Related papers: Multidimensional optical singularities and their a…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. Partial results obtained in a previous paper are completed to represent accurately…
The aim of this paper is to provide a discussion on current directions of research involving typical singularities of 3D nonsmooth vector fields. A brief survey of known results is presented. The main purpose of this work is to describe the…
The use of coherent wave phenomena to enhance device performance is a cornerstone of modern optics. In juxtaposition to (locally) periodic metasurfaces, their disordered counterparts exhibit an interplay of destructive and constructive…
The mathematical notion of a spectral singularity admits a physical interpretation as a zero-width resonance. It finds an optical realization as a certain type of lasing effect that occurs at the threshold gain. We explore spectral…
Oscillons are long-lived, spatially localized field configurations, which are supported by attractive non-linearities in the scalar potential. We study oscillons comprised of multiple interacting fields, each having an identical potential…
We give simple criteria for the singularities appearing on surfaces codimension less than or equal to two. As applications, we give conditions for codimension two singularities that appear in ruled surfaces and center maps of surfaces in…
We give an overview of the fundamental definitions and results concerning hypersurface singularities, defined by convergent power series over an arbitrary real valued field. This approach combines, on the one hand, the classical case of…
The focus of this article is the study of a certain type of singularities and their transfer properties in a universally equidimensional morphism (i.e. an open morphism with constant pure-dimensional fibers). The singularities of interest…
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…
Counter-propagating light fields have the ability to create self-organized one-dimensional optically bound arrays of microscopic particles, where the light fields adapt to the particle locations and vice versa. We develop a theoretical…
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…
Optical cavities are of central importance in numerous areas of physics, including precision measurement, cavity optomechanics and cavity quantum electrodynamics. The miniaturisation and scaling to large numbers of sites is of interest for…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. Firstly derived in the static case, the result is generalized to the dynamic one.…
M\"{o}bius strips with one, two, three, and four, half-twists are shown to be generic features of three-dimensional (nonparaxial) elliptically polarized light. The geometry and topology of these unusual singularities is described and the…
Optical systems capable of generating fields with sub-wavelength spatial features have become standard in science and engineering research and industry. Pertinent examples include atom- and ion-based quantum computers and optical…
Disordered many-particle hyperuniform systems are exotic amorphous states characterized by anomalous suppression of large-scale density fluctuations. Here we substantially broaden the hyperuniformity concept along four different directions.…
Topological singularities are ubiquitous in many areas of physics. Polarization singularities are locations at which an aspect of the polarization ellipse of light becomes undetermined or degenerate. At C points the orientation of the…
The main purpose of this article is to lay the foundations for a classification of isolated hypersurface singularities in positive characteristic. Although our article is in the spirit of Arnol'd who classified real an complex hypersurfaces…
We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-\epsilon$…
Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation…