Proof of polarisation independence and nonexistence of crosspolar terms for targets presenting n-fold (n>2) rotational symmetry with special reference to frequency-selective surfaces

A simple proof is given on symmetry grounds to show that any electromagnetic scatterer that has an axis of n-fold rotational symmetry (for n>2) about a common direction of incidence and observation must have transmission/reflection coefficients that are independent of the polarisation of the incident wave. Furthermore, that there can exist no cross-polarisation.