Polarization properties of light multiply scattered by non-spherical Rayleigh particles

Multiple scattering of incoherent polarized light propagating through a random medium comprised of spheroidal Rayleigh particles is studied using Monte Carlo simulations. Two approaches are taken for the implementation of the simulation: the first uses individual realizations of particle orientation and the second, an accelerated method, averages over the particle orientation. These different methods produce results that are indistinguishable within statistical errors. The depolarization of light is examined in both transmission and backscatter for media comprised of spheroids of different polarizability ratios. In media containing spheroidal particles the depolarization is greater than that for spherical particles. Media containing prolate spheroids are more depolarizing than media comprising oblate particles of the same polarizability ratio. The extra depolarization due to asphericity is much less pronounced in the multiple scattering regime than for single scattering.     

On scattering of light by small axially symmetric particles

Light scattering by small dielectric particles of an arbitrary axially symmetric shape is analyzed. A simple approximate expression that governs the polarizability of the particle is found under the assumption of field homogeneity inside of these particles. The expression includes four relatively simple one-dimensional integrals that can be calculated analytically for some types of particles (except for spheroids). A comparison with the numerical data obtained for various Chebyshev particles and finite cylinders showed that the obtained approximation yields acceptable results, even when the shape of scatterers is significantly different from spheroidal. For spheroids, our approximation coincides with the Rayleigh one.     

On the applicability of a spherical basis for spheroidal layered scatterers

The applicability of an analog of the extended boundary condition method, which is popular in light-scattering theory, is studied in combination with the standard spherical basis for the solution of an electrostatic problem appearing for spheroidal layered scatterers the sizes of which are small as compared to the incident radiation wavelength. In the case of two or more layers, polarizability and other optical characteristics of particles in the far zone are shown to be undeterminable if the condition under which the appearing systems of linear equations for expansion coefficients of unknown fields are Fredholm systems solvable by the reduction method is broken. For two-layer spheroids with confocal boundaries, this condition is transformed into a simple restriction on the ratio of particle semiaxes a/b< $\sqrt 2 $ + 1. In the case of homogeneous particles, the solvability condition is that the radius of convergence of the internal-field expansion must exceed that of the expansion of an analog of the scattering field. Since homogeneous spheroids (ellipsoids) are unique particles inside which the electrostatic field is homogeneous, it is shown that the solution can be always found in this case. The obtained results make it possible to match in principle the results of theoretical and numerical determinations of the domain of applicability for the extended boundary condition method with a spherical basis for spheroidal scatterers.     

Light Scattering by Small Multilayer Particles: A Generalized Separation of Variables Method

A Rayleigh approximation is constructed for light scattering by small multilayer axisymmetric particles, in which their polarizability is determined by the generalized separation of variables method (SVM). In this method, scalar potentials, the gradients of which yield the electric-field strengths, are represented as expansions in spherical harmonics of the Laplace equation. Unknown coefficients of expansions are determined from the boundary conditions, which are reduced to infinite systems of linear algebraic equations (ISLAEs), since the separation of variables is incomplete. The T matrix of the electrostatic problem, principal element T₁₁ of which is proportional to the particle polarizability, is determined. The necessary condition for the ISLAEs solvability for the SVM coincides with the condition of the correct application of the extended boundary conditions method (EBCM). However, numerical calculations in which finite-dimensional (i.e., reduced) systems are solved, yield different results in ranges of variation of parameters that are close to the boundary of the range of applicability. An analysis of the numerical calculations of the scattering and absorption cross sections for two-layer confocal spheroids, an exact solution for which can be obtained using spheroidal harmonics, shows that the SVM is preferable to the EBCM. It turned out that the proposed method yields workable results in a wider range of variation of parameters. Even outside the range of applicability, in which it should be regarded as a certain approximate solution, its use in a number of cases is quite acceptable. Additional calculations for three-layer nonconfocal spheroids, as well as for three-layer similar pseudospheroids and Pascal’s snails, which can be obtained from spheroids as a result of the inversion with respect to the coordinate origin and one of the foci, respectively, confirm these inferences. We note that, for certain values of the parameters, the shapes of the latter particles are nonconvex.     

Spheroidal particle plasmons in amplifying media

The effect of a surrounding gain medium on the localized surface plasmon resonance in spheroidal metal particles is analyzed in the quasi-static limit of the Maxwell equations. It is shown that the gain required to create a singularity in the dynamic polarizability of the particle is significantly lower for non-spherical spheroids than for spheres, and can be as low as several hundred inverse centimeters for noble metals in the near infrared region of the spectrum. Resonant aspect ratios and gain values are calculated as a function of frequency for various metals. The use of non-spherically shaped nano-particles, along with gains achievable in semiconductors and dyes, can result in surface enhanced Raman scattering (SERS) signals which are dramatically enhanced. PACS 61.46.Df; 73.21.Hb; 78.67.Hc     

Imaging and multiple scattering through media containing optically active particles

Abstract

This paper examines the behaviour of polarized light scattered by a medium containing small chiral spheroidal particles. We show that for single scattering the observed phenomena of optical activity may be interpreted in terms of an averaged Mueller matrix and describe how the degree of polarization is affected by such a medium. The polarization properties of multiply scattered light by chiral particles are considered through the use of Monte Carlo simulations. It is shown that the effects of chirality under multiple scattering can be interpreted as an order-preserving influence in a disordered system and that this influence can, in principle, be exploited for the purposes of imaging.     

Constraints on PSC particle microphysics derived from lidar observations

Based on extensive T-matrix computations of light scattering by polydispersions of randomly oriented, rotationally symmetric nonspherical particles, we analyze existing lidar observations of polar stratospheric clouds (PSCs) and derive several constraints on PSC particle microphysical properties. We show that sharp-edged nonspherical particles (finite circular cylinders) exhibit less variability of lidar backscattering characteristics with particle size and aspect ratio than particles with smooth surfaces (spheroids). For PSC particles significantly smaller than the wavelength, the backscatter color index and the depolarization color index β are essentially shape independent. Observations for type Ia PSCs can be reproduced by spheroids with aspect ratios larger than 1.2, oblate cylinders with diameter-to-length ratios greater than 1.6, and prolate cylinders with length-to-diameter ratios greater than 1.4. The effective equal-volume-sphere radius for type Ia PSCs is about 0.8 μm or larger. Type Ib PSCs are likely to be composed of spheres or nearly spherical particles with effective radii smaller than 0.8 μm. Observations for type II PSCs are consistent with large ice crystals (effective radius greater than 1 μm) modeled as cylinders or prolate spheroids.     

An Ellipsoidal Model for Small Multilayer Particles

This paper presents an ellipsoidal model that is constructed for small layered nonspherical particles and methods for constructing “effective” multilayer ellipsoids, the light-scattering properties of which would be close to the corresponding properties of original particles. In the case of axisymmetric particles, prolate or oblate spheroids (ellipsoids of revolution) are implied. Numerical calculations of the polarizability and scattering cross sections of small layered nonspherical particles, including nonconfocal (similar) spheroids, Chebyshev particles, and pseudospheroids, are performed by different approximate and rigorous methods. Approximate approaches involve the use of an ellipsoidal model, in which the polarizability of a layered particle is determined in two ways. In the first case, the polarizability is calculated in the approximation of confocal spheroids, while, in the second case, it is sought as a linear combination of the polarizabilities of embedded spheroids proportionally to the volumes of layers. Among rigorous methods, the extended boundary conditions method and the generalized separation of variables method are applied. On the basis of a comparison of the results obtained with rigorous and approximate approaches, their drawbacks and advantages are discussed.     

Polarization of light backscattered by small particles

We study scattering of light by wavelength-scale spherical, cubic, and spheroidal particles as well as clusters of spherical particles for equal-volume-sphere size parameters 4≤x≤10 and refractive indices 1.1≤m≤2.0. Such particles exhibit three specific features in the regime of backscattering: first, the intensity shows a backscattering peak; second, the degree of linear polarization for unpolarized incident light is negative; and, third, the depolarization ratio is double-lobed. We find that the overall characteristics of the scattering-matrix elements can be explained by an internal field composed of waves propagating in opposite directions near the particle perimeter and forming standing waves, as well as a wave propagating forward with the wavelength of the internal medium. When moving from the central axis of the particle toward its perimeter, the internal field changes from a forward-propagating wave with a wavelength dictated by the particle refractive index toward a standing wave with an apparent wavelength of the surrounding medium. The mapping of the internal field to the scattered far field is like an interference dial where rotation of the dial by a quarter of a wavelength on the particle perimeter results in a change from a destructive to constructive interference feature in the angular patterns (or vice versa). The dial is a manifestation of a well-known rule of thumb: the number of maxima or minima in the scattering-matrix elements is given by the size parameter. We explain the backscattering peak as deriving from the backward-propagating internal wave near the particle perimeter. Negative polarization follows from the spatial asymmetry of the internal fields: inside the particle, the fields are amplified near the central plane perpendicular to the polarization state of incident light, resulting in more pronounced interference effects for the perpendicular polarization than for the parallel polarization. The double-lobe feature in the depolarization results from the same internal-field structure with leading cross-polarized fields located slightly different from the copolarized fields. We discuss practical implications of these findings for the retrieval of particle sizes, shapes, and refractive indices from observations and laboratory experiments.     

Extended boundary condition method in combination with field expansions in terms of spheroidal functions

The problem of light scattering by nonspherical particles, which arises in many applications, is nowadays most frequently solved by the method of extended boundary conditions in combination with the expansion of the fields in terms of spherical wave functions. However, such an approach encounters difficulties if the shape of particles is far from spherically symmetric, even in the simplest case of spheroids with the semiaxis ratio a/b > 5?10. A new approach to solving this problem is proposed, which also applies the extended boundary condition method but involves the expansion of the fields in terms of spheroidal functions. In this case, to obtain effective solutions for strongly prolate and oblate particles, the fields are divided in two parts with known properties and specific scalar potentials are used for each part. The basic relations of the approach are presented and some results of calculations of the optical properties of spheroids and spheroidal Chebyshev particles that are performed using computer codes realizing this approach are given. The convergence of the results for different cases and the domain of applicability of the method are discussed.     

On the interrelation of the characteristic scales of depolarization and decorrelation of optical fields under multiple-scattering conditions

The interrelation of depolarization and decorrelation of optical fields in multiply scattering Brownian media is studied on the basis of the notion of the probability density of optical path lengths of the partial components of the scattered field under multiple-scattering conditions. To describe such media a universal parameter that is independent of the density (concentration) of scattering particles is introduced — the characteristic correlation time. Experimental results obtained with aqueous suspensions of polystyrene beads as model media are presented which demonstrate the constancy of this parameter at different concentrations of scattering particles. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 455–460 (10 April 1998)     

Impact of particle shape on refractive-index dependence of scattering in resonance domain

The impact of particle shape on how scattering, in particular the asymmetry parameter g, depends on the refractive index m is studied. Light scattering simulations for spheres and 16 different spheroids with varying refractive indices and sizes are carried out using an exact T-matrix method to establish how m affects scattering for different shapes. In addition to single shapes, shape distributions of spheroids are used to mimic scattering properties of ensembles of irregularly shaped particles. The results show that Δg resulting from Δm are both size and shape dependent, and spheroids are not universally less or more sensitive to m than the corresponding spheres are. While shape distributions of spheroids show much weaker and much more consistent m-dependence of g than the spheres of the same size, an integration over a size distribution (SD) largely eliminates these differences. Thus, the use of spheres for estimating Δg resulting from Δm for a collection of nonspherical particles appears to be safe except for very narrow SDs. The actual g-values tend to be, however, considerably and consistently in error.     

Theory of scanning near-field magnetooptical microscopy

An analytical theory of scanning near-field magnetooptical microscopy is developed. The theory is based on the elastic scattering of light by small, resonantly polarizable particles, which are used to scan the plane surface of a nonuniformly magnetized medium. The effective polarizability of the particles is calculated with the effect of dynamic “image forces” taken into account in all orders of perturbation theory with respect to the interaction of the particle with a demagnetized ferromagnet, and the magnetooptical perturbation is calculated to first order in the magnetization. The major contributions to the magnetooptical light scattering for a ferromagnetic structure magnetized perpendicular to the surface are found, including a quasistatic approximation for the near-field particle-magnet interaction. The optical size resolution of a magnetic (dielectric) inhomogeneity is estimated. Zh. Tekh. Fiz. 68, 86–91 (July 1998)     

Electrooptical properties of aqueous suspensions of nickel hydrosilicate nanotubes

We present the results of our investigations of electrooptical effects that occur as a result of light scattering by an aqueous polydisperse system the disperse phase of which consists of nickel hydrosilicate nanotubes with a chrysotile structure. Multilayer nanotubes were synthesized by the hydrothermal method and had the composition Ni₃Si₂O₅. The dimensions of nanotubes were as follows: the length was 0.1–1 μm or more, the outer diameter was 10–15 nm, and the inner diameter was 3 nm. We have studied relative changes in the intensities of light transmitted and scattered by the suspension that were caused by the orientation of nanotubes in an external electric field. Experiments have been performed at different directions of the linear polarization of the incident and scattered light, different scattering angles, and different degrees of orientation of nanotubes along the field. These measurements allowed us to determine the magnitude of electrooptical effects, such as the conservative dichroism, the light scattering, and the influence of the orientation of nanotubes in the field on the intensity and degree of depolarization of light scattered by them. Curves of free relaxation of electrooptical effects and their field dependences allowed us to determine the distributions of nanotubes and their aggregates in the colloid over lengths and polarizability anisotropy values. The dependences of the degree of depolarization of the scattered radiation on the scattering angle and the relaxation dependences of electrooptical effects allowed us to characterize the aggregation stability of nanotubes in water.     

Axisymmetric scattering of scalar waves by spheroids

A phase shift formulation of scattering by oblate and prolate spheroids is presented, in parallel with the partial-wave theory of scattering by spherical obstacles. The crucial step is application of a finite Legendre transform to the Helmholtz equation in spheroidal coordinates. In the long-wavelength limit the spheroidal analog of the spherical scattering length immediately gives the cross section. Analytical results are readily obtained for scattering of Schro?dinger particle waves by impenetrable spheroids, and for scattering of sound waves by acoustically soft spheroidal objects. The method is restricted to scattering by spheroids whose symmetry axis is coincident with the direction of the incident plane wave.     

A theoretical study of hot plasma spheroids in the presence of low-frequency electromagnetic waves

While taking into account thermal motion of electrons, scattering of electromagnetic waves with low frequency from hot plasma spheroids is investigated. In this theoretical research, ions are heavy to respond to electromagnetic fluctuations. The solution of scalar wave equation in spheroidal coordinates for electric potential inside the plasma spheroids are obtained. The variations of resonance frequencies vs. Debye length are studied and consistency between the obtained results in this paper and the results for the well-known plasma objects such as plasma column and spherical plasma have been proved.     

Effect of electric field on light scattering by aqueous colloids of diamond and graphite

We present the results of our experimental investigation of light scattering by polydisperse colloids of diamond and graphite. The scattering is studied at a random orientation of particles and in an external radiofrequency electric field, which orients particles along the strength. The average dimensions of particles in both colloids are close to each other and comparable with the wavelength of the incident light. The shape of particles and the optical and electrooptical properties of diamond and graphite colloids are significantly different. We analyze the polarization components of scattered light energy when the light incident on the colloids is linearly polarized. We show that the quadrupole light scattering by isotropic diamond particles has the main effect on angular dependences of depolarization of scattered light. For light scattering by anisotropic graphite particles, the depolarization of scattered light is mainly determined by a particular feature of the dipole scattering of particles. It is shown that, in both colloids, the orientational order of particles considerably reduces the depolarization of light scattered by particles. We show that relative changes in the intensity and depolarization of scattered light, which depend on the scattering angle and polarization direction of light, as well as on the parameters of particles, can be used as a measure of electrooptical effects observed in colloids.     

Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?

We address the question if and how observations of scattered intensity and polarisation can be employed for retrieving particle shape information beyond a simple classification into spherical and nonspherical particles. To this end, we perform several numerical experiments, in which we attempt to retrieve shape information of complex particles with a simple nonspherical particle model based on homogeneous spheroids. The discrete dipole approximation is used to compute reference phase matrices for a cube, a Gaussian random sphere, and a porous oblate and prolate spheroid as a function of size parameter. Phase matrices for the model particles, homogeneous spheroids, are computed with the T-matrix method. By assuming that the refractive index and the size distribution is known, an optimal shape distribution of model particles is sought that best matches the reference phase matrix. Both the goodness of fit and the optimal shape distribution are analysed. It is found that the phase matrices of cubes and Gaussian random spheres are well reproduced by the spheroidal particle model, while the porous spheroids prove to be challenging. The “retrieved” shape distributions, however, do not correlate well with the shape of the target particle even when the phase matrix is closely reproduced. Rather, they tend to exaggerate the aspect ratio and always include multiple spheroids. A most likely explanation why spheroids succeed in mimicking phase matrices of more irregularly shaped particles, even if their shape distributions display little similarity to those of the target particles, is that by varying the spheroids’ aspect ratio one covers a large range of different phase matrices. This often makes it possible to find a shape distribution of spheroids that matches the phase matrix of more complex particles.     

Propagation of circularly polarized light in media with large-scale inhomogeneities

Small-angle multiple scattering of circularly polarized waves in disordered systems composed of large (larger than the light wavelength) spherical particles is discussed. The equation for Stokes’s fourth parameter V — the difference between the intensities of the left-and right-hand polarized light — is shown to have the form similar to that of the scalar transport equation for intensity I, the only difference being the presence of an additional “non-small-angle” term responsible for depolarization. In the case of small-angle scattering, depolarizing collisions are relatively rare and, in contrast to the scalar case, the problem contains an additional spatial scale, namely the depolarization depth. The polarization degree and helicity of the scattered light are calculated for the case of purely elastic scattering and in the presence of absorption in the medium. For strong absorption, depolarization is shown to follow the transition to the asymptotic regime of wave propagation. The features appearing in strong (non-Born) single scattering are also discussed. Zh. éksp. Teor. Fiz. 115, 769–790 (March 1999)