A monochromatic plane wave polarized along y is normally incident from z < 0 onto a two-dimensional

Question:

A monochromatic plane wave polarized along ˆy is normally incident from z < 0 onto a two-dimensional conducting scatterer confined to the z = 0 plane. Use Kirchoff’s approximation but do not use the Fraunhofer approximation.

(a) Let the scatterer be a conducting disk of radius a. Find E_disk(0, 0, z > 0).
(b) Let the scatterer be an infinite conducting sheet with a circular aperture of radius a centered on the z-axis. Find E_aperture(0, 0, z > 0).
(c) Confirm that E_aperture(0, 0, z > 0) = E_inc − E_disk(0, 0, z > 0). Explain why Babinet’s principle is not the reason this is true.