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.     

Optical extinction by closely spaced parallel cylinders inside a finite dielectric slab

The formulation for the extinction and scattering cross sections of closely spaced parallel infinite cylinders in a dielectric medium of finite thickness is presented. We consider the general case of dissimilar refractive indices for the half-spaces on both sides of the slab, and the diameter and refractive index of each cylinder can be different. The formulation accounts for the coherent scattering between the cylinders and scattering of the multiply reflected internal waves inside the slab. Discontinuity in the refractive index across the dielectric slab interfaces results in boundary reflections that modify the angular distribution of the scattered intensity in both forward and backward directions. The extinction cross section, which is derived by a formal application of the optical theorem, is shown to consist of both a forward and a backward component. The general solution is applied to obtain the formulas for the cases of cylinders in front of a reflecting plane, cylinders inside a semi-infinite dielectric medium, and cylinders in free space.     

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.     

Response of acoustic imaging systems using convergent leaky waves to cylindrical flaws

A theoretical study of imaging systems utilizing focused leaky surface acoustic waves (SAWs), and their response to certain kind of defects is presented. In particular, circular cylindrical inhomogeneities with axes perpendicular to the surface are considered. The scattering of the SAW from this cylinder is formulated with some approximations. The surface wave incident on the inhomogeneity is initially found as an angular spectrum of plane waves. However, to apply the boundary conditions at the cylindrical surface, the incident field has to be transformed into a superposition of cylindrical waves. Similarly, the scattered field, which is found in the form of outgoing cylindrical SAWs, is converted back to a plane wave spectrum. A formula is obtained for the transducer output voltage in terms of the position and the radius of the cylinder, and it is suitable for computer evaluation. By considering various locations for the cylinder, the sensitivity of the system around the focal point is studied. By comparing the output voltages for cylinders of different radii, the sensitivity of the system to the size of the inhomogeneity is examined. The numerical results are in agreement with the experimental observations.     

Scattering from cylinders using the two-dimensional vector plane wave spectrum

The two-dimensional vector plane wave spectrum (VPWS) is scattered from parallel circular cylinders using a boundary value solution with the T-matrix formalism. The VPWS allows us to define the incident, two-dimensional electromagnetic field with an arbitrary distribution and polarization, including both radiative and evanescent components. Using the fast Fourier transform, we can quickly compute the multiple scattering of fields that have any particular functional or numerical form. We perform numerical simulations to investigate a grating of cylinders that is capable of converting an evanescent field into a set of propagating beams. The direction of propagation of each beam is directly related to a spatial frequency component of the incident evanescent field.     

Wave forces on arrays of floating bodies

Summary Previous work on the scattering of an incident wave field by an array of fixed vertical cylinders is extended to calculate the added-mass and damping coefficients for an array of floating axisymmetric bodies. The method is based upon a large spacing approximation where diverging waves are replaced by plane waves. It is shown that, given the scattering and radiation properties of a single body, the interaction effects within an array can be calculated both simply and accurately.     

Formulation and validation of Berenger's PML absorbing boundary forthe FDTD simulation of acoustic scattering

Berenger's perfectly matched layer (PML) absorbing boundary condition for electromagnetic (EM) waves is derived to absorb 2-D and 3-D acoustic waves in finite difference time domain (FDTD) simulation of acoustic wave propagation and scattering. A PML medium suitable for acoustic waves is constructed. Plane wave propagation in the PML medium is solved for both 2-D and 3-D cases and explicit FDTD boundary conditions are derived. The equations show that a matched PML medium is a perfect simulation of free space in that a plane wave does not change its direction of propagation or its speed when it propagates from free space into a matched PML medium. FDTD simulation of a pulsed point source propagating in two dimensions is carried out to test the performance of the PML boundary for acoustic waves. Results show that an eight layer PML boundary condition reduces the reflected error 40 dB over Mur's second order boundary condition     

Excitation with a focused, pulsed optical beam in scattering media: diffraction effects

To gain a better understanding of the spatiotemporal problems that are encountered in two-photon excitation fluorescence imaging through highly scattering media, we investigate how diffraction affects the three-dimensional intensity distribution of a focused, pulsed optical beam propagating inside a scattering medium. In practice, the full potential of the two-photon excitation fluorescence imaging is unrealized at long scattering depths, owing to the unwanted temporal and spatial broadening of the femtosecond excitation light pulse that reduces the energy density at the geometric focus while it increases the excitation energy density in the out-of-focus regions. To analyze the excitation intensity distribution, we modify the Monte Carlo-based photon-transport model to a semi-quantum-mechanical representation that combines the wave properties of light with the particle behavior of the propagating photons. In our model the propagating photon is represented by a plane wave with its propagation direction in the scattering medium determined by the Monte Carlo technique. The intensity distribution in the focal region is given by the square of the linear superposition of the various plane waves that arrive at different incident angles and optical path lengths. In the absence of scattering, the propagation model yields the intensity distribution that is predicted by the Huygens-Fresnel principle. We quantify the decrease of the energy density delivered at the geometric focus as a function of the optical depth to the mean-free-path ratio that yields the average number of scattering events that a photon encounters as it propagates toward the focus. Both isotropic and anisotropic scattering media are considered. Three values for the numerical aperture (NA) of the focusing lens are considered: NA = 0.25, 0.5, 0.75.     

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.     

Reflection and refraction of an arbitrary electromagnetic wave at a plane interface separating an isotropic and a biaxial medium.

Exact solutions are obtained for the reflected and transmitted fields resulting when an arbitrary electromagnetic field is incident on a plane interface separating an isotropic medium and a biaxially anisotropic medium in which one of the principal axes is along the interface normal. From our exact solutions for the reflected fields resulting when a plane TE or TM wave is incident on the plane interface, it can be inferred that the reflected field contains both a TE and a TM component. This gives a change in polarization that can be utilized to determine the properties of the biaxial medium. The time-harmonic solution for the reflected field is in the form of two quadruple integrals, one of which is a superposition of plane waves polarized perpendicular to the plane of incidence and the other a superposition of plane waves polarized parallel to the plane of incidence. The time-harmonic solution for the transmitted field is also in the form of two quadruple integrals. Each of these is a superposition of extraordinary plane waves with displacement vectors that are perpendicular to the direction of phase propagation.     

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.     

Ultrasonic wave scattering from rough,imperfect interfaces. Part II. Incoherent and coherent scattered fields

A theoretical model for ultrasonic wave scattering for geometrically irregular and imperfectly bonded interfaces is presented. Part I presents the stochastic interface characterization and a model for its mechanical response based on a micromechanics model of asperity contact. Part II uses this interface representation to write the well used quasi-static boundary conditions for scattering from a.flat imperfect interface¹ directly on the irregular interface profile. The boundary conditions are then expanded in an asymptotic series in the roughness parameter (standard deviation of the surface height) which is small compared to wavelength. The slope of the profile must also be everywhere small. These equations are solved exactly for the zero-th and second order terms, which are the flat coherent solution and its' first coherent correction, and the first order term, which is the first term in the expansion for the incoherently scattered solution. Results for obliquely incident longitudinal and shear waves show a strong dependence on the roughness in both the coherent and incoherent reflected fields, but little if any dependence on the roughness in the transmitted fields. In particular, the reflected coherent fields show markedly increasing attenuation compared to the flat compliant interface with increasing roughness and increasing ultrasonic frequency, the latter result being in qualitative agreement with results for scattering from an inhomogeneous array of individual scatterers.² There is evidence in the incoherent reflected fields for the existence of an incoherent leaky interface disturbance which manifests itself as a bulk incoherent shear wave at a scattering angle equal to the critical longitudinal angle. A coherent true interface wave is also supported by the rough interface which is shown to further attenuate the coherent reflected fields compared to the flat compliant interface solution.     

Wave scattering by a horizontal circular cylinder in a two-layer fluid with an ice-cover

In a two-layer fluid wherein the upper layer is of finite depth and bounded above by a thin but uniform layer of ice-cover modelled as a thin elastic sheet and the lower layer is infinitely deep below the interface, time-harmonic waves with a given frequency can propagate with two different wavenumbers. The wave of smaller wavenumber propagates along the ice-cover while wave of higher wavenumber propagates along the interface. In this paper problems of wave scattering by a horizontal circular cylinder submerged in either the lower or in the upper layer due to obliquely as well as normally incident wave trains of both the wave numbers are investigated by using the method of multipole expansions. The effect of the presence of ice-cover on the various reflection and transmission coefficients due to incident waves at the ice-cover and the interface is depicted graphically in a number of figures.     

Effects of incident illumination on in-line phase-contrast imaging

Effects of incident illumination on phase-contrast images obtained by means of free-space propagation are investigated under the "transport-of-intensity" approximation. Analytical expressions for image intensity distribution are derived in the cases of coherent quasi-plane and quasi-spherical incident waves, as well as for spatially incoherent and quasi-homogeneous sources and some other types of sources. Practical methods for measuring the relevant parameters of the incident radiation are discussed together with formulas allowing one to calculate the effect of these parameters on the image intensity distribution. The results are expected to be useful in quantitative in-line imaging, phase retrieval, and tomography with polychromatic and spatially partially coherent radiation. As an application we present a method for simultaneous "automatic" phase retrieval and spatial deconvolution in in-line imaging of homogeneous objects using extended polychromatic x-ray sources.     

层理面对水压爆破应力波传播规律的影响

水压爆破应力波的传播过程决定了爆破的作用效果及影响范围,层状岩体中的层理面特征对水压爆破应力波的传播路径及衰减具有直接影响.为明确水压爆破应力波在层状岩体内的传播规律及影响因素,采用理论分析和数值模拟相结合的方法,研究了层理面位置及其介质属性对水压爆破应力波传播的影响规律.结果表明:水压爆破相对于常规爆破产生的初始应力...     

Scattering of inhomogeneous wave by viscoelastic interface crack

Summary The reflection, refraction and scattering of inhomogeneous plane waves of SH type by an interface crack between two dissimilar viscoelastic bodies are investigated. The singular integral equation method is used to reduce the scattering problem into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Then, the singular integral equation is solved numerically by Kurtz's piecewise continous function method. The crack opening displacement and dynamic stress intensity factor characterizing the scattered near-field are estimated for various incident angles, frequencies and relaxation times. The differences on crack opening displacement and stress intensity factor between elastic and viscoelastic interface crack are contrasted. And the effects of incident angle, incident frequency and relaxation time of the viscoelastic material are analyzed and explained by the features of phase lag and energy dissipation of the viscoelastic wave.     

Wave dispersion and attenuation in fiber composites

 This work deals with the dispersion and attenuation of elastic plane waves propagating in a single layer fiber reinforced composite, in a direction which is perpendicular to the fibers. An iterative effective medium model, based on single scattering considerations, for the quantitative estimation of wave dispersion and attenuation is proposed. The single scattering problem is solved numerically by means of a 2-D boundary element methodology. Numerical results concerning the plane velocity and the attenuation coefficient of longitudinal or transverse SH, SV waves propagating in two types of fiber reinforced composite materials, are presented. The obtained results are compared to those taken either experimentaly or numericaly by other investigators.     

Scattering of antiplane shear waves in a fiber-reinforced composite medium with interfacial layers

Summary This paper deals with the scattering of antiplane shear waves in a metal matrix composite reinforced by fibers with interfacial layers. We assume same-size cylindrical inclusions and same-thickness interface layers with nonhomogeneous elastic properties. The effective complex wave numbers follow from the coherent wave equation which depends only upon the scattering amplitude of the single scattering problem. Effective elastic constants can be obtained from phase velocities of coherent waves. Numerical calculations for an SiC-fiber-reinforced Al composite are carried out, and the effect of interface properties on scattering cross section, phase velocity, attenuation of coherent plane wave, and effective elastic constant is shown graphically.     

Hyper-Rayleigh light scattering from an aqueous suspension of purple membrane

Here we report the first observation of hyper-Rayleigh light scattering from bacteriorhodopsin in the form of an aqueous suspension of unoriented purple membranes. A typical purple membrane suspension used in our experiments contains approximately 10(8) randomly oriented purple membranes. Each purple membrane contains approximately 10(5) bacteriorhodopsin molecules in a two-dimensional crystallinearray. Hyper-Rayleigh light scattering is observed when the purple membrane suspension is illuminated with light that has a wavelength of 1064 nm. We propose that the 532-nm scattered light from each of the bacteriorhodopsin molecules in a single purple membrane is coherent, and that the scattered light from different purple membranes is incoherent. This proposal is supported by the following experimental observations: (a) the 532-nm light intensity is proportional to the square of the incident power, (b) the intensity of the 532-nm signal is linearly proportional to the concentration of purple membrane in solution, (c) the scattered 532-nm light is incoherent, (d) the scattered 532-nm light intensity decreases if the size of the purple membranes is reduced while the bacteriorhodopsin concentration is kept constant, and (e) the 532-nm light is due to the retinal chromophore of the bacteriorhodopsin molecule. The ratio of horizontal polarized hyper-Rayleigh scattered light to vertically polarized hyper-Rayleigh scattered light gives the angle (23 ± 4°) of the retinal axis with respect to the plane of the purple membrane. The hyperpolarizability of the bacteriorhodopsin molecule is found to be 5 ± 0.4 × 10(-27) esu.