Parallel plate waveguide time domain spectroscopy to study terahertz conductivity of ultrathin materials

The newly discovered atomically thin and layered materials which host electronic system that respond to long wavelength light in extraordinary manner can lead to a major breakthrough in the field of terahertz (THz) optics and photonics. However, their low conductivities due to either low densities or low mobility make it challenging to characterize their basic THz properties with the standard spectroscopic method. Here, we develop a THz spectroscopic technique based on parallel plate waveguide (PPWG) to overcome the limitations of the conventional THz time domain spectroscopy (TDS) technique. The present method is particularly suitable to ultrathin conductive materials with low carrier density. We report in details the derivation of the dispersion equations of the terahertz wave propagation in a PPWG loaded by a thin conductive materials with zero -thickness. These dispersion equations for transverse magnetic (TM) and transverse electric (TE) waveguide modes are the core of the optical parameters extraction algorithm in the THz-PPWG-TDS analysis. We demonstrate the effectiveness of the waveguide approach by characterizing low conductive CVD graphene. The high sensitivity of THz-PPWG-TDS technique enables us to study the carrier dynamics in graphene with Drude and Drude-Smith model.