Gyrotropic effects in hyperbolic metamaterials

Hyperbolic metamaterials (HMs) have recently been one of the most prominent impetus to infrared and optical applications for their broadband spontaneous emission enhancement and super absorption of near fields. It has been shown that plasmonic layers stacked with subwavelength dielectric spacers can be homogenized as a uniaxial electric media, with negative transverse permittivity for a wide range of parameters, which gives rise to a hyperbolic wavevector dispersion characteristics. In this premise, we investigate an HM implementation that utilize thin in-plane anisotropic structures in a multilayer configuration. Such anisotropic materials can be implemented, depending on the desired operating wavelength, using anistropically-patterned metasurfaces, or by exploiting the Hall effect in magnetically-biased metals, semiconductors or graphene sheets. We explore the possibility of observing non-vanishing off-diagonal elements in the effective permittivity tensor, in other words, obtaining an effective gyrotropic and nonreciprocal media with negative transverse permittivity. Moreover, we demonstrate how the propagation wavenumber inside the effective gyrotropic medium can be derived using a transmission line formalism, where a new set of wave solutions is formed as a result of the peculiar coupling between the TE and TM polarizations. We also validate our analysis with the rigorous transfer matrix approach by cascading the multilayers and constructing a four port network that accounts for the mode-coupling, and we show good agreement with the effective medium description in calculating plane wave transmission and reflection spatial spectrum of the multilayer.