相关论文: Rayleigh-Sommerfeld Fraunhofer Diffraction

We apply the stationary phase method developed in (Assier, Shanin \& Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written as a double Fourier transform of an unknown spectral…

The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…

This report aims to present my research updates on distance function wavelets (DFW) based on the fundamental solutions and the general solutions of the Helmholtz, modified Helmholtz, and convection-diffusion equations, which include the…

Ultrafast X-ray diffraction by the LCLS free-electron laser has been used to probe Charge Density Wave (CDW) systems under applied external currents. At sufficiently low currents, CDW wavefronts bend in the direction transverse to the…

We consider an optical diffraction grating in which the spatial distribution of open slits forms a fractal set. The Fraunhofer diffraction patterns through the fractal grating are obtained analytically for the simplest triad Cantor type and…

Fourier transform spectroscopy (FTS) has been widely used as an analytical tool for many applications in science and engineering. In this paper, we describe the operation principle and practical implementation of an FTS prototype. First,…

An elegant and convenient rigorous approach for solving circular open-ended dielectric-loaded waveguide diffraction problems is presented. It uses the solution of corresponding Wiener-Hopf-Fock equation and leads to an infinite linear…

This dissertation is concerned with understanding and analyzing some of the effects of diffraction in the near field. The contributions of homogeneous and of evanescent waves to two-dimensional near-field diffraction patterns of scalar…

The division of the near-field and far-field zones for electromagnetic waves is important for simplifying theoretical calculations and applying far-field results. In this paper, we have studied the far-field asymptotic behaviors of dipole…

Several papers have been published recently, particularly in the field of topological insulators, that use a Fourier-transform technique in a way that can be misleading or otherwise inaccurate, and the processing is not always described in…

Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…

We study sampling of Fourier Integral Operators $A$ at rates $sh$ with $s$ fixed and $h$ a small parameter. We show that the Nyquist sampling limit of $Af$ and $f$ are related by the canonical relation of $A$ using semiclassical analysis.…

The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of…

Context. Narrow-band interference filters can be tuned toward shorter wavelengths by tilting them from the perpendicular to the optical axis. This can be used as a cheap alternative to real tunable filters, such as Fabry-P\'erot…

Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…

This tutorial is designed to clarify a few misconceptions in the field of ultrafast optics. (1) Analytic signal that underlies the complex-conjugate decomposition of the field is discussed, as well as the misunderstanding between…

We study concentration operators associated with either the discrete or the continuous Fourier transform, that is, operators that incorporate a spatial cut-off and a subsequent frequency cut-off to the Fourier inversion formula. Their…

We have analytically obtained the theoretical results for the Rayleigh-Sommerfeld (R-S) scalar diffraction by apertures, such as single-slit, double-slit, grating and circular aperture, moving at relativistic speeds with the velocities…

We construct a minimal theory describing the optical activity of a thin sheet of a twisted material, the simplest example of which is twisted bilayer graphene. We introduce the notion of "twisted electrical conductivity", which parametrizes…

We investigate estimating scalar oscillatory integrals by integrating by parts in directions based on $(x_1 \partial_{x_1} f(x) ,..., x_n \partial_{x_n}f(x))$, where $f(x)$ is the phase function. We prove a theorem which provides estimates…