DISSIPATION IN THICK FREQUENCY SELECTIVE STRUCTURES Bj¨ orn Widenberg, Anders Karlsson, Gerhard Kristensson Department of Electroscience, Electromagnetic Theory, Lund Institute of Technology, P.O. Box 118 S-221 00 Lund, Sweden, fax: +46-462227508. E-mail: bjorn.widenberg@es.lth.se, anders.karlsson@es.lth.se, gerhard.kristensson@es.lth.se ABSTRACT Dissipation in Frequency Selective Structures (FSS) of aperture/slot type is studied. The dissipation in an FSS is due to losses in the dielectric material, and losses due to finite conductivity in the metallic plate. The dissipation in the dielectric medium is modeled by the complex permittivity. The dissipation on the metallic structure arises both on the plane metallic surface and on the walls of the apertures. The attenuation and the power losses are calculated for a number of different FSS, and based on these results the performance of an FSS with losses is discussed. INTRODUCTION E incident E reflected E transmitted Lossy dielectric sheet (ǫ d ,µ d ) Lossy dielectric puck (ǫ w ,µ w ) Metallic plate with finite conductivity (σ m ) Fig. 1. A Thick Frequency Selective Structure (FSS). The presence of dissipation in the dielectric medium and the metallic surfaces in an FSS modifies the usual description of scattering by an FSS. This modification takes the form of a complex rather than an real propagation constant, and by introduction of a surface resistance. The transmitted power is approximately given by P trans = P inc t dl t dw t c L f , (1) where t dl is the transmittance due to dissipation in the dielectric layers, t dw is the transmittance due to dissipation in the dielectric waveguide puck , t c is the transmittance due to finite conductivity in the walls of the waveguide, and L f is the loss factor due to finite conductivity in the plane metallic surface. The transmissivities and the loss factor can with good accuracy be determined separately. The transmissivities due to dissipation in the dielectric medium, t dl and t dw , are determined by assuming infinite conductivity for the metallic surfaces, and the transmittance due to finite conductivity in the walls of the waveguide t c and the loss factor due to finite conductivity in metallic medium L f is determined by assuming lossless dielectric medium. GEOMETRY AND METHOD The geometry of a simple FSS, that consists of a perforated conducting plate sandwiched between two dielectric slabs, is depicted in Fig. 1. The screen can have an arbitrary number of aperture layers and dielectric layers. An aperture layer consists of an electrically conducting plate perforated with a periodic array of apertures. The apertures are treated as waveguides, can be filled with a dielectric material, and can have arbitrary cross-section. The method for analyzing the FSS is based on a general mode-matching technique. The FSS is divided into a number of boundaries and uniform layers. The electric and magnetic fields outside the screen and inside the dielectric layers are expanded in tangential plane waves, Floquet modes. The tangential fields inside the aperture layers, are expanded in