We show that the blockage in transmission of a screen with a periodic microstructure integrated over all wavelengths is bounded by the static polarizability per unit area of the screen. Physical bounds on the co-polarized transmission coefficient over a wavelength interval are presented using only information from the zero-frequency properties of the microstructure. The theoretical results are compared to and verified by measurements on a screen composed of a large number of split ring resonators printed on a dielectric substrate.

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