Scattering Width of an Infinite Cylinder

Calculate the scattering width of an infinite cylinder. The infinite cylinder is modelled using an one-dimensional periodic boundary condition (PBC).

Figure 1. 3D view of the infinite cylinder defined as a unit cell with a one-dimensional PBC with a plane wave (source).

The scattering by a circular cylinder1 is computed by:

S W = 1 λ   lim ρ [ 2 π ρ E z s 2 E z i 2 ] .
1 C. A. Balanis, Advanced Engineering Electromagnetics, Wiley, 1989, pp. 607.