A linearly polarized plane wave of amplitude E0 and wave number k is incident on a circular opening of radius a in an otherwise perfectly conducting flat screen. The incident wave vector makes an angle α with the normal to the screen. The polarization vector is perpendicular to the plane of incidence.
(a) Calculate the diffracted fields and the power per unit solid angle transmitted through the opening, using the vector Smythe--Kirchhoff formula (10.101) with the assumption that the tangential electric field in the opening is the unperturbed incident field.
(b) Compare your result in part a with the standard scalar Kirchhoff approximation and with the result in Section 10.9 for the polarization vector in the plane of incidence.