The study investigates the mathematical background of the method of auxiliary sources (MAS) employed in electromagnetic diffraction. Here, the mathematical formulation is developed for E-polarized plane wave diffraction by perfectly conducting two-dimensional objects of arbitrary smooth shape, and the comparison with an analytical and a numerical approach is provided in the numerical part. The results reveal a quite high accuracy among all methods. The importance of the study is to develop the complete mathematical background of MAS for two-dimensional TM-polarized electromagnetic scattering problems by conducting objects. Different from the method of moments (MoM) and other integral equation approaches in electromagnetic scattering problems, here the integral equation resulting from the boundary condition on the scatterer is solved by expanding the current density as orthonormalized Hankel's function with the argument of the distance between the scatterer actual and auxiliary surfaces. The approach can be summarized by that first the sources are shifted inside the scatterer and second, the boundary condition is employed as the total tangential electric field is zero on the surface and inside the object. Then, such expansion leads to eliminating the singularity problems by shifting the sources from the actual surface.
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