Abstract

A metamaterial made by stacked hole-array layers, known as a fishnet metamaterial, behaves as a hyperbolic metamaterial at a wavelength much longer than the hole-array period. However, the analytical formulae of the effective parameters of a fishnet metamaterial have not been reported, hindering the design of deep-subwavelength imaging devices using this structure. We report the new closed-form formulae of effective parameters comprising the anisotropic dispersion relation of a fishnet metamaterial working at terahertz or microwave frequency. These effective parameters of a fishnet metamaterial are consistent with those obtained by quasi-full solutions using known effective parameters of a hole-array layer working at a frequency below its spoof plasma frequency with the superlattice period much smaller than the hole-array period. We also theoretically demonstrate deep-subwavelength focusing at $\lambda /83$ using a composite structure of a slit-array layer and a fishnet metamaterial. It is found that the focused intensity inside a fishnet metamaterial is several times larger than that without the fishnet metamaterial, but the transmitted intensity is still restricted by a large-wavevector difference in air and a fishnet metamaterial. Our effective parameters may aid next-generation deep-subwavelength imaging devices working under terahertz or microwave radiation.

© 2017 Optical Society of America

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