I. Introduction
High transmission through periodically perforated metal screens occurs at certain frequencies associated with various resonance phenomena. Those can be intrinsic resonances of the apertures, related to their size and geometry, or resonances related to the periodicity. Some transmission peaks, referred to as extraordinary transmission (EoT) [1]–[3], have been explained from a theoretical perspective by surface plasmon polaritons at optical frequencies [2], [4], and by spoof plasmons at radio frequencies [5]. From the practical perspective it is desirable to know what is the maximum attainable transmission bandwidth, regardless of the nature of the transmission. Here, we formulate a fundamental bound on the transmission bandwidth in the form of a sum rule.