Light scattering by an infinite circular cylinder immersed in an absorbing medium

Analytic solutions are developed for the single-scattering properties of an infinite dielectric cylinder embedded in an absorbing medium with normal incidence, which include extinction, scattering and absorption efficiencies, the scattering phase function, and the asymmetry factor. The extinction and scattering efficiencies are derived by the near-field solutions at the surface of the particle. The normalized scattering phase function is obtained by use of the far-field approximation. Computational results show that, although the absorbing medium significantly reduces the scattering efficiency, it has little effect on absorption efficiency. The absorbing medium can significantly change the conventional phase function. The absorbing medium also strongly affects the polarization of the scattered light. However, for large absorbing particles the degrees of polarization change little with the medium's absorption. This implies that, if the transmitting lights are strongly weakened inside the particle, the scattered polarized lights can be used to identify objects even when the absorption property of the host medium is unknown, which is important for both active and passive remote sensing.     

Finite-difference time-domain solution of light scattering and absorption by particles in an absorbing medium

The three-dimensional (3-D) finite-difference time-domain (FDTD) technique has been extended to simulate light scattering and absorption by nonspherical particles embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. When computing the single-scattering properties of a particle in an absorbing dielectric medium, we derive the single-scattering properties including scattering phase functions, extinction, and absorption efficiencies using a volume integration of the internal field. A Mie solution for light scattering and absorption by spherical particles in an absorbing medium is used to examine the accuracy of the 3-D UPML FDTD code. It is found that the errors in the extinction and absorption efficiencies from the 3-D UPML FDTD are less than approximately 2%. The errors in the scattering phase functions are typically less than approximately 5%. The errors in the asymmetry factors are less than approximately 0.1%. For light scattering by particles in free space, the accuracy of the 3-D UPML FDTD scheme is similar to a previous model [Appl. Opt. 38, 3141 (1999)].     

Light scattering by a coated infinite cylinder in an absorbing medium

The scattering formulation for a coated infinite cylinder in an absorbing medium is presented in this paper. The cylinder is subjected to an arbitrarily polarized plane wave propagating in a general direction at the cylinder. The refractive index and magnetic permeability of the host medium, as well as those for the core and coating of the cylinder, can be real or complex. The scattering and extinction efficiencies and the scattering amplitudes are derived for both the near field and the far field. As the medium is absorbing, the "true" extinction and scattering efficiencies are derived based on the radiative energy outflow at the surface of the cylinder. The radiative efficiencies in the far field are denoted as "apparent" properties because they include absorption by the intervening medium. The influence of the refractive index and permeability of the host medium on the scattering properties of a coated cylinder is illustrated by numerical examples.     

Finite-difference time-domain solution of light scattering by an infinite dielectric column immersed in an absorbing medium

The two-dimensional (2-D) finite-difference time-domain (FDTD) method is applied to calculate light scattering and absorption by an arbitrarily shaped infinite column embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. The single-scattering properties of the infinite column embedded in the absorbing medium, including scattering phase functions and extinction and absorption efficiencies, are derived by use of an area integration of the internal field. An exact solution for light scattering and absorption by a circular cylinder in an absorbing medium is used to examine the accuracy of the 2-D UPML FDTD code. With use of a cell size of 1/120 incident wavelength in the FDTD calculations, the errors in the extinction and absorption efficiencies and asymmetry factors from the 2-D UPML FDTD are generally smaller than approximately 0.1%. The errors in the scattering phase functions are typically smaller than approximately 4%. With the 2-D UPML FDTD technique, light scattering and absorption by long noncircular columns embedded in absorbing media can be accurately solved.     

Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles

Exact mathematical expressions for the intrinsic electromagnetic (EM) cross–sections (i.e. extinction, scattering and absorption) for a pair of perfectly conducting circular cylinders in a homogeneous non–absorptive medium are derived. The multipole expansion method in cylindrical coordinates and the translational addition theorem, applicable to any range of frequencies or particle sizes are used. An effective EM field, incident on the probed cylinder is defined first, which includes the initial and re-scattered field from the second cylinder. It is used jointly with the scattered field to derive the mathematical expressions for the intrinsic/local cross–sections. Numerical computations for the intrinsic extinction (or scattering) energy efficiencies per unit-length for a pair of conducting circular cylinders with different radii in a homogeneous medium are considered. The results computed a priori can be useful in the full characterization of a multiple scattering system of many particles, in conjunction with experimental data for the extrinsic cross–sections.     

Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium

The conventional Lorenz-Mie formalism is extended to the case for a coated sphere embedded in an absorbing medium. The apparent and inherent scattering cross sections of a particle, derived from the far field and near field, respectively, are different if the host medium is absorptive. The effect of absorption within the host medium on the phase-matrix elements associated with polarization depends on the dielectric properties of the scattering particle. For the specific cases of a soot particle coated with a water layer and an ice sphere containing an air bubble, the phase-matrix elements -P12/P11 and P33/P11 are unique if the shell is thin. The radiative transfer equation for a multidisperse particle system embedded within an absorbing medium is discussed. Conventional multiple-scattering computational algorithms can be applied if scaled apparent single-scattering properties are applied.     

Light scattering by a random distribution of particles embedded in absorbing media: diagrammatic expansion of the extinction coefficient

We address the problem of the modeling of the extinction coefficient into an absorbing medium, including a random distribution of identical scatterers of arbitrary size. We show that the extinction coefficient, including losses in the host medium, can be derived from a diagrammatic expansion arising from the rigorous multiple-scattering theory of electromagnetic waves in random media. While in previous approaches the contribution to the extinction coefficient due to the absorption in the host medium and due to the absorption and scattering by the particles were evaluated separately and heuristically, our approach is based on a derivation from first principles.     

Modeling radiation characteristics of semitransparent media containing bubbles or particles

Modeling of radiation characteristics of semitransparent media containing particles or bubbles in the independent scattering limit is examined. The existing radiative properties models of a single particle in an absorbing medium using the approaches based on (1) the classical Mie theory neglecting absorption by the matrix, (2) the far field approximation, and (3) the near field approximation are reviewed. Comparison between models and experimental measurements are carried out not only for the radiation characteristics but also for hemispherical transmittance and reflectance of porous fused quartz. Large differences are found among the three models predicting the bubble radiative properties when the matrix is strongly absorbing and/or the bubbles are optically large. However, these disagreements are masked by the matrix absorption during calculation of radiation characteristics of the participating medium. It is shown that all three approaches can be used for radiative transfer calculations in an absorbing matrix containing bubbles.     

Mie-scattering formalism for spherical particles embedded in an absorbing medium

Most of the Mie-scattering calculations have been done for a particle embedded in a nonabsorbing host medium. Generalization to an absorbing host medium can be achieved (a) by modifying the calculation of the spherical Bessel functions to account for a complex argument and (b) by accounting properly for the net rate of incident, scattered, and absorbed energy. We present an extended formalism of Mie scattering for the case of an absorbing host medium. Numerical calculations show that for a large spherical particle embedded in an absorbing host medium the extinction efficiency approaches 1 compared with 2 for a nonabsorbing host medium. We conjecture that this difference is due to the suppression of diffraction when the radius of the sphere is large.     

Efficiency factors and radiation characteristics of spherical scatterers in an absorbing medium

The radiative properties of bubbles or particles embedded in an absorbing medium are investigated. We aim first to determine the conditions under which absorption by the surrounding medium must be accounted for in the calculation of the efficiency factors by comparing results from Mie theory and the far-field and near-field approximations. Then, we relate these approximations for a single particle to the effective radiation characteristics required for solving the radiative transfer in an ensemble of scatterers embedded in an absorbing medium. The results indicate that the efficiency factors for a spherical particle can differ significantly from one model to another, in particular for large particle size parameter and matrix absorption index. Moreover, the effective scattering coefficient should be expressed based on the far-field approximation. Also, the choice of the absorption efficiency factor depends on the model used for estimating the effective absorption coefficient. However, for small void fractions, absorption by the matrix dominates, and models for the absorption coefficient and efficiency factor are unimportant. Finally, for bubbles in water, the conventional Mie theory can be used between 0.2 and 200 mum except at some wavelengths at which absorption by water must be accounted for.     

Multicomponent aerosol mass efficiency with various mixture types for polydispersed aerosol

Based on the filter-sampled chemical composition data the seasonal variation of the optical properties of polydispersed aerosols, extinction, scattering, and absorption coefficient, are estimated for various types of aerosol mixtures. The mixtures considered in this study are the internal mixture, elemental carbon (EC)/non-EC external mixture, and fully external mixture. This study also evaluated the sensitivity of the aerosol optical properties for different size distributions. The results show that the extinction coefficient can be mostly accounted for scattering and generally shows a good agreement with each mixture type in this case study. However, the absorption coefficient shows a different tendency for internal and external mixtures. This study also shows that the aerosol optical properties vary as a function of particle diameter at the same composition and mass concentration. This means that mass extinction, scattering, and absorption efficiencies, which were considered as constants in general, should be reassessed and more specifically described as a function of particle size.     

Yet another look at light scattering from particles in absorbing media

We examine the scattering properties of particles contained in absorbing media. Rather than consider energy fluxes through arbitrary integrating spheres, we examine the extinction from its fundamental definition: the energy removed from the plane wave, or incident beam. The resulting energy received by a detector contains two terms: one the result of the incident beam traversing through the medium that would have occurred if the particle were not present, and a correction term due to the presence of the particle. Both terms have the same dependence on the pathlength that the beam travels between two arbitrarily located parallel planes and are independent of where the particle is located within the medium. The result is that the definition of the extinction cross section is not dependent on a reference plane or the particle location within the medium.     

Effective medium theories for irregular fluffy structures: aggregation of small particles

The extinction efficiencies as well as the scattering properties of particles of different porosity are studied. Calculations are performed for porous pseudospheres with small size (Rayleigh) inclusions using the discrete dipole approximation. Five refractive indices of materials covering the range from 1.20+0.00i to 1.75+0.58i were selected. They correspond to biological particles, dirty ice, silicate, and amorphous carbon and soot in the visual part of the spectrum. We attempt to describe the optical properties of such particles using Lorenz-Mie theory and a refractive index found from some effective medium theory (EMT) assuming the particle is homogeneous. We refer to this as the effective model. It is found that the deviations are minimal when utilizing the EMT based on the Bruggeman mixing rule. Usually the deviations in the extinction factor do not exceed approximately 5% for particle porosity P = 0 - 0.9 and size parameters x(porous) = 2 pi r(s,porous)/lambda < or approximately = 25. The deviations are larger for scattering and absorption efficiencies and smaller for particle albedo and the asymmetry parameter. Our calculations made for spheroids confirm these conclusions. Preliminary consideration shows that the effective model represents the intensity and polarization of radiation scattered by fluffy aggregates quite well. Thus the effective models of spherical and nonspherical particles can be used to significantly simplify the computations of the optical properties of aggregates containing only Rayleigh inclusions.     

Examination of surface roughness on light scattering by long ice columns by use of a two-dimensional finite-difference time-domain algorithm

Natural particles such as ice crystals in cirrus clouds generally are not pristine but have additional microroughness on their surfaces. A two-dimensional finite-difference time-domain (FDTD) program with a perfectly matched layer absorbing boundary condition is developed to calculate the effect of surface roughness on light scattering by long ice columns. When we use a spatial cell size of 1/120 incident wavelength for ice circular cylinders with size parameters of 6 and 24 at wavelengths of 0.55 and 10.8 microm, respectively, the errors in the FDTD results in the extinction, scattering, and absorption efficiencies are smaller than approximately 0.5%. The errors in the FDTD results in the asymmetry factor are smaller than approximately 0.05%. The errors in the FDTD results in the phase-matrix elements are smaller than approximately 5%. By adding a pseudorandom change as great as 10% of the radius of a cylinder, we calculate the scattering properties of randomly oriented rough-surfaced ice columns. We conclude that, although the effect of small surface roughness on light scattering is negligible, the scattering phase-matrix elements change significantly for particles with large surface roughness. The roughness on the particle surface can make the conventional phase function smooth. The most significant effect of the surface roughness is the decay of polarization of the scattered light.     

Separation of scattering and absorption contributions in UV/visible spectra of resonant systems.

Resonance light scattering (RLS) is a phenomenon due to an enhancement of the scattered light in close proximity to an absorption band. The effect is easily detectable in the case of strongly absorbing chromophores, which are able to interact, thus leading to large aggregates (Pasternack, R. F.; Collings, P. J. Science 1995, 269, 935). The measurement of absorption spectra from solutions containing such resonant systems can lead to misleading results. In this paper, a simple method is described to obtain absorption spectra of aggregated species with a fairly good correction of the scattering component. The RLS spectrum, obtained using a common spectrofluorimeter, is correlated to the extinction spectrum of the same sample, allowing for an estimation of the scattering contribution to the total extinction spectrum. The method has been successfully applied both on real samples containing aggregated chromophores, such as porphyrins, chlorophyll a and gold colloids, and by simulating extinction spectra.     

Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition

A three-dimensional finite-difference time-domain (FDTD) program has been developed to provide a numerical solution for light scattering by nonspherical dielectric particles. The perfectly matched layer (PML) absorbing boundary condition (ABC) is used to truncate the computational domain. As a result of using the PML ABC, the present FDTD program requires much less computer memory and CPU time than those that use traditional truncation techniques. For spheres with particle-size parameters as large as 40, the extinction and absorption efficiencies from the present FDTD program match the Mie results closely, with differences of less than ~1%. The difference in the scattering phase function is typically smaller than ~5%. The FDTD program has also been checked by use of the exact solution for light scattering by a pair of spheres in contact. Finally, applications of the PML FDTD to hexagonal particles and to spheres aggregated into tetrahedral structures are presented.     

Finite-difference time-domain solution of light scattering by dielectric particles with large complex refractive indices

The finite-difference time-domain (FDTD) technique is examined for its suitability for studying light scattering by highly refractive dielectric particles. It is found that, for particles with large complex refractive indices, the FDTD solution of light scattering is sensitive to the numerical treatments associated with the particle boundaries. Herein, appropriate treatments of the particle boundaries and related electric fields in the frequency domain are introduced and examined to improve the accuracy of the FDTD solutions. As a result, it is shown that, for a large complex refractive index of 7.1499 + 2.914i for particles with size parameters smaller than 6, the errors in extinction and absorption efficiencies from the FDTD method are generally less than ~4%. The errors in the scattering phase function are less than ~5%. We conclude that the present FDTD scheme with appropriate boundary treatments can provide a reliable solution for light scattering by nonspherical particles with large complex refractive indices.     

Study of optical parameters of polystyrene spheres in dense aqueous suspensions

We investigated the dependence of the scattering and absorption coefficients of particles in dense suspensions by the low-coherence fiber optic dynamic light scattering (FODLS) technique. The estimated particle size was used to calculate the scattering coefficient of particles suspended in dense suspensions. The path-length resolved intensity distributions of light backscattered from absorbing dense suspensions were investigated experimentally. The absorption coefficient can be obtained by applying the measured path-length resolved intensity distributions to the modified Lambert-Beer law. As a result, the low-coherence FODLS technique can simultaneously measure the scattering and absorption coefficients of particles in absorbing dense suspensions, and the scattering and absorption coefficients are independent of each other in dense suspensions in the low-scattering regime of 2l(d) < 10?*.     

Extinction cross-section for elastic wave scattering in energy-absorbing media: revisited

A rigorous derivation of the extinction cross-section for elastic wave scattering by an object in an absorbing medium is given. It is necessary to readdress this problem because the assumption of a small detector made in our previous derivation, which essentially leads to the extinction cross-section that is valid strictly in the short wavelength limit, is found to be unnecessary. The detector is now assumed to be infinitely large. This assumption endows the extinction cross-section with a physical meaning that it is a property of the scatterer, independent of the nature of the detector, and is valid in the entire frequency range. Using an integral representation for scattered wave fields instead of using the wave functions for a specific dimension, two- and three-dimensional scattering problems are treated in a unified way. Numerical results are given to demonstrate why the exact extinction cross-section should be used. Applications of the present result to the analysis of wave propagation in inhomogeneous materials are also discussed.