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Phase information on wave scattering is not unique and greatly depends on a choice of the origin of coordinates in the measurement system. The present paper argues that the center of scattering for polygonal cylinders should not be a geometrical center of the obstacle such as a center of gravity but be a position that acts as a balance to the electrostatic field effects from edge points. The position is exactly determined in terms of edge positions, edge parameters and lengths of side of polygons. A few examples are given to illustrate a difference from the center of geometry.
A numerical scheme for the analytic continuation of radiation patterns of the azimuthal coordinate θ into the whole space over the complex plane is given. The scattering data given over the real space [0, 2π] are extended into the complex plane by using the recurrence formulas. An example shows the validity of mathematically exact evaluation for the scattering from polygonal cylinders.
Scattering of the two dimensional electromagnetic waves is studied by the infinite sequences of zeros arising on the complex plane, which just correspond to the null points of the far field pattern given as a function of the azimuthal angle θ. The convergent sequences of zeros around the point of infinity are evaluated when the scattering objects are assumed to be N-polygonal cylinders. Every edge condition can be satisfied if the locations of zeros are determined appropriately. The parameters, which allow us to calculate the exact positions of zeros, are given by the asymptotic analysis. It is also shown that there are N-directions of convergence, which tend to infinity. An illustrative example is presented.