Related papers: Hermite-Laguerre-Gaussian Vector Modes
Let $K$ be a number field, $\OK$ be its ring of integers. We introduce the notion of compactified representation of $GL_N(\OK)$ and, we see how to associate to a hermitian vector bundle $\E$ over $\Spec(\OK)$ and a compactified…
A new n-dimensional vector space of the DNA sequences on the Galois field of the 64 codons (GF(64)) is proposed. In this vector space gene mutations can be considered linear transformations or translations of the wild type gene. In…
Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and…
Gravitational waves in general relativity contain two polarization degrees of freedom, commonly labeled plus and cross. Besides those two tensor modes, generic theories of gravity predict up to four additional polarization modes: two scalar…
In this paper we consider the complex vector spaces of holomorphic cross-sections of homogeneous holomorphic vector bundles over elliptic adjoint orbits, and provide a sufficient condition for the vector spaces to be finite dimensional in…
We numerically study the filamentation of femtosecond vector beams with spatially varying polarization profiles in air. The vector beams include azimuthal, radial, and spiral cylindrical vector beams (CVBs), as well as low-order Full…
The localization of vector multiplets is examined using the {\cal N}=1 supersymmetric U(1) gauge theory with the Fayet-Iliopoulos term coupled to charged chiral multiplets in four dimensions. The vector field becomes localized on a BPS wall…
Gaussian Schell-model fields are examples of spatially partially coherent fields, which in recent years have found several unique applications. The existing techniques for generating Gaussian Schell-model (GSM) fields are based on…
With higher-order neighborhood information of graph network, the accuracy of graph representation learning classification can be significantly improved. However, the current higher order graph convolutional network has a large number of…
Localized vectorial modes, with equal frequencies and mutually orthogonal polarizations, are investigated both analytically and experimentally in a one-dimensional photonic lattice with saturable nonlinearity. It is shown that these modes…
Model equations for describing and efficiently computing the radiation profiles of tightly spherically-focused higher-order electromagnetic beams of vortex nature are derived stemming from a vectorial analysis with the complex-source-point…
In the field of computer graphics, the use of vector graphics, particularly Scalable Vector Graphics (SVG), represents a notable development from traditional pixel-based imagery. SVGs, with their XML-based format, are distinct in their…
Optical orbital angular momentum transformation and corresponding azimuthal-mode selection rules have been studied exhaustively for various nonlinear optical interactions. However, nonlinear transformation of radial mode has not been…
We completely classify the possible extensions between semistable vector bundles on the Fargues-Fontaine curve (over an algebraically closed perfectoid field), in terms of a simple condition on Harder-Narasimhan polygons. Our arguments rely…
Realistic human geometry generation is an important yet challenging task, requiring both the preservation of fine clothing details and the accurate modeling of clothing-body interactions. To tackle this challenge, we build upon Geometry…
Physical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences. These naturally occurring vector fields are often subject to physical constraints, such as being curl-free or…
We consider a vector gauge theory in 2 + 1 dimensions of the type recently proposed by Radzihovsky and Hermele [1] to describe fracton phases of matter. The theory has U(1)XU(1) vector gauge fields coupled to an additional vector field with…
Hermite-Gaussian (HG) beams are standard modes delivered by continuous or pulsed lasers systems, and pulse-front tilt is one of the most common, detrimental or beneficial, spatiotemporal couplings affecting ultrashort pulses. Combining…
I study vector solitons involving two incoherently-coupled field components in periodic PT-symmetric optical lattices. The specific symmetry of the lattice imposes the restrictions on the symmetry of available vector soliton states. While…
We construct a new category of vector spaces which contains both the standard category of vector spaces and Grassmannians. Its space of objects classifies vector bundles, its space of morphisms classifies bundle isomorphisms, and it can be…