Scattering by a dense layer of infinite cylinders at normal incidence

The solution for scattering by a layer of densely distributed infinite cylinders is presented. The layer is irradiated by an arbitrarily polarized plane wave that propagates in the plane perpendicular to the axes of the cylinders. The theoretical formulation utilized the effective field and quasi-crystalline approximation to treat the multiple scattering interactions in the dense finite medium. Governing equations for the propagation constants and amplitudes of the effective fields are derived for TM and TE mode incident waves, from which the scattered intensity distribution and scattering cross section for arbitrary polarization are obtained. The dense medium gives rise to coherent and incoherent scattered radiation that propagates in the plane normal to the axes of the cylinders. The coherent scattered radiation includes the forward component in the direction of the incident wave and the backward component in the direction of specular reflection. The incoherent scattered intensity distribution shows a pronounced forward peak that coincides with the angle of refraction of the effective waves inside the medium. Numerical results are presented to illustrate the scattering characteristics of a dense layer of cylinders as a function of layer thickness for a given solid volume fraction.     

Solution of convergence problem in ultrasound inverse scattering tomography

When the product of contrast and size of an object, which is to be reconstructed by using the ultrasound inverse scattering tomography algorithm, is large, it is well known that those algorithms fail to converge to a unique global minimum. In order to solve this well known and difficult convergence problem, in this paper we present a new method, which converges to the true solution, for obtaining the scattering potential without using the Born or Rytov approximation. This method converts the nonlinear nature of the problem into a linear one. Through computer simulations we will show the validity of the new approach for high contrast two-dimensional scattering objects which are insonified by an incident ultrasound plane wave. Numerical results show that the reconstruction error is very small for circularly symmetric two-dimensional cylindrical objects whose refractive indices range from small to even sufficiently large values for which the previous inverse scattering algorithms fail to converge.     

Modeling Ultrasonic Pulse-Echo Signals from a Flat-Bottom Hole in Immersion Testing Using a Multi-Gaussian Beam

This paper proposes an ultrasonic measurement model that can predict the pulse-echo signals from a flat-bottom hole in an isotropic, homogeneous solid specimen immersed in water in a computationally efficient manner. To develop such a model, a measurement model approach is adopted based on two important assumptions: the paraxial approximation for the transducer beam and the small flaw assumption for the flat-bottom hole. The modular model that results from these two assumptions contains three terms: a diffraction correction term, a far-field scattering amplitude term and a system efficiency factor term. The diffraction correction is defined based on a multi-Gaussian beam model which allows the rapid evaluation of the wave field incident on the hole. The far-field scattering amplitude of the flat-bottom hole is obtained using the Kirchhoff approximation together with the small flaw assumption. The system efficiency factor is determined by deconvolution of an experimental front surface reflection signal by a reference reflector model. Here, the contribution of each of these three terms to the overall measurement model are described in detail and the accuracy of the proposed model is verified by the comparison of the model-based predictions to experiments.     

Iterative solution of inverse scattering for a two-dimensional dielectric object

Two-dimensional inverse scattering for a dielectric cylinder was investigated. The problem was to reconstruct the dielectric constant distribution of a scatterer from the scattered field measured outside under the illumination of an incident wave. Theoretically, the inversion algorithm is derived using integral equation formulations together with the iterative technique. Note that the inverse problem is solved in the angular spectral domain instead of in the space domain. Therefore, the ill-posedness can be reduced and no regularization is needed. Numerical results show that with only one incident wave generated by a line source, good reconstruction is obtained even when the dielectric constant is fairly large and the Born approximation is no longer valid. The effects of random noise and measurement distance on imaging reconstruction were also investigated. © 1996 John Wiley & Sons, Inc.     

Boundary-integral equation method for elastodynamic scattering by a compact inhomogeneity

The set of singular integral equations which relates unknown fields on the surface of the scatterer to a time-harmonic incident wave is solved by the boundary element method. The general method of solution is discussed in some detail for scattering by an inclusion. Results are presented for a spherical cavity, and for a soft and a stiff spherical inclusion. Fields on the surface of the scatterer are compared with previous results obtained by different methods. Back-scattered and forward-scattered displacement fields are presented, both as a function of position at fixed frequency, and as a function of frequency at fixed position. The quasi-static approximation is briefly discussed.     

The role of coherent effects in mode bistability of a gas laser in inhomogeneous medium

Abstract

We have studied microscopic effects leading to mode competition in an inhomogeneously broadened medium of a gas laser with a weakly anisotropic cavity. The polarization bistability observed in some lasers, which is believed to be caused by hole burning, we attribute to microscopic coherent effects induced by two light fields. Due to these effects one field can be coupled with another. Hole burning is found to be important, but not crucial. The exact solution of the equation of motion for field amplitudes is compared with the third order approximation of perturbation theory. The role of four wave mixing, important for bistability of axial modes in a homogeneously broadened medium, is discussed.     

Non-linear Resonant Transient and Steady-state Response in a Classical Model

The Doppler-broadened steady state and transient response of a thermal ensemble of anharmonic oscillators to incident laser radiation is investigated. Non-linear polarization of this classical system is obtained by analytically solving the dynamical equations up to third order in the electric field. Except for the sign of the third-order transient polarization, the results are in striking contrast to those obtained in semi-classical theory. In particular, the classical response at resonance is unsaturated up to this order. The Doppler-integrated third-order free induction decay (FID) signal vanishes in the usual approximation of the homogeneous width being smaller than the Doppler width. The physical conclusion of the paper is negative: resonant non-linear and coherent effects such as saturation and nutation typical of the quantum mechanical two-level atoms do not arise for classical anharmonic oscillators.     

Spatial coherence effects in light scattering from metallic nanocylinders

We study the scattering of a partially coherent electromagnetic beam from metallic nanocylinders and analyze the effects of plasmon resonances on the coherence and polarization properties of the optical near field. We employ the coherent-mode representation for the incident field and solve the scattering problem independently for each mode by using a boundary-integral method. Our results show that the plasmon resonances may significantly affect the coherence and polarization characteristics of the near field and that partial coherence influences the energy flow in nanocylinder arrays.     

某小型潜航器的声散射特性研究

运用目标回声强度预报的板块元方法,研究某小型潜航器的水下回声特性。计算并分析了入射波频率和方位对其声散射特性的影响规律;利用板块元法得到的散射特性,根据频域间接法仿真出水下声成像结果;完成外场试验,将试验结果与计算结果进行对比,吻合较好。研究表明潜航器中的桅杆结构对其散射有较明显影响。     

Interpretation of single-particle negative polarization at intermediate scattering angles

We study the interrelation of the internal field of irregular particles to the far-field scattering characteristics by modifying the internal field of dipole groups. In this paper, we concentrate on the longitudinal component, i.e., the internal-field component parallel to the incident wave vector. We use the discrete-dipole approximation to determine the internal field and switch off the longitudinal component from the dipoles that have the highest energy density above a preset cutoff value. We conclude that only a relatively small number of core dipoles, about 5% of all dipoles, contribute to the negative linear polarization at intermediate scattering angles. These core dipole groups are located at the forward part of the particles. The number of core dipoles in the group becomes greater as particle asphericity increases. We find that the interference between the scattered waves from the core dipole groups, which was studied previously for spherical particles, is preserved to a large extent for nonspherical particles.     

Scattering of the Lowest Lamb Wave Modes by a Corrosion Pit

Scattering of time-harmonic Lamb wave modes by a partial spherical corrosion pit in a plate is investigated. By using superposition, the total field consists of the incident and scattered fields, where the latter is generated by tractions on the surface of the cavity. In the approximation advanced in this article these tractions are represented by time-harmonic body forces on a trace of the cavity in the interior of the plate. The acoustic radiation from the resultants of these body forces applied to the surface of the plate approximates the scattered field. The resultant forces are decomposed in symmetric and anti-symmetric systems, which generate symmetric and anti-symmetric radiating modes. The time-harmonic elastodynamic form of the reciprocity theorem is employed to obtain an analytical solution to the scattered field amplitudes. We obtain the ratio of scattered to incident Lamb mode amplitudes, which in a closed generalized form include material properties, geometry of the pit and layer, and angular frequency of the incident wave. Results of this study yield graphical representations for the amplitude ratios with respect to pit geometry and has the potential to lead to a unique solution of the inverse problem under some conditions.     

大粗糙度起伏下一维海面声散射建模与分析

针对起伏海面高频声散射计算问题,提出了一种改进的基尔霍夫(Kirchhoff)近似方法。该方法考虑了海面的阴影区和亮区之间的多次散射声场,可对小入射角下大粗糙度起伏海面的散射声场进行计算。以一维余弦和高斯谱海面散射声场的有限元计算结果为标准解验证了所提方法的准确性和适用性。利用该方法计算了一维余弦海面的散射强度,分析了不同入射声波频率和角度下海面散射强度的分布情况,并解释了Bragg散射的产生机理,同时讨论了不同海面均方根高度和相关长度情况下高斯谱海面散射强度的变化规律。     

Spherical wave scattering by slender bodies

The problem of the scattering of a spherical acoustic wave by rigid slender bodies of revolution is investigated theoretically from a formalism based on the matched asymptotic expansion method. It is an extension of a formulation that was originally derived for incident plane waves with the so-called slender-body approximation. Simple and practical formulas are obtained for the scattered pressure in the near- and far-fields: they are valid at low and medium frequencies when the reduced wavenumber Ka is less or of the order of unity. Computations of the monostatic and bistatic angular distributions for a spheroid are presented to illustrate the sensitivity of the scattered field with respect to the distance source and observation point.     

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.     

Polarization of transmission scattering simulated by using a multiple-facets model

A Mueller matrix for scattering by a rough plane surface of a glass hemisphere was simulated by using a micro-facet model. The algorithms are formulated in vector representation in terms of the input and output directions. The single-facet scattering simulation used the results of the Kirchhoff integral for medium rough surfaces with exponential height distribution. Scatterings by two or more facets were also simulated. For a fixed angle between the incident and the detection directions, the transmission scattering and its polarization properties were symmetric when plotted against the off-specular incident angle. The single-facet model generated no depolarization or polarization change. When double-facet scattering was included, polarizations were changed appreciably while depolarization was still very small. Depolarization increased appreciably when scattering by higher orders was included. The simulated results that include all orders of scattering fit excellently to the measured scattering transmittance and its polarization and depolarization.     

Scattering of plane electromagnetic waves by a chiral-metal cylinder

The problem of scattering of E-and H-polarized plane electromagnetic waves by a metal cylinder covered with a chiral layer is solved by the method of partial regions. The scattering field is studied in the near and far zones. The correlation between the type of polarization of the incident electromagnetic wave and the magnitude of the depolarized component of the scattered field is considered.     

Low frequency electromagnetic scattering by a perfectly conducting moving sphere

The paper investigates the propagation of a plane electromagnetic waves in the exterior of a moving obstacle. Under the assumption that the obstacle moves with uniform velocity and more slowly than the incident field, we apply the Lorentz transformation. In the object’s frame, where the scatterer is stationary, we introduce the low-frequency approximation technique. For the near electromagnetic field we obtain the Rayleigh low-frequency coefficients while in the far field we derive the leading non-vanishing terms for the scattering amplitude and scattering cross-section. Finally, using the inverse transformation we express the same quantities in the observer’s frame.     

小斜率近似方法分析粗糙界面声散射问题

利用小斜率近似方法计算了起伏海面的声散射特性,得到了具有高斯分布粗糙海面的平均反射系数（即镜反射系数）计算公式,并与微扰法和Kirchhoff近似做了比较,结果表明小斜率近似是一种非常有效的分析起伏表面散射特性的近似方法。最后讨论了海面镜反射系数随海面的不平整度（波浪的均方根高度）、声波频率和声波入射方向的变化关系,得出了只有在声波波长和起伏波浪高度可比拟时,才有明显的镜反射的结论。这为分析浅海目标声散射特性时,选择是否需要考虑海面（海底）所引起的多途效应提供了理论依据。     

Scattering of light from the random interface between two dielectric media with low contrast

We calculate the coherent and incoherent scattering of p- and s-polarized light incident from a dielectric medium characterized by a real, positive, dielectric constant epsilon0 onto its one-dimensional, randomly rough interface with a dielectric medium characterized by a real, positive, dielectric constant epsilon. We use a perturbation theory with a new small parameter, namely, the dielectric contrast eta = epsilon0 - epsilon between the medium of incidence and the scattering medium. The proper self-energy entering the expression for the reflectivity is obtained as an expansion in powers of eta through the second order in eta, and the reducible vertex function in terms of which the scattered intensity is expressed is obtained as an expansion in powers of eta through the fourth. The roughness-induced shifts of the Brewster angle (in p polarization) and of the critical angle for total internal reflection (epsilon0 > epsilon) are obtained. The angular dependence of the intensity of the incoherent component of the scattered light displays an enhanced backscattering peak, which is due to the coherent interference of multiply scattered lateral waves supported by the interface and their reciprocal partners. Analogs of the Yoneda peaks observed in the scattering of x rays from solid surfaces are also present. The results obtained by our small-contrast perturbation theory are in good agreement with those obtained in computer simulation studies.     

Inverse design of anti-reflection coatings using the nonlinear approximate inverse

We consider a multi-frequency inverse scattering problem arising in the design of anti-reflection coatings. These thin films are deposited onto photovoltaic solar cells to enhance their performance. The objective is to determine the space-dependent refractive index in an inhomogeneous optical layer from the reflection coefficients at the surface. The relevant model yields a boundary value problem for the one-dimensional (1D) Helmholtz equation, which we formulate as an equivalent integral equation. The resulting inverse problem is nonlinear and ill-posed. We consider a series expansion of the field depending on the order of nonlinearity of the model. The first-order solution is obtained by using the Born approximation which is valid for weak scattering. Stronger scatterers are sought by considering a nonlinearity of higher order. The mathematical and numerical framework is provided by the (noniterative) method of the approximate inverse (AI) for nonlinear inverse problems. Numerical results are presented to attest the efficiency and stability of the method.