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Topology of the spatial coherence function is considered in details. The phase singularity (coherence vortices) structures of coherence function are classified by Hopf index and Brouwer degree in topology. The coherence flux quantization…
Knotted fields enrich a variety of physical phenomena, ranging from fluid flows, electromagnetic fields, to textures of ordered media. Maxwell's electrostatic equations, whose vacuum solution is mathematically known as a harmonic field,…
We classify the finite groups of orthogonal transformations in 4-space, and we study these groups from the viewpoint of their geometric action, using polar orbit polytopes. For one type of groups (the toroidal groups), we develop a new…
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…
In this article, we unravel an intimate relationship between two seemingly unrelated concepts: elasticity, that defines the local relations between stress and strain of deformable bodies, and topology that classifies their global shape.…
We introduce new three-dimensional topological phases of two-band models using the Pontryagin-Thom construction. In symmetry class A these are the infinitely many Hopf-Chern topological insulators, which are hybrids of layered Chern…
Scroll waves exist ubiquitously in three-dimensional excitable media. It's rotation center can be regarded as a topological object called vortex filament. In three-dimensional space, the vortex filaments usually form closed loops, and even…
The goal of this paper is to put the theory of approximate fibrations into the framework of higher topos theory. We define the notion of an approximate fibration for a general geometric morphism of $\infty$-topoi, give several…
Magnetic hopfions are topologically protected three-dimensional solitons that are constituted by a tube which exhibits a topologically nontrivial spin texture in the cross-section profile and is closed to a torus. Here we show that the…
Dispersions of rodlike colloidal particles exhibit a plethora of liquid crystalline states, including nematic, smectic A, smectic B, and columnar phases. This phase behavior can be explained by presuming the predominance of hard-core volume…
Atom optics demonstrates optical phenomena with coherent matter waves, providing a foundational connection between light and matter. Significant advances in optics have followed the realisation of structured light fields hosting complex…
Toroidal vortices in fluid and gas dynamics underpin a broad spectrum of scientific and technological fields, from elementary particle physics to condensed matter systems, and have recently garnered significant attention in optics because…
Photonic crystal fibres (PCFs) are optical fibres that guide light using a modulated dielectric medium. They provide an exceptionally versatile platform for various applications, thanks to the flexibility with which light-guiding can be…
Structured light beams with space-variant polarization can be efficiently generated using voltage-tunable nematic liquid-crystal (Q-plate). By appropriately selecting the input state and the retardation of the Q-plate, an optical field…
In this paper, we present a topology optimization (TO) framework to simultaneously optimize the matrix topology and fiber distribution of functionally graded continuous fiber-reinforced composites (FRC). Current approaches in density-based…
We study photonic crystal fibers and ring resonators with topological features induced by Aubry- Andre-Harper modulations of the cladding. We find non trivial gaps and edge states at the interface between regions with different Chern…
In this work, we investigate the topological properties of knotted defects in smectic liquid crystals. Our story begins with screw dislocations, whose radial surface structure can be smoothly accommodated on $S^3$ for fibred knots by using…
An elastic membrane with embedded nematic molecules is considered as a model of anisotropic fluid membrane with internal ordering. By considering the geometric coupling between director field and membrane curvature, the nematic texture is…
Chirality, an inherent property of most objects of the universe, is a dynamic research topic in material science, physics, chemistry, and biology. The fundamental appeal of this extensive study is supported by the technological quest to…
Topological photonics harnesses the physics of topological insulators to control the behavior of light. Photonic modes robust against material imperfections are an example of such control. In this work, we propose a soft-matter platform…