Related papers: Hermite-Laguerre-Gaussian Vector Modes
Multiple-degrees-of-freedom free-space communication combining polarization and high-order spatial modes promises high-capacity communication channel. While high-order spatial modes have been widely exploited for dense coding and…
Polarization (P), angular index (l), and radius index (p) are three independent degrees of freedom (DoFs) of vector vortex beams, which have been widely used in optical communications, quantum optics, information processing, etc. Although…
A well-known shortcoming of High Harmonic Generation (HHG) is the strong dependence of the broadband HHG spectra (HGS) on the carrier envelope phase (CEP) of the driver. Here we numerically show that compared to the current well-established…
With the increased transverse mode degrees of freedom, spatiotemporal mode-locked (STML) fiber lasers exhibit more intricate and richer nonlinear dynamics, making them an ideal platform for studying complex nonlinear phenomena. However,…
The present paper introduces a method of basis transformation of a vector space that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such as Hermite, Laguerre and Legendre…
The dimension of the state space for information encoding offered by the transverse structure of light is usually limited by the finite size of apertures. The widely used orbital angular momentum (OAM) number of Laguerre-Gaussian (LG) modes…
We investigate a class of spatially covariant vector field theories on a flat background, where the Lagrangians are constructed as polynomials of first-order derivatives of the vector field. Because Lorentz and $\mathrm{U}(1)$ invariances…
We found that small perturbations of the optical vortex core in the Laguerre-Gaussian (LG) beams generate a fine structure of the Hermite-Gauss (HG) mode spectrum. Such perturbations can be easily simulated by weak variations of amplitudes…
The methods of mode decomposition and Fourier analysis of classical and quantum fields on curved spacetimes previously available mainly for the scalar field on Friedman- Robertson-Walker (FRW) spacetimes are extended to arbitrary vector…
Some time ago, we published the full count of degrees of freedom in the linearised weak gravity limit of arbitrary New GR models. We did it by considering the linear equations of motion and presented a thorough analysis with no ambiguity…
High harmonic generation (HHG) is a manifestation of the strongly nonlinear response of matter to intense laser fields and has, as the basis for coherent XUV sources a variety of applications. Recently, HHG from atoms in a phase and…
Scalable Vector Graphics (SVG) is a popular format on the web and in the design industry. However, despite the great strides made in generative modeling, SVG has remained underexplored due to the discrete and complex nature of such data. We…
Light's spatial properties represent an infinite state space, making it attractive for applications requiring high dimensionality, such as quantum mechanics and classical telecommunications, but also inherently spatial applications such as…
Laguerre-Gaussian (LG) modes are solutions of the paraxial Helmholtz equation in cylindrical coordinates and are associated with light fields carrying orbital angular momentum (OAM). It is customary to modulate such beams using phase-only…
This paper presents the method for the first time to generate intense high-order optical vortices that carry orbital angular momentum in the extreme ultraviolet region. In three-dimensional particle-in-cell simulation, both the reflected…
The transverse structure of light is recognized as a resource that can be used to encode information onto photons and has been shown to be useful to enhance communication capacity as well as resolve point sources in superresolution imaging.…
The far-field intensity distribution of spatiotemporal Laguerre-Gaussian (STLG) modes propagating in free space exhibits a multi-petal pattern analogous to that observed in tilted Hermite-Gaussian modes. Here, we show that this phenomenon…
We study the projective geometry of homogeneous varieties $X= G/P\subset P(V)$, where $G$ is a complex simple Lie group, $P$ is a maximal parabolic subgroup and $V$ is the minimal $G$-module associated to $P$. Our study began with the…
This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an…
In the theory of so called "Covariant Quantum Mechanics" a basic role is played by Hermitian vector fields on a complex line bundle in the frameworks of Galilei and Einstein spacetimes. In fact, it has been proved that the Lie algebra of…