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A metamaterial made by stacked hole-array layers known as a fishnetmetamaterial behaves as a hyperbolic metamaterial at wavelength much longerthan hole-array period. However, the analytical formulae of effectiveparameters of a fishnet metamaterial have not been reported hindering thedesign of deep-subwavelength imaging devices using this structure. We reportthe new closed-form formulae of effective parameters comprising anisotropicdispersion relation of a fishnet metamaterial working at terahertz or microwavefrequency. These effective parameters of a fishnet metamaterial are consistentwith those obtained by quasi-full solutions using known effective parameters ofa hole-array layer working at frequency below its spoof plasma frequency withthe superlattice period much smaller than the hole-array period. We alsotheoretically demonstrate the deep-subwavelength focusing at {\lambda}/83 usingthe composite structure of a slit-array layer and a fishnet metamaterial. It isfound that the focused intensity inside a fishnet metamaterial is several timeslarger than that without the fishnet metamaterial, but the transmittedintensity is still restricted by large-wavevector difference in air and afishnet metamaterial. Our effective parameters may aid the next-generationdeep-subwavelength imaging devices working at terahertz or microwave radiation.

Closed-form formulae of hyperbolic metamaterial made by stacked hole-array layers working at terahertz or microwave radiation