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 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.     

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 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.     

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.     

Mie theory for light scattering by a spherical particle in an absorbing medium

Analytic equations are developed for the single-scattering properties of a spherical particle embedded in an absorbing medium, which include absorption, scattering, extinction efficiencies, the scattering phase function, and the asymmetry factor. We derive absorption and scattering efficiencies by using the near field at the surface of the particle, which avoids difficulty in obtaining the extinction based on the optical theorem when the far field is used. Computational results demonstrate that an absorbing medium significantly affects the scattering of light by a sphere.     

A MoM solution for TM scattering by dielectric cylinders above an infinite flat surface

A simple solution method is presented for transverse magnetic plane wave scattering by a dielectric cylinder of arbitrary cross-section in front of an infinite flat dielectric surface. The interface between two semi-infinite, dissimilar half-spaces is considered by a perturbed equivalent magnetic current. Coupled integral equations are obtained from a special form of surface equivalence principles and are solved numerically by the Method of Moments. The scattered tangential electric field at interface is displayed and far-zone fields are compared to the results available in the literature.     

Mie scattering by a spherical particle in an absorbing medium

We show that the large-size parameter limit of the scattering efficiency of a spherical particle of relative refractive index m(r) embedded in an absorbing medium is equal to [m(r) - 1[2/]m(r) + 1]2 and not to zero as has been claimed in a recent article [J. Appl. Opt. 40, 1354-1361 (2001)].     

Finite-difference time-domain and steady-state analysis with novel boundary conditions of optical transport in a three-dimensional scattering medium illuminated by an isotropic point source

We evaluate the numerical accuracy of finite-difference time-domain (FDTD) analysis of optical transport in a three-dimensional scattering medium illuminated by an isotropic point source. This analysis employs novel boundary conditions for the diffusion equation. The power radiated from an isotropic point source located at a depth equal to the reciprocal of the reduced scattering coefficient (1/μ'(s)) below the surface at the irradiated position is introduced to the integral form of the diffusion equation. Finite-difference approximations of the diffusion equation for a surface cell are derived by utilizing new boundary conditions that include an isotropic source even in a surface cell. Steady-state and time-resolved reflectances are calculated by FDTD analysis for a semi-infinite uniform scattering medium illuminated by an isotropic point source. The numerical results agree reasonably with the analytical solutions for μ'(s)=1-3 mm(-1) without resizing the mesh elements.     

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.     

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。     

Electromagnetic scattering by an infinite cylinder of material or metamaterial coating eccentrically a dielectric cylinder

The electromagnetic scattering by an infinite cylinder of dielectric material or metamaterial, coating eccentrically another infinite dielectric cylinder, is treated in this work. The problem is solved using classical separation of variables techniques. No use is made of the translational addition theorem. For small eccentricities h = d/a(? 1), where d is the distance between the axes of the cylinders and a the radius of the outer cylinder, we use instead the cosine and the sine laws to satisfy the boundary conditions at the surface of the outer cylinder. Keeping terms up to the order h2 we finally obtain exact, closed-form expressions for the expansion coefficients g(1) and g(2) in the relation S(h) = S(0)[1 + g(1)h + g(2)h2 + O(h3)], giving the scattered field and the scattering cross sections of the problem, where S(0) corresponds to the coaxial geometry, with h = 0 (d = 0). Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters, corresponding to materials or metamaterials. Our method is an alternative of the one using the translational addition theorem in the case of small eccentricities h.     

The light scattering of dielectric films

The Rayleigh scattering of dielectric films was measured at 441.6 nm wavelength. The total scattering losses of TiO₂, SiO₂, ZnS and MgF₂ films show a close correlation with the evaporation parameters. The light scattering of the TiO₂SiO₂ and ZnSMgF₂ film systems can be explained by scattering at the interfaces. By comparing curves of the light scattering as a function of scattering angle with the results of a numerical computing method the statistical parameters of the interfaces were obtained and were found to be in good agreement with electron microscope results.     

Application of the exact solution for scattering by an infinite cylinder to the estimation of scattering by a finite cylinder

A new algorithm for cylindrical Bessel functions that is similar to the one for spherical Bessel functions allows us to compute scattering functions for infinitely long cylinders covering sizes ka = 2πa/λ up to 8000 through the use of only an eight-digit single-precision machine computation. The scattering function and complex extinction coefficient of a finite cylinder that is seen near perpendicular incidence are derived from those of an infinitely long cylinder by the use of Huygens's principle. The result, which contains no arbitrary normalization factor, agrees quite well with analog microwave measurements of both extinction and scattering for such cylinders, even for an aspect ratio p = l/(2a) as low as 2. Rainbows produced by cylinders are similar to those for spherical drops but are brighter and have a lower contrast.     

Dynamic stress intensity factors due to scattering of harmonic waves by a crack in an infinite medium

An analytical method for calculating dynamic stress intensity factors in the mixed mode (combination of opening and sliding modes) using complex functions theory is presented. The crack is in infinite medium and subjected to the plane harmonic waves. The basis of the method is grounded on solving the two‐dimensional wave equations in the frequency domain and complex plane using mapping technique. In this domain, solution of the resulting partial differential equations is found in the series of the Hankel functions with unknown coefficients. Applying the boundary conditions of the crack, these coefficients are calculated. After solving the wave equations, the stress and displacement fields, also the J‐integrals are obtained. Finally using the J‐integrals, dynamic stress intensity factors are calculated. Numerical results including the values of dynamic stress intensity factors for a crack in an infinite medium subjected to the dilatation and shear harmonic waves are presented.     

The numerical solution of radiative heat transfer for grey bodies in an absorbing medium

A new approximate analytical method for solving the integral radiation equations [1, 2] is used for the numerical calculation and investigation of the local and average characteristics of radiative heat transfer in systems of grey bodies separated by an isothermal absorbing medium.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 3, pp 520–525, September, 1969.     

Numerical solution of the radiative-transfer equation for an absorbing,emitting, and scattering medium with a complex 3-D geometry

A method is proposed for numerically solving the integro-differential, radiative-transfer equation with the use of its piecewise-analytic solutions obtained by the discrete-ordinate method and grids constructed by the finite-element method. The advantages of the method proposed and some results of calculation of the radiative-transfer characteristics for one-, two-, and three-dimensional problems are discussed.__________Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 1, pp. 138–147, January–February, 2005.     

Superposition states of light in a three-photon absorbing dissipative medium

We consider the process of simultaneous absorption of three photons in a medium in the presence of weak one-photon absorption. We show that in such a system stationary three-component superposition states of light may be formed in the range of small values of state amplitude (weak perturbation). This circumstance is associated with the fact that in this range of interaction the field spends more time in one of the three types of superposition states of light (constituting an ensemble of quantum trajectories of the system) than in two other types. We also show that in the range of large values of state amplitude it is possible to obtain three types of non-stationary superposition states of light. By using numerical simulation of quantum trajectories of the system we study the dynamics of the quantum entropy of the field. We calculate the Wigner functions of the field states. We also obtain analytical results for the density matrix of the steady state of the system.     

Finite-difference time-domain analysis of frequency-selective surfaces in the mid-infrared

We use the finite-difference time-domain (FDTD) method to model the spectral properties of frequency-selective surfaces (FSSs) at normal incidence in the 1-10 microm wavelength. At these wavelengths the usual assumption that the metallic portions of a FSS are infinitesimally thin perfect conductors are no longer valid. We include the effects of dispersive complex conductivity for real metals and dispersive permittivity for dielectric materials by developing a unified approach that is especially suited for use in FDTD simulations. We concentrate on the finite nature of the metallic conductivity and its variation with wavelength in FSS structures. Our simulation results indicate that the resonant spectrum of a FSS in this wavelength range depends not only on the geometry of the structure and the dielectric substrate present, but also critically on the dispersive properties of the metal species used for the conductors.