相关论文: Singularities and Poincar\'{e} Indexes of Electrom…

Electromagnetic multipoles can be continuously mapped to tangent vectors on the momentum sphere, the topology of which guarantees the existence of isolated singularities. For pure (real or imaginary) vectors, those singularities correspond…

Indices of singular points of a vector field or of a 1-form on a smooth manifold are closely related with the Euler characteristic through the classical Poincar\'e--Hopf theorem. Generalized Euler characteristics (additive topological…

Using full-wave numerical simulations and analytical multipole expansions we investigated the properties of real-space polarization singularities that emerge in light scattering by subwavelength particles. We considered spherical and torus…

Polarization singularities of vectorial electromagnetic fields locate at the positions (such as points, lines, or surfaces) where properties of polarization ellipses are not defined. They are manifested as circular and linear polarization,…

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…

Singularities, i.e. places of discontinuities of parameters are extremely general objects appearing in electromagnetic waves and thus are the key to understanding fundamental wave processes. These structures commonly occur in purely…

We show that combined permanent and induced electric dipole interactions of polar and polarizable molecules with collinear electric fields lead to a sui generis topology of the corresponding Stark energy surfaces and of other observables -…

We consider 1-forms on, so called, essentially isolated determinantal singularities (a natural generalization of isolated ones), show how to define analogues of the Poincar\'e--Hopf index for them, and describe relations between these…

Bound states in the continuum in periodic photonic systems like photonic crystal slabs are proved to be accompanied by vortex polarization singularities on the photonic bands in the momentum space. The winding structures of polarization…

A boundary singularity is a singularity of a function on a manifold with boundary. The simple and unimodal boundary singularities were classified by V. I. Arnold and V. I. Matov. The McKay correspondence can be generalized to the simple…

Classical beams of light with non-uniform polarization patterns (e.g. radially and azimuthally polarized doughnut beams) may exhibit quantum-like features as, for instance, inseparability. We establish an exact correspondence between…

The Poincar\'e-Hopf Theorem relates the Euler characteristic of a 2-dimensional compact manifold to the local behavior of smooth vector fields defined on it. However, despite the importance of Filippov vector fields, concerning both their…

We define the concepts of topological particles and topological radiation. These are nothing more than connected components of defects of a vector field. To each topological particle we assign an index which is an integer which is conserved…

We introduce a method, based on the Poincare-Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear…

Topological properties of photonic structures described by Hamiltonian matrices have been extensively studied in recent years. Photonic systems are often open systems, and their coupling with the environment is characterized by scattering…

We reveal how to exploit joint spatial-electromagnetic duality symmetries to obtain invariant scattering properties (including extinction, scattering, absorption) of self-dual scattering systems for incident waves of arbitrary…

Electromagnetic waves are described by not only polarization ellipses but also cyclically rotating vectors tracing out them. The corresponding fields are respectively directionless steady line fields and directional instantaneous vector…

In the canonical model of a pulsar, rotational energy is transmitted through the surrounding plasma via two electrical circuits, each connecting to the star over a small region known as a "polar cap." For a dipole-magnetized star, the polar…

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…

We investigate theoretical properties of beams of light with non-uniform polarization patterns. Specifically, we determine all possible configurations of cylindrically polarized modes (CPMs) of the electro-magnetic field, calculate their…