Symmetry Properties of Electromagnetic Planar Arrays in Transfer Matrix Description

We analyze in this paper symmetry properties of planar arrays in the long-wave approximation and for general case of oblique incidence of electromagnetic waves. We introduce the concept of the group of wave vectors for scattering problems in transfer matrix description. Using formalism of magnetic groups we define all the possible symmetries for planar arrays and show how to calculate the structure of 4 × 4 transfer matrix for nonmagnetic and magnetic arrays. We discuss also the reciprocity conditions for the transfer matrices which are different from those in scattering matrix description. Application of the theory is illustrated by some examples.