Scattering of a surface wave by a submerged sphere

Summary The problem of the scattering of a surface wave in a nonviscous, incompressible fluid of infinite depth by a fully submerged, rigid, stationary sphere has been reduced to the solution of an infinite set of linear algebraic equations for the expansion coefficients in spherical harmonics of the velocity potential. These equations are easily solved numerically, so long as the sphere is not too close to the surface. The approach has been to formulate the problem as an integral equation, expand the Green's function, the velocity potential of the incident wave, and the total velocity potential in spherical harmonics, impose the boundary condition at the surface of the sphere, and carry out the integrations. The scattering cross section has been evaluated numerically and is shown to peak for values of the product of radius and wave number somewhat less than unity. Also, the Born approximation to the cross section is obtained in closed form.Supported by the Department of the Navy, Naval Sea Systems Command under Contract No. N00017-72-C-4401.     

Analysis of electromagnetic scattering by uniaxial anisotropic bispheres

Based on the generalized multiparticle Mie theory and the Fourier transformation approach, electromagnetic (EM) scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes is investigated. By introducing the Fourier transformation, the EM fields in the uniaxial anisotropic spheres are expanded in terms of the spherical vector wave functions. The interactive scattering coefficients and the expansion coefficients of the internal fields are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. Some selected calculations on the effects of the size parameter, the uniaxial anisotropic absorbing dielectric, and the sphere separation distance are described. The backward radar cross section of two uniaxial anisotropic spheres with a complex permittivity tensor changing with the sphere separation distance is numerically studied. The authors are hopeful that the work in this paper will help provide an effective calibration for further research on the scattering characteristic of an aggregate of anisotropic spheres or other shaped anisotropic particles.     

Scattering of elastic waves by an elastic sphere

The problem of scattering of plane compressional wave by an elastic sphere embedded in an isotropic elastic medium of different material properties is solved. Approximate formulas are derived for the displacement field, stress tensor, stess intensity factors, far-field amplitudes and the scattering cross section. It is assumed that the wave length is large compared to the radius of the scatterer. Various elastostatic limits are also presented.     

Low-frequency scattering of coated spherical obstacles

This work deals with the scattering of a plane harmonic elastic wave by a penetrable spherical scatterer with a concentric spherical penetrable inclusion. We evaluate the zeroth and first-order approximations of the Rayleigh expansion of the displacement fields. The major line of applications belongs to the science of the particulate composite material. So, as an application of the method, a typical particulate composite material is examined and the behaviour of the scattering cross section with respect to the elastic properties of the medium is presented.     

Light scattering at oblique incidence on two coaxial cylinders

A solution for the problem of a plane wave at oblique incidence on two coaxial cylinders is presented. The solution of the wave equation is determined for various geometric regions, and boundary conditions are applied at the material interfaces. The resulting solution consists of a system of eight equations in eight unknown coefficients. Expressions for two of the Mueller-scattering matrix elements (S(11) and S(12)) and the extinction, scattering, and backscattering cross sections are derived. A numerical algorithm for the solution is developed and implemented. The algorithm is tested for several limiting cases: homogeneous, hollow, and metal-core cylinders at various angles of incidence for TM and TE waves. Comparisons of the results of the algorithm with the results of studies reported in the literature are made. The comparisons are favorable, achieving good agreement with published work. For two coaxial cylinders, the numerical calculations show that if one is to use light scattering as a diagnostic tool, both of the Mueller-scattering matrix elements S(11) and S(12) must be measured simultaneously. In addition, the backscattering cross section is very sensitive for monitoring change in the radii of the cylinders.     

Coil impedance due to a sphere of arbitrary radial conductivity andpermeability profiles

This paper presents analytical expressions for coil impedance due to a spherical workpiece consisting of concentric spherical shells. The expressions are used to simulate the nondestructive inspection of a sphere having arbitrary radial conductivity and magnetic permeability profiles by a circular coil of rectangular cross section. The simulation replaces continuous profiles with piecewise constant profiles. The paper compares the results to published experimental measurements and the results of other analytical solutions     

Absolute interferometric test of aspheres by use of twin computer-generated holograms

A complete absolute interferometric test of axially symmetric aspheres is presented. The method is based on a specially designed computer-generated hologram (CGH) that reconstructs an aspherical wave as well as a spherical auxiliary wave. Since both phase functions have the same symmetry and their pattern is simultaneously encoded, we call this type of multiplex hologram a Twin-CGH. The spherical wave is used for calibration. The aberrations of the spherical auxiliary wave are measured absolutely with either a spherical mirror or an absolute test for Fresnel zone plates. Thus the two types of aberration inherent in the CGH can be identified and separated from each other. The errors of the spherical wave can be transferred to those of the aspherical wave. Two different methods thatuse Twin-CGHs for absolute testing of aspheric surfaces are described. Test procedures are explained, equations are derived, and experimental results are presented. A mutual comparison of the two results and a comparison with the established N-position rotation test are given.     

Electromagnetic scattering by an aggregate of spheres

We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.     

A New Closed-Form Solution to Light Scattering by Spherical Nanoshells

Light or electromagnetic wave scattered by a single sphere or a coated sphere has been considered as a classic Mie theory. There have been some further extensions that were made further based on the Mie theory. Recently, a closed-form analytical model of the scattering cross section of a single nanoshell has been considered. The present paper is documented further, based on the work in 2006 by Alam and Massoud, to derive another different closed-form solution to the problem of light scattered by the nanoshells using polynomials of up to order 6. Validation is made by comparing the present closed-form solution to the exact Mie scattering solution and also to the other closed-form solution by Alam and Massoud. This study is found to be, however, more generalized and also more accurate for the coated spheres of either tiny/small or medium sizes than that of Alam and Massoud. Therefore, the derived formulas can be used for accurately characterizing both surface plasmon resonances of nanoparticles (of small sizes) or nanoantenna near-field properties (of medium sizes comparable with half wavelength).     

Light scattering by a multilayer sphere

The recurrence algorithm for calculating electromagnetic scattering from a multilayer sphere, which was described recently by Wu and Wang [Radio Sci. 26, 1393, (1991)], is derived in a slightly modified form and extended to include a calculation of the internal field and the absorption cross sections of the individual layers. The original algorithm calculates the scattering by a recurrence procedure that propagates the log derivatives of the Debye potentials outward from the core to the outer layer. The extended algorithm then continues the calculation by an inward recurrence procedure that propagates the Debye potentials from the outer layer to the core. Concurrent with the inward propagation, a separate algorithm calculates the absorption cross sections of the imbedded concentric spheres. The results of several example calculations are presented, including the differential cross section and internal electric field of a Luneburg lens.     

Vibration analysis of a poroelastic composite hollow sphere

Vibrations in a poroelastic composite hollow sphere are investigated employing Biot’s theory of wave propagation in poroelastic media. A composite hollow poroelastic sphere consists of two concentric poroelastic spherical layers both of which are made of different poroelastic materials with each poroelastic material being homogeneous and isotropic. The boundaries of the composite hollow poroelastic sphere are free from stress. The frequency equations of both radial and rotatory vibrations are obtained each for pervious and impervious surfaces. The frequency equation of vibrations of a poroelastic composite hollow sphere with rigid core is derived as a particular case. The non-dimensional frequency for propagating modes is computed as a function of ratio of thickness to inner radius of core. The results are presented graphically for two types of poroelastic composite spheres and then discussed.     

Estimate for the effect of forward scattering on the measurement of extinction for particles by cavity ringdown spectroscopy

An analytical model is formulated for the extinction of light by particles in a cavity ringdown spectroscopy measurement. The electromagnetic field inside the cavity is assumed to be the lowest-order Gaussian beam, and the scattering by the particles is incorporated using van de Hulst's approximation for the scattering by a sphere. This model includes both coherent scattering in the forward direction and strong scattering in the forward direction for electrically large particles. The model is used to estimate the amount of energy scattered by the particles that is coupled back into the incident beam. The consequences of this coupling for the measurement of the extinction cross section of spherical particles are examined.     

Scattering of electromagnetic waves by a coated not perfectly conducting sphere

We consider the low-frequency scattering problem of a plane electromagnetic wave by a sphere, which is covered by a penetrable concentric spherical shell. The medium, occupying the shell, is lossless while on the surface of the core an impedance boundary condition is satisfied. The impedance boundary condition was introduced by Leontovich (Investigations of Radiowave Propagation. Part II, Academy of Science, Moscow, 1948) and it accounts for situations where the obstacle is not perfectly conducting but the exterior field will not penetrate deeply into the scatterer. For the near electromagnetic field we obtain the low-frequency coefficients of the zeroth and the first orders while in the far field we derive the leading non-vanishing terms for the scattering amplitude and the scattering cross-section. Spherical coated obstacles are very important in applications. Small particles in biological suspensions, cells, some human organs, atmospheric particles and granules within composite materials are only a few examples of applied interest in science and technology.     

Scattering of elastic P and SV waves by a rigid elliptic cylindrical inclusion

The 2-dimensional problem of scattering of obliquely incident $\text{P}$ and SV waves by an infinite rigid elliptic cylinder embedded in an infinite, isotropic and homogeneous elastic medium is solved. Approximate formulas are derived for the displacement field, stress tensor, far-field amplitudes and the scattering cross section when the wave lengths are large compared to the distance between the two focii of the elliptic cylinder.     

Stress intensity factor for the cylindrical interface crack between nonhomogeneous coaxial finite elastic cylinders

The problem of determining the stress intensity factor for a cylindrical interface crack between two dissimilar nonhomogeneous coaxial finite elastic cylinders under axially symmetric longitudinal shear stress is considered. The mixed boundary conditions lead to a pair of dual series equations which are reduced to a Fredholm integral equation of the second kind and then finally to a system of algebraic equations. Numerical values of the stress intensity factor are presented graphically.     

Electromagnetic-wave scattering by a sphere with multiple spherical inclusions

An exact solution to the problem of electromagnetic-wave scattering from a sphere with an arbitrary number of nonoverlapping spherical inclusions is obtained by use of the indirect mode-matching technique. A set of linear equations for the wave amplitudes of the electric field intensity throughout the inhomogeneous sphere and in the surrounding empty space is determined. Numerical results are calculated by truncation and matrix inversion of that set of equations. Specific information about the truncation number pertaining to the multipole expansions of the electric field intensity is given. The theory and the accompanying computer code successfully reproduce the results of other pertinent papers. Some numerical results [Borghese et al., Appl. Opt. 33, 484 (1994)] were not reproduced well, and that discrepancy is discussed. Our numerical investigation is focused on an acrylic sphere with up to four spherical inclusions. This is the first time that numerical results are presented for a sphere with more than two spherical inclusions. Interesting remarks are made about the effect that the look direction and the structure of the inhomogeneity have on backscattering by the acrylic host sphere.     

Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid

The theory of an arbitrarily oriented, shaped, and located beam scattered by a homogeneous spheroid is developed within the framework of the generalized Lorenz-Mie theory (GLMT). The incident beam is expanded in terms of the spheroidal vector wave functions and described by a set of beam shape coefficients (G(m)(n),(TM),G(m)(n),(TE)). Analytical expressions of the far-field scattering and extinction cross sections are derived. As two special cases, plane wave scattering by a spheroid and shaped beam scattered by a sphere can be recovered from the present theory, which is verified both theoretically and numerically. Calculations of the far-field scattering and cross sections are performed to study the shaped beam scattered by a spheroid, which can be prolate or oblate, transparent or absorbing.     

Scattering of a plane wave by an anisotropic ferrite-coated conducting sphere

On the basis of the three-dimensional spherical vector wave functions in ferrite anisotropic media, and the fact that the first and second spherical vector wave functions in ferrite anisotropic media satisfy the same differential equations, the electromagnetic fields in homogeneous ferrite anisotropic media can be expressed as the addition of the first and second spherical vector wave functions in ferrite anisotropic media. Applying the continue boundary condition of the tangential component of electromagnetic fields in the interface between the ferrite anisotropic medium and free space, and the tangential electric field vanishing in the interface of the conducting sphere, the expansion coefficients of electromagnetic fields in terms of spherical vector wave function in ferrite medium and the scattering fields in free space can be derived. The theoretical analysis and numerical result show that when the radius of a conducting sphere approaches zero, the present method can be reduced to that of the homogeneous ferrite anisotropic sphere. The present method can be applied to the analyses of related microwave devices, antennas and the character of radar targets.     

膨胀石墨的毫米波二维平面散射截面研究

本文报道了不同平面密度下或不同长度的膨胀石墨蠕虫的毫米波二维平面散射截面的实验结果，并将其与镀铝玻璃纤维和铝箔条的相关实验结果作了对比研究。结果表明，膨胀石墨蠕虫虽然在物理形状上与镀铝玻璃纤维和铝箔条有相似之处，并且具有一定的导电性能，但其对毫米波的散射特性并不符合半波谐振子模型所推导的结论，且其毫米波散射截面远远小于镀铝玻璃纤维和铝箔条。