Related papers: Building ideal paraxial optical skyrmions using ra…
The optical counterparts of skyrmions have recently been constructed with diverse topological types and by different degrees of freedom, such as field, spins, and Stokes vectors, exhibiting extensive potential in modern information science.…
In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is…
The Skyrme crystal is built up of repeating units similar to the cubic Skyrmion of baryon number 4. Using this as guide, we construct new Skyrmion solutions in the massive pion case, with various baryon numbers up to 108. Most of our…
Optical skyrmions formed in terms of polarization are topological quasi-particles and have garnered much interest in the optical community owing to their unique inhomogeneous polarization structure and simplicity in their experimental…
We consider multiskyrmion configurations in 2D ferromagnets with Dzyaloshinskii-Moriya (DM) interaction and the magnetic field, using the stereographic projection method. In the absence of DM interaction, $D$, and the field, $B$, the…
The potential for manipulating characteristics of skyrmions in a CrI$_3$ monolayer using circularly polarised light is explored. The effective skyrmion-light interaction is mediated by bright excitons whose magnetization is selectively…
Discovery of polar skyrmions on the (PbTiO$_3$)$_n$/(SrTiO$_3$)$_n$ superlattice in the absence of any known interaction, which can orient electric polarizations at a point with respect to its neighboring points, is enigmatic. We here show…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space. This problem is first turned into the computation of the finite…
Skyrmions are extended field configurations, initially proposed to describe baryons as topological solitons in an effective field theory of mesons. We investigate and confirm the existence of skyrmions within the electroweak sector of the…
A new method is introduced to construct approximations to Skyrmions that are explicit rational functions of the spatial Cartesian coordinates. The scheme uses ADHM data of a Yang-Mills instanton to produce a Skyrmion with a baryon number…
We present 4D topological textures in (quasi)monochromatic nonparaxial optical lattices that contain all possible polarization ellipses with every combination of ellipticity and orientation in 3D space. These fields span the nonparaxial…
We review and develop the construction of crosscap states associated with parity symmetries in rational conformal field theories. A general method to construct crosscap states in abelian orbifold models is presented. It is then applied to…
We complete the `paraxial' (small-angle) ray optics cloaking formalism presented previously [Choi and Howell, Opt. Express 22, 29465 (2014)], by extending it to the full-field of light. Omnidirectionality is then the only relaxed parameter…
We present an integrability criterion for rational mappings based on two requirements. First, that a given point should have a unique preimage under the mapping and, second, that the spontaneously appearing singularities be confined to a…
The aim of this paper is to present a simple way to generate proper monomial rational maps between generalized balls and via the relations between generalized balls and bounded symmetric domains of type I, we suggest new examples of proper…
We construct discrete analogs of Skyrmions in nonlinear dynamical lattices. The Skyrmion is built as a vortex soliton of a complex field, coupled to a dark radial soliton of a real field. Adjusting the Skyrmion ansatz to the lattice setting…
Chiral fields with large optical chirality are very important in chiral molecules analysis, sensing and other measurements. Plasmonic nanostructures have been proposed to realize such super chiral fields for enhancing weak chiral signals.…
The Euclidean Algorithm is the often forgotten key to rational approximation techniques, including Taylor, Lagrange, Hermite, osculating, cubic spline, Chebyshev, Pade and other interpolation schemes. A unified view of these various…
Skyrmions, merons, bimerons, and skyrmionic hopfions are quasiparticles which have stable topological textures. They have been observed across multiple physical domains including nucleons, water waves, magnetic materials, electromagnetic…