The role of low and high frequency asymptotes when deriving physical bounds for electromagnetically functional surfaces

Surfaces can be designed to have intentional electromagnetic functionality, for instance absorption, frequency or polarization selectivity, focusing, pulse shaping etc. These functions are often characterized in terms of some performance parameter like minimum acceptable absorption level, and the bandwidth over which this performance is achieved. Based on the physical principles of linearity, passivity, and time translational invariance, it can often be shown that the product of performance and bandwidth is bounded by a number which can be computed from knowledge of the low and high frequency asymptotes of the electromagnetic function in question. In this contribution, we show how these asymptotes (in particular the low frequency limit) can be computed or estimated for a number of canonical structures, and highlight the fundamental difficulties that arise when simplified models like PEC boundary conditions can not be applied. For instance, to compute the low frequency reflection and transmission coefficients for a perforated infinite periodic structure with finite conductivity proves to require significantly different local problems than the corresponding PEC structure, due to the partial transmission of electromagnetic waves in the static limit.