Related papers: Geometry and Topological photonics
Topological photonics has emerged as a novel route to engineer the flow of light. Topologically-protected photonic edge modes, which are supported at the perimeters of topologically-nontrivial insulating bulk structures, have been of…
Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems…
Electronic topological insulators are one of the breakthroughs of the 21st century condensed matter physics. So far, the search for a light counterpart of an electronic topological insulator has remained elusive. This is due to the…
The flourishing of topological photonics in the last decade was achieved mainly due to developments in linear topological photonic structures. However, when nonlinearity is introduced, many intriguing questions arise. For example, are there…
Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…
Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in…
We investigate the occurrence of topologically protected waves in classical fluids confined on curved surfaces. Using a combination of topological band theory and real space analysis, we demonstrate the existence of a system-independent…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
Photonics, dealing with the generation, manipulation, and detection of photons in various systems, lays the foundation of many advanced technologies. A key task of photonics is to know how photons propagate in complex media such as periodic…
Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for quantum many-body states of matter that previously had not been accessible. Here we introduce a symmetry-based method of…
The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of…
We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph - its topology. We consider generic open graphs and show that any cycle leads…
We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations…
The field of topological photonics emerged as one of the most promising areas for applications in transformative technologies: possible applications are in topological lasers or quantum optics interfaces. Nevertheless, efficient and simple…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
In recent years, twisting has emerged as a new degree of freedom that plays an increasingly important role in Bloch bands of various physical systems. However, there is currently a lack of reports on the non-trivial physics of topological…
Topological band theory establishes a standardized framework for classifying different types of topological matters. Recent investigations have shown that hyperbolic lattices in non-Euclidean space can also be characterized by hyperbolic…
This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital…
The main focus of this paper is a nonparametric filtering technique for the estimation of interface geometry in bulk materials obtainable from modern imaging measurements. The filtering methodology relies on an assumed hierarchy of…
We outline an approach to endow a plain vanilla material with topological properties by creating topological bands in stacks of manifestly nontopological atomically thin materials. The approach is illustrated with a model system comprised…