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.     

Investigation of ultrasonic wave scattering by a randomly rough solid-solid interface

An imperfect interface between two dissimilar materials is modeled by a random interface profile. A theoretical study of the interaction of ultrasonic waves with the rough solid-solid interface is presented. The reflection and transmission coefficients for longitudinal and shear coherent waves are calculated as a function of the angle of incidence within the framework of a second order perturbation theory. The effects of the statistical interface parameters, as well as the interface spectral density on the scattered fields, are investigated. These results are used to determine the roughness-induced attenuation of the coherent fields as a function of the above parameters. In addition, the relation between the incoherent part of the scattering cross-section, and interface roughness is examined.     

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.     

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.     

Separation of surface and volume effects in scattering from heterogeneous rough surfaces: derivation of a splitting rule

We give theoretical support to the splitting rule, which was recently observed numerically for the scattering from heterogeneous rough surfaces. Under certain general conditions, the incoherent intensity of a composite medium with a rough interface is the sum of the incoherent intensity of the rough homogeneous surface with an effective permittivity and the incoherent intensity of the same composite medium below a flat interface. The coherent intensity is merely that of the rough effective homogeneous surface. The effective permittivity is given accurately by the Bruggemann mixing rule, provided that the scale of fluctuations in the volume is small with respect to the electromagnetic wavelength.     

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.     

Spatial coherence of forward-scattered light in a turbid medium

We study spatially coherent forward-scattered light propagating in a turbid medium of moderate optical depth (0-9 mean free paths). Coherent detection was achieved by using a tilted heterodyne geometry, which desensitizes coherent detection of the attenuated incident light. We show that the degree of spatial coherence is significantly higher for light scattered only once in comparison with that for multiply scattered light and that it approaches a small constant value for large numbers of scattering events.     

Slope distribution of a rough surface measured by transmission scattering and polarization

Transmission scattering from medium to air was used to measure the slope distribution of the rough plane surface of a transparent glass hemisphere. A facet model successfully explained the measured results of refraction, scattering, and polarization: Transmission scattering existed for incident angles greater than the critical angle, all measured curves for the normalized scattered intensity versus the facet slope angle for different detection directions overlapped, and the measured polarization of scattering was approximately constant for >99% of the facets. The slope distribution obtained by transmission scattering agrees with those of the surface profiles in the valid range of the profiler and can represent the slope distribution of the rough surface.     

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.     

Spatial correlations between chromophores in thin films by femtosecond hyper-Rayleigh scattering

Femtosecond hyper-Rayleigh scattering has been used to probe the spatial orientational fluctuations between nonlinear optical chromophores as dopants in spincoated polymer films. The fluctuation in the second-order incoherently scattered light intensity upon translating the sample is indicative of the degree of spatial correlation between the chromophores. The decay of the autocorrelation function of this fluctuating signal is characterized by a spatial correlation length. Electric-field poling of chromophores is shown to increase this length. The temporal characteristics of this correlation length have been studied and compared with relaxation times, obtained with coherent second-harmonic generation. This correlation length decays much faster than the second-harmonic intensity. The difference in relaxation time between the incoherent and the coherent process is explained by translational diffusion of free volume over the wavelength and over the coherence length, respectively.     

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.     

Angular range for reflection of p-polarized light at the surface of an absorbing medium with reflectance below that at normal incidence.

The range of incidence angle, 0 < phi < phi(e), over which p-polarized light is reflected at interfaces between transparent and absorbing media with reflectance below that at normal incidence is determined. Contours of constant phi(e) in the complex plane of the relative dielectric constant epsilon are presented. A method for determining the real and imaginary parts of the complex refractive index, epsilon(1/2) = n + jk, which is based on measuring phi(e) and the pseudo-Brewster angle phi(pB), is viable in the domain of fractional optical constants, n, k < 1.     

The effect of phase modulation of scattered radiation on the asymptotic behavior of the contrast ratio of partially coherent speckle fields

We analyze the influence of a weak phase modulation of multiply scattered partially coherent light fields on the variance of fluctuations of the scattered field intensity. It is suggested to perform diagnostics of scattering media by analyzing the probing radiation scattered from a “modulating” medium and determining the speckle intensity index (or contrast ratio) upon introduction of an object studied into the scheme of measurements. The proposed method is experimentally verified on model scattering media.     

Scattering of a partially coherent Gaussian-Schell beam from a diffuse target in slant atmospheric turbulence

On the basis of the extended Huygens-Fresnel principle, the scattering of partially coherent Gaussian-Schell-model (GSM) beams from a diffuse target in slant double-passage atmospheric turbulence is studied and compared with that of fully coherent Gaussian beams. Using the cross-spectral density function of the GSM beams, we derive the expressions of the mutual coherence function, angle-of-arrival fluctuation, and covariance and variance of the intensity of the scattered field, taking into account the fluctuations of both the log-amplitude and phase. The numerical results are presented, and the influences of the wavelength, propagation distance, and waist radius on scattering properties are discussed. The perturbation region of the normalized intensity variance of the partially coherent GSM beam is smaller than that of the fully coherent Gaussian beam at the middle turbulence level. The normalized intensity variance of long-distance beam propagation is smaller than that of beam propagation along a short distance.     

Microwave thickness measurement of lossy layered dielectric slabs using incoherent reflectivity

Radiative transfer theory is used to calculate the incoherent effective reflectivity (_e) for a multilayer lossy dielectric medium backed by a conducting plate. The theoretical results of this formulation are compared with that of the coherent approach. Several test cases are presented to show the characteristics of _e as a function of thickness, and dielectric constant of the dielectric layers, and frequency. The results can ultimately be used in nondestructive dielectric thickness measurement.     

Enhanced backscattering from a free-standing dielectric film

It has been known theoretically for a few years that not only a rough metallic surface but also a rough dielectric surface can produce an enhanced backscattering peak. Because of difficulty in the fabrication of one- or two-dimensional rough dielectric surfaces with a high index of refraction, no experiments to date have been able to reveal such a peak in scattering from a rough dielectric surface. We present experimental results showing enhanced backscattering from a free-standing dielectric film and compare them with the results of numerical simulations of such scattering. The vacuum-dielectric interface is a one-dimensional, randomly rough surface, and the dielectric-vacuum interface is approximately planar.The results of the numerical simulations of scattering from a one-dimensional, randomly rough free-standing dielectric film are in qualitative agreement with the experimental data, and it is believed that the main mechanism responsible for the enhanced backscattering peak is the reflection from the flat dielectric-vacuum interface. The coherent addition of a given light path that interacts with the rough dielectric surface at two different points because of its partial reflection from the back surface and its time-reversed partner leads to an enhancement of the intensity of scattering in the retroreflection direction with respect to the intensity of scattering in other directions.     

Analytical approximations in multiple scattering of electromagnetic waves by aligned dielectric spheroids

In a dense medium, the failure to properly take into account multiple-scattering effects could lead to significant errors. This has been demonstrated in the past from extensive theoretical, numerical, and experimental studies of electromagnetic wave scattering by densely packed dielectric spheres. Here, electromagnetic wave scattering by densely packed dielectric spheroids with aligned orientation is studied analytically through quasicrystalline approximation (QCA) and QCA with coherent potential (QCA-CP). We assume that the spheroids are electrically small so that single-particle scattering is simple. Low-frequency QCA and QCA-CP solutions are obtained for the average Green's function and the effective permittivity tensor. For QCA-CP, the low-frequency expansion of the uniaxial dyadic Green's function is required. The real parts of the effective permittivities from QCA and QCA-CP are compared with the Maxwell-Garnett mixing formula. QCA gives results identical to those with the mixing formula, while QCA-CP gives slightly higher values. The extinction coefficients from QCA and QCA-CP are compared with results from Monte Carlo simulations. Both QCA and QCA-CP agree well with simulations, although qualitative disagreement is evident at higher fractional volumes.     

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.     

Light scattering by microscopic spheres behind a glass-air interface

Scattering of light from single spheres placed behind a glass-air interface with light incident through the glass is examined. This scattering is investigated for both p- and s-polarized light incident at angles below the glass-air critical angle. The intensity of light scattered into the air half-space from each sphere is measured as a function of scattering angle, and this response is compared in situ with the background scatter produced by the planar substrate. A detailed comparison between data and established theory are thereby obtained. This system is of interest in the field of optical biosensing.     

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.