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An analysis of a periodic screen consisting of one or more periodic surfaces sandwiched between homogeneous dielectric layers is presented. A periodic surface is defined to be a free-standing array of patches, or an array of apertures within a metallic surface. The dielectric layers may be lossy. The analysis treats a screen component (periodic surface or dielectric layer) as an element characterized by its scattering parameters. The cascade connection of the scattering parameters of all elements that comprise the screen then gives the overall transmission and reflection coefficients of the structure. This analysis allows for the calculation of the fields and, hence, power dissipation within lossy layers at any point within the screen.