We discuss the differences and similarities in the interaction of scalar and vector wave fields with particles and holes. Analytical results are provided for the transmission of isolated and arrayed small holes as well as surface modes in hole arrays for light, electrons and sound. In contrast to the optical case, small-hole arrays in perforated perfect screens cannot produce acoustic or electronic surface-bound states. However, unlike electrons and light, sound is transmitted through individual holes approximately in proportion to their area, regardless of their size. We discuss these issues with a systematic analysis that allows one to explore both common properties and unique behavior in wave phenomena for different material realizations.
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Abajo et al. (2009) studied this question.
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