Title: Closed-form formulae of hyperbolic metamaterial made by stacked hole-array layers working at terahertz or microwave radiation,
Abstract: A metamaterial made by stacked hole-array layers known as a fishnet
metamaterial behaves as a hyperbolic metamaterial at wavelength much longer
than hole-array period. However, the analytical formulae of 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 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 frequency below its spoof plasma frequency with
the superlattice period much smaller than the hole-array period. We also
theoretically demonstrate the deep-subwavelength focusing at {\lambda}/83 using
the 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 large-wavevector difference in air and a
fishnet metamaterial. Our effective parameters may aid the next-generation
deep-subwavelength imaging devices working at terahertz or microwave radiation.