The solution of electromagnetic scattering by a homogeneous prolate (or oblate) spheroidal particle with an arbitrary size and refractive index is obtained for any angle of incidence by solving Maxwell's equations under given boundary conditions. The method used is that of separating the vector wave equations in the spheroidal coordinates and expanding them in terms of the spheroidal wavefunctions. The unknown coefficients for the expansion are determined by a system of equations derived from the boundary conditions regarding the continuity of tangential components of the electric and magnetic vectors across the surface of the spheroid. The solutions both in the prolate and oblate spheroidal coordinate systems result in a same form, and the equations for the oblate spheroidal system can be obtained from those for the prolate one by replacing the prolate spheroidal wavefunctions with the oblate ones and vice versa. For an oblique incidence, the polarized incident wave is resolved into two components, the TM mode for which the magnetic vector vibrates perpendicularly to the incident plane and the TE mode for which the electric vector vibrates perpendicularly to this plane. For the incidence along the rotation axis the resultant equations are given in the form similar to the one for a sphere given by the Mie theory. The physical parameters involved are the following five quantities: the size parameter defined by the product of the semifocal distance of the spheroid and the propagation constant of the incident wave, the eccentricity, the refractive index of the spheroid relative to the surrounding medium, the incident angle between the direction of the incident wave and the rotation axis, and the angles that specify the direction of the scattered wave.

Light Scattering by a Spheroidal Particle

An overview is given over some of the most widely used numerical techniques for solving the electromagnetic scattering problem that start from rigorous electromagnetic theory. In particular, the theoretical foundations of the separation of variables method, the finite-difference time-domain method, the finite-element method, the method of lines, the point matching method, the method of moments, the discrete dipole approximation, and the null-field method (or extended boundary condition method) are reviewed, and the advantages and disadvantages of the different methods are discussed. Aspects concerning the T matrix formulation and the surface Green's function formulation of the electromagnetic scattering problem are addressed.

Numerical methods in electromagnetic scattering theory

Recently, by introducing locally resonant scatterers with spherical shape proposed in phononic crystals into design of underwater sound absorption materials, the low-frequency underwater sound absorption phenomenon induced by the localized resonances is observed. To reveal this absorption mechanism, the effect of the locally resonant mode on underwater sound absorption should be studied. In this paper, the finite element method, which is testified efficiently by comparing the calculation results with those of the layer multiple scattering method, is introduced to investigate the dynamic modes and the corresponding sound absorption of localized resonance. The relationship between the resonance modes described with the displacement contours of one unit cell and the corresponding absorption spectra is discussed in detail, which shows that the localized resonance leads to the absorption peak, and the mode conversion from longitudinal to transverse waves at the second absorption peak is more efficient than that at the first one. Finally, to show the modeling capability of FEM and investigate shape effects of locally resonant scatterers on underwater sound absorption, the absorption properties of viscoelastic materials containing locally resonant scatterers with ellipsoidal shape are discussed.

Effects of locally resonant modes on underwater sound absorption in viscoelastic materials

The problem of underwater target detection and classification from acoustic backscatter is the central focus of this paper. It has been shown that at certain frequencies the acoustic backscatter from elastic targets exhibits certain resonance behavior which closely relates to the physical properties of the target such as dimension, thickness, and composition. Several techniques in both the time domain and frequency domain have been developed to characterize the resonance phenomena in acoustic backscatter from spherical or cylindrical thin shells. The purpose of this paper is to develop an automated approach for identifying the presence of resonance in the acoustic backscatter from an unknown target by isolating the resonance part from the specular contribution. An adaptive transversal filter structure is used to estimate the specular part of the backscatter and consequently the error signal would provide an estimate of the resonance part. An important aspect of this scheme Lies in the fact that it does not require an underlying model for the elastic return. The adaptation rule is based upon fast Recursive Least Squares (RLS) learning. The approach taken in this paper is general in the sense that it can be applied to targets of unknown geometry and thickness and, further, does not require any a priori information about the target and/or the environment. Test results on acoustic data are presented which indicate the effectiveness of the proposed approach.

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Isolation of resonance in acoustic backscatter from elastic targets using adaptive estimation schemes

A novel laser-based ultrasonic technique for the inspection of thin plates and membranes is presented, in which a modulated continuous-wave laser source is used to excite narrow bandwidth Lamb waves. The dominant feature in the acoustic spectrum is a sharp resonance peak that occurs at the minimum frequency of the first-order symmetric Lamb mode, where the group velocity of the Lamb wave goes to zero while the phase velocity remains finite. Experimental results with the laser source and receiver on epicenter demonstrate that the zero-group velocity resonance generated with a low-power modulated excitation source can be detected using a Michelson interferometer coupled to a lock-in amplifier. This resonance peak is sensitive to the thickness and mechanical properties of plates and may be suitable, for example, for the measurement and mapping of nanoscale thickness variations.

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Laser-based ultrasonic generation and detection of zero-group velocity Lamb waves in thin plates

The acoustic scattering by thin‐walled, evacuated, elastic spherical shells immersed in water is studied. The analytic structure of the scattering amplitude in the complex‐k plane is directly analyzed using Cauchy’s residue theorem, and dispersion curves are presented for the lowest elastic modes of the fluid‐loaded shell. It is found that fluid loading has a profound effect on the vacuum dynamical characteristics of the shell; the spherical equivalent of the first antisymmetric, flat‐plate Lamb wave for the fluid‐loaded shell bifurcates into two distinct modes near the frequency that the vacuum dispersion curve transitions from a subsonic to a supersonic phase velocity. By way of contrast, the spherical equivalent of the first symmetric Lamb wave is essentially unaffected. The salient features of the free‐field scattering process are also analyzed in terms of the resonance excitation of these modes.

The acoustic scattering by a submerged, spherical shell. I: The bifurcation of the dispersion curve for the spherical antisymmetric Lamb wave

A multiple‐scattering approach is developed for the acoustic scattering from a target in a range‐independent oceanic waveguide. The multiple‐scattering series is explicitly summed and a solution is obtained in closed form. The final result is algebraically much simpler than that obtained in earlier work, and the individual terms may be straightforwardly interpreted in terms of scattering events in the waveguide. The formalism is applied to the scattering from a target (1) near a sound‐soft boundary, and (2) in a waveguide with a single, homogeneous fluid layer over a homogeneous, fluid half‐space. Numerical examples are given that illustrate the importance of contributions involving rescattering among the target and the waveguide boundaries.

Multiple scattering analysis for a target in an oceanic waveguide

The scattering of sound by objects buried in underwater sediments is studied in the context of an exactly soluble model. The model consists of two fluid half‐spaces separated by a planar, fluid, transition layer of arbitrary thickness. Attenuation is included in any of these regions by using complex wave numbers. A directional source field, generated in the upper half‐space by a continuous line array, insonifies an object placed in the lower half‐space. The scattered field detected by another line array placed anywhere in the system may be calculated. The solution is determined from the T matrix for the bounded scattering system and is exact (in linear acoustics) to all orders of multiple scattering among the interfaces and object. Numerical results are presented to investigate the effect of the local acoustic environment on the free‐field, in‐water scattering resonances of thin spherical shells. The field scattered by a shallowly buried object is discussed with emphasis on the importance of evanescent wa...

Scattering by objects buried in underwater sediments: Theory and experiment

A spheroidal‐coordinate‐based transition matrix is derived for acoustic and elastic wave scattering. The formalism is based on Betti’s third identity and an appropriately chosen set of vector spheroidal basis functions. Transition matrices are obtained for the scattering from an elastic inclusion in an elastic medium and in an inviscid fluid.

The transition matrix for acoustic and elastic wave scattering in prolate spheroidal coordinates

A transition matrix formalism is developed for the acoustic scattering from a target in a layered, inhomogeneous waveguide. The connection is made with the normal mode model of propagation and the total acoustic wave is expressed as a sum over waveguide modes. For a target in a deep ocean environment, the scattering solution may be expressed in terms of the free‐field T matrix and the normal mode wavefunctions for the empty waveguide. Both homogeneous and inhomogeneous layers are considered.

Roger H. Hackman

Papers

The acoustic scattering by a submerged, spherical shell. I: The bifurcation of the dispersion curve for the spherical antisymmetric Lamb wave

Multiple scattering analysis for a target in an oceanic waveguide

Scattering by objects buried in underwater sediments: Theory and experiment

The transition matrix for acoustic and elastic wave scattering in prolate spheroidal coordinates

Acoustic scattering in an inhomogeneous waveguide: Theory