Elemental derivation of the Babinet principle in electromagnetic form

Abstract

Two complementary, thin screens treated in the Babinet principle have one thing in common, the line of their edges. Employing the assumption that scattering of electromagnetic waves from a thin, conducting screen is solely from the elements of the edges, we have made a simple derivation of the Babinet principle in electromagnetic form. We needed to treat but one element of edge with the aperture and conductor interchanged. The factors which affect the amplitudes and phases of the electric and magnetic scattered wavelets reaching any point of observation from the common element of edge of the complementary screens are identical except for phase factors of 0° or 180° caused by polarization effects at the conducting edge. Symmetry conditions from electromagnetic theory yield those factors. We have illustrated the Babinet principle in electromagnetic form by tabularly expressing the scattered waves from two complementary half-planes. These results also were based on the assumption that scattering by a thin screen is solely from the edges.