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Topological photonics has attracted increasing attention in recent years due to the unique opportunities it provides to manipulate light in a robust way immune to disorder and defects. Up to now, diverse photonic platforms, rich physical…
Topological defects play a key role in a variety of physical systems, ranging from high-energy to solid state physics. They yield fascinating emergent phenomena and serve as a bridge between the microspic and macroscopic world. A skyrmion…
Topological materials provide a platform that utilizes the geometric characteristics of structured materials to control the flow of waves, enabling unidirectional and protected transmission that is immune to defects or impurities. The…
Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, non-reciprocal chiral edge states and cavity-like confined states that have applications in both linear and…
Topological quasiparticles such as skyrmions and merons have recently attracted enormous attentions in the form of diverse optical degrees of freedom. However, these structures have not been explored in the fundamental momentum vectors of…
The ideas of topology have found tremendous success in Hermitian physical systems, but even richer properties exist in the more general non-Hermitian framework. Here, we theoretically propose and experimentally demonstrate a new…
Topological photonics is developed based on the analogy of Schr\"{o}dinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they…
In nonparaxial, monochromatic light the electric and magnetic fields generally have different energy densities, different singularities and different polarisation structures. A topological picture of the electric field or magnetic field in…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
Topological photonic crystals have received considerable attention for their ability to manipulate and guide light in unique ways. They are typically designed by hand based on careful analysis of their bands and mode profiles, but recent…
Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium. Recent experimental progress is much from optical, cold-atomic, and classical platforms due to the vast tunability and clear identification…
This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…
Chirality is more than a geometric curiosity; it governs measurable asymmetries across nature, from enantiomer-selective drugs and left-handed fermions in particle physics to handed charge transport in Weyl semimetals. We extend this…
Topological features - global properties not discernible locally - emerge in systems from liquid crystals to magnets to fractional quantum Hall systems. Deeper understanding of the role of topology in physics has led to a new class of…
Electric dark spots are point singularities at which the electric field amplitude vanishes. These singularities usually emerge in real space accidentally and are unstable due to the vectorial property of the electric field. In this paper,…
Singular optics aims to understand and manipulate light's topological defects, pioneered by the discovery that phase vortex lines, strands of destructive interference, naturally occur in scalar wave fields. Monochromatic electromagnetic…
One of the most striking manifestations of electronic properties of topological insulators is the dependence of the photocurrent direction on the helicity of circularly polarized optical excitation. The helicity dependent photocurrents,…
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…
Topological spin and polar textures have fascinated people in different areas of physics and technologies. However, the observations are limited in magnetic and solid-state ferroelectric systems. Ferroelectric nematic is the first…
We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…