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 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)].     

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.     

Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols

We have examined the Maxwell-Garnett, inverted Maxwell-Garnett, and Bruggeman rules for evaluation of the mean permittivity involving partially empty cells at particle surface in conjunction with the finite-difference time-domain (FDTD) computation. Sensitivity studies show that the inverted Maxwell-Garnett rule is the most effective in reducing the staircasing effect. The discontinuity of permittivity at the interface of free space and the particle medium can be minimized by use of an effective permittivity at the cell edges determined by the average of the permittivity values associated with adjacent cells. The efficiency of the FDTD computational program is further improved by use of a perfectly matched layer absorbing boundary condition and the appropriate coding technique. The accuracy of the FDTD method is assessed on the basis of a comparison of the FDTD and the Mie calculations for ice spheres. This program is then applied to light scattering by convex and concave aerosol particles. Comparisons of the scattering phase function for these types of aerosol with those for spheres and spheroids show substantial differences in backscattering directions. Finally, we illustrate that the FDTD method is robust and flexible in computing the scattering properties of particles with complex morphological configurations.     

Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data

The diameter and refractive index of micrometer sized spherical dielectric particles are simultaneously deduced using the wavelength dependence of backscattering data from optically levitated particles. The accuracy of the results is set by experimental errors in the determination of the wavelength of backscatter resonance peaks and the ratio of slopes of specified peaks. At present the refractive index and diameter can be deduced with relative errors of 5 x 10(-5). This represents the most accurate determination of absolute size and refractive index yet made by light scattering. A reduction of these errors by an order of magnitude is possible. We assume a priori knowledge of diameter and refractive index with accuracy of 10(-1) and 5 x 10(-3), respectively.     

Scattering by particles with radially variable refractive indices

The problem of scattering by a spherical particle whose refractive index arbitrarily depends on the distance from its center has been solved. A computational scheme for determining the scattering coefficients for the refractive-index profiles given by some piecewise smooth function is constructed, and the models to use it are presented. The simple algorithm for evaluating the scattered and internal field vectors is elaborated. The exact expression for the scattering cross section in terms of the generated Debye partial potentials that are dependent on the given refractive index has been obtained.     

Application of the symplectic finite-difference time-domain method to light scattering by small particles

A three-dimensional fourth-order finite-difference time-domain (FDTD) program with a symplectic integrator scheme has been developed to solve the problem of light scattering by small particles. The symplectic scheme is nondissipative and requires no more storage than the conventional second-order FDTD scheme. The total-field and scattered-field technique is generalized to provide the incident wave source conditions in the symplectic FDTD (SFDTD) scheme. The perfectly matched layer absorbing boundary condition is employed to truncate the computational domain. Numerical examples demonstrate that the fourth-order SFDTD scheme substantially improves the precision of the near-field calculation. The major shortcoming of the fourth-order SFDTD scheme is that it requires more computer CPU time than a conventional second-order FDTD scheme if the same grid size is used. Thus, to make the SFDTD method efficient for practical applications, one needs to parallelize the corresponding computational code.     

Concept of the equiphase sphere for light scattering by nonspherical dielectric particles

We introduce the concept of the equiphase sphere for light scattering by nonspherical dielectric particles. This concept facilitates the derivation of a simple analytical expression for the total scattering cross section of such particles. We tested this concept for spheroidal particles and obtained a bound on the minor-to-major axis ratio for the valid application of this technique. We show that this technique yields results that agree well with the rigorous numerical solution of Maxwell's equations obtained with the finite-difference time-domain method. The new technique has the potential to be extended to the study of light scattering by arbitrarily shaped convex dielectric particles.     

三维介质体的时域散射分析

用时间递推（marching—on in-time，MOT）方法求解了电磁场时域耦合积分方程，计算了均匀介质体的表面等效电流和表面等效磁流，得到时域散射远场并给出了详细推导过程。举例比较了将时域散射用Fourier变化后在频域的RCS和频域直接求得的RCS，以说明该算法的正确性。     

Comparison of Cartesian grid configurations for application of the finite-difference time-domain method to electromagnetic scattering by dielectric particles

Two grid configurations can be employed to implement the finite-difference time-domain (FDTD) technique in a Cartesian system. One configuration defines the electric and magnetic field components at the cell edges and cell-face centers, respectively, whereas the other reverses these definitions. These two grid configurations differ in terms of implication on the electromagnetic boundary conditions if the scatterer in the FDTD computation is a dielectric particle. The permittivity has an abrupt transition at the cell interface if the dielectric properties of two adjacent cells are not identical. Similarly, the discontinuity of permittivity is also observed at the edges of neighboring cells that are different in terms of their dielectric constants. We present two FDTD schemes for light scattering by dielectric particles to overcome the above-mentioned discontinuity on the basis of the electromagnetic boundary conditions for the two Cartesian grid configurations. We also present an empirical approach to accelerate the convergence of the discrete Fourier transform to obtain the field values in the frequency domain. As a new application of the FDTD method, we investigate the scattering properties of multibranched bullet-rosette ice crystals at both visible and thermal infrared wavelengths.     

Analytical solution to the optical transfer function of a scattering medium with large particles

A new analytical expression for the optical transfer function of multiple-scattering media such as clouds, mists, and dust aerosols is given in terms of their microphysical characteristics. The geometrical optics approximation is used to find local optical parameters of a scattering medium, including the simple approximation of the phase function, which is the key to the solution of the problem considered here. The optical transfer function is taken within a small-angle approximation of the radiative transfer theory. A comparison with Monte Carlo data shows a fairly satisfactory accuracy of our analytic formulas.     

Peculiarities in light scattering by spherical particles with radial anisotropy

Light scattering by a spherical particle with radial anisotropy is discussed by extending Mie theory to diffraction by an anisotropic sphere, including both the electric and the magnetic anisotropy ratio. It is shown that radial anisotropy may lead to great modifications in scattering efficiencies and field enhancement, elucidating the importance of anisotropies in the control of scattering. The capacity for nondissipating damping is demonstrated for anisotropic spheres with different signs in radial and transversal permittivities.     

Optical detection of small changes in refractive indices in water by single-beam scattering

We studied forward-scattered laser light that is produced when the light strikes an abrupt interface (air bubble in water) and when it passes unimpeded through diffused water layers caused by temperature gradients. Measured intensities of the scattered light indicated patterns that are due to both geometrical and physical optics. Distribution of intensities within the scattered beam changed with the average vertical temperature gradient. Shifts in locations of intensities indicated small changes in the index of refraction in the diffused scattering case.     

Computation of light scattering by axisymmetric nonspherical particles and comparison with experimental results

A laboratory prototype of a novel experimental apparatus for the analysis of spherical and axisymmetric nonspherical particles in liquid suspensions has been developed. This apparatus determines shape, volume, and refractive index, and this is the main difference of this apparatus from commercially available particle analyzers. Characterization is based on the scattering of a monochromatic laser beam by particles [which can be inorganic, organic, or biological (such as red blood cells and bacteria)] and on the strong relation between the light-scattering pattern and the morphology and the volume, shape, and refractive index of the particles. To keep things relatively simple, first we focus attention on axisymmetrical particles, in which case hydrodynamic alignment can be used to simplify signal gathering and processing. Fast and reliable characterization is achieved by comparison of certain properly selected characteristics of the scattered-light pattern with the corresponding theoretical values, which are readily derived from theoretical data and are stored in a look-up table. The data in this table were generated with a powerful boundary-element method, which can solve the direct scattering problem for virtually arbitrary shapes. A specially developed fast pattern-recognition technique makes possible the on-line characterization of axisymmetric particles. Successful results with red blood cells and bacteria are presented.     

Light scattering by optically soft large particles of arbitrary shape

Light scattering by chaotically oriented optically soft large particles of arbitrary shape is considered within the framework of the Rayleigh-Gans approximation. It has been shown that outside the forward direction, the scattering pattern has the dependence of Δk??(1+cos2θ), where is an average particle surface area, Δk is the difference between scattered and initial wave vectors, θ is the scattering angle, and this pattern is independent of particle shape. A simple approximating formula is suggested, which correctly describes the scattering pattern in the entire range of scattering angles. This formula is compared to the particular case of size-distributed spherical particles and is shown to have high accuracy. Also, it is shown that the inherent optical properties, as total, transport, and backward scattering coefficients, are determined by the specific particle surface area and the effective particle size.     

Geometrical-optics solution to light scattering by droxtal ice crystals

We investigate the phase matrices of droxtals at wavelengths of 0.66 and 11 microm by using an improved geometrical-optics method. An efficient method is developed to specify the incident rays and the corresponding impinging points on the particle surface necessary to initialize the ray-tracing computations. At the 0.66-microm wavelength, the optical properties of droxtals are different from those of hexagonal ice crystals. At the 11-microm wavelength, the phase functions for droxtals are essentially featureless because of strong absorption within the particles, except for ripple structures that are caused by the phase interference of the diffracted wave.     

Polarized light scattering by dielectric and metallic spheres on silicon wafers

The polarization and intensity of light scattered by monodisperse polystyrene latex and copper spheres, with diameters ranging from 92 to 218 nm, deposited on silicon substrates were measured with 442-, 532-, and 633-nm light. The results are compared with a theory for scattering by a sphere on a surface, originally developed by others [PhysicaA 137,209 (1986)], and extended to include coatings on the sphere and the substrate. The results show that accurate calculation of the scattering of light by a metal sphere requires that the near-field interaction between the sphere and its image be included in acomplete manner. The normal-incidence approximation does not suffice for this interaction, and the existence of any thin oxide layer on the substrate must be included in the calculation.     

Polarized light scattering by microroughness and small defects in dielectric layers

The polarization of light scattered by the surface of a material contains information that can be used to identify the sources of that scatter. Theories for light scattering from interfacial roughness of a dielectric layer and from defects in that dielectric layer are reviewed. Methods for calculating the Mueller matrix or the Stokes vector for scatter from multiple sources and for decomposing a Stokes vector into contributions from two nondepolarizing scattering sources are derived. The theories are evaluated for a specific sample and geometry. Results show that some incident polarizations are more effective than others at discriminating among scattering sources, with s-polarized light being least effective. The polarization of light scattered from interfacial roughness depends upon the relative roughness of the two interfaces and the degree of correlation between the two interfaces. The scattering from defects in the film depends on the depth of the defect and differs from that from any one of the cases of interfacial roughness. The scattering from defects randomly distributed in the film and for small dielectric permittivity variations in the film is also calculated. Experimental results are presented for a 52-nm SiO2 film thermally grown on microrough silicon.     

Local-field resonance in light scattering by a single water droplet with spherical dielectric inclusions

Light scattering by an evaporating water droplet several micrometers in size with spherical dielectric inclusions was investigated. The evolution of the droplet radius and the effective refractive index was determined. A deviation from predictions by standard effective-medium theories in the form of a resonance was encountered. Simple analysis of the phenomenon was conducted, and a qualitative explanation was proposed.