Improved recursive algorithm for light scattering by a multilayered sphere

An improved recurrence algorithm to calculate the scattering field of a multilayered sphere is developed. The internal and external electromagnetic fields are expressed as a superposition of inward and outward waves. The alternative yet equivalent expansions of fields are proposed by use of the first kind of Bessel function and the first kind of Hankel function instead of the first and the second kinds of Bessel function. The final recursive expressions are similar in form to those of Mie theory for a homogeneous sphere and are proved to be more concise and convenient than earlier forms. The new algorithm avoids the numerical difficulties, which give rise to significant errors encountered in practice by previous methods, especially for large, highly absorbing thin shells. Various calculations and tests show that this algorithm is efficient, numerically stable, and accurate for a large range of size parameters andrefractive indices.     

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.     

Scattering of plane electromagnetic waves by a chiral-metal cylinder

The problem of scattering of E-and H-polarized plane electromagnetic waves by a metal cylinder covered with a chiral layer is solved by the method of partial regions. The scattering field is studied in the near and far zones. The correlation between the type of polarization of the incident electromagnetic wave and the magnitude of the depolarized component of the scattered field is considered.     

Approximation of the solution of inverse problem of scattering of electromagnetic waves on plane dielectrics

We propose a method for the determination of the material parameters of dielectric coatings according to the measured values of scattered electromagnetic fields which enables us to introduce an efficient procedure of processing of the data of measurements in the methods of nondestructive testing. As a specific feature of the proposed method for the solution of the formulated inverse problem, we can mention the possibility of reconstruction of piecewise continuous profiles of dielectric permittivity for laminated materials. The procedure of reconstruction is based on the method of integral equations. The solution of the problem is obtained approximately. The measured values of the coefficient of reflection of plane electromagnetic waves are extrapolated to the high-frequency region, which enables us to guarantee higher accuracy of reconstruction of the functions of dielectric permittivity for the analyzed structures.     

MIE散射系数的改进算法

提出一种新的计算MIE散射系数的算法。该算法使用了改进的后向递推公式,可对MIE系数中的消光系数Kext和散射系数Ksca进行精确计算。由于新算法能显著地减少计算循环次数,因此明显缩短了计算时间。对广泛运用的递推法和连分式法进行了比较详细的讨论。并且把新算法的计算结果和已有的成果进行了比较。结果表明:(1)计算的循环次数与粒子的复折射率基本没有关系;(2)连分式得到的结果通常最准确;(3)新算法在尺度系数较大时(>1000),计算时间仅为连分式算法的10-2~10-3,计算的误差小于10-5;(4)算法的适用范围广,对于尺度系数从10-6到106,复折射率从从10-6到106都能很好地进行计算。     

On the theory of elastic scattering of electromagnetic waves by atoms

A Hamiltonian describing the elastic interaction of electromagnetic radiation (EMR) with an atom is obtained using the invariant theory of perturbations in the limit of EMR wavelengths λ significantly exceeding the atom size a₀. An exact expression for the interaction amplitude is obtained, and the probability of EMR scattering on the atom is calculated. It is established that the scattering probability at large λ is proportional to the squared frequency of monochromatic EMR. It is shown that, in the limit of large wavelengths, the formula h∼(ω/c)⁴ v ₀ for the extinction coefficient is inapplicable and the relation h=Aω² becomes valid, where A is a definite coefficient.     

Finely stratified cylinder model for radially inhomogeneous cylinders normally irradiated by electromagnetic plane waves

A finely stratified cylinder model (FSCM) for calculation of the scattered fields of infinitely long, radially inhomogeneous, circular cylinders normally illuminated by electromagnetic plane waves is introduced for the first time, to our knowledge. Because of its capability of using a very large number of layers (more than 80,000), the model is useful for both continuous and discontinuous refractive-index profiles. Numerical results agree well with published solutions for radially inhomogeneous cylinders; for cylinders with a dimensionless size parameter larger than 60, results obtained with the FSCM agree with the geometric optics for both continuous and discontinuous refractive-index profiles.     

Boundary element method calculation for coherent electromagnetic scattering from two and three dielectric spheres

A quadratic, isoparametric boundary element formulation has been used to calculate the multiple scattering of electromagnetic waves from systems of two and three dielectric spheres. Extinction efficiency results for the scattering of a plane wave are presented for variations of the separation of the two spheres in three kinds of orientations of the system with respect to the incident wave. These have been verified against analytical calculations based on Mie's theory and calculations by other authors. The results demonstrate a large side scattering resonance (the so-called specular resonance). Agreement between the results establishes the boundary element method as a very powerful tool for solving multiple scattering problems because the method applies to arbitrarily shaped objects having a homogeneous dielectric constant in any configuration. To illustrate the versatility of the method, scattering from three spheres is calculated.     

Analytical approximations in multiple scattering of electromagnetic waves by aligned dielectric spheroids

In a dense medium, the failure to properly take into account multiple-scattering effects could lead to significant errors. This has been demonstrated in the past from extensive theoretical, numerical, and experimental studies of electromagnetic wave scattering by densely packed dielectric spheres. Here, electromagnetic wave scattering by densely packed dielectric spheroids with aligned orientation is studied analytically through quasicrystalline approximation (QCA) and QCA with coherent potential (QCA-CP). We assume that the spheroids are electrically small so that single-particle scattering is simple. Low-frequency QCA and QCA-CP solutions are obtained for the average Green's function and the effective permittivity tensor. For QCA-CP, the low-frequency expansion of the uniaxial dyadic Green's function is required. The real parts of the effective permittivities from QCA and QCA-CP are compared with the Maxwell-Garnett mixing formula. QCA gives results identical to those with the mixing formula, while QCA-CP gives slightly higher values. The extinction coefficients from QCA and QCA-CP are compared with results from Monte Carlo simulations. Both QCA and QCA-CP agree well with simulations, although qualitative disagreement is evident at higher fractional volumes.     

Debye series for light scattering by a multilayered sphere

We have derived the formula for the Debye-series decomposition for light scattering by a multilayered sphere. This formulism permits the mechanism of light scattering to be studied. An efficient algorithm is introduced that permits stable calculation for a large sphere with many layers. The formation of triple first-order rainbows by a three-layered sphere and single-order rainbows and the interference of different-order rainbows by a sphere with a gradient refractive index, are then studied by use of the Debye model and Mie calculation. The possibility of taking only one single mode or several modes for each layer is shown to be useful in the study of the scattering characteristics of a multilayered sphere and in the measurement of the sizes and refractive indices of particles.     

Diffraction of electromagnetic waves on two spheres: Application to designing antennas for space vehicles

Designing the antenna systems for space vehicles employing electrojet thrusters has to be based on a strict solution of the problem of electromagnetic wave diffraction on two bodies. Here, the problem of diffraction on two spherical surfaces is strictly solved in terms of the scalar field potentials. A method for the transformation of wave amplitudes upon a shift of the spherical coordinate system is proposed. The results of numerical calculations are presented.     

The reflection and transmission of elastic waves through a plane of spheres in periodic arrangement

The work presented in this paper focuses on the reflection and transmission coefficients of an incident plane wave which impinges obliquely a plane of identical spheres arranged periodically in a homogeneous host with infinite extension. The Bloch theorem of periodic structure and the addition theorem of spherical wave functions are used to obtain the total scattering wave from all spherical scatterers periodically arranged in a plane. The total scattering wave in series form of spherical wave functions is then transformed into plane wave form in order to derive the reflection and transmission coefficients. Some numerical examples are given for different size, material constants and array patterns of spherical scatterers, and their influences on the reflection and transmission coefficients of a plane of spheres are discussed based on the numerical results. This study implies that a plane of spheres can be elaborately designed to serve as a sound barrier at a certain frequency range.     

一种改进的红外焦平面非均匀性校正算法

针对红外焦平面探测器现有非均匀性校正算法在实际应用中存在的问题,结合实际系统的开发,提出了一种改进算法——一点加两点校正算法。先求两点校正算法的校正增益和校正偏置,再求一点校正算法的校正偏置,求取一点校正算法的偏置参数时的图像数据来自前面求得的两点校正之后的数据,即最后的校正结果是两点校正后的再校正。理论分析和应用表明该算法与目前流行的算法相比具有实时性好、误差小、处理效果好等特点。     

Debye series for Gaussian beam scattering by a multilayered sphere

The Debye series has been a key tool for the understanding of light scattering features, and it is also a convenient method for understanding and improving the design of optical instruments aimed at optical particle sizing. Gouesbet has derived the Debye series formulation for generalized Lorenz-Mie theory (GLMT). However, the scattering object is a homogeneous sphere, and no numerical result is provided. The Debye series formula for plane-wave scattering by multilayered spheres has been derived before. We have devoted our work to the Debye series of Gaussian beam scattering by multilayered spheres. The integral localized approximation is employed in the calculation of beam-shape coefficients (BSCs) and allows the study of the scattering characteristics of particles illuminated by the strongly focused beams. The formula and code are verified by the comparison with the results produced by GLMT and also by the comparison with the result for the case of plane-wave incidence. The formula is also employed in the simulation of the first rainbow by illuminating the particle with one or several narrow beams.     

Electromagnetic scattering by an aggregate of spheres

We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.     

Comparison of exact and asymptotic results for the focusing of electromagnetic waves through a plane interface

Recently, exact Kirchhoff solutions and the corresponding asymptotic solutions for the focusing of electromagnetic waves through a plane interface between two different dielectrics were reported. But the computation of exact results takes a long time because it requires the quadruple integration of a rapidly oscillating integrand. By using asymptotic techniques to perform two of the integrations, one can reduce the computing time dramatically. Therefore it is important to establish the accuracy and the range of validity of the asymptotic technique. To that end, we compare the exact and the asymptotic results for high-aperture, near-field focusing systems with a total distance from the aperture to the focal point of a few wavelengths and with a distance from the aperture to the interface as small as a fraction of a wavelength. The systems examined have f-numbers in the range from 0.6 to 0.9 and Fresnel numbers in the range from 0.4 to 3.5. Our results show that the accuracy of the asymptotic method increases with the aperture-interface distance when the aperture-focus distance is kept fixed and that it increases with the aperture-focus distance when the aperture-interface distance is kept fixed. To an accuracy of 7.8%, the asymptotic techniques are valid for aperture-interface distances as small as 0.5lambda as long as the total distance from the aperture to the focal point exceeds 8lambda. It is also shown that an accuracy of better than 1% can be obtained for the same aperture-interface distance of 0.5lambda and for interface-observation-point distances as small as 0.1lambda as long as the total distance from the aperture to the focal point exceeds 12lambda. By use of the asymptotic technique the computing time is reduced by a factor of 10(3).     

Modeling of the scattering of electromagnetic waves by a thin dielectric coating on a cylinder

Double-sided boundary conditions containing only tangential components of a diffracted field are used to model the interaction of electromagnetic waves with a cylinder of arbitrary cross section covered with a thin dielectric layer. The obtained boundary-value problem is reduced to a system of two singular integral equations of the second kind with kernels whose structure is similar to the kernels of integral equations of the first kind for a perfectly conducting scatterer. The numerical solution of the integral equations of the problem is obtained by the method of mechanical quadratures. The scattering properties of an elliptic cylinder with different dielectric coatings are studied in the superhigh-frequency band. It is shown that the coating strongly affects the diffraction properties of the cylinder. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 1, pp. 96–104, January–February, 2006.     

Frequency modulated thermal wave imaging for visualizing power density of electromagnetic waves on plane surfaces

In this article, Frequency Modulated Thermal Wave Imaging (FMTWI) [1–6] is introduced for the first time for determining power distribution of electromagnetic waves on plane surfaces. The advantage with this technique is that we can extract multiple amplitude and phase images from a single run of experiment. The applied excitation signal in this technique is a frequency modulated chirp signal instead of a single frequency signal used in conventional lock-in infrared (IR) thermography [7–11].

The thermal images obtained using FMTWI can be used qualitatively, e.g., to detect field leakage near electromagnetic junctions and microstrip feed lines. As a practical demonstration of this technique, an example of 2 × 2 patch antenna array at 8 GHz is considered. First, amplitude images at various modulation frequencies are obtained. Next, signal to noise ratio (SNR) values at each frequency are calculated. It is seen that SNR is lower at higher frequencies. It is observed that at higher modulation frequencies, micro-strip lines feeding the individual patch antennas of the array, are not visible in amplitude images, while at lower frequencies they are clearly visible

Mathematical modeling of the microwave absorption screen has also been carried out to show variations of incident, reflected, and transmitted powers as a function of screen surface impedance. It is also observed that the screen minimally perturbs the electromagnetic fields.