Related papers: Hermite-Laguerre-Gaussian Vector Modes
Photons propagating in Laguerre-Gaussian modes have characteristic orbital angular momentums, which are fundamental optical degrees of freedom. The orbital angular momentum of light has potential application in high capacity optical…
We study generalized Hermite polynomials with rectangular matrix arguments arising in multivariate statistical analysis and the theory of zonal polynomials. We show that these are well-suited for expressing the Wiener-Ito chaos expansion of…
We experimentally observe longer than long trajectory influence in high order harmonic generation (HHG) by varying the peak intensity of the driving laser field through either direct attenuation, or by chirping the laser pulse. Using a…
The purpose of this paper is to extend the Donaldson-Corlette theorem to the case of vector bundles over cell complexes. We define the notion of a vector bundle and a Higgs bundle over a complex, and describe the associated Betti, de Rham…
We propose and experimentally demonstrate the generation of pseudo-high-order group velocity locked vector solitons (GVLVS) in a fiber laser using a SESAM as the mode locker. With the help of an external all-fiber polarization resolved…
This article lays the foundations for the study of modular forms transforming with respect to representations of Fuchsian groups of genus zero. More precisely, we define geometrically weighted graded modules of such modular forms, where the…
Hierarchies of Lagrangians of degree two, each only partly determined by the choice of leading terms and with some coefficients remaining free, are considered. The free coefficients they contain satisfy the most general differential…
In this work, we demonstrate that the mixing of scalar and vector condensates produces spatially oscillating, but exponentially damped correlation functions in fermionic theories at finite density and temperature. We find a regime…
In this paper we describe an approach to construct large extendable collections of vectors in predefined spaces of given dimensions. These collections are useful for neural network latent space configuration and training. For classification…
While recent advances in generative latent spaces have driven substantial progress in single-image generation, the optimal latent space for novel view synthesis (NVS) remains largely unexplored. In particular, NVS requires geometrically…
Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward…
The task of multi-label image classification involves recognizing multiple objects within a single image. Considering both valuable semantic information contained in the labels and essential visual features presented in the image, tight…
We show how to make precise the vague idea that for compact metric spaces that are close together for Gromov-Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach…
Harnessing the spontaneous emission of incoherent quantum emitters is one of the hallmarks of nano-optics. Yet, an enduring challenge remains-making them emit vector beams, which are complex forms of light associated with fruitful…
We have experimentally studied the distribution of the spatial extent of modes, and the crossover from essentially single-mode to distinctly multi-mode behavior inside a porous gallium phosphide random laser. This system serves as a paragon…
We introduce \emph{hierarchical depth}, a new invariant of line bundles and divisors, defined via maximal chains of effective sub-line bundles. This notion gives rise to \emph{hierarchical filtrations}, refining the structure of the Picard…
The vector electric-field Helmholtz equation, containing cross-polarization terms, is factored to produce both pseudo-differential and exponential operator forms of a three-dimensional, one-way, vector, wave equation for propagation through…
Solitons are non-dispersing localized waves that occur in diverse physical settings. A variety of optical solitons have been observed, but versions that involve both spatial and temporal degrees of freedom are rare. Optical fibers designed…
We develop a geometric description of structured Gaussian beams, a form a structured light, by applying geometric quantisation and symplectic reduction to the 2D harmonic oscillator. Our results show that the geometric quantisation of the…
A vectorial optical mode converter that can transform an orthogonal set of multiple input vector beams into another orthogonal set of vector beams is attractive for a wide range of applications in optics and photonics. While multi-plane…