Related papers: Half-integer order Bessel beams
Conventional method for Gaussian beam collimation is to expand the beam waist to achieve a smaller divergence angle. Recent transformation optics offers an unconventional path to control the electromagnetic field. In this paper we show that…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
Optical pin beams (OPBs) represent a novel class of structured light fields engineered for resilient, long-distance propagation. Their exceptional stability and strong resistance to atmospheric turbulence make them a compelling alternative…
Perfect (optical) vortex (PV) beams are fields which are mooted to be independent of the orbital angular momentum (OAM) they carry. To date, the best experimental approximation of these modes is obtained from passing Bessel-Gaussian beams…
Perfect (optical) vortices (PVs) have the mooted ability to encode orbital angular momentum (OAM) onto the field within a well-defined annular ring. Although this makes the near-field radial profile independent of OAM, the far-field radial…
In this paper, we report about recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs), by using energy-conserving line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class. In…
Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…
We present an algorithm for holographic shaping of partially coherent light, bridging the gap between traditional coherent and geometric optical approaches. The description of partially coherent light relies on a mode expansion formalism,…
Solving partial differential equations (PDEs) and their inverse problems using Physics-informed neural networks (PINNs) is a rapidly growing approach in the physics and machine learning community. Although several architectures exist for…
We propose a single phase-only optical element that transforms different orbital angular momentum (OAM) modes into localized spots at separated angular positions on a transverse plane. We refer to this element as an angular lens since it…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been…
A mathematical model in terms of partial differential equations (PDE) for the calculation of double freeform surfaces for irradiance and phase control with predefined input and output wavefronts is presented. It extends the results of…
Coherent nonlinear optical micro-spectroscopy is a frequently used tool in modern material science, as it is sensitive to many different local observables, which comprise, among others, crystal symmetry and vibrational properties. The…
We introduce a novel spectral, finite-dimensional approximation of general Sobolev spaces in terms of Chebyshev polynomials. Based on this polynomial surrogate model (PSM), we realise a variational formulation, solving a vast class of…
We consider the variational formulation of the electric field integral equation (EFIE) on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on div-conforming Raviart-Thomas boundary elements…
Speckle patterns are formed by random interferences of mutually coherent beams. While speckles are often considered as an unwanted noise in many areas, they also formed the foundation for the development of numerous speckle-based imaging,…
The exact formulas for the induced electric surface current (in the scattering phenomenon) and the equivalent electric surface current (in the diffraction phenomenon) on the open cylindrical surface due to an arbitrary narrow-band beam have…
There is significant interest in tailoring wave packets that transversely accelerate during propagation. The first realisation was in the optical domain, the Airy beam. Valid in the paraxial approximation, such beams were shown to…
We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a…