相关论文: A Higher-Order Poincar\'e Ellipsoid representation…

The Poincar\'e sphere is a graphical representation in a three-dimensional space for the polarization of light. Similarly, an optical element with spatially varying birefringence can be represented by a surface on a four-dimensional…

Holographic displays are widely regarded as the "ultimate" display technology, promising immersive 3D visuals with natural depth cues, continuous parallax, and perceptual realism. Realizing this potential, however, has remained elusive due…

Optical vortex beam of fractional order is generated by the diffraction of a Gaussian beam using computer generated hologram embedded with mixed screw-edge dislocation. Unfolding of the generated fractional vortex beam into…

We investigate interesting symmetry properties verified by the down-converted beams produced in optical parametric amplification with structured light. We show that the Poincar\'e sphere symmetry, previously demonstrated for first-order…

We propose a method for generating hollow beams using higher-order cylindrical vector modes of the form R-TEMpl, where the radial index p is varied from 1 to 3 while the azimuthal index is fixed at l = 1. It is found that this scheme…

We develop a triangular formulation of the hierarchical Poincar\'e-Steklov (HPS) method for elliptic partial differential equations on surfaces, allowing high-order discretizations on unstructured meshes and complex geometries. Classical…

The connection between Poincar\'e spheres for polariz-ation and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic 2-dimensional harmonic oscillator in Hamiltonian mechanics, its…

Increasing demand for practical applications is forcing deeper research into optical vortices (OVs): from the generation and measurement to shaping and multiple singularities manipulation of OVs. Herein, we propose a new type of phase…

We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh;…

We provide the first experimental demonstration of geometric phase generated in association with closed Poincar\'e Sphere trajectories comprised of geodesic arcs that do not start, end, or necessarily even include, the north and south poles…

This paper is devoted to investigating the fundamental properties of the high-order proximal operator (HOPE) and the high-order Moreau envelope (HOME) in the nonconvex setting, where the quadratic regularization ($p=2$) is replaced by a…

The Poincar\'e-Hopf Theorem is a conservation law for real-analytic vector fields, which are tangential to a closed surface (such as a torus or a sphere). The theorem also governs real-analytic vector fields, which are tangential to…

In this paper, we propose a novel model for high-dimensional data, called the Hybrid Orthogonal Projection and Estimation (HOPE) model, which combines a linear orthogonal projection and a finite mixture model under a unified generative…

This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an…

We investigate higher-order geometric $k$-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudinal studies of Computational Anatomy. Our…

The Ince-Gauss beams, separable in elliptic coordinates, are studied through a ray-optical approach. Their ray structure can be represented over a ray-Poincar\'e sphere by generalized Viviani curves (intersections of a cylinder and a…

We propose and experimentally demonstrate a polarization--based steganographic scheme using partially polarized vector beams. In our approach, the spatially dependent polarization structure of the optical field serves as the carrier through…

Load forecasting is a fundamental task in smart grid. Many techniques have been applied to developing load forecasting models. Due to the challenges such as the Curse of Dimensionality, overfitting, and limited computing resources,…

Autonomous systems need to understand the semantics and geometry of their surroundings in order to comprehend and safely execute object-level task specifications. This paper proposes an expressive yet compact model for joint object pose and…

Like the ordinary power spectrum, higher-order spectra (HOS) describe signal properties that are invariant under translations in time. Unlike the power spectrum, HOS retain phase information from which details of the signal waveform can be…