As is usual in the method of moments, we assume an expansion for the source currents over some known set of basis functions with unknown weighting coefficients Jj (Scott [1989]): Substituting () into () and then testing the resulting equation with the i-th current basis function (i.e., dotting from the left and integrating over the domain of the i-th current basis function, thereby completing the quadratic form) produces the i-th row of the matrix equation as (Scott [1989]): This is the i-th row of the electric field integral equation (EFIE) for a free-standing metallic FSS. Equation () may be readily modified for analyzing FSS with surrounding dielectric sheets (substrates and/or superstrates), and even complex multi-layer FSS structures (Scott [1989]). All of these matrix equations are very simple to implement and require only that the 2D Fourier transform (FT) of the basis functions be computed, preferably in closed form. There is a striking similarity between eqn. () above, and the Bloch wave - MoM method eqn. () for computing ω–β diagrams for triply-periodic electromagnetic media such as photonic crystals (Scott [1998], Scott [2002], available on researchgate.net). Given this similarity, eqn. () and its numerous variants in dielectric-layered FSS structures (Scott [1989]) could also be used (with the RHS set to zero) to find surface waves in complex FSS structures. The RWG (Rao–Wilton–Glisson) basis functions (Rao, Wilton and Glisson [1982]) are a very versatile choice for many purposes and have a transform that is readily computed using area coordinates. Computing reflection and transmission coefficients Equations () and () have been used to solve for the electric current J and then the scattered fields E to compute reflection and transmission from various types of FSS (Scott[1989]). The reflected field is due to the currents on the FSS (the field radiated by the FSS) and the transmitted field is equal to the radiated field plus the incident field, and differs from the reflected field only for the , order (the zero order). Or else the numerical method with periodical boundary conditions can serve as a powerful tool to compute the coefficients of FSS. Equivalent circuits – introduction Background Overview For wavelengths greater than the FSS lattice dimensions, only one – out of the infinitude of Floquet modes – actually propagates. All of the others are (exponentially decaying in the z-direction, normal to the plane of the FSS, since the quantity under the root in