Multiple scattering of electromagnetic waves by an aggregate of uniaxial anisotropic spheres

An exact analytical solution is obtained for the scattering of electromagnetic waves from a plane wave with arbitrary directions of propagation and polarization by an aggregate of interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes. The expansion coefficients of a plane wave with arbitrary directions of propagation and polarization, for both TM and TE modes, are derived in terms of spherical vector wave functions. The effects of the incident angle α and the polarization angle β on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres are numerically analyzed in detail. The characteristics of the forward and backward RCSs in relation to the incident wavelength are also numerically studied. Selected results on the forward and backward RCSs of several types of square arrays of SiO? spheres illuminated by a plane wave with different incident angles are described. The accuracy of the expansion coefficients of the incident fields is verified by comparing them with the results obtained from references when the plane wave is degenerated to a z-propagating and x- or y-polarized plane wave. The validity of the theory is also confirmed by comparing the numerical results with those provided by a CST simulation.     

Effects of fiber ellipticity and orientation on dynamic stress concentrations in porous fiber-reinforced composites

Interaction of time harmonic fast longitudinal and shear incident plane waves with an elliptical fiber embedded in a porous elastic matrix is studied. The novel features of Biot dynamic theory of poroelasticity along with the classical method of eigen-function expansion and the pertinent boundary conditions are employed to develop a closed form series solution involving Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the non-orthogonality of angular Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with appearance of additional angular dependent terms in the boundary conditions are all avoided by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. A MATHEMATICA code is developed for computing the Mathieu functions in terms of complex Fourier coefficients which are themselves calculated by numerically solving appropriate sets of eigen-systems. The analytical results are illustrated with numerical examples in which an elastic fiber of elliptic cross section is insonified by a plane fast compressional or shear wave at normal incidence. The effects of fiber cross sectional ellipticity, angle of incidence (fiber two-dimensional orientation), and incident wave polarization (P, SV, SH) on dynamic stress concentrations are studied in a relatively wide frequency range. Limiting cases are considered and fair agreements with well-known solutions are established.     

Polarization effects on scatterer sizing accuracy analyzed with frequency-domain angle-resolved low-coherence interferometry

Angle-resolved low-coherence interferometry (a/LCI) enables us to make depth-resolved measurements of scattered light that can be used to recover subsurface structural information such as the size of cell nuclei. Endoscopic frequency-domain a/LCI (fa/LCI) acquires data by using a novel fiber probe in a fraction of a second, making it a clinically practical system. However, birefringent effects in fiber-based systems can alter the polarization state of the incident light and potentially skew the collected data. We analyze the effect the polarization state of the incident light has on scattering data collected from polystyrene microsphere tissue phantoms and in vitro cell samples and examine the subsequent accuracy of the determined sizes. It is shown that the endoscopic fa/LCI system accurately determines the size of polystyrene microspheres without the need to control the polarization of the incident beam, but that epithelial cell nuclear sizes are accurately determined only when the polarization state of the incident light is well characterized.     

Mechanism and symmetry properties of depolarization in weak scattering of light

The mechanism and some symmetry properties of depolarization upon weak scattering of light from a class of random media were studied theoretically. Departing from the angular distribution of the degree of polarization, our derivations showed the mechanism that induces the change of polarization can be split into two parts of different nature. One is the vectorial effect that redistributes the original light components, and the other is the interaction effect of the medium that modulates the correlation properties of the incident field. We also showed that there is dependence of the angular distribution on the incident polarization state; i.e., the angular pattern and its symmetry depend on both the orientation and ellipticity of the incident polarization. Random light was analyzed in the space-frequency domain.     

Polarization conversion by reflection in a thin-film grating.

A dielectric-film waveguide with a grating etched on its film-cover interface can be used as a polarization converter. The e wave can be converted into the h wave and vice versa if the guided wave is incident obliquely to the grating vector. The polarization converter is analyzed by use of a quasi-optic technique. A high degree of polarization-conversion efficiency is achieved by a suitable choice of the grating length. The Bragg angles of incidence and observation, the maximum polarization-conversion efficiency, and the frequency and the angular selectivity are all found to increase with an increase in the grating period. An illustrative numerical example is presented.     

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence

On the basis of our previous work on the extension of the geometrical-optics approximation to Gaussian beam scattering by a spherical particle, we present a further extension of the method to the scattering of a transparent or absorbing spheroidal particle with the same symmetric axis as the incident beam. As was done for the spherical particle, the phase shifts of the emerging rays due to focal lines, optical path, and total reflection are carefully considered. The angular position of the geometric rainbow of primary order is theoretically predicted. Compared with our results, the M?bius prediction of the rainbow angle has a discrepancy of less than 0.5 degrees for a spheroidal droplet of aspect radio kappa within 0.95 and 1.05 and less than 2 degrees for kappa within 0.89 and 1.11. The flux ratio index F, which qualitatively indicates the effect of a surface wave, is also studied and found to be dependent on the size, refractive index, and surface curvature of the particle.     

Retrieval of the scattering and microphysical properties of aerosols from ground-based optical measurements including polarization. I. Method

A method has been developed for retrieving the scattering and microphysical properties of atmospheric aerosol from measurements of solar transmission, aureole, and angular distribution of the scattered and polarized sky light in the solar principal plane. Numerical simulations of measurements have been used to investigate the feasibility of the method and to test the algorithm's performance. It is shown that the absorption and scattering properties of an aerosol, i.e., the single-scattering albedo, the phase function, and the polarization for single scattering of incident unpolarized light, can be obtained by use of radiative transfer calculations to correct the values of scattered radiance and polarized radiance for multiple scattering, Rayleigh scattering, and the influence of ground. The method requires only measurement of the aerosol's optical thickness and an estimate of the ground's reflectance and does not need any specific assumption about properties of the aerosol. The accuracy of the retrieved phase function and polarization of the aerosols is examined at near-infrared wavelengths (e.g., 0.870 mum). The aerosol's microphysical properties (size distribution and complex refractive index) are derived in a second step. The real part of the refractive index is a strong function of the polarization, whereas the imaginary part is strongly dependent on the sky's radiance and the retrieved single-scattering albedo. It is demonstrated that inclusion of polarization data yields the real part of the refractive index.     

Analysis of ultrasonic wave scattering for characterization of defects in solids: I. Spherical inclusions and reciprocity

This paper, as part of a series on elastic wave scattering, presents results of measurements and calculations on scattering of ultrasonic waves by a solid spherical inclusion (tungsten carbide) embedded in titanium alloy by the diffusion bonding process. Both direct scattering and mode-converted scattering angular distributions are reported for shear and compressional incident waves. The consequences upon the signals when transmitter and receiver were interchanged are explored in a reciprocity rule.     

Rigorous model of the scattering of a focused spot by a grating and its application in optical recording

We describe a rigorous model for the scattering of a three-dimensional focused spot by a one-dimensional periodic grating. The incident field is decomposed into a sum of quasi-periodic fields, and the scattering of each of these is computed inside one unit cell of the grating. The model is applied to the simulation of the readout of a DVD disk. The polarization dependence of the reflected near and far fields is studied, and, for a TM-polarized incident spot, plasmons are observed in the reflected far-field intensity.     

Effect of laser-radiation polarization on the nonlinear scattering of light in nanodiamond suspensions

The effect of laser radiation polarization on the nonlinear scattering of light in aqueous suspensions of detonation nanodiamonds (DNDs) in a regime of optical power limiting (OPL) has been studied. It is established that the nonlinear transmission coefficient of DND suspension in the OPL regime in a field of nanosecond laser pulses with a wavelength of 532 nm is independent of the polarization of incident radiation. The nonlinear scattering of light observed at an angle of 90° in the plane perpendicular to the plane of polarization of the incident radiation depends on the polarization angle in accordance with a trigonometric law. It is shown that the ratio of the signals of scattered radiation for the vertical and horizontal polarizations exhibits nonmonotonic dependence on the laser-beam power density. The results are explained by the Rayleigh-Mie scattering and a change in the size of scattering centers as a result of the effect of a laser upon the DND suspension.     

Scattering-induced changes in the degree of polarization of a stochastic electromagnetic plane-wave pulse

The scattering of a stochastic electromagnetic plane-wave pulse on a deterministic spherical medium is investigated. An analytical formula for the degree of polarization (DOP) of the scattered field in the far zone is derived. Letting pulse duration T(0) → ∞, our formula can be applied to study the scattering of a stationary stochastic electromagnetic light wave. Numerical results show that the DOP of the far zone field is closely determined by the size of the spherical medium when the incident field is a stochastic electromagnetic plane-wave pulse. This is much different from the case when the incident field is a stationary stochastic electromagnetic light wave, where the DOP of the far zone field is independent of the size of the medium. One may obtain the information of the spherical medium by measuring the scattering-induced changes in the DOP of a stochastic electromagnetic plane-wave pulse.     

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.     

Angular-scattering characteristics of ferroelectric liquid-crystal electro-optical devices operating in the transient-scattering and the extended-scattering modes

The angular distribution of forward-scattered light in transient-scattering-mode (TSM) and extended-scattering-mode (ESM) ferroelectric liquid-crystal (FLC) devices was evaluated by use of circularly polarized incident light. For both modes the intensity and the distribution of forward-scattered light depended primarily on the FLC birefringence, spontaneous polarization, and the cell path length. In the FLC materials examined, the forward-scattering intensity under ESM drive conditions increased with longer FLC pitch lengths, whereas under TSM conditions stronger forward scattering was observed with increasing FLC spontaneous polarization. Although both TSM and ESM drive conditions displayed a similar angular distribution for forward-scattered light, the intensity of ESM scattering over a 0 degrees -6 degrees range was considerably smaller than that observed in earlier experiments with linearly polarized incident light.     

The disturbance of a plane dyadic wave by a small spherical cavity

Dyadic scattering offers a general setting for solving wave-obstacle interaction problems in Continuum Mechanics, because it eliminates the direction of polarization from the scattering formulation. Once the dyadic problem has been solved, any classical scattering problem for the displacement field is recoverable through a contraction with the given polarization. In the present work we solve the scattering problem of a plane dyadic incident field which is disturbed by a spherical cavity in the medium of propagation. The cavity is considered to be small in the sense that its characteristic dimension is much less than the wave length of the incident field. The zeroth and the first order low-frequency approximations of the near field as well as the leading approximation of the far-field (which is of the third order) are obtained explicitly via an appropriate generalization of the Papkovich representation for dyadic fields. The leading approximation of the scattering cross-section is also provided. The results are then used to check the credibility of related vector results obtained from the Boundary Element Method and an amazing coincidence is observed, at least for small enough frequencies.     

Localizable imaging study for the noninvasive diagnosis of lesions with the backscattering polarized light

The asymmetry appearing in the degree of polarization (DOP) distribution of the backscattering polarized light from tissues is investigated by using polarized Monte Carlo simulation. When the incident point is close to the boundary of the lesion inside the tissue, high asymmetry emerges regardless of the polarized direction of the incident light. A noninvasive method based upon the DOP asymmetry of the backscattering light is proposed to locate lesions hidden in live tissues by scanning a point light source. Imaging of the front projection on complicated lesion structures is demonstrated with this method. Its transverse resolution, which is affected by the wavelength of incident light and the size of the scattering particle, can reach the diameter of the lesion scattering particle theoretically while the best longitudinal detection depth can be achieved by choosing a suitable incident wavelength according to the scattering characters of the tissue.     

Geometrical-optics approximation of forward scattering by gradient-index spheres

By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.     

Angular spectrum method and ray algorithm for the acoustic field of a focusing transducer in an anisotropic solid

The angular spectrum method is applied to calculating the acoustic field of a liquid-coupled focusing transducer in an anisotropic slab-shaped solid with surfaces normal to the axis of the transducer. The stationary phase approximation (SPA) is used to determine the dominant contributions to this field and calculate the echo signals produced by waves that have been reflected off the rear surface of the solid. The dominant features of this field and of the echoes are reproduced well by a hybrid ray method devised to simulate the finite point-spread function of the lens. Both approaches in the paraxial approximation yield a split focus for each wave polarization branch for a general direction of the surface normal. Echo arrival times and amplitudes calculated by the two methods are in good agreement. The hybrid ray method is shown to be particularly suited to handling multiple stationary phase points within the angular spectrum of the incident field and stationary phase points not associated with the normally incident ray, and should be useful for dealing with scattering from cracks and other defects. Pulse echo calculations for different crystallographic directions in a nickel-based superalloy are shown to be in good agreement with measurements carried out on single crystal specimens of the alloy     

Confocal fluorescence polarization microscopy in turbid media: effects of scattering-induced depolarization

We present an experimental and theoretical study of confocal fluorescence polarization microscopy in turbid media. We have performed an experimental study using a fluorophore-embedded polymer rod immersed in aqueous suspensions of 0.1 and 0.5 microm diameter polystyrene microspheres. A Monte Carlo approach to simulate confocal fluorescence polarization imaging in scattering media is also presented. It incorporates a detailed model of polarized fluorescence generation that includes sampling of elliptical polarization, excited-state molecular rotational Brownian motion, and dipole fluorescence emission. Using both approaches, we determine the effects of the number of scattering events, target depth, photon scattering statistics, objective numerical aperture, and pinhole size on confocal anisotropy imaging. From this detailed analysis and comparison of experiment with simulation, we determine that fluorescence polarization is maintained to depths at which meaningful intensity images can be acquired.     

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.     

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.