Scattering from a Dielectric Circular Cylinder of Finite Length

Electromagnetic scattering by dielectric cylindrical objects is an important research subject and has been considered by many authors for over three decades. Among the analytical models, to solve the dielectric cylinders with finite length, a typical model is the generalized Rayleigh-Gans (GRG) approximation. It approximates the induced current in a finite cylinder by that in an infinitely long cylinder with the same radius and electrical properties and is valid for a nontenuous scatterer with at least one dimension small compared to the wavelength, e.g., needles or thin disks. Stiles and Sarabandi proposed a more general solution for long and thin dielectric cylinders of arbitrary cross section as extension to GRG approximation. In a more general setting, the T-matrix method introduced by Waterman, which is based on the extended boundary condition method (EBCM), is one of the most powerful and widely used tools for rigorously computing electromagnetic scattering by resonance particles and has been applied to particles of various shapes, such as spheroids, finite cylinders, Chebyshev particles, clusters of spheres, cubes, and so on. However, when any of the parameters defining the scattering particle (size, eccentricity, or refractive index) takes extreme values, this method is reported to suffer from convergence problems. For instance, regular EBCM computation becomes an ill-conditioned procedure for particles with dimensions much larger than the wavelength, and for particles with extreme geometries represented by very large aspect ratios. The round-off errors may become increasingly significant with increasing size parameter. One approach for overcoming the problem of numerical instability in computing the T matrix for spheroids with large aspect ratio is the so-called iterative extended boundary condition method (IEBCM). It has been shown that in some cases the use of IEBCM instead of the regular EBCM allows to more than quadruple the maximum convergent size parameter. However, IEBCM is still restricted by the maximum convergent size parameter of EBCM for PEC particles. Another technique to solve scattering from highly elongated spheroids, general multipole technique (GMT), represents EM field vectors by multiple expansions. The limit of the method is its requirement for continuously differentiable function of position at all points on particle surface. Recently, null field method with discrete sources (NF-DS) is proposed to deal with the instability. Its numerical stability is achieved at the expense of considerable increase in computer complexity, and the resolution of this method can be affected by the localization of the sources. As far as dielectric cylindrical objects are considered, to ensure the regular T-matrix method applicable, traditionally the cylinders were limited to objects with only moderate aspect ratios. In this paper, we propose a new iterative technique applicable for electromagnetic scattering by finite dielectric cylinders with large aspect ratio. For such a cylinder, a direct application of the EBCM often leads to numerical instability, so we divide it into several identical cylinders to reduce the aspect ratio for each sub-cylinder to which the EBCM can be applied. T matrix needs to be solved only once for the identical sub-cylinders. Then we employ an iterative method for different parts of the cylinder, in which the basic framework is as follows. The scattered field can be expressed in the form of spherical vector wave functions referring to the center of one part, yet the problem of interacting volumes requires the representations of the scattered field by the use of the same set of spherical harmonic vector wave functions which refer to the center of another part. Thus the scattered properties of different parts can be connected through translational addition theorem. By using the translational addition theorem, a set of linear algebraic equations can be obtained by matching the boundary conditions on the surface of each particle. Meanwhile, the convergence property of translational addition theorem thus bears its influence on the convergence of the linear system; such effect is carefully treated in this paper. On the other hand, the new method holds the potential for multi-cylinder problems, especially for the cases of closely placed cylinders. To validate this proposed method, comparisons are currently made between the theoretical predictions and numerical simulations, as well as measurements for scattering from circular cylinders with finite length. The results show good agreements and clearly demonstrate that the new method can extend regular T-matrix method to solve the rod cases with any aspect ratio, thus bridges the gap between the regular T-matrix method and other analytical methods such as GRG approximation. The new method can also be used for finite dielectric cylinders with arbitrary cross section as long as the T matrix of each sub-cylinder can be accurately obtained.