Analysis of multifunctional graphene-based hyperbolic metamaterials at mid-infrared frequencies

We conceptualize and theoretically explore a compact, tunable, and multifunctional device using graphene-based hyperbolic metamaterials (HMMs). We model our device using an effective medium theory and apply a standard transfer matrix approach to calculate the reflectance spectrum at mid-infrared frequencies. Our theoretical analysis suggests that by carefully tailoring the properties of graphene, the dispersion profile of the HMM is switchable between ellipse and hyperbola, where two types (Type-I and Type-II) of hyperbolic dispersion profile can be obtained simultaneously: Type-I HMM is located in the wavelength range of $1.4\mu m$ to $1.6\mu m$ whilst Type-II HMM ranges from $3.3\mu m$ to $8\mu m$. We show that by changing the chemical potential (${\mu }_c$) of the graphene, the reflectance spectra of the device can be shifted to the shorter wavelengths. Our analysis also demonstrates that for a fixed ${\mu }_c$, the reflectance spectra of the device can be further blue-shifted by increasing the number of graphene monolayers. Notably, we find that the reflectance spectra remain largely unaffected by the transverse polarization (TE/TM modes) of the incoming waves. We also test the transmission properties of two sub-wavelength slits through a straight section of the graphene-based metamaterial slab at $1.5\mu m$, observing that our device is capable of resolving the deep sub-wavelength features at the output end of the slab. At $1.5\mu m$, we also examine the propagation of light through a graphene-based magnifying hyperlens, achieving a three-fold image magnification at the output surface. Finally, we compare the calculated intensity profile for two-slits with the numerical simulation, finding good agreement between them. We believe that our proposed metamaterial-based multifunctional device would be a suitable candidate for creating imaging devices and tunable filters.