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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…

Optics · Physics 2023-06-21 Jie Peng , Ruo-Yang Zhang , Shiqi Jia , Wei Liu , Shubo Wang

When two topologically trivial and nontrivial systems are brought together, a localized energy state is formed at the interface. For crystalline quantum and classical systems, their topology can be determined by studying the eigenmode…

Optics · Physics 2026-05-11 T. H. Chan , Y. H. Guan , C. Liu , H. C. Ong

Electronic flat bands have localized Wannier-like orbitals as zero modes. In the Lieb or the kagome models, the localized orbitals satisfy a topological condition that entails two non-contractible loop eigenstates along $x/y$-axis in real…

Mesoscale and Nanoscale Physics · Physics 2026-03-27 Rui-Heng Liu , Jiangping Hu , Chen Fang

On the basis of the "molecular-orbital" representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models,…

Mesoscale and Nanoscale Physics · Physics 2020-09-30 Tomonari Mizoguchi , Yasuhiro Hatsugai

In polarization optics, various topological constructs, namely Poincar\'e spheres of different orders, are used to represent uniform and structured polarization distributions. Similarly, there are also structured polarization optical…

Optics · Physics 2025-07-08 Mohammad Umar , P. Senthilkumaran

After more than 70 years of development, holography has become an essential tool of modern optics in many applications. In fact, for various applications of different kinds of holographic techniques, stability and antijamming ability are…

Optics · Physics 2023-05-18 Ling-Jun Kong , Jingfeng Zhang , Furong Zhang , Xiangdong Zhang

While energy band topology in spatial photonic crystals (PCs) and momentum-band topology in temporal crystals have each served as powerful probes of topological phases in their respective domains, their unification in a static platform…

Optics · Physics 2026-02-06 Zimeng Zeng , Zhuoyang Li , Jiayao Liu , Zelong He , Zhaona Wang

The topological invariants of a periodic system can be used to define the topological phase of each band and determine the existence of topological interface states within a certain bandgap. Here, we propose a scheme based on the full phase…

Topology plays an important role in non-hermitian systems. How to characterize a non-hermitian topological system under open-boundary conditions(OBCs) is a challenging problem. A one-dimensional(1D) topological invariant defined on a…

Strongly Correlated Electrons · Physics 2023-06-21 ChunChi Liu , LiuHao Li , Jin An

We numerically investigate and experimentally demonstrate an in-situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its inter-particle stiffness in a…

Pattern Formation and Solitons · Physics 2017-07-19 Rajesh Chaunsali , Aman Thakkar , Eunho Kim , Panayotis G. Kevrekidis , Jinkyu Yang

Exceptional points as branch singularities describe peculiar degeneracies of non-Hermitian systems that do not obey energy conservation. This work shows that exceptional points can emerge in a topological photonic system, for example, the…

Optics · Physics 2021-07-13 Junhua Dong , Chang-Yin Ji , Qingmei Hu , Bingsuo Zou , Yongyou Zhang

The nonlinear optical responses from topological semimetals are crucial in both understanding the fundamental properties of quantum materials and designing next-generation light-sensors or solar-cells. However, previous work was focusing on…

Valley pseudospin, a new degree of freedom in photonic lattices, provides an intriguing way to manipulate photons and enhance the robustness of optical networks. Here we experimentally demonstrated topological waveguiding, refracting,…

Applied Physics · Physics 2019-08-13 Jingwen Ma , Xiang Xi , Xiankai Sun

Topological photonics sheds light on some of the surprising phenomena seen in condensed matter physics that arise with the appearance of topological invariants. Optical waveguides provide a well-controlled platform to investigate effects…

Mesoscale and Nanoscale Physics · Physics 2020-09-16 Adrian J Menssen , Jun Guan , David Felce , Martin J Booth , Ian A Walmsley

Topological phases of matter is an exotic phenomena in modern condense matter physics, which has attracted much attention due to the unique boundary states and transport properties. Recently, this topological concept in electronic materials…

Quantum Physics · Physics 2021-08-06 Zheng-Yuan Xue , Yong Hu

Topologically engineered optical materials support robust light transport. Herein, the investigated non-Hermitian lattice is trimerized and inhomogeneously coupled using uniform intracell coupling. The topological properties of the coupled…

Mesoscale and Nanoscale Physics · Physics 2018-03-20 L. Jin

Over the past decade, topological photonics has emerged as a vibrant field, attracting significant attention and witnessing remarkable advancements. This growth can be attributed to its fundamental appeal and the unique opportunities it…

Research on two-dimensional van der Waals materials has demonstrated that the layer degree of freedom can significantly alter the physical properties of materials due to the substantial modification of bulk bands. Inspired by this concept,…

The lack of a unified theoretical framework for characterizing band inversions across different crystal symmetries hinders the rapid development of topological photonic band engineering. To address this issue, we have constructed a…

Optics · Physics 2025-09-11 Ze Tao , Fujun Liu

We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…

Exactly Solvable and Integrable Systems · Physics 2013-09-30 Mikhail P. Kharlamov