(a) Consider the electric field diffracted by a circular aperture of radius a using a Kirchoff approximation where E_inc = E₀ exp(−ρ²/ω²)ŷ in the plane of the aperture. Show that the far-zone field still has a Gaussian profile when the beam waist ω << a.
(b) Repeat the calculation for a square aperture with side length a in the same limit and compare to part (a).