An Improved Theoretical Model to Extract the Optical Conductivity of Two-Dimensional Material from Terahertz Transmission or Reflection Spectroscopy

The technique of terahertz time-domain spectroscopy (THz-TDS) enables us to simultaneously determine the real and imaginary parts of optical parameters. However, it is still a challenge to extract the optical parameters of a two-dimensional (2D) material (or an ultra-thin film) on a substrate accurately and flexibly for an arbitrary incident angle and different polarization. By treating a 2D material as a conductive boundary without thickness, we propose an improved theoretical model to extract the optical conductivity of the 2D material on a substrate from THz transmission or reflection spectroscopy. Importantly, the effects of wave polarization, incident angle, and multiple reflections in the substrate are considered in our model and the analytical formulae associated with the optical conductivity of the 2D material are provided. Furthermore, we verify the validation of our model based on the THz transmission and reflection experiments for mono- and few-layer MoS2 on sapphire substrates. These results not only are of practical significance for investigating the THz properties of 2D materials but can also be extended to the situations of ultra-thin films and/or incoherent detection such as Fourier transform infrared spectroscopy.