arXiv subjects

Alexander Neuhaus

Publications and source records attributed to Alexander Neuhaus.

7 recordsLinked to original sources

arXiv2026

Topological Classification of Non-Normalizable Vector Fields

Topological classification of physical vector fields conventionally relies on field normalization and homotopy-based invariants. However, when field amplitudes vanish, normalization becomes ill-defined, preventing a direct topological characterization. Here, we introduce a general framework for the topological classification of non-normalizable $n$-dimensional vector fields with compactifiable base spaces by transforming them into $(n+1)$-dimensional normalized vector fields. This construction extends homotopy-based classification to fields containing amplitude zeros. We explicitly demonstrate the approach for one-, two-, and three-dimensional non-normalized vector fields and derive the corresponding topological invariants. The resulting topological charges are robust under continuous deformations and can change only when the embedding structure becomes singular. Our framework provides a unified route to the topological characterization of non-normalizable fields and opens the door to the study of topological phenomena in a broad range of systems, including magnetic textures, ferroelectrics, electromagnetic fields, and wave systems.

cond-mat.other↗

arXiv2026

Analysis of the Topology of a Plasmonic Target-Skyrmion Texture

Topological concepts are frequently used to describe structured optical fields, including plasmonic near fields. Topological descriptions in terms of skyrmion numbers implicitly assume the compactness of the underlying manifold. Even when skyrmion-like textures appear locally, the compactness is usually not fulfilled in extended optical fields. Here, we use photoemission electron microscopy to investigate a plasmonic nano-focus that exhibits a sequence of radially extending alternating skyrmion and antiskyrmion textures. The full spatio-temporal reconstruction of the electric field vectors and their topology is accessible by vector polarimetry. The experiments confirm the expected oscillatory behavior of the skyrmion number and demonstrate that a global skyrmion number cannot be assigned in such non-compact fields.

physics.optics↗

arXiv2024

Plasmonic Twistronics: Discovery of Plasmonic Skyrmion Bags

The study of van der Waals heterostructures with an interlayer twist, known as "twistronics", has been instrumental in advancing contemporary condensed matter research. Most importantly, it has underpinned the emergence of a multitude of strongly-correlated phases, many of which derive from the topology of the physical system. Here, we explore the application of the twistronics paradigm in plasmonic systems with nontrivial topology, by creating a moir\'e skyrmion superlattice using two superimposed plasmonic skyrmion lattices, twisted at a "magic" angle. The complex electric field distribution of the moir\'e skyrmion superlattice is measured using time-resolved vector microscopy, revealing that each super-cell possesses very large topological invariants and harbors a "skyrmion bag", the size of which is controllable by the twist angle and center of rotation. Our work shows how twistronics leads to a diversity of topological features in optical fields, providing a new route to locally manipulate electromagnetic field distributions, which is crucial for future structured light-matter interaction.

physics.optics↗

arXiv2024

Spatio-temporal topology of plasmonic spin meron pairs revealed by polarimetric photo-emission microscopy

Topology is the study of geometrical properties and spatial relations unaffected by continuous changes, and has become an important tool for understanding complex physical systems. Although recent optical experiments have inferred the existence of vector fields with the topologies of merons, the inability to extract the full three dimensional vectors misses a richer set of topologies that have not yet been fully explored. In our work, we extend the study of the topology of electromagnetic fields on surfaces to a spin quasi-particle with the topology of a meron pair, formed by interfering surface plasmon polaritons, and show that the in-plane vectors are constrained by the embedding topology of the space as dictated by the Poincare-Hopf theorem. In addition we explore the time evolution of the three dimensional topology of the spin field formed by femtosecond laser pulses. These experiments are possible using our here developed method called polarimetric photoemission electron microscopy (polarimetric PEEM) that combines an optical pump-probe technique and polarimetry with photo-emission electron microscopy. This method allows for the accurate generation of surface plasmon polariton fields and their subsequent measurement, revealing both the spatial distribution of the full three-dimensional electromagnetic fields at deep sub-wavelength resolution and their time evolution.

physics.optics↗

arXiv2023

Angle-resolved photoelectron spectroscopy in a low energy electron microscope

Spectroscopic photoemission microscopy is a well-established method to investigate the electronic structure of surfaces. In modern photoemission microscopes the electron optics allows imaging of the image plane, momentum plane, or dispersive plane, depending on the lens setting. Furthermore, apertures allow filtering of energy-, real-, and momentum space. Here, we describe how a standard spectroscopic and low energy electron microscope can be equipped with an additional slit at the entrance of the already present hemispherical analyzer to enable an angle- and energy resolved photoemission mode with micrometer spatial selectivity. We apply a photogrammetric calibration to correct for image distortions of the projective system behind the analyzer and present spectra recorded on Au(111) as a benchmark. Our approach makes data acquisition in energy-momentum space more efficient, which is a necessity for laser-based pump-probe photoemission microscopy with femtosecond time resolution.

cond-mat.mtrl-sci↗

arXiv2022

Stabbing balls with line segments and polygonal paths

We study the problem of ordered stabbing of $n$ balls (of arbitrary and possibly different radii, no ball contained in another) in $\mathbb{R}^d$, $d \geq 3$, with either a directed line segment or a (directed) polygonal curve. Here, the line segment, respectively polygonal curve, shall visit (intersect) the given sequence of balls in the order of the sequence. We present a deterministic algorithm that decides whether there exists a line segment stabbing the given sequence of balls in order, in time $O(n^{4d-2} \log n)$. Due to the descriptional complexity of the region containing these line segments, we can not extend this algorithm to actually compute one. We circumvent this hurdle by devising a randomized algorithm for a relaxed variant of the ordered line segment stabbing problem, which is built upon the central insights from the aforementioned decision algorithm. We further show that this algorithm can be plugged into an algorithmic scheme by Guibas et al., yielding an algorithm for a relaxed variant of the minimum-link ordered stabbing path problem that achieves approximation factor 2 with respect to the number of links. We conclude with experimental evaluations of the latter two algorithms, showing practical applicability.

cs.CG↗

arXiv2020

Computing the Fréchet distance of trees and graphs of bounded tree width

We give algorithms to compute the Fréchet distance of trees and graphs with bounded tree width. Our algorithms run in $O(n^2)$ time for trees of bounded degree, and $O(n^2\sqrt{n \log n})$ time for trees of arbitrary degree. For graphs of bounded tree width we show one can compute the Fréchet distance in FPT (fixed parameter tractable) time.

cs.CG↗