A rectangular opening with sides of length and b > defined by x = (/2),

A rectangular opening with sides of length α and b > α defined by x = ±(α/2), у = ±(b/2) exists in a flat, perfectly conducting plane sheet filling the x-y plane. A plane wave is normally incident with its polarization vector making an angle β with the long edges of the opening.

(a) Calculate the diffracted fields and power per unit solid angle with the vector Smythe-Kirchhoff relation (10.109), assuming that the tangential electric field in the opening is the incident unperturbed field.

(b) Calculate the corresponding result of the scalar Kirchhoff approximation.

(c) For b = α, β = 45°, kα = 4π, compute the vector and scalar approximations to the diffracted power per unit solid angle as a function of the angle θ for ф = 0. Plot a graph showing a comparison between the two results.