内容将会推动近红外波段光场调控技术的发展。
仇成伟教授表示：“外尔半金属是具有拓扑非平庸能带结构的一类新颖的量子材料，在量子器件中具有广阔的应用前景。这项工作通过独特的设计将磁性外尔半金属和BICs结合起来，实现动态调控的高效单向传输和辐射，这是将该材料应用到光子器件中的一项重要探索，其有望为片上集成光学的设计提供新的思路和视野。”