We reveal the existence of a type of surface electromagnetic wave supported by hyperbolic metasurfaces, described by a conductivity tensor with an indefinite signature. We demonstrate that the spectrum of the hyperbolic metasurface waves consists of two branches corresponding to hybrid transverse electric–transverse magnetic waves with a polarization that varies from linear to elliptic or circular depending on the wave frequency and propagation direction. The shape of the equal-frequency contours drastically depends on the frequency and changes from the elliptical to hyperbolic—a topological transition takes place. We derive asymptotic formulas describing the losses of the surface waves for capacitive, inductive, and hyperbolic regimes of the metasurface. We analyze numerically the generation of surface waves by a point electric dipole placed in the vicinity of the metasurface with numerical simulations, and also reveal wave-front peculiarities in strong anisotropic hyperbolic and $\sigma$-near-zero regimes of the metasurface.

Transverse spin angular momentum is an inherent feature of evanescent waves which may have applications in nanoscale optomechanics, spintronics, and quantum information technology due to the robust spin-directional coupling. Here we analyze local spin angular momentum density of hybrid surface waves propagating along anisotropic hyperbolic metasurfaces. We reveal that, in contrast to bulk plane waves and conventional surface plasmons at isotropic interfaces, the spin of the hybrid surface waves can be engineered to have an arbitrary angle with the propagation direction. This property allows us to tailor directivity of surface waves via the magnetic control of the spin projection of quantum emitters, and it can be useful for optically controlled spin transfer.

Hyperbolic metasurfaces have gained significant attention due to their extraordinary electromagnetic properties to control propagating plane waves, but the excitation and propagation of surface plasmon-polaritons at hyperbolic metasurfaces, called hyperbolic plasmons, have been experimentally observed only recently. However, the advantages of the hyperbolic plasmons, such as hybrid TE-TM polarization discussed below, are not yet fully revealed and analyzed. In this paper, we focus on the numerical and experimental characterization of surface waves in the frequency range from 2 to 8 GHz supported by a hyperbolic metasurface composed of anisotropic metallic Jerusalem crosses printed on a thin dielectric substrate. We show different shapes of equal frequency contours, which correspond to a plethora of excitation and propagation regimes of surface waves. The principal novelty of this work consists in the experimental demonstration of surface waves with hybrid, i.e., mixed TE-TM, polarization. Surface waves with hybrid polarization are a promising tool in a number of applications and phenomena, including polarization converters, plasmonic sensors, plasmon steering over a surface, optical forces, and spin-orbit photonics, and they highlight the impact of on-chip and planar networks.

Self-complementary metasurfaces have gained significant attention due to their unique frequency-independent transmission and reflection properties and the possibility of the polarization transformation of plane waves. In this paper, we focus on the near-field spectrum to investigate, both theoretically and experimentally, the properties of surface waves supported by anisotropic self-complementary metasurfaces. We show that as a consequence of the electromagnetic Babinet’s duality, such a structure is hyperbolic for any frequency. We demonstrate the possibility of switching the canalization direction of surface waves with ultimately flat phase fronts for 90° by a very small frequency shift, paving the way to the extreme tunability and surface-wave routing. We reveal the polarization degree of freedom inherent to plane waves by demonstrating the all-frequency TE-TM polarization degeneracy of the surface waves along two principal directions. The results obtained open a plethora of opportunities for practical applications, including flat polarization devices, optical data-processing systems, sensing, holography and antennas.

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.