Mie scattering in the time domain. Part II. The role of diffraction

The p=0 term of the Mie-Debye scattering amplitude contains the effects of external reflection and diffraction. We computed the reflected intensity in the time domain as a function of the scattering angle and delay time for a short electromagnetic pulse incident on a spherical particle and compared it to the predicted behavior in the forward-focusing region, the specular reflection region, and the glory region. We examined the physical consequences of three different approaches to the exact diffraction amplitude, and determined the signature of diffraction in the time domain. The external reflection surface wave amplitude gradually replaces the diffraction amplitude in the angular transition region between forward-focusing and the region of specular reflection. The details of this replacement were studied in the time domain.     

Time-domain boundary element analysis of elastic wave interaction with a crack

The mathematical formulation of the problem of transient wave interaction with a crack in a homogeneous, isotropic, linearly elastic solid has been reduced to the solution of an integral equation over the insonified crack face. The integral equation relates the unknown crack-opening displacement, which depends on time and position, to the incident wave field. The integral equation has been solved numerically by a time-stepping method in conjunction with a boundary element discretization of the crack surface. For normal incidence of a longitudinal step-stress wave on a penny-shaped crack, results as functions of time have been obtained for the crack-opening displacement, the elastodynamic Mode-I stress intensity factor and the scattered far-field.     

Cross-wind profiling based on the scattered wave scintillation in a telescope focus

The problem of wind profile reconstruction from scintillation of an optical wave scattered off a rough surface in a telescope focus plane is considered. Both the expression for the spatiotemporal correlation function and the algorithm of cross-wind velocity and direction profiles reconstruction based on the spatiotemporal spectrum of intensity of an optical wave scattered by a diffuse target in a turbulent atmosphere are presented. Computer simulations performed under conditions of weak optical turbulence show wind profiles reconstruction by the developed algorithm.     

Pulse distortion of a scattered chirped pulse

We have studied the time-dependent properties of a chirped short pulse when the pulse is scattered by a spherical particle. We used generalized Lorentz-Mie formulas to study the scattered electrical field and pulse distortion. Plane wave Gaussian pulses of different chirps with a constant pulse-filling coefficient l(0) = 1.98 have been studied. A morphology-dependent resonance causes a prolonged trailing edge (small scattering angle) and oscillations (large scattering angle) in the scattered pulse. When frequency sweeping superimposes on a morphology-dependent resonance, the pulse chirp affects the scattered pattern and distorts the scattered intensity. Multisecondary pulses are generated because of the pulse chirp and even subsecondary pulses occur if the incident pulse is deeply chirped. The pulse widths of secondary and subsecondary pulses are shorter than those of an incident pulse.     

Quantitative use of Rayleigh waves to locate and size subsurface holes

An ultrasonic inspection method is used to obtain the circumference of a subsurface hole and the depth of the hole below the surface. A pitch-catch Rayleigh wave transducer set-up was used to launch a Rayleigh surface wave at the flaw and to capture and record the scattered waves. The frequency spectrum of the scattered waves can be used to obtain the depth of the hole. The ligament of material between the hole and the surface is sent into resonance, and this feature can be extracted from the scattered waves' frequency spectrum. The frequency is a function of the ligament length; thus the hole depth can be obtained. The circumference of the hole is found from a time of flight measurement. A Rayleigh wave is formed that travels around the hole's surface. The length of time required for the wave to travel around the hole is a measure of the circumference.     

Near-field intensity distribution of waves scattered from slightly rough surfaces

The near fields of electromagnetic waves scattered from two-dimensional slightly rough surfaces are studied by using the stochastic functional approach. The correlation coefficient between the surface and the intensity of the scattered-wave field is investigated to estimate the fidelity of near-field intensity images. We show that the fidelity depends on both the polarization and the angle of incidence and that high fidelity can be obtained by a TM-polarized incident wave whose incident angle is not close to the critical angle of the total reflection.     

Statistical moments for rough surface scatter from two-way parabolic integral equation at low grazing angles

The moments of a plane wave scattered at low grazing angles from a one-dimensional perfectly reflecting rough surface are considered. The mean intensity and autocorrelation of the scattered field and the corresponding angular spectrum are obtained to second order in surface height. The derivations are based on an operator expansion of the extended (two-way) parabolic integral equation solution. The resulting operator series describes successively higher-order surface interactions between forward and backward going components. The expressions derived may be regarded as backscatter corrections to those obtained via the standard (one-way) parabolic integral equation method.     

Optical cross-sectional imaging with pulse ultrasound wave assistance.

We have developed an optical cross-sectional imaging method for turbid media with the aid of a pulse ultrasound wave. Observation of deep regions in turbid media, such as tissue samples, is difficult owing to the rapid dispersion of an incoming laser beam by scattering. A pulse ultrasound wave, which is less scattered in tissues, can indicate the measuring point on the basis of the change of the optical scattering properties in a localized region. A depth-resolving capability can be achieved from the time-dependent measurement of the scattered-light intensity as the pulse ultrasound wave propagates in the sample. We verified the method by observing absorptive objects embedded in silicone rubber and by obtaining the cross-sectional image of an absorbing object surrounded by a strong scattering medium.     

Nonstationary scattering of electromagnetic pulses by spherical particles

We have studied time variances of the shape of an electromagnetic pulse scattered by a spherical particle. General formulas are derived for a pulse with an arbitrary envelope, for momentary values of scattered-light fields and light intensity, and for efficiencies of extinction and scattering. It is possible, by the use of these formulas, to obtain by routine integration the sensitivity reaction of a receiver with any time dependence. The formulas are illustrated with examples of scattering of a Gaussian pulse with a carrier wave λ(0) = 0.6328 μm and of multisized water drops. Pulses of different durations are studied. However, only those pulses that have all significant values of the Fourier density in the domain of positive frequencies ω are considered.     

Patterns in Mie scattering: evolution when normalized by the Rayleigh cross section

An alternative to using the traditional scattering angle theta to describe light scattering from a uniform dielectric sphere is the dimensionless parameter qR, where R is the radius of the sphere, q = 2k sin(theta/2), and k is the wavenumber of the incident light. Simple patterns appear in the scattered intensity if qR is used in place of theta. These patterns are characterized by the envelopes approximating the scattered intensity distributions and are quantified by the phase-shift parameter rho = 2kR/m - 1/, where m is the real refractive index of the sphere. Here we find new patterns in these envelopes when the scattered intensity is normalized to the Rayleigh differential cross section. Mie scattering is found to be similar to Rayleigh scattering when p < 1 and follows simple patterns for p > 1, which evolve predictably as a function of p. These patterns allow us to present a unifying picture of the evolution of Mie scattering for changes in kR and m.     

Patterns in the ripple structure of Mie scattering.

We study the ripple structure in the scattered intensity predicted by Mie scattering theory in the angular behavior of the scattered intensity for homogeneous, dielectric spheres. We find that for small values of the phase shift parameter rho = 2kR absolute value(m - 1), where k = 2 pi/lambda, R is the sphere radius, and m is the relative refractive index, the ripples are periodic with spacing equal to pi when plotted versus the dimensionless qR, where q = 2k sin(theta/2) and theta is the scattering angle. However, as rho increases, this outcome switches to nonuniform spacing of approximately pi cos(theta/2). The latter spacing is equivalent to a uniform spacing of pi/kR when plotted versus theta.     

双层弹性-非弹性封闭腔体的内部声场研究

从球坐标中声波波动方程出发，利用本征函数展开方法和界面边界条件，导出了双层弹性封闭球壳的内部散射声场表达式。对于单位源强度的点声源，本文计算了分别由弹性/粘弹性和弹性/吸声材料组成的双层封闭球壳的内部散射声压随频率的变化关系。计算结果表明，粘弹性材料和吸声材料在某些频段对散射声压有十分明显的抑制作用。     

Scattering of light by thermal ripplons on superfluid helium

It is well known that thermally excited waves on the free surface of a liquid can cause light to be diffusely scattered. In order to investigate the possible effects of the superfluid transition in liquid helium, we have measured the intensity of the surface scattering from the free surface of liquid helium as a function of temperature (1.3–2.1 K) and as a function of the scattering angle. The surface was illuminated vertically from above with a He-Ne laser. A measuring technique was devised which could not only distinguish among background scattering, scattering from the bulk liquid, and scattering from the surface, but could determine the ratio of surface to bulk scattering also. We have found that our results can be described by the theory of Mandelshtam, which is valid for classical liquids. According to this theory, the surface-scattered intensity is given by the ratio of temperature to surface tension. The angular dependence is determined by the characteristic wave vector dependence of the mean square amplitude of the fluctuations. The ratio between surface- and bulk-scattered intensity is calculated on the basis of the classical theory. The data indicate that in the frequency range around about 1 MHz no influence of the two-fluid nature of the superfluid is detectable.     

Scattering of light by a periodic structure in the presence of randomness. V. Detection of successive peaks in a periodic structure

We address the problem of detecting periodic structures hidden behind roughness. We have shown that if r(0) is the coherence length of the scattered radiation, due to the random part of the surface, and Lambda is the wavelength of the periodic part of the surface, then with a matched filtering method that we introduce, and by using simple computations with the intensity data, it is possible to detect the hidden first-order peak even when (r(0)/Lambda) approximately 0.11. Here we advance the method to bring out very weak second-order peaks, which we demonstrate for what we believe is the first time. The unmistakable presence of both the first- and second-order peaks, which have identical shapes as the zeroth-order peak, is strong evidence of the hidden periodicity and serves as a novel method for the detection of weak periodicities hidden behind strong randomness.     

High-frequency acoustic interaction of resonant systems using SAWs

A planar array of microspheres was deposited on the surface of a surface-acoustic-wave (SAW) device. Arrays of polymer microspheres with mode number m=1 and 2 were observed to resonate with the acoustic wave, thus absorbing or scattering the wave such that transmission is reduced at the resonant frequency. Comparing the quality factor determined from the transmission spectra (Q~15) and that determined from rapid pulse shut-off experiments (Q<15) also indicated that the surface wave was either scattered by the array or absorbed via enhanced coupling to the atmosphere.     

Scattering from rough inhomogeneous media: splitting of surface and volume scattering

The intensity scattered by particles randomly placed beneath a rough interface is studied with rigorous simulations. It is shown that the angular intensity pattern is close to that obtained by adding the intensity scattered by particles under a flat surface to that scattered by a rough homogeneous surface whose permittivity is evaluated with an effective-medium theory. This heuristic splitting rule is accurate for a large range of parameters that are well beyond any perturbative treatment.     

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.     

High-order perturbation theory for light scattering from a rough metal surface.

The angular distribution of the mean diffuse intensity scattered from a metal surface with one-dimensional roughness is studied with perturbation theory. From an approach based on the reduced Rayleigh equations in p polarization, exact perturbation terms up to eighth order in the height parameter are developed for surface roughness consistent with a stationary Gaussian process. The theory is evaluated for a number of cases in which surface plasmon polariton excitation is significant and produces effects such as backscattering enhancement. For surface roughness having a wide Gaussian power spectrum, it is found that the high-order terms lead to roughness-induced broadening of the backscattering peak. For rectangular spectra, two cases are studied in which backscattering effects are due to sixth- and eighth-order terms; both cases provide good comparisons with previously unexplained experimental results. Further, because of an eighth-order term, the diffuse intensity is shown to contain a specular peak that also relies on polariton excitation. This new effect is studied in detail and is found to arise from the constructive interference of contributions produced by multiple-scattering processes, although the time-reversed paths that produce backscattering enhancement are not essential to the specular effect.     

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.     

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.