Related papers: The Broken Ray Transform in $n$ Dimensions with Fl…
X-ray Bragg coherent diffraction imaging has been demonstrated as a powerful three-dimensional (3D) microscopy approach for the investigation of sub-micrometer-scale crystalline particles. It is based on the measurement of a series of…
We propose and investigate an "interface-flattening" transformation, hinging upon Transformation Optics (T.O.) techniques, to facilitate the rigorous analysis of electromagnetic (EM) fields radiated by sources embedded in tilted,…
We derive new general expressions for the fluctuating electromagnetic field outside a homogeneous material surface. The analysis is based on general results from the thermodynamics of irreversible processes, and requires no consideration of…
In a series of two papers, we make a comparative analysis of the performance of conventional perturbation theory to analyze electroweak phase transition in the real triplet extension of Standard Model ($\Sigma$SM). In Part I (this paper),…
We study the microlocal inversion of the ray transform on symmetric $m$-tensor fields restricted to all lines passing through a curve in $\mathbb{R}^{n}$. From this incomplete data, we show that the wavefront set of the solenoidal component…
We introduce a Bargmann transform on the space of hyperplanes by applying the Plancherel formula of the Radon transform to the definition of the Bargmann transform on the Euclidean space. Some basic facts on microlocal analysis are also…
Epsilon-near-zero (ENZ) media disclose the peculiarities of electrodynamics in the limit of infinite wavelength but non-zero frequency for experiments and applications. Theory suggests that wave interaction with obstacles and disturbances…
We consider integrals of spherical harmonics with Fourier exponents on the sphere $S^n ,\, n \geq 1$. Such transforms arise in the framework of the theory of weighted Radon transforms and vector diffraction in electromagnetic fields theory.…
In this manuscript, we obtain a plane wave decomposition for the delta distribution in superspace, provided that the superdimension is not odd and negative. This decomposition allows for explicit inversion formulas for the super Radon…
For a piecewise linear version of the periodic map with anomalous diffusion, the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions…
Let $\bbK=\mathbb R, \mathbb C, \mathbb H$ be the field of real, complex or quaternionic numbers and $M_{p, q}(\bbK)$ the vector space of all $p\times q$-matrices. Let $X$ be the matrix unit ball in $M_{n-r, r}(\bbK)$ consisting of…
A numerical study of the features of the scattering of incident radiation at a periodically modulated hyperbolic metamaterial boundary was carried out. We have found optimal - sawtooth-shaped profile of the interface which provides minimal…
We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary…
The Eulerian transformation is the linear operator on polynomials in one variable with real coefficients which maps the powers of this variable to the corresponding Eulerian polynomials. The derangement transformation is defined similarly.…
A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. As an example, we apply this formalism to study the…
1-loop quantum corrections are shown to induce large effects on the refraction index n inside a graphene strip in the presence of an external magnetic field B orthogonal to it. To this purpose, we use the tools of Quantum Field Theory to…
An atomically flat interface is achieved between face-centered cubic Al and diamond lattice Ge via molecular beam epitaxy (MBE). Based on the measurements of scanning tunneling microscopy (STM), we demonstrate an atomically resolved lateral…
We study higher-rank Radon transforms that take functions on $j$-dimensional totally geodesic submanifolds in the $n$-dimensional real constant curvature space to functions on similar submanifolds of dimension $k >j$. The corresponding dual…
Reflection high-energy electron diffraction (RHEED) is a powerful tool for characterizing crystal surface structures. However, the setup geometry leads to distorted and complicated patterns, which are not straightforward to link to the…
Flat lens concept based on negative refraction proposed by Veselago in 1968 has been mostly investigated in monochromatic regime. It was recently recognized that time development of the super-lensing effect discovered in 2000 by Pendry is…