Analysis of arbitrary frequency selective surfaces: analytic constraints

Constraining equations for the reflection coefficient of any arbitrary periodic surface of infinitesimal thickness is presented. These constraints can help verify the accuracy of the numerical results and give further insight into the FSS. The constraints allow shoe that there is a theoretical limit on the amount of energy that can be lost. The analysis presented can be extended to any number of substrates and superstrates but it cannot be extended to multiple periodic surfaces. The field scattered from the FSS is a summation of plane waves (called Floquet modes) that satisfy the periodic boundary condition. The Floquet modes are also orthogonal to each other. As a result, the total power is the sum of the power in each Floquet mode. In addition, each Floquet mode must independently satisfy the electric and magnetic field boundary conditions. We therefore enforce the boundary conditions only on the lowest order Floquet mode (that is the mode that propagates along the specular direction).