Analytical derivation of the stationarity and the ergodicity of a field scattered by a slightly rough random surface

In the framework of the small perturbation method, we present a new theoretical derivation of the statistical and spatial properties of a field scattered by a one-dimensional slightly rough random surface. The work concerns the intermediate field zone where the scattered field is reduced to the contribution of the progressive plane waves. The surface is assumed to be stationary, ergodic and Gaussian. First, from a statistical point of view, we demonstrate that under oblique incidence the scattered field is not stationary while it is strictly stationary under normal incidence. For an infinite surface, the scattered field modulus obeys to Hoyt law and the phase is not uniform. Second, from a spatial point of view, for a given altitude and under all incidences, we show that the scattered field is ergodic. Under oblique incidence, the phase is spatially uniform and the modulus is given by a Rayleigh law. Under normal incidence, the phase is not uniform and the modulus is given by a Hoyt law. Third, from a practical point of view, we show that the field measured by a directional antenna is ergodic and stationary if the angular transfer function of the antenna does not contain the specular direction.     

Acoustic response from a bubble pulsating near a fluid layer of finite density and thickness

A theory is developed that allows one to consider the dynamics of an acoustically induced bubble near a fluid layer of finite density and thickness. The theory reveals that, as far as the scattered field of a bubble in the far-field zone is concerned, the layer thickness is a very important factor because the behavior of the scattered field in the cases of infinite and finite layers is qualitatively different even if both layers are of the same density. The amplitude of the scattered pressure from a bubble pulsating in the vicinity of an infinite layer is larger than that for the same bubble in an unbounded fluid, while in the case of a finite layer, on the contrary, the amplitude of the scattered pressure for a bubble near the layer is smaller than that in an unbounded fluid. It is also shown that the higher the layer density, the greater the difference between the scattered pressure amplitudes for infinite and finite layers.     

Integral equation method in near-field optical microscopy of scattering

Based on the integral equation method, the boundary problem of classical optics of finding the strength of the electromagnetic field scattered by a probe positioned in the near zone of a plane surface is solved in the context of application in near-field optical microscopy of scattering. Only the dipole component of the scattered field was taken into account in the calculations. The obtained theoretical expressions were compared to the known experimental data on scanning the surface of SiC. Good agreement between the experimental and the theoretical results was obtained outside the region of the resonant interaction of the probe of a near-field microscope and the surface under study.     

Scattering of low-frequency pulsed sound signals from elastic cylindrical shells

A method and experimental setup intended for measuring the amplitude and phase of acoustic field in the near zone of a scatterer are described. The results of measuring the scattering characteristics of low-frequency sound signals scattered by elastic cylindrical shells are analyzed.     

Single-metal-cluster local imaging: polarized scattered electric field calculation compared to the field’s modulus and phase observed in the optical near-field

Simultaneous topographical and near-field optical imaging have been performed on single gold particles of diameters close to 12 nm. The optical source is a linearly polarized laser diode operating at λ=780 nm away from the plasmon resonance of the particles. The experimental optical image is recorded with an apertureless scanning near-field optical microscope (ASNOM) operating in transmission mode. It is compared to the components of the polarized scattered electric field around a single cluster calculated using Mie formalism. We show that the tip used in the experiments is sensitive to the axial component of the scattered field, thus allowing us to obtain the amplitude and the phase of the local field. Our derivation brings out new information, usually shaded when applied to an ensemble of particles. In particular, the dipole model widely used to describe the scattered field by a spherical particle is not suitable to describe the three components of the scattered field in the near zone. Our results are of interest for fundamental studies of the optical properties of single metal clusters and the control of local phenomena such as enhancement, extinction, etc. PACS 07.79.Fc; 78.67.Bf; 78.35.+c     

Scattering of a plane electromagnetic wave by an infinite wedge with a truncated circular cylinder coated coaxially with a magnetodielectric layer

We formulate and solve the problem of scattering of a plane electromagnetic wave by an infinite, perfectly conducting wedge with a truncated, perfectly conducting circular cylinder which is coated coaxially with a magnetodielectric layer and located along the wedge edge. The rigorous solution is obtained and reduced to a system of linear algebraic equations of the second kind for unknown coefficients of Fourier expansions of the scattered field. The results of calculating the scattered field in the far zone with a specified accuracy are presented for the case of an H-polarized wave. It is shown that for certain values of the electric radius of the cylinder, the backscattering cross section of such a structure has pronounced maxima.     

Generalization of the optical theorem for an arbitrary multipole in the presence of a transparent half-space

The optical theorem is generalized to the case of excitation of a local inhomogeneity introduced in a transparent substrate by a multipole of arbitrary order. It is shown that, to calculate the generalized extinction cross section, it is sufficient to calculate the derivatives of the scattered field at a single point by adding a constant and a definite integral. Apart from general scientific interest, the proposed generalization makes it possible to calculate the absorption cross section by subtracting the scattering cross section from the extinction cross section. The latter fact is important, because the scattered field in the far zone contains no Sommerfeld integrals. In addition, the proposed generalization allows one to test computer modules for the case where a lossless inhomogeneity is considered.     

Shape reconstruction of metallic objects from intensity scattered field data only

We address an inverse scattering problem using only amplitude information of the scattered field. In particular, we are concerned with the reconstruction of the shape of a metallic planar obstacle, located in a known plane (aperture plane), starting from the knowledge of the intensity of the scattered field over two measurement planes in near zone and parallel to the aperture plane, when a single-frequency incident plane wave is exploited. The formulation of the inverse scattering problem is given under the physical optics approximation, and thus the resulting phase retrieval problem is quadratic. This allows us to apply some phase retrieval techniques already developed for antenna diagnostics. Reconstruction results with synthetic data indicate the feasibility of the proposed approach.     

Scattering of a Generic Two-Dimensional Field by Cylindrical Structures in the Presence of a Plane Interface

A new method for treating the scattering of a two-dimensional electromagnetic field, expressed by means of its plane-wave spectrum, by an arbitrary configuration of circular cylinders in the presence of a plane interface between two different media, is presented. The proposed method allows us to solve the problem for both polarizations and to calculate the scattered field both in the near and in the far zone. Numerical results relevant to vacuum-dielectric interfaces are presented and compared with previous known results.     

Spectral-energy characteristics of sound fields scattered by fine-structured inhomogeneities of sound velocity into the geometrical shadow zone

In analyzing experimental results obtained with explosive sources in the tropical zone of the Indian Ocean, a good agreement was obtained for spectral-energy characteristics of signals observed in the first geometrical shadow zone with computer calculations of the sound field scattered by fine structure inhomogeneities of the fractal type. From the comparison of the results of calculating the frequency characteristics of sound fields in the shadow zone by the wave code and by the method combining ray acoustics with the wave theory of sound scattering, it was found that both methods are appropriate for describing the real processes of scattering and propagation of sound in the ocean with fine-structured stratification and that these methods can be used for solving inverse problems.     

Rotationally symmetric scattering from anisotropic media

It is reported that the rotationally symmetric distributions of the spectral density and the spectral degree of coherence of the scattered field in the far zone can be produced by appropriate choices of the effective radius and the correlation length of the scatterer, when a polychromatic plane light wave is incident upon a Gaussian-correlated, quasi-homogeneous, anisotropic medium. The necessary and sufficient conditions are presented. Our results are illustrated by numerical examples.     

Scattering of short electromagnetic radiation pulses on an infinitely long conductive cylinder

A method of numerical solution of the complete system of Maxwell equations is used to investigate the process of interaction of a short electromagnetic pulse with a long conductive cylinder (a two-dimensional scattering problem). Reflected signal waveforms and spectra are calculated for various relationships between the pulse length and the sizes of the scatterer. It is demonstrated that for incident pulse length smaller than the diameter of the cylinder, two pulses of scattered radiation are formed in the far field zone.     

一种半导体表面上微粒缺陷散射场的计算方法

本文通过分析半导体表面上微粒缺陷散射场的光波传播规律,建立了表面上微粒缺陷场的传输模型和数学模型,使定量计算表面上微粒缺陷的散射场成为可能。进一步将入射场和散射场都表达成球矢量波函数的形式,并考虑表面的二次散射作用,用T矩阵将入射场和散射场的展开项系数连系起来。从而得到散射场与入射场之间的一系列定量表达式,并给出计算结果。     

Measuring the characteristics of backscattering of sound on a rough surface in the near-field zone of a phased array

The paper presents the results of an experiment on measuring the characteristics of backscattering of sound waves by a rough surface. Measurements were conducted in the near zone of a vertical array, which made it possible with a high degree of accuracy to control the propagation conditions and the angles of incidence of an acoustic wave onto the surface. Tonal signals were emitted in a constant mode at frequencies of 0.5–3.5 kHz. The Doppler spectrum of the scattered signal was analyzed in detail, the spectral component corresponding to Bragg scattering was isolated, and the width of this component was determined. The possibilities of calculating the scattered field using two forms of the sea state spectrum are studied and compared: the two-dimensional spatiotemporal sea state spectrum, which was measured optically, and the conventional one-dimensional time spectrum, measured with a single surveying mark.     

A characterization of the scattered acoustic intensity field in the resonance region for simple spheres

The properties of the scattered acoustic vector fields generated by simple spheres illuminated by monotonic continuous wave (CW) plane waves are investigated. Analytical solutions are derived from general acoustic pressure scattering models and analyzed for wave numbers in the resonance region. Of particular interest is the understanding of the characteristics of the scattered acoustic vector field in the near-to-far-field transition region. The separable active and reactive components of the acoustic intensity are used to investigate the structural features of the scattered field components. Numerical results are presented for the near and transition regions for a rigid sphere. A method of mapping nulls in the scattered intensity field components is described. The analysis is then extended to include a simple fluid-filled boundary and finally the evacuated thin-walled shell. Near field acoustic intensity field structures are compared against mechanical material properties of vacuous shells. The ability to extract scattered field features is illustrated with measurements obtained from a recent in-air experiment using an anechoic chamber and acoustic vector sensor probes to measure the scattered acoustic vector field from rigid spheres.     

The diffraction of light at ultrasonic waves in acoustic resonators

A theoretical treatment is given of the diffraction of light by hypersonic waves excited in solid prismatic samples. For a fixed frequency, a set of modes exists in such a resonator. The modes differ in the spatial distribution of the field, which corresponds to a set of partial waves propagating over an entire solid angle. The diffraction occurs only at the partial waves which satisfy the Bragg condition and the diffraction pattern has the form of a circle consisting of a large number of points. An expression is found for the angular separation of adjacent points which correspond to different modes. It is shown experimentally that for the scattered light field in the far zone the diffraction patterns are similar to Shaefer-Bergmann patterns. Explanations are given for the shape and fine structure of these patterns. The structure of the diffracted light beams in the near zone is also studied and the frequency intervals between the excitation of the various resonator modes are measured. The experimental results are in qualitative agreement with the theory.     

Role of the probe quadrupole moment in apertureless near-field optical microscopy

A theory of an apertureless scanning near-field optical microscope is developed that takes into account the quadrupole moment of the probe in forming the near field and the scattered wave in the far-field zone. It is shown that the quadrupole moment can lead to a change in the conditions for the resonant coupling of the probe tip with the sample surface, as well as to the appearance of additional resonances in the frequency dependence of the response of a near-field microscope. The theory developed is found to be in good agreement with known experimental data in the region of resonant tip—sample coupling.     

Scattering of a Plane Electromagnetic Wave by an Infinite Dihedral Wedge with a Slotted Cylinder at the Apex

The problem of scattering of a plane electromagnetic wave by a perfectly conducting dihedral wedge with a slotted cylinder at the apex in rigorous formulation is reduced to solving a system of linear algebraic equations for unknown coefficients of the Fourier expansion of the scattered field. The results of calculation of the far-zone field with a given accuracy are presented in the case of an E-polarized incident wave. It is shown that for a slot with a large opening angle, the radiation patterns of the field in the long-wavelength far zone has a shape similar to a cardioid and does not depend on the incident-wave direction and the dielectric permittivity of the cylinder. In the case of a narrow slot, the radiation-pattern shape depends significantly on the incidence angle of the wave.     

Features of the Sound Field Structure in a Two-Channel Oceanic Waveguide

The results of experimental studies of the energy and angular structure of a sound field in the region of the Iberian Basin in the northeastern Atlantic are discussed. The experiments are carried out in a two-channel waveguide whose axes are located at depths of approximately 450 and 2000 m. A continuous pseudonoise signal in the frequency range 2.52–4.0 kHz is emitted. The signals are received by the omnidirectional hydrophones and, simultaneously, by a 10-m-long vertical array, which allows one to realize a narrow beam reception (～2.5°) in the vertical plane. The source and the receiver are located in a 500-m-thick layer within the upper sound channel. The field characteristics are measured in the course of a continuous change of distance from 1 to 65 km. The comparison of the experimental data with calculations shows that the sound field structure formed by the lower channel is much closer to the theoretical results than the structure formed by the upper channel. In the upper sound channel, the shadow zone manifests itself only slightly and the first convergence zone begins approximately 72–11 km nearer to the source than predicted by the calculations. The corresponding angular sound field structure is fairly pronounced in the vertical plane and bears no evidence of the random behavior that is peculiar to the fields scattered by the inhomogeneities.     

Coherence properties of the scattered electromagnetic field generated by anisotropic quasi-homogeneous media

The coherence properties of the scattered field generated by linearly polarized and uniformly unpolarized electromagnetic plane waves incident on anisotropic quasi-homogeneous media are studied. The analytical expressions for the spectral density and the spectral degree of coherence of the three dimensional scattered field are derived. The results of the numerical simulations indicate that not only the properties of the anisotropic media have a great effect on the coherence properties of the scattered field, but also the polarization of the incident wave. And most important, the effect of the polarization of the incident wave on the coherence properties of the scattered field nearly concerns the properties of the anisotropic media. There are also close and interesting relations between the coherence properties of the scattered field that generated by the anisotropic media and by the corresponding isotropic media.