A negative index metamaterial driven by phonons on a ZnO platform

Abstract

Negative index metamaterials (NIMs) can be achieved with uniaxial hyperbolic metamaterials (HMMs) featuring $\epsilon_{parallel}>0$ and $\epsilon_{perpendicular}<0$. This type of approach has been traditionally realized using stacked doped/undoped semiconductor layers. Only recently surface phonon polaritons (SPhPs) have emerged as a promising low-loss alternative to surface plasmon polaritons (SPPs). Despite this advantage, the SPhP-based approach has been underexplored due to the challenges associated with ensuring high crystal quality in the heterostructure when using alloys with different phonon frequencies. In this work, we design a phononic-driven NIM using a ZnO/(Zn,Mg)O heterostructure, demonstrating control over its hyperbolic behavior through the precise selection of the Mg content and the relative layer thicknesses. Our study shows that increasing the Mg content in the ternary layers enhances the type I behavior, and that the optimal layer thickness varies depending on the Mg content. After analyzing the conditions for achieving type I hyperbolic dispersion, we experimentally demonstrate this concept with a sample featuring equal layer thicknesses and a 32% Mg concentration. We characterize the structure by means of polarized reflectance spectroscopy and use attenuated total reflectance spectroscopy to report the presence of a SPhP mode located within the type I hyperbolic region. By employing the transfer matrix method, we demonstrate that this mode exhibits negative frequency dispersion, a hallmark of type I hyperbolic modes, and isofrequency curve calculations further confirm this behavior. Controlling the design of a phononic hyperbolic type I metamaterial lays the groundwork for exploring its potential applications in attaining low-loss, sub-diffraction-limited optical modes using SPhP excitations.