Scattering of a spheroidal particle illuminated by a gaussian beam

An approach to expanding a Gaussian beam in terms of the spheroidal wave functions in spheroidal coordinates is presented. The beam-shape coefficients of the Gaussian beam in spheroidal coordinates can be computed conveniently by use of the known expression for beam-shape coefficients, g(n), in spherical coordinates. The unknown expansion coefficients of scattered and internal electromagnetic fields are determined by a system of equations derived from the boundary conditions for continuity of the tangential components of the electric and magnetic vectors across the surface of the spheroid. A solution to the problem of scattering of a Gaussian beam by a homogeneous prolate (or oblate) spheroidal particle is obtained. The numerical values of the expansion coefficients and the scattered intensity distribution for incidence of an on-axis Gaussian beam are given.     

Off-axis scattering of an ultrasound bessel beam by a sphere

In this paper, the scattering of an ultrasound zero-order Bessel beam by a rigid sphere in the off-axis configuration is studied. The beam is described through the partial wave expansion. The beam-shape coefficients which represent the amplitude of each multipole mode of the partial wave expansion are computed by numerical quadrature. Calculations are presented for both near- and far-field off-axis scattering. The far-field scattering is examined in both Rayleigh and geometrical acoustic limits. Results demonstrate that the scattered pressure in the off-axis case may significantly deviate from that in the on-axis configuration. In addition, the directive pattern of the scattered pressure is highly dependent on the relative position of the beam to the sphere.     

Scattering by a dense finite layer of infinite cylinders at oblique incidence

This paper presents the scattering solution for a finite dense layer of cylinders irradiated by an arbitrarily polarized plane wave at a general incident direction. The theoretical formulation utilizes the effective field approach and quasi-crystalline approximation to derive the governing equations for the propagation constant and amplitudes of the effective waves. The finite layer thickness gives rise to effective waves propagating in both the forward and backward directions inside the dense medium. Formulas are developed for the far-field coherent and incoherent scattered intensities, as well as the extinction and scattering cross sections of the dense layer. The forward peak of the incoherent scattered intensity is shown to be shifted to the propagating direction of the effective waves. The influence of incident direction, layer thickness, and solid volume fraction on the scattering properties is illustrated by means of a numerical example.     

Scattering of he-ne laser light by an average-sized red blood cell

The scattering of He-Ne laser light by an average-sized human red blood cell (RBC) is investigated numerically. The RBC is modeled as an axisymmetric, low-contrast dielectric, biconcave disk. The interaction problem is treated numerically by means of a boundary-element methodology. The differential scattering cross sections (DSCS's) corresponding to various cell orientations are calculated. The numerical results obtained for the exact RBC geometry are compared with those corresponding to a scattering problem in which the cell is assumed to be either a volume-equivalent sphere or an oblate spheroid. A parametric study demonstrating the dependence of the DSCS on the wavelength of the incident wave and the cell's refractive index is presented.     

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.     

Electromagnetic fields for a spheroidal particle with an arbitrary embedded source

A spheroidal coordinate separation-of-variables solution has been developed for the determination of the internal, near-surface, and scattered fields of a spheroid (either prolate or oblate) with an embedded source of arbitrary type, location, and orientation. Presented results for (1,0) and (1,1) electric multipoles embedded in 2:1 axis ratio prolate and oblate spheroids (equal volume sphere size parameter equal to 20) illustrate that the presence of the spheroid interface can have a profound effect on the corresponding far-field scattering pattern. The calculation procedure could be used, for example, to model the emission of inelastic scattered light (Raman, fluorescence, etc.) from biological particles of appreciably elongated (prolatelike) or appreciably flattened (oblatelike) geometries.     

Effective phase function for light scattered by blood

The scattering process induced in blood by a collimated laser beam is theoretically investigated. An individual red blood cell (RBC) has a scattering phase function strongly peaked in the forward direction. For far-field experiments, the small scattering volumes can be considered as "macroscopic particles" characterized by an effective scattering phase function. Using the single-cell phase function as "input data" the angular distribution of light scattered at small angles by the whole scattering volume, containing RBCs in suspension, is calculated analytically. The angular dispersion of the light scattered by blood can be approximately described by the same formula used to characterize the light scattered by a single cell but with an effective, hematocrit-dependent anisotropy parameter.     

焦区附近球形粒子对高斯光束的弹性散射

本文应用复源球面波理论,将高斯光束场按矢量球波函数展开,对高斯光束入射到单个球形粒子上时的弹性散射问题进行了理论分折。并对球形粒子在波束传播轴上时的远场散射光强角分布进行了数值计算,同时还与平面波散射的结果进行了比较。     

Internal, near-surface, and scattered electromagnetic fields for a layered spheroid with arbitrary illumination

A spheroidal coordinate separation-of-variables solution has been developed for the determination of internal, near-surface, and scattered electromagnetic fields of a layered spheroid (either prolate or oblate) with arbitrary monochromatic illumination (e.g., plane wave or focused Gaussian beam). Calculated results are presented for layered 2:1 axis ratio prolate and oblate spheroids with an equivalent sphere size parameter of 20.     

Aerosol and cloud backscatter at 1.06, 1.54, and 0.53 mum by airborne hard-target-calibrated Nd:YAG /methane Raman lidar

A lidar instrument was developed to make simultaneous measurements at three distinct wavelengths in the visible and near infrared at 0.532, 1.064, and 1.54 mum with high cross-sectional calibration accuracy. Aerosol and cloud backscatter cross sections were acquired during November and December 1989 and May and June 1990 by the NASA DC-8 aircraft as part of the Global Backscatter Experiment. The instrument, methodology, and measurement results are described. A Nd:YAG laser produced 1.064- and 0.532-mum energy. The 1.54-mum transmitted pulse was generated by Raman-shifted downconversion of the 1.064-mum pulse through a Raman cell pressured with methane gas. The lidar could be pointed in the nadir or zenith direction from the aircraft. A hard-target-based calibration procedure was used to obtain the ratio of the system calibration between the three wavelengths, and the absolute calibration was referenced to the 0.532-mum lidar molecular backscatter cross section for the clearest scattering regions. From the relative wavelength calibration, the aerosol backscatter cross sections at the longer wavelengths are resolved for values as small as 1% of the molecular cross section. Backscatter measurement accuracies are better than 10(-9) (m sr)(-1) at 1.064 and 1.54 mum. Results from the Pacific Ocean region of the multiwavelength backscatter dependence are presented. Results show extensive structure and variation for the aerosol cross sections. The range of observed aerosol cross section is over 4 orders of magnitude, from less than 10(-9) (m sr)(-1) to greater than 10(-5) (m sr)(-1).     

T-matrix computations of light scattering by red blood cells

The electromagnetic far field, as well as the near field, originating from light interaction with a red blood cell (RBC)volume-equivalent spheroid, was analyzed by utilizing theT-matrix theory. This method is a powerful tool thatmakes it possible to study the influence of cell shape on the angulardistribution of scattered light. General observations were that thethree-dimensional shape, as well as the optical thickness apparent tothe incident field, affects the forward scattering. Thebackscattering was influenced by the shape of the surface facing theincident beam. Furthermore sphering as well as elongation of anoblate RBC into a volume-equivalent sphere or a prolate spheroid, respectively, was theoretically modeled to imitate physiologicalphenomena caused, e.g., by heat or the increased shear stress offlowing blood. Both sphering and elongation were shown to decreasethe intensity of the forward-directed scattering, thus yielding lowerg factors. The sphering made the scattering patternindependent of azimuthal scattering angle phi(s), whereas the elongation induced more apparent phi(s)-dependent patterns. The lightscattering by a RBC volume-equivalent spheroid was thus found to behighly influenced by the shape of the scattering object. Anear-field radius r(nf) was evaluated as thedistance to which the maximum intensity of the total near field haddecreased to 2.5 times that of the incident field. It was estimatedto 2-24.5 times the maximum radius of the scattering spheroid, corresponding to 12-69 mum. Because the near-field radiuswas shown to be larger than a simple estimation of the distance betweenthe RBC's in whole blood, the assumption of independent scattering, frequently employed in optical measurements on whole blood, seemsinappropriate. This also indicates that one cannot extrapolate theresults obtained from diluted blood to whole blood by multiplying witha simple concentration factor.     

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle

The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.     

Three-dimensional electromagnetic diffraction of a Gaussian beam by a perfectly conducting half-plane

Formulas are derived for the diffraction of a three-dimensional electromagnetic Gaussian beam by a perfectly conducting half-plane. The beam can be incident from any direction, and the main component of the electric field can point in any direction on the plane of the beam waist. The center of the beam waist is on the edge of the half-plane. The incident beam is constructed as a superposition of plane waves, and the total diffracted field is obtained from a superposition of the diffracted fields that are due to each plane wave. Physical constraints that limit the size and direction of the beam relative to the half-plane are described and incorporated into the theory. The scattered field in the far zone is obtained by asymptotic evaluation of the general formulas. Graphical results for the near-field as well as far-field patterns are presented and discussed.     

Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis

We use the semiclassical limit of electromagnetic wave scattering theory to determine the properties of the exterior caustics of a diagonally incident plane wave scattered by an infinitely long homogeneous dielectric circular cylinder in both the near zone and the far zone. The transmission caustic has an exterior/interior cusp transition as the tilt angle of the incident beam is increased, and each of the rainbow caustics has a farzone rainbow/exterior cusp transition and an exterior/interior cusp transition as the incident beam tilt angle is increased. We experimentally observe and analyze both transitions of the first-order rainbow. We also compare the predictions of the semiclassical approximation with those of ray theory and exact electromagnetic wave scattering theory.     

Reflection symmetry of a sphere's internal field and its consequences on scattering: a microphysical approach

We examine the reflection symmetries of the electromagnetic wave inside of a uniform spherical particle and identify the consequences of the symmetries for the Stokes parameters describing the polarization state of the far-field scattered wave. The connection between the two waves is described from a microphysical perspective that illustrates the wavelet-superposition origin of the scattered wave. In contrast to more conventional approaches, this microphysical perspective yields new insight into the physical character of the scattering of a plane wave by a sphere. The results of simulations are presented, which graphically demonstrate the relation between the symmetries present in the internal wave and the polarization state of the scattered wave.     

功能梯度材料亚表面缺陷的热波多重散射问题

基于热传导波动模型,采用波函数展开法,研究了半无限功能梯度材料亚表面球形缺陷的热波多重散射.给出了热波散射的一般解.温度波由调制光束在材料表面激发,球形缺陷表面的边界条件为绝热,非均匀参数为指数函数变化.分析了结构几何参数和物理参数对温度分布的影响,并给出了温度变化的数值结果.本研究可为功能梯度材料的分析研究、物理反问题和红外热波成像等提供理论基础和参考数据.     

Scattering of electromagnetic waves by a perfect electromagnetic conducting sphero

An exact solution to the problem of scattering of electromagnetic waves from a perfect electromagnetic conducting spheroid is presented, using the method of separation of variables. The formulation of the problem is realised by expanding the incident as well as the scattered electromagnetic fields in terms of appropriate spheroidal vector wave functions and imposing the appropriate boundary conditions at the surface of the spheroid. This generates a set of simultaneous equations, the solution of which yields the unknown coefficients associated with the expansion of the scattered electromagnetic field. Results are presented in the form of normalised bistatic and backscattering cross-sections for spheroids of different axial ratios, sizes and admittances, for both transverse electric and transverse magnetic polarisations of the incident wave.     

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).     

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.     

Electromagnetic scattering from a multilayered sphere located in an arbitrary beam

A solution is given for the problem of scattering of an arbitrary shaped beam by a multilayered sphere. Starting from Bromwich potentials and using the appropriate boundary conditions, we give expressions for the external and the internal fields. It is shown that the scattering coefficients can be generated from those established for a plane-wave illumination. Some numerical results that describe the scattering patterns and the radiation-pressure behavior when an incident Gaussian beam or a plane wave impinges on a multilayered sphere are presented.