Related papers: Direct S-matrix calculation for diffractive struct…
A spatio-temporal metasurface is proposed to decompose in real time the temporal frequencies of electromagnetic waves into spatial frequencies onto a two-dimensional plane. The metasurface is analyzed and demonstrated using Fourier…
Development generating diffraction-related valuable expressions and formulas capable of initiating new era for diffraction and for scientific domains that use it provided. The main expression, among these, gives diffracted intensity as…
The resonant mode approximation of the scattering matrix is considered for calculating the optical properties of multilayered periodic structures within the formalism of the Fourier-modal method for two diffraction thresholds in close…
The Fourier-based diffraction approach is an established method to extract order and symmetry propertiesfrom a given point set. We want to investigate a different method for planar sets which works in direct spaceand relies on reduction of…
The S-matrix in the static limit of a dispersion relation has a finite order N and is a matrix of meromorfic functions of energy in the complex plane with cuts. In the elastic case it reduces to N functions connected by the crossing…
Chord diagrams and combinatorics of word algebras are used to model products of Dirac matrices, their traces, and contractions. A simple formula for the result of arbitrary contractions is derived, simplifying and extending an old…
We present a new computation method for simulating reflection high-energy electron diffraction and the total-reflection high-energy positron diffraction experiments. The two experiments are used commonly for the structural analysis of…
We describe efficient differentiation methods for computing Jacobians and gradients of a large class of matrix functions including the matrix logarithm $\log(A)$ and $p$-th roots $A^{\frac{1}{p}}$. We exploit contour integrals and conformal…
X-ray scattering patterns from emerging single particle experiments have commonly many missing or contaminated pixels. This complicates different analyses including projections on Fourier or other basis functions (for noise suppression,…
We present a formalism for understanding the elecromagnetism of metasurfaces, optically thin composite films with engineered diffraction. The technique, diffractive interface theory (DIT), takes explicit advantage of the small optical…
The analytical solving dynamic problems of elasticity theory for piecewise homogeneous half-space is found. The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S-matrix is meromorphic. We can express it in terms of its poles, and then calculate the quantum mechanical second virial coefficient…
We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the…
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
This report shows formulation of wave scattering in frequency domain. The formulation provides an understanding of S-matrix solver which is named as Scattering Matrix Analyzer (SMatrAn). The S-matrix has the whole of amplitude and phase…
The usual derivations of the S and K matrices for two-particle reactions proceed through the Lippmann-Schwinger equation with formal definitions of the incoming and outgoing scattering states. Here we present an alternative derivation that…
Scattering by an isolated defect embedded in a dielectric medium of two dimensional periodicity is of interest in many sub-fields of electrodynamics. Present approaches to compute this scattering rely either on the Born approximation and…
Fourier optics, the principle of using Fourier Transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and has been widely applied to optical information processing, imaging, holography etc.…
We optimize optical performance of metasurfaces based on periodically corrugated silicon layers by adjusting the Fourier coefficients of their surface profile. For smooth corrugations, we demonstrate an excellent quantitative accuracy of…