Electromagnetic Scattering by a Finite Metallic Circular Cylinders Set

Abstract

The problem of electromagnetic scattering by cylinders is an old problem that has been studied in many configurations. The present publication provides a theoretical study on a not yet investigated general case: the set of finite metallic circular cylinders. A model which takes into account both the finiteness of the cylinders and their electromagnetic coupling is provided. The total field is written in a two dimensional problem in terms of cylindrical harmonics and is used to define current densities which are integrated in a three dimensional problem. The finiteness is taken into account assuming current densities that are identical from those of the two dimensional problem. Coupling effects are naturally taken into account via the matrix formulation of the boundary condition that binds together the cylindrical harmonic coefficients. The proposed closed-form is valid for great cylinder lengths and any cylinder radii. Numerical experiments are also provided in various configurations in order to evaluate the accuracy of the model. The model computational times happens to be 5 orders of magnitude shorter than a full-wave reference simulation, without significant loss of accuracy.

Figures (8)

• Figure 1: Illustration of the scattering by a set of cylinders. They are finite and of arbitrary radius, height and position. The scattered field is the result of the interaction between the incident wave and the coupled cylinders.
• Figure 2: The two dimensional configuration which consists of a set of $\hat{\boldsymbol{z}}$ oriented infinite cylinders. Each cylinder is associated with both cylindrical local basis and spherical local basis which are represented in the zoomed rectangle.
• Figure 3: A set of finite cylinders illuminated by a plane wave propagating along $\hat{\boldsymbol{x}}$. This figure is the three dimension extension of Figure \ref{['fig_infinite_conf']}. The current density calculated in the 2D configuration is used to calculate the radiation integral over the finite surface of a cylinder.
• Figure 4: Scattering by a thick cylinder. (a) Illumination scene, (b) model, $x = 2d_\mathrm{far}$, (c) error, $x = 2d_\mathrm{far}$, (d) $r = 2d_\mathrm{far}$, $\phi = 0^\circ$ and (e) $z = 0$, $x = 2d_\mathrm{far}$. Blue (---) and orange (---) arrows of (a) are the x-axes of (d) and (e) subplots respectively, which are associated with the same model curve color.
• Figure 5: Scattering by a set of 9 identical cylinders. (a) Illumination scene, (b) model, $x = 2d_\mathrm{far}$, (c) error, $x = 2d_\mathrm{far}$, (d) $r = 2d_\mathrm{far}$, $\phi = 0^\circ$ and (e) $z = 0$, $x = 2d_\mathrm{far}$.