Related papers: The Light Scattering and Fast Mie Algorithm
This paper introduces a fast algorithm, applicable throughout the electromagnetic spectrum, for the numerical solution of problems of scattering by periodic surfaces in two-dimensional space. The proposed algorithm remains highly accurate…
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…
In this tutorial paper, we formulate a two-dimensional integral-equation based method of moments approach for numerically computing the electromagnetic fields scattered from an azimuthally-rough dielectric cylinder or an axially-rough…
In this paper, we review the main problem concerning the calculation of X-ray scattering of simulated model systems, namely their finite size. A novel method based on the Rayleigh-Debye-Gans approximation was derived, which allows…
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions…
We provide a theoretical description of light scattering by a spherical particle whose permittivity is modulated in time at twice the frequency of the incident light. Such a particle acts as a finite-sized photonic time crystal and, despite…
We propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector…
We consider an inverse scattering problem for time-harmonic acoustic or electromagnetic waves. The goal is to localize several small penetrable objects embedded inside an otherwise homogeneous background medium from observations of far…
We present a fast general-purpose algorithm for high-throughput clustering of data "with a two dimensional organization". The algorithm is designed to be implemented with FPGAs or custom electronics. The key feature is a processing time…
We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…
In this paper we introduce a new fix point iteration scheme for solving nonlinear electromagnetic scattering problems. The method is based on a spectral formulation of Maxwell's equations called the Bidirectional Pulse Propagation…
We develop an imaging algorithm that exploits strong scattering to achieve super-resolution in changing random media. The method processes large and diverse array datasets using sparse dictionary learning, clustering, and multidimensional…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed…
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…
Finding hidden order within disorder is a common interest in material science, wave physics, and mathematics. The Riemann hypothesis, stating the locations of nontrivial zeros of the Riemann zeta function, tentatively characterizes…
The numerically stable evaluation of scattering matrix elements near the infrared limit of gauge theories is of great importance for the success of collider physics experiments. We present a novel algorithm that utilizes double precision…
Clustering is a concept used in a huge variety of applications. We review a conceptually very simple algorithm for hierarchical clustering called in the following the {\it mutual information clustering} (MIC) algorithm. It uses mutual…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
We propose a method based on sinc series approximations for computing the Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The diffraction integrals are given in terms of a convolution, and our proposed numerical approach is…