Effective surface conductivity of optical hyperbolic metasurfaces: from far-field characterization to surface wave analysis.

Metasurfaces offer great potential to control near- and far-fields through engineering optical properties of elementary cells or meta-atoms. Such perspective opens a route to efficient manipulation of the optical signals both at nanoscale and in photonics applications. In this paper we show that a local surface conductivity tensor well describes optical properties of a resonant plasmonic hyperbolic metasurface both in the far-field and in the near-field regimes, where spatial dispersion usually plays a crucial role. We retrieve the effective surface conductivity tensor from the comparative analysis of experimental and numerical reflectance spectra of a metasurface composed of elliptical gold nanoparticles. Afterwards, the restored conductivities are validated by semi-analytic parameters obtained with the nonlocal discrete dipole model with and without interaction contribution between meta-atoms. The effective parameters are further used for the dispersion analysis of surface plasmons localized at the metasurface. The obtained effective conductivity describes correctly the dispersion law of both quasi-TE and quasi-TM plasmons in a wide range of optical frequencies as well as the peculiarities of their propagation regimes, in particular, topological transition from the elliptical to hyperbolic regime with eligible accuracy. The analysis in question offers a simple practical way to describe properties of metasurfaces including ones in the near-field zone with effective conductivity tensor extracting from the convenient far-field characterization.