Related papers: 4D topological textures in light

This paper introduces two-dimensional diagrams that are slight generalizations of moment map images for toric four-manifolds and catalogs techniques for reading topological and symplectic properties of a symplectic four-manifold from these…

We mostly determine which closed smooth oriented 4-manifolds fibering over lower dimensional manifolds are virtually symplectic, i.e. finitely covered by symplectic 4-manifolds.

In the present research, we demonstrate the usage of plasmonic effects in thin film structures to control magnetic topological textures, specifically skyrmions and skyrmioniums. We investigate numerically the generation and alteration of…

Transmitting structured light robustly through complex random media is crucial in many applications, from sensing to communication. Unfortunately, the spatial structure of light is distorted in such media due to refractive index…

We present a general analysis of two-dimensional optical lattice models that give rise to topologically non-trivial insulating states. We identify the main ingredients of the lattice models that are responsible for the non-trivial…

The program of understanding Shape Theory layer by layer topologically and geometrically -- proposed in Part I -- is now addressed for 4 points in 1-$d$. Topological shape space graphs are far more complex here, whereas metric shape spaces…

We view conformal surfaces in the 4--sphere as quaternionic holomorphic curves in quaternionic projective space. By constructing enveloping and osculating curves, we obtain new holomorphic curves in quaternionic projective space and thus…

This paper develops a rigorous mathematical framework for light propagation by constructing the optical phase space with its symplectic structure and the extended phase space with its contact structure. We prove that light rays in…

Topological photonic systems offer light transport that is robust against defects and disorder, promising a new generation of chip-scale photonic devices and facilitating energy-efficient on-chip information routing and processing. However,…

Three-dimensional (3D) topological spin textures emerge as promising quasi-particles for encoding information in future spintronic devices. The third dimension provides more malleability regarding their magnetic properties as well as more…

The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial dimensions. We use electric circuits to…

We present an analytical method to achieve highly non-paraxial, azimuthally polarized structured beams that, when propagating through an absorbing stratified media, can assume in the last semi-infinite layer approximately any desired…

Skyrmions are topological defects belonging to nontrivial homotopy classes in particle theory. Their remarkably stable topology has recently been observed in electromagnetic waves. For the evanescent fields near a surface, this has been…

Thurston's boundary to the universal Teichm\"uller space $T(\mathbb{D})$ is the space $PML_{bdd}(\mathbb{D})$ of projective bounded measured laminations of $\mathbb{D}$. A geodesic ray in $T(\mathbb{D})$ is of Teichm\"uller type if it…

We propose a nanophotonic platform for topological quantum optics. Our system is composed of a two-dimensional lattice of non-linear quantum emitters with optical transitions embedded in a photonic crystal slab. The emitters interact…

One-dimensional Thue-Morse (ThMo) lattices are examples of self-similar structures that exhibit bandgap phenomena. ThMo multilayers may also possess fractal photonic bandgaps that give rise to large omnidirectional reflectance and light…

Rich topological phenomena, edge states and two types of corner states, are unveiled in a two-dimensional square-lattice dielectric photonic crystal without both $C_4$ and $M_{x(y)}$ symmetries. Specifically, non-trivial type-I corner…

Lagrangian curves in 4-space entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic…

Vector light beams, characterised by a spatially varying polarisation, can exhibit localised structures reminiscent of the Skyrmions familiar from the study of magnetic media. We present a theory of such Skyrmions within paraxial optics,…

Nonlinear optical processes of spatially structured light, including optical vortex and vector optical fields, have stimulated a lot of interesting physical effects and found a variety of important applications ranging from optical imaging…