() is negative. And for FSS spacings greater than roughly a tenth of a wavelength or so, these evanescent wave fields have negligible effect on FSS stack performance. So, for practical purposes, in the frequency bands for which we'll be likely to use the FSS, a single propagating wave will be sufficient to capture the significant properties of a multi-layer FSS stack. This single propagating wave can be modeled in terms of an equivalent transmission line. The FSS sheet may be represented in terms of lumped RLC networks placed in parallel across the transmission line. The shunt admittance FSS model is exact only for an infinitesimally thin FSS, for which the tangential electric field is continuous across the FSS; for finite thickness FSS, a tee or pi network can be used as a better approximation. Free space as a transmission line Both free space and transmission lines admit TEM traveling wave solutions, and even the TE/TM plane waves in free space can be modeled using equivalent transmission line models. The main thing is that both free space and transmission lines admit traveling wave solutions with a z-dependence of the form: One can construct equivalent transmission lines as follows: For TEM waves, For TE waves, For TM waves, where θ is the angle off-normal that the incident wave makes with respect to the FSS. Z0 for free space is 377 Ohms. Shunt circuit resonators and FSS Circuit elements placed in parallel across an equivalent transmission line have some factors in common with thin FSS. The continuity of tangential electric field condition for thin FSS mirrors the voltage continuity condition on either side of the shunt circuit elements. The magnetic field jump condition for the FSS mirrors the Kirchhoff current division law for the equivalent circuit. For sufficiently thick FSS sheets, a more general pi or tee model will likely be required for good approximation to the real FSS. Resonant circuits can approximately model resonant scatterers. For all but the most tightly packed dipole arrays (the brickwork-like "gangbuster" low-pass filters), a first order understanding of FSS operation can be achieved by simply considering the scattering properties of a single periodic element in free space. A dipole or patch in free space will strongly reflect energy for wavelengths comparable in size to the object itself, for example when the dipole is 1/2 wavelength in length. For frequencies below this first resonance (and for