Scatterers Of Arbitrary Shape Research Articles

Limits to surface-enhanced Raman scattering near arbitrary-shape scatterers: erratum.

In this erratum, we correct two minor algebraic errors from our previous published manuscript [Opt. Express 27, 35189 (2019)], which do not affect the main results or conclusions, and make a corresponding small change to one figure.

Limits to surface-enhanced Raman scattering near arbitrary-shape scatterers.

The low efficiency of Raman spectroscopy can be overcome by placing the active molecules in the vicinity of scatterers, typically rough surfaces or nanostructures with various shapes. This surface-enhanced Raman scattering (SERS) leads to substantial enhancement that depends on the scatterer that is used. In this work, we find fundamental upper bounds on the Raman enhancement for arbitrary-shaped scatterers, depending only on its material constants and the separation distance from the molecule. According to our metric, silver is optimal in visible wavelengths while aluminum is better in the near-UV region. Our general analytical bound scales as the volume of the scatterer and the inverse sixth power of the distance to the active molecule. Numerical computations show that simple geometries fall short of the bounds, suggesting further design opportunities for future improvement. For periodic scatterers, we use two formulations to discover different bounds, and the tighter of the two always must apply. Comparing these bounds suggests an optimal period depending on the volume of the scatterer.

Inverse design of acoustic devices: From flat lenses without negative refraction to acoustic cloaks based on scattering cancellation

Inverse design is currently applied to obtain unusual acoustical devices based on ordered and non-ordered scatterers. Recently, flat and lenticular acoustic lenses, de-multiplexors, directional sound sources and acoustic cloaks have been designed using a variety of optimization methods like genetic algorithms, simulated annealing and shape or topology optimizations among others. For example, feasible one-directional cloaks were first designed in two- and three-dimensions using high symmetry objects like cylinders [Appl. Phys. Lett. 99, 074102 (2011)] and toroidal scatterers [Phys. Rev. Lett. 110, 124301 (2013)], respectively. Recently, an extraordinary simple one-directional acoustic cloak has been reported using a technique that combines the method of fundamental solutions with arbitrary shape scatterers [Sci. Rep. 8, 12924 (2018)]. Here, we report a further improvement of the method by combining the Boundary Element Method (BEM) with shape optimization to obtain quasi-omnidirectional cloaks in two-dimensions. The shapes of the scatterers are optimized for the cloaking of the whole setup with waves impinging on the stealth object (a cylinder) from many different directions. An important feature of the method is the possibility of including visco-thermal acoustic losses in the optimization process [J. Sound Vib. 447, 120–136 (2019)].

Acoustic cloak based on B\xe9zier scatterers

Among the different approaches proposed to design acoustic cloaks, the one consisting on the use of an optimum distribution of discrete scatters surrounding the concealing object has been successfully tested. The feasibility of acoustic cloaks mainly depends on the number and shape of the scatterers surrounding the object to be cloaked. This work presents a method allowing the reduction of the number of discrete scatterers by optimizing their external shape, which is here defined by a combination of cubic Bézier curves. Based on scattering cancellation, a two-dimensional directional cloak consisting of just 20 Bézier scatters has been designed, fabricated and experimentally characterized. The method of fundamental solutions has been implemented to calculate the interaction of an incident plane wave with scatterers of arbitrary shape. The acoustic cloak here proposed shows a performance, in terms of averaged visibility, similar to that consisting of 120 scatterers with equal circular cross sections. The operational frequency of the proposed cloak is 5940 Hz with a bandwidth of about 110 Hz.

Wave propagation through penetrable scatterers in a waveguide and through a penetrable grating

A multimodal method based on the admittance matrix is used to analyze wave propagation through scatterers of arbitrary shape. Two cases are considered: a waveguide containing scatterers, and the scattering of a plane wave at oblique incidence to an infinite periodic row of scatterers. In both cases, the problem reduces to a system of two sets of first-order differential equations for the modal components of the wavefield, similar to the system obtained in the rigorous coupled wave analysis. The system can be solved numerically using the admittance matrix, which leads to a stable numerical method, the basic properties of which are discussed (convergence, reciprocity, energy conservation). Alternatively, the admittance matrix can be used to get analytical results in the weak scattering approximation. This is done using the plane wave approximation, leading to a generalized version of the Webster equation and using a perturbative method to analyze the Wood anomalies and Fano resonances.

Light propagation in finite-sized photonic crystals: multiple scattering using an electric field integral equation

We present an accurate, stable, and efficient solution to the Lippmann-Schwinger equation for electromagnetic scattering in two dimensions. The method is well suited for multiple scattering problems and may be applied to problems with scatterers of arbitrary shape or non-homogenous background materials. We illustrate the method by calculating light emission from a line source in a finite-sized photonic crystal waveguide.

Time Domain Scattering of Scalar Waves by Two Spheres in Free-Space

The importance of the T-matrix method is well known when frequency domain scattering problems are of interest. With the relatively recent and wide-spread interest in time domain scattering problems, similar applications of the T-matrix method are expected to be useful in the time domain. In this paper, the time domain spherical scalar wave functions are introduced, translational addition theorems for the time domain spherical scalar wave functions necessary for the solution of multiple scattering problems are given, and the formulation of time domain scattering of scalar waves by two scatterers of arbitrary shape is presented. The whole analysis is performed in the time domain requiring no inverse Fourier integrals to be evaluated. Scattering by two soft spheres in free-space is studied as an application to check the numerical accuracy and demonstrate the utility of the expressions.

Double Higher Order Method of Moments for Surface Integral Equation Modeling of Metallic and Dielectric Antennas and Scatterers

A novel double higher order Galerkin-type method of moments based on higher order geometrical modeling and higher order current modeling is proposed for surface integral equation analysis of combined metallic and dielectric antennas and scatterers of arbitrary shapes. The technique employs generalized curvilinear quadrilaterals of arbitrary geometrical orders for the approximation of geometry (metallic and dielectric surfaces) and hierarchical divergence-conforming polynomial vector basis functions of arbitrary orders for the approximation of electric and magnetic surface currents within the elements. The geometrical orders and current-approximation orders of the elements are entirely independent from each other, and can be combined independently for the best overall performance of the method in different applications. The results obtained by the higher order technique are validated against the analytical solutions and the numerical results obtained by low-order moment-method techniques from literature. The examples show excellent accuracy, flexibility, and efficiency of the new technique at modeling of both current variation and curvature, and demonstrate advantages of large-domain models using curved quadrilaterals of high geometrical orders with basis functions of high current-approximation orders over commonly used small-domain models and low-order techniques. The reduction in the number of unknowns is by an order of magnitude when compared to low-order solutions.

A semi-numerical method for elastic wave scattering calculations

This paper is concerned with the calculation of elastic wavefields in strongly heterogeneous media containing scatterers of arbitrary shape and size. A hybrid method is described in which the elastodynamic field within a finite region enclosing the scatterers is modelled by finite elements while the field away from this region is represented by means of a suitable set of wave functions. Application of a variational principle and the continuity conditions at the interface between the two regions lead to a system of linear equations that is solved by standard techniques. The hybrid method extends the applicability of the finite element method to wave propagation problems in unbounded media by rigorously modelling the radiation field. The method is used to calculate the elastodynamic field in a plate of finite thickness and infinite lateral dimensions containing geometric discontinuities.

Electromagnetic Wave Scattering From Small Scatterers of Arbitrary Shape

Scattering of electromagnetic waves from arbitrary shaped dielectric particles that are small compared to the wavelength in surrounding medium is studied theoretically by means of the local perturbation method generalized for vector equations. The resonance conditions are formulated, and the resonant frequency and the width of the resonance are calculated. As an example scattering of electromagnetic waves radiated by a moving charged particle is considered.

Transient scattering from arbitrary conducting surfaces by iterative solution of the electric field integral equation

This paper presents a numerical time-marching solution of the electric field integral equation (EFIE) suitable for simulation of transient scattering and radiation from perfectly conducting three-dimensional surfaces in a lossless isotropic medium. The method is capable of treating metallic scatterers of arbitrary shape modeled by arbitrary polygonal patches. Backscattering results for scatterers under an arbitrary time-dependent electromagnetic excitation may be obtained provided the tangential electric fields incident on the scatterer surface are known. By applying an expanded form of the EFIE free of spatial derivatives to simple piecewise-constant patch basis functions on polygonal surface patches, analytical simplifications then facilitate an iterative solution technique producing results free of numerical instabilities. Both near- and far-field transient scattering and radiation results can be obtained using this method.

On sound energy scattered by a rigid body near a compliant surface

A theorem is derived which generalizes the classical extinction theorem (also known as the optical theorem) to cases where a rigid scatterer of arbitrary shape is lo­cated near a large compliant surface which has quite general mechanical properties, including dissipation and wave-bearing features, and where the acoustic media on both sides of the compliant surface may have different densities and sound speeds. The theorem relates the sound energy scattered from incident planar acoustic waves to the far field pressure in the specular reflection direction and that in the transmis­sion direction, determined by the Snell’s law. From this simple relation, the scattered energy can be found almost trivially from the far field pressures in these two partic­ular directions; the energy calculation then completely avoids integration of energy flux over control surfaces.

Numerical solutions of TM scattering using an obliquely cartesian finite difference time domain algorithm

The conventional finite difference time domain (FDTD) algorithm for solving electromagnetic scattering problems, which uses a uniform Cartesian grid for enmeshing the problem domain, is limited in its ability to model scatterers of arbitrary shapes. In this paper, we extend the FDTD algorithm to a general obliquely Cartesian coordinate system, and apply it in conjunction with an edge-type absorbing boundary condition (ABC) to solve a number of representative TM scattering problems. In addition to extending the FDTD algorithm to obliquely Cartesian grids, we also derive the stability condition for the twodimensional obliquely Cartesian FDTD algorithm.

Convergent Long Wavelength Expansion Method for Two-Dimensional Scattering Problems

A conformal transformation is used to map the exterior of a scatterer of arbitrary shape into the exterior of a circle. This mapping replaces the problem of scattering from an awkwardly shaped scatterer in a medium of constant index of refraction (constant k2) by the problem of scattering from a circle in a medium of varying index of refraction (varying k2). The variation in the index of refraction is treated perturbatively by taking for the unperturbed problem the problem of scattering by a circle in a medium of constant index of refraction. Generally applicable bounds on the region of convergence of the perturbative solution are obtained and evaluated numerically for the case of Dirichlet boundary conditions. Error bounds on the remainder after n iterations are given. The method is illustrated by explicit calculation of the scattering from an infinite strip.

Scattering of Stress Waves by a Circular Elastic Cylinder Embedded in an Elastic Medium

Scattering of stress waves by a circular elastic cylinder embedded in an elastic medium is investigated. The axis of the scatterer is perpendicular to the propagation vector of the incident plane compressional stress pulse wave. Making use of modified Kirchhoff’s integral formulas developed for elastodynamics by Ko [1], wave-front stresses and displacements during the early stage of interaction are obtained for both interior and exterior fields, and for the scatterer-medium interface. The solutions are valid for the whole spectrum of material properties of the scatterer ranging from void to infinitely dense materials. It is found that Kirchhoff’s method of retarded potentials predicts singular wave-front response at caustics as does the geometrical acoustics. The basic integral equations presented are applicable to a scatterer of arbitrary shape and do not only give the wave-front solution, but also the solutions after the arrival of the wave front.