Characteristic Far-Field Analysis of Scattering due to Plane Wave Excitations

In the theory of characteristic modes, a set of modes was derived such that the corresponding far fields are orthogonal over the infinite sphere. We exploit the orthogonality of these far fields to derive relationships between the modal parameters, such as the modal excitation coefficients, when a plane wave is incident on the obstacle. These results provide a useful framework for visualizing how each mode contributes to the overall scattering over a range of plane wave parameters, such as the wave-vectors and polarization. Validations were performed by comparing the theoretical analysis with simulations.