Analysis of Multifunctional Graphene-Based Hyperbolic Metamaterials at Mid-Infrared Frequencies

Abstract

We conceptualize and theoretically explore a compact, tunable, and multifunctional device using graphene-based hyperbolic metamaterials. 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 rage of 1.4 𝜇m to 1.6 𝜇m whilst Type-II HMM ranges from 3.3 𝜇m to 8 𝜇m. We show that by changing the chemical potential of the graphene, the reflectance spectra of the device can be shifted to the shorter wavelengths. Our analysis also demonstrates that for a fixed 𝜇𝑐 , 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 test the transmission properties of two sub-wavelength slits through a straight section of the graphene-based metamaterial slab at 1.5 𝜇m, observing that our device is capable of resolving the deep sub-wavelength features at the output end of the slab. At 1.5 𝜇m, we also examine the propagation of light through a graphene-based magnifying hyperlens, achieving a three-fold image magnification. Finally, we compare the calculated intensity profile for two-slits with the numerical simulation, finding good agreement between them.

Keywords: Metamaterial, Hyperlens, Diffraction