Related papers: Paraxial Sharp-Edge Diffraction of Vortex Beams by…
We construct the first measure-preserving affine actions with spectral gap on surfaces of arbitrary genus $g > 1$. We achieve this by finding geometric representatives of multi-twists on origami surfaces. As a major application, we…
We report on the experimental realization of flat mirrors enabling the broadband generation of optical vortices upon reflection. The effect is based on the geometric Berry phase associated with the circular Bragg reflection phenomenon from…
Partitioning an image into superpixels based on the similarity of pixels with respect to features such as colour or spatial location can significantly reduce data complexity and improve subsequent image processing tasks. Initial algorithms…
We describe a research project carried out with a group of undergraduate physics students and aimed at exploring the use of a neural network to study a classical problem in wave optics whose analytical solution is well known: the…
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…
Multiple image gravitational lens systems, and especially quads are invaluable in determining the amount and distribution of mass in galaxies. This is usually done by mass modeling using parametric or free-form methods. An alternative way…
A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld…
Closed form solutions for the computation of the solid angle from polygonal cross-sections are well known, however similar formulae for computation of projected solid angle are not generally available. Formulae for computing the projected…
We investigate the mechanism of the nonparaxial propagation of the tightly focused beams in the view of Fourier optics. It shows that it is the phase of the angular spectrum which induces the interesting evolution of the tightly focused…
A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lame curves with double reduction and in the explicit…
We present a simple method for calculation of diffraction effects in a beam passing an aperture. It follows the well-known approach of Miyamoto and Wolf, but is simpler and does not lead to singularities. It is thus shown that in the…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
The rapid scale broadening and divergence increasing of vortex beams (VBs) with orbital angular momentum (OAM), e.g., Laguerre-Gaussian beams, severely impede the wide applications of VBs ranging from optical manipulation to…
We for the first time report the truncated diffraction with a triangular aperture of the SU(2) geometric modes and propose a method to detect the complicated orbital angular momentum (OAM) of an SU(2) wave-packet, to the best of our…
Phase-Stretch Adaptive Gradient-Field Extractor (PAGE) is an edge detection algorithm that is inspired by physics of electromagnetic diffraction and dispersion. A computational imaging algorithm, it identifies edges, their orientations and…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack…
A novel approach based on the two-channel moir\'e deflectometry has been used to measure both wave-front and transverse component of the Poynting vector of an optical vortex beam. Generated vortex beam by the q-plate, an inhomogeneous…
We study the Schr\"odinger equation which comes from the paraxial approximation of the Helmholtz equation in the case where the direction of propagation is tilted with respect to the boundary of the domain. In a first part, a mathematical…
The analysis of ultrafast electron diffraction (UED) data from low-symmetry single crystals of small molecules is often challenged by the difficulty of assigning unique Laue indices to the observed Bragg reflections. For a variety of…