Complex multipole beam approach to electromagnetic scattering problems

An approach which attempts to combine the advantages of both the IML (impedance matrix localization) and the MMP (multiple multipole) methods is introduced. The strategy followed in this method is to expand the scattered fields in terms of beams, generated by a judiciously selected set of multipole sources located in the complex space. The method can be viewed as a numerical approach to finding an approximate Gabor representation of the boundary field. Since the completeness properties and other characteristics of the Gabor expansion functions are well understood, the task of developing a set of simple rules for choosing the orders and locations of the multipoles is greatly facilitated. And yet, in common with the IML and MMP methods, the present approach retains the advantage in terms of the number of unknowns over the MoM, as it typically uses less than four unknowns per wavelength. The formulation presented here has been employed to solve the problem of scattering by a variety of cylindrical shapes.<>