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.     

Computation of the beam-shape coefficients in the generalized Lorenz-Mie theory by using the translational addition theorem for spherical vector wave functions

The generalized Lorenz-Mie theory describes the electromagnetic scattering of a Gaussian laser beam by a spherical particle. The most intensive computational aspect of the theory concerns the evaluation of the beam-shape coefficients in the general case of an off-axis location of the scatterer. These beam-shape coefficients can be computed starting from the set of beam-shape coefficients for an on-axis location by using the addition theorem for the spherical vector wave functions of the first kind under a translation of the coordinate origin.     

Mean-field approximation of Mie scattering by fractal aggregates of identical spheres

We apply the recent exact theory of multiple electromagnetic scattering by sphere aggregates to statistically isotropic finite fractal clusters of identical spheres. In the mean-field approximation the usual Mie expansion of the scattered wave is shown to be still valid, with renormalized Mie coefficients as the multipolar terms. We give an efficient method of computing these coefficients, and we compare this mean-field approach with exact results for silica aggregates of fractal dimension 2.     

Inverse Mie problem

We apply functional analysis to the scattered electromagnetic field of a particle with spherical symmetry to obtain a pair of integral transforms for converting the Mie-scattering amplitudes S perpendicular (theta) and S parallel (theta) into the Mie coefficients an and bn. In the case of a homogeneous sphere, a simple mathematical construction is derived that uniquely inverts the Mie coefficients to find the refractive index and the radius of the particle. A more general method for construction of the refractive-index profile of an arbitrary sphere is discussed that follows from the treatment of Newton and Sabatier.     

Attenuation of an electromagnetic wave by charged dust particles in a sandstorm

We calculate the light scattering properties of the partially charged dust particles with the Mie theory for electromagnetic waves with different frequencies, and the attenuation coefficients of an electromagnetic wave propagating in a sandstorm are also calculated. The results show that the electric charges distributed on the sand surface have a significant effect on the attenuation of the electromagnetic wave, especially for a frequency lower than 40 GHz, and attenuation coefficients increase with the magnitude of charges carried by the dust particles (expressed by the charge-to-mass ratio in this paper). For the higher frequency electromagnetic wave, such as visible light, the effect of charges carried by sand particles on its attenuation is very little, which can be ignored.     

Mie scattering by an anisotropic object. Part I. Homogeneous sphere

Establishing a vector spherical harmonic expansion of the electromagnetic field propagating inside an arbitrary anisotropic medium, we extend Mie theory to the diffraction by an anisotropic sphere, with or without losses. The particular case of a uniaxial material leads to a simpler analysis. This work opens the way to the construction of a differential theory of diffraction by a three-dimensional object with arbitrary shape, filled by an arbitrary anisotropic material.     

Note on the use of localized beam models for light scattering theories in spherical coordinates

Localized beam models provide the most efficient and enlightening ways to evaluate beam shape coefficients of electromagnetic arbitrary shaped beams for use in light scattering theories. At the present time, they are valid in spherical and (circular and elliptical) cylindrical coordinates. A misuse of localized beam models in spherical coordinates recently appeared several times in the literature. We therefore present a warning to avoid the propagation of an incorrect use of localized beam models.     

Optical response of a single spherical particle in a tightly focused light beam: application to the spatial modulation spectroscopy technique

We develop a new and numerically efficient formalism to describe the general problem of the scattering and absorption of light by a spherical metal or dielectric particle illuminated by a tightly focused beam. The theory is based on (i) the generalized Mie theory equations, (ii) the plane-wave decomposition of the converging light beam, and (iii) the expansion of a plane wave in terms of vector spherical harmonics. The predictions of the model are illustrated in the case of silver nanoparticles. The results are compared with the Mie theory in the local approximation. Finally, some effects related to the convergence of the beam are analyzed in the context of experiments based on the spatial modulation spectroscopy technique.     

Improved Gaussian beam-scattering algorithm

The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.     

Generalized theory of resonance excitation by sound scattering from an elastic spherical shell in a nonviscous fluid

This work presents the general theory of resonance scattering (GTRS) by an elastic spherical shell immersed in a nonviscous fluid and placed arbitrarily in an acoustic beam. The GTRS formulation is valid for a spherical shell of any size and material regardless of its location relative to the incident beam. It is shown here that the scattering coefficients derived for a spherical shell immersed in water and placed in an arbitrary beam equal those obtained for plane wave incidence. Numerical examples for an elastic shell placed in the field of acoustical Bessel beams of different types, namely, a zero-order Bessel beam and first-order Bessel vortex and trigonometric (nonvortex) beams are provided. The scattered pressure is expressed using a generalized partial-wave series expansion involving the beam-shape coefficients (BSCs), the scattering coefficients of the spherical shell, and the half-cone angle of the beam. The BSCs are evaluated using the numerical discrete spherical harmonics transform (DSHT). The far-field acoustic resonance scattering directivity diagrams are calculated for an albuminoidal shell immersed in water and filled with perfluoropropane gas, by subtracting an appropriate background from the total far-field form function. The properties related to the arbitrary scattering are analyzed and discussed. The results are of particular importance in acoustical scattering applications involving imaging and beam-forming for transducer design. Moreover, the GTRS method can be applied to investigate the scattering of any beam of arbitrary shape that satisfies the source-free Helmholtz equation, and the method can be readily adapted to viscoelastic spherical shells or spheres.     

Multiple scattering of electromagnetic waves by an aggregate of uniaxial anisotropic spheres

An exact analytical solution is obtained for the scattering of electromagnetic waves from a plane wave with arbitrary directions of propagation and polarization by an aggregate of interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes. The expansion coefficients of a plane wave with arbitrary directions of propagation and polarization, for both TM and TE modes, are derived in terms of spherical vector wave functions. The effects of the incident angle α and the polarization angle β on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres are numerically analyzed in detail. The characteristics of the forward and backward RCSs in relation to the incident wavelength are also numerically studied. Selected results on the forward and backward RCSs of several types of square arrays of SiO? spheres illuminated by a plane wave with different incident angles are described. The accuracy of the expansion coefficients of the incident fields is verified by comparing them with the results obtained from references when the plane wave is degenerated to a z-propagating and x- or y-polarized plane wave. The validity of the theory is also confirmed by comparing the numerical results with those provided by a CST simulation.     

Mie scattering in the time domain. Part 1. The role of surface waves

We computed the Debye series p=1 and p=2 terms of the Mie scattered intensity as a function of scattering angle and delay time for a linearly polarized plane wave pulse incident on a spherical dielectric particle and physically interpreted the resulting numerical data. Radiation shed by electromagnetic surface waves plays a prominent role in the scattered intensity. We determined the surface wave phase and damping rate and studied the structure of the p=1,2 surface wave glory in the time domain.     

Analytical solutions to light scattering by plasmonic nanoparticles with nearly spherical shape and nonlocal effect

We derive analytical solutions for the scattering of electromagnetic waves by a nanoparticle with nearly spherical shape and nonlocal dielectric function by using an extended Mie scattering theory with additional boundary conditions. A perturbation method is used to treat the correction due to deviation from the spherical shape. A surface characteristic function is introduced to describe the non-spherical surface profile of the nanoparticle, and it plays an important role in our analytical formulation. Complex surface plasmon modes are obtained. It is found that not only the transverse but also the longitudinal surface plasmon modes of the nanoparticle are excited due to the nonlocal effect. Our analytical formulation provides an alternative method for investigating the optical behaviors of the surface plasmon of nanoparticles with nearly spherical shape and nonlocal effect.     

The reflection and transmission of elastic waves through a plane of spheres in periodic arrangement

The work presented in this paper focuses on the reflection and transmission coefficients of an incident plane wave which impinges obliquely a plane of identical spheres arranged periodically in a homogeneous host with infinite extension. The Bloch theorem of periodic structure and the addition theorem of spherical wave functions are used to obtain the total scattering wave from all spherical scatterers periodically arranged in a plane. The total scattering wave in series form of spherical wave functions is then transformed into plane wave form in order to derive the reflection and transmission coefficients. Some numerical examples are given for different size, material constants and array patterns of spherical scatterers, and their influences on the reflection and transmission coefficients of a plane of spheres are discussed based on the numerical results. This study implies that a plane of spheres can be elaborately designed to serve as a sound barrier at a certain frequency range.     

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.     

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).     

Coherent reflectance in a system of random Mie scatterers and its relation to the effective-medium approach

We consider the coherent reflection and transmission of electromagnetic waves from a slab of a dilute system of randomly located, polarizable, spherical particles. We focus our attention on the case where the size of the spheres is comparable to the wavelength of the incident radiation. First, using wave-scattering and Mie theories, we derive expressions for the coherent fields that are transmitted and reflected by a very thin slab. Then we find the effective-current distribution that would act as a source of these fields. We conclude that if the effective currents were induced in an effective medium, this medium must possess, besides an effective electric permittivity, also an effective magnetic permeability. We find that both of these optical coefficients become functions of the angle of incidence and the polarization of the incident wave. Then we calculate the reflection coefficient of a half-space by considering a semi-infinite pile of thin slabs and compare the result with Fresnel relations. Numerical results are presented for the optical coefficients as well as for the half-space reflectance as a function of several parameters. The reflectance is compared with that obtained without considering the magnetic response. Finally, we discuss the relevance and the physics behind our results and indicate as well the measurements that could be performed to obtain an experimental verification of our theory.     

Radiation pressure cross sections and optical forces over negative refractive index spherical particles by ordinary Bessel beams

When impinged by an arbitrary laser beam, lossless and homogeneous negative refractive index (NRI) spherical particles refract and reflect light in an unusual way, giving rise to different scattered and internal fields when compared to their equivalent positive refractive index particles. In the generalized Lorenz-Mie theory, the scattered fields are dependent upon the Mie scattering coefficients, whose values must reflect the metamaterial behavior of an NRI scatterer, thus leading to new optical properties such as force and torque. In this way, this work is devoted to the analysis of both radial and longitudinal optical forces exerted on lossless and simple NRI particles by zero-order Bessel beams, revealing how the force profiles are changed whenever the refractive index becomes negative.     

Nonstationary scattering of electromagnetic pulses by spherical particles

We have studied time variances of the shape of an electromagnetic pulse scattered by a spherical particle. General formulas are derived for a pulse with an arbitrary envelope, for momentary values of scattered-light fields and light intensity, and for efficiencies of extinction and scattering. It is possible, by the use of these formulas, to obtain by routine integration the sensitivity reaction of a receiver with any time dependence. The formulas are illustrated with examples of scattering of a Gaussian pulse with a carrier wave λ(0) = 0.6328 μm and of multisized water drops. Pulses of different durations are studied. However, only those pulses that have all significant values of the Fourier density in the domain of positive frequencies ω are considered.