Terahertz characterization of graphene conductivity via time-domain reflection spectroscopy on metal-backed dielectric substrates

A theoretical and experimental framework for the characterization of the terahertz (THz) conductivity of graphene on metal-backed substrates is presented. Analytical equations are derived for the general problem of oblique incidence of the THz beam in a time-domain spectroscopic (TDS) setup working in reflection. The recorded time-domain signals are post-processed in order to retrieve the substrate thickness, its dielectric frequency dispersion, and the complex graphene conductivity frequency dispersion, which is described by a generalized Drude-Smith model. The method is tested on two samples of chemical vapor deposited graphene, transferred on polyethylene terephthalate and cyclo-olefin polymeric substrates of sub-millimetric thickness, and characterized by Raman spectroscopy. By working only with the amplitude spectra, the proposed method circumvents issues stemming from phase uncertainties that typically affect TDS measurements in reflection mode. More important, it allows for a rapid, nondestructive characterization of graphene sheets that can be directly integrated in the production flow of graphene-based passive or active components employing metal-backed resonant cavities, such as THz absorbers, metasurface lenses, or leaky-wave antennas.