Related papers: Optical M\"{o}bius Singularities
I give various criteria for singularities to appear on geometric generic fibers of morphism between smooth schemes in positive characteristics. This involves local fundamental groups, jacobian ideals, projective dimension, tangent and…
A brief overview of the current state of the problem of electromagnetic field singularities arising from the refraction and scattering of light by material objects is given. The discussion begins with caustics arising from ray tracing in…
Phase singularities are locations where light is twisted like a corkscrew, with positive or negative topological charge depending on the twisting direction. Among the multitude of singularities arising in random wave fields, some can be…
In this paper, we study tropicalisations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximal-dimensional type, show that they can generically have only finitely many singular points, and…
In algebraic topology, we usually represent surfaces by mean of cellular complexes. This representation is intrinsic, but requires to identify some points through an equivalence relation. On the other hand, embedding a surface in a…
In this article we show that in a three dimensional (3D) optical field there can exist two types of hidden singularities, one is spin density (SD) phase singularity and the other is SD vector singularity, which are both unique to 3D fields.…
We give examples of open 3-manifolds and 3-orbifolds that exhibit pathological behavior with respect to splitting along surfaces (2-suborbifolds) with nonnegative Euler characteristic.
HI spectral line mapping studies are a unique probe of morphologically peculiar systems. Not only does HI imaging often reveal peculiarities that are totally unsuspected at optical wavelengths, but it opens a kinematic window into the outer…
We systematically examine the topological, valleytronic, and optical properties of experimentally accessible PbS (001) few-layers, with a focus on the monolayer. With even-odd layer-dependent oscillations and without band inversions, the…
A topologically minimal surface may be isotoped into a normal form with respect to a fixed triangulation. If the intersection with each tetrahedron is simply connected, then the pieces of this normal form are triangles, quadrilaterals, and…
We count the number of isomorphism classes of degree $d$-twists of some polarized abelian varieties over finite fields of odd prime dimension. This can be seen as a higher dimensional analogue of the counting problem for elliptic curves…
We characterize finite-dimensional Lie algebras over an arbitrary field of characteristic zero which admit a non-trivial (quasi-) triangular Lie bialgebra structure.
Brewster-reflection of a post-paraxial optical beam at a plane dielectric interface unravels fundamentally significant optical singularity dynamics. We express the simulated field-component profiles of a Brewster-reflected post-paraxial…
Polarization is a fundamental property of light that can be engineered and controlled efficiently with optical metasurfaces. Here, we employ chiral metasurfaces with monoclinic lattice geometry and achiral meta-atoms for resonant…
Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring…
We study orientifold projections of families of four-dimensional $\mathcal{N}=1$ toric quiver gauge theories. We restrict to quivers that have the unusual property of being associated with multiple periodic planar diagrams which give rise,…
We consider families of B\"or\"oczky tilings in hyperbolic space in arbitrary dimension, study some basic properties and classify all possible symmetries. In particular, it is shown that these tilings are non-crystallographic, and that…
A characterization of the focused space-time structures of radially chirped beams is provided, detailing different tunable properties such as: variable on-axis centroid velocity, symmetric pulse front tilt, transverse intensity modulations,…
The work is devoted to the self-action of laser beams propagating in the isotropic phase of a cholesteric liquid crystal near the transition temperature to the mesophase in a wide range of parameter values characterizing the nonlocality of…
We characterize singularities of focal surfaces of wave fronts in terms of differential geometric properties of the initial wave fronts. Moreover, we study relationships between geometric properties of focal surfaces and geometric…