Topological near fields generated by topological structures

Abstract

The central idea of metamaterials and metaoptics is that, besides their base materials, the geometry of structures offers a broad extra dimension to explore for exotic functionalities. Here, we discover that the topology of structures fundamentally dictates the topological properties of optical fields and offers a new dimension to exploit for optical functionalities that are irrelevant to specific material constituents or structural geometries. We find that the nontrivial topology of metal structures ensures the birth of polarization singularities (PSs) in the near field with rich morphologies and intriguing spatial evolutions including merging, bifurcation, and topological transition. By mapping the PSs to non-Hermitian exceptional points and using homotopy theory, we extract the core invariant that governs the topological classification of the PSs and the conservation law that regulates their spatial evolutions. The results bridge singular optics, topological photonics, and non-Hermitian physics, with potential applications in chiral sensing, chiral quantum optics, and beyond photonics in other wave systems.

Progress on chiral optical near fields

“…Copyright © 2023 American Chemical Society; (c) 横向自旋锁模导致的近场不对称几何相位调控 [75] , Copyright © 2023 by the American Physical Society phase induced by the interference of two linearly polarized fundamental modes [73] , Copyright © 2023 American Chemical Society; (c) near-field asymmetric geometric phase caused by transverse spin-momentum locking [75] , Copyright © 2023 by the American Physical Society 近场干涉产生的偏振奇点携带奇异的特性，近年来吸引了研究人员的广泛关注。Peng 等人 [13] 系 统地研究了散射体近场偏振奇点的性质，计算了不同结构的散射近场的偏振奇点，并在此基础 上进一步建立了近场偏振奇点拓扑性质和光学结构拓扑性质之间普遍而精确的联系。有趣的 是，光滑金属散射体的近场偏振奇点的全局拓扑性质由散射体的欧拉示性数决定，与激励场、 结构对称性或细节没有任何关系(图 5(a)) [11] 。这一发现首次将光学近场的拓扑性质与光学结构 的拓扑性质联系在一起，为调控近场偏振提供了一个全新的自由度。近场偏振奇点的实验观测 可以利用具有高柱对称性孔径的近场探头来实现 [76] 。近场偏振奇点通常具有光学手性，在与粒 子相互作用时可以产生复杂的光力矩，因此可以用来操控粒子在近场的运动，在生物、医学以 及化学领域具有重要的应用价值 [77] 。 光学近场的偏振奇点还能诱导产生相位涡旋、斯格明子和莫比乌斯环等拓扑构型。Yang 等 人 [78] 利用具有旋转对称性和镜面对称性的谐振器实现了具有不同拓扑性质的相位涡旋，证明了 系统的对称性直接影响近场拓扑构型的性质。Tsesses 等人 [79] 利用表面等离激元倏逝场产生斯格 明子晶格，晶格原胞中心存在偏振奇点，当晶格中的拓扑畴壁连续变化时，斯格明子的空间构 型可以从气泡型变为 Né el 型，并且表现出对缺陷的鲁棒性，如图 5(b)所示。等离激元波的叠加 和干涉可形成等离激元涡旋，进一步形成类磁介子准粒子 [80] 。此外，围绕偏振奇点的偏振椭圆 长轴可以形成莫比乌斯环。例如，图 5(c)展示了一个介质球粒子散射场中的偏振奇点线，围绕 奇点线环路上的偏振椭圆长轴形成莫比乌斯环结构 [81] 。当系统满足镜像对称性或旋转对称性 时，高阶偏振奇点的出现还会进一步诱导产生奇异的双扭莫比乌斯偏振带 [11] 。这些新颖的近场 偏振拓扑构型为调控实空间光场的亚波长性质提供了具鲁棒性的物理机制和自由度。 图 5 (网络版彩色)手性光学近场的偏振结构。(a) 不同拓扑光学结构产生的偏振奇点 [11] , under a Creative Commons license CC BY 4.0; (b) 等离激元倏逝场形成的斯格明子晶格 [79] , Reprinted with permission from AAAS; (c) 电介质球体散射产生的圆偏振奇点线和围绕奇点线的偏振莫比乌斯带 [81] , Copyright © 2017 American Chemical Society topological structures [11] , under a Creative Commons license CC BY 4.0; (b) Skyrmion lattice formed by the evanescent fields of surface plasmons [79] , Reprinted with permission from AAAS; (c) polarized Mobius strip around C lines induced by the scattering of a dielectric sphere [81] , Copyright © 2017 American Chemical Society 近场手性增强还有助于实现手性分子的不对称光合成，在生物传感、细胞操纵和光治疗等领域 具有潜在应用 [82] 。 [83] 。与自由空间 中的圆偏振光相比，超手性光具有更强的归一化光学手性，它与手性粒子相互作用时可以产生 更大的吸收不对称度，因此可以实现增强的手性探测信号。这种超手性光可以在非均匀光场的 局部区域产生，例如，两束具有相反手性和传播方向的圆偏振光干涉，可以在驻波节点上产生 超手性光 [84] ；等离子或高折射率电介质纳米结构的局域共振也可以产生超手性光 [85] 。其中，等 离子纳米结构与入射光的手性匹配决定近场手性的大小，但其受限于较弱的磁共振和较大的欧 姆损耗 [86] ，而电介质纳米结构的电磁共振可以进一步增强超手性光 [87,88] 图 6 (网络版彩色)光学近场的手性增强和探测。(a) 利用超表面实现超手性光 [89] , Copyright © 2018 by ...…”

Half‐Integer Topological Charge Polarization of Quasi‐Dirac Bound States in the Continuum

“…As instance, a V‐point, that is, a state with undetermined linear polarization, is the intersection of two C‐lines running in opposite directions with opposite circular polarization. [ 8 ] The C‐lines separate when the symmetry of the system is broken as a function of a continuously varied parameter. Thus, a V‐point with TC = +1 will break into two C‐points with TC = +1/2 and opposite circular polarization.…”