Fundamental bounds on transmission through periodically perforated metal screens with experimental validation

TL;DR

This paper establishes fundamental physical limits on the transmission bandwidth of periodically perforated metal screens using a sum rule, validated through numerical simulations and experimental measurements.

Contribution

It derives a general sum rule for transmission through periodic apertures, providing a physical bound on bandwidth and guiding the design of frequency selective surfaces.

Findings

Sum rule relates transmission bandwidth to static polarizability.

Numerical verification of the bandwidth bound for various aperture designs.

Experimental validation with measurements of a horseshoe-shaped slot array.

Abstract

This paper presents a study of transmission through arrays of periodic sub-wavelength apertures. Fundamental limitations for this phenomenon are formulated as a sum rule, relating the transmission coefficient over a bandwidth to the static polarizability. The sum rule is rigorously derived for arbitrary periodic apertures in thin screens. By this sum rule we establish a physical bound on the transmission bandwidth which is verified numerically for a number of aperture array designs. We utilize the sum rule to design and optimize sub-wavelength frequency selective surfaces with a bandwidth close to the physically attainable. Finally, we verify the sum rule and simulations by measurements of an array of horseshoe-shaped slots milled in aluminum foil.