Retrieval of material parameters for uniaxial metamaterials

Abstract

We present a general method for retrieving the effective tensorial permittivity of uniaxially anisotropic metamaterials. By relaxing the usually-imposed constraint of assuming non-magnetic metal/dielectric metamaterials, we also retrieve the effective permeability tensor and show that multilayer hyperbolic metamaterials exhibit a strong and broadband diamagnetic response in the visible regime. The method provides the means for designing magnetically anisotropic metamaterials for studying magnetic topological transitions in the visible regime. We obtain orientation-independent effective material parameters, which are distinguishable from mere wave parameters. We analytically validate this method for Ag/SiO 2 planar metamaterials with a varying number of layers and filling fractions, and compare to the results from effective medium theory and Bloch theory. KeywordsEffective medium theory, transfer matrix, uniaxial anisotropy, hyperbolic metamaterials (HMM), isofrequency contour, density of optical states

Field-effect induced tunability in hyperbolic metamaterials

“…1, calculated through the utilized retrieval method [1] to the dispersion of an infinite stack of unit cells, calculated through the generalized Bloch wave vector. Specifically, the unit cell of Fig.…”

“…This changes Maxwell's boundary conditions on those interfaces, which affects the effective metamaterial parameters, which are obtained through a parameter retrieval method [1]. The optical parameter affected the most through this modulation is the extraordinary permittivity ε e as we show in Part B.…”

“…It is characterized through a tensorial electric permittivity and magnetic permeability , where ε ο and μ ο refer to the ordinary parameters in the inplane direction, while ε e and μ e correspond to the direction of the optical axis. The strong anisotropy along the optical axis causes the TM polarized bulk modes, containing an electric field component in this direction, to experience strong birefringence expressed via the dispersion equation 1 :…”

“…Recent studies [1,21] have shown that planar HMMs can be engineered to exhibit hyperbolic dispersion…”

“…The latter idea arises from the consideration that Dirac-like dispersion cones can be realized in a linear dispersion regime where the metamaterial effective parameters approach zero, allowing for topological transitions to occur in metamaterials. Hyperbolic metamaterials also support ENZ and epsilon near pole (ENP) spectral regions [1,21] that induce band splitting and support such topological transitions [22]. Thus, active tuning of the effective parameters can tune the spectral regions of topological transitions along with the possibility to dynamically study topological transitions in photonic systems.…”