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We theoretically investigate the transmission of electromagnetic radiation through a metal plate with a zero-$ϵ$ metamaterial slit, where the permittivity tends towards zero over a given bandwidth. Our analytic results demonstrate that the transmission coefficient can be substantial for a broad range of slit geometries, including subwavelength widths that are many wavelengths long. This resonant effect has features quite unlike the Fabry-Perot-like resonances that have been observed in conductors with deep channels. We further reveal that ultranarrow zero-$ϵ$ channels can have significantly greater transmission compared to slits with no wave impedance difference across them.
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Halterman et al. (2008) studied this question.
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