Bridging the Gap Between the Babinet Principle and the Physical Optics Approximation: Scalar Problem

For a two-dimensional (2-D) problem, this paper shows that the Babinet Principle (BP) can be derived from the physical optics (PO) approximation. Indeed, following the same idea as Ufimtsev, from the PO approximation and in far-field zone, the field scattered by an object can be split up into a field that mainly contributes around the specular direction (illuminated zone) and a field that mainly contributes around the forward direction (shadowed zone), which is strongly related to the scattered field obtained from the BP. The only difference relies on the integration surface. We also show mathematically that the involved integral does not depend on the shape of the object, which then corresponds to the BP. Simulations are provided to illustrate the link between the BP and PO.