Electromagnetic Scattering from Multiple Cylinders

During the last several decades, electromagnetic scattering from multiple cylinders has been an active research topic of in many areas, such as microwave remote sensing, theory of photonic crystals, atmospheric sciences, and so on. Rigorous theoretical treatment is therefore of critical importance. A large body of available studies in the literature concerns with two dimensional scattering, such as the scattering matrix method (SMM) [1-2]. The typical treatment is to represent fields (incident, exciting, and scattered) using vector cylindrical harmonic waves, and set up the multi-scatterer equation with the aid of translational addition theorem. For such cases, the circumscribing sphere of each particle is degenerated to a circle, and the mutual exclusive condition of the circumscribing spheres is usually fulfilled. However, when 3-D scattering problems are considered, the issues become more complicated. The problems of 3-D scattering of multiple spheres can be similarly treated using the multi-scatterer equation, with varying technical delicacy attached to the solution process. Examples include the special cases in the iterative algorithms by Mackowski [3] or the recursive T-matrix algorithm (RTMA) by Chew [4]. Yet regardless of the underlying technical details, several benevolent features hold for such setting, including fulfillment of the mutual exclusive condition of the circumscribing spheres of each scatterer (actually the sphere itself in these cases) and the favorable behavior of the T matrix for spheres. It is not the case when scattering from multiple cylinders is considered. One, the mutual exclusive condition of the circumscribing spheres is often found violated (as in the case when any pair of reasonably long cylinders are close to each other), and two, the T matrix of a dielectric cylinder of arbitrary length, equivalent volumetric radius, and dielectric contrast with the ambient environment can have poor convergent property or even fail to converge. Partly for these reasons, in [5], the 3D problem was first converted to a 2D problem by assuming infinite length of the cylinders to obtain the exciting fields and then to use the Huygen's principle to bring back the 3D scattering. Yet such convenience for technical treatment may compromise the rigorousness and fidelity of the scattering characterization. Another approach without resorting to the multi-scatterer equation in