Related papers: Building ideal paraxial optical skyrmions using ra…
Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation,…
In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, and a stationary point of a particular energy functional. This paper describes lattice analogues of the aforementioned skyrmions, namely a natural way…
Prototype optical microscopes, built to pursue developments in advanced imaging techniques, need specific optomechanical constructions: preferably with high flexibility in the elements arrangement, easy access to the optical paths,…
We put forward a powerful technique that allows generating quasi-non-diffracting light beams with a variety of complex transverse shapes and topologies. We show that, e.g., spiraling patterns, patterns featuring curved or bent bright…
Magnetic skyrmions and their anti-particles, the antiskyrmions, are stable magnetic solitons existing down to the nanometer scale. Their stability and size as well as the possibility to propel them by, e.g., electric currents make them…
We consider multishell configurations in the Skyrme model within the rational map ansatz. We show that equations for the Skyrme field are linearized in the limit of large number of shells, thus allowing for a simple analytic solution.…
Let $X,Y$ be two irreducible subvarieties of the projective space $\mathbb{P}^n$, and $d\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\bf explicitly}, in terms of $d$ and the ideals defining $X$ and…
Generation and propagation of optical skyrmions provide a versatile plalform for topologically nontrivial optical informatics and light-matter interactions, but their acceleration along curved trajectories is to be studied. In this study,…
Various superpositions of Bessel-Gaussian beams and modified Bessel Gaussian beams are considered. Two selected parameters characterizing these beams, with respect to which the superpositions are constructed, are the topological index $n$…
The identification of general principles for stabilizing magnetic skyrmion phases in bulk materials over wide ranges of temperatures is a prerequisite to the development of skyrmion-based spintronic devices. Lacunar spinels with the formula…
We prove that any smooth rational projective surface over the field of complex numbers has an open covering consisting of 3 subsets isomorphic to affine planes.
In this paper, we construct geometrically finite rational maps with buried critical points on the boundaries of some hyperbolic components by using the pinching and plumbing deformations.
We develop an analytical model for calculation of optical spectra for metal nanostructures of arbitrary shape supporting localized surface plasmons (LSPs). For plasmonic systems with characteristic size below the diffraction limit, we…
The antiferromagnetic coupling and entanglement between skyrmion lattices are treated in magnetic bilayer systems. We first formulate the problem of large bilayer skyrmions using $\mathbb{CP}^{1}\otimes \mathbb{CP}^{1}$ theory. We have…
Recently, magnetic skyrmion has emerged as an active topic of fundamental study and applications in magnetic materials research. Magnetic skyrmions are vortex-like spin excitations with topological protection and therefore are more robust…
Skyrmions, as quasiparticles with topological spin textures, has recently garnered great attention for both condensed matter and structured wave communities, promising next-generation large-density robust information technologies. However,…
Strong magneto-electric coupling in two-dimensional helical materials leads to a peculiar type of topologically protected solutions -- skyrmions. Coupling between the net ferroelectric polarization and magnetization allows control of the…
This is the second of two papers on the birational geometry of $\bar{M}_{g,1}$. We construct rational maps from $\bar{M}_{5,1}$ and $\bar{M}_{6,1}$ to lower-dimensional moduli spaces. As a consequence, we identify geometric divisors that…
Optical skyrmions are members of the emerging topological branch of solid-state physics and photonics, allowing for control over topological light textures through light-matter interactions. However, in nanophotonics their practical…
Effective field theories have been developed for the description of light, shallow nuclei. I review results for two- and three-nucleon systems, and discuss their extension to halo nuclei.