Mapping the complex refractive index of single layer graphene on semiconductor or polymeric substrates at terahertz frequencies

Assessing experimentally the main optical parameters of graphene (e.g. complex refractive index, carrier density, mobility) in the far-infrared (0.1-10 THz) is important for quantum science, due to the possibility to devise miniaturized devices (frequency combs, random lasers), components (optical switches, spatial light modulators, metamaterial mirrors and modulators) or photonic circuits, in which graphene can be integrated with existing semiconductor technologies to manipulate their optical properties and induce novel functionalities. Here, we combine time domain terahertz (THz) spectroscopy and Fourier transform infrared spectroscopy to extract the complex refractive index of large (similar to 1cm(2)) area single layer graphene on thin (similar to 0.1-1 mu m) polymeric suspended substrates, flexible and transparent films, and high reflectivity Si substrates in the 0.4-1.8 THz range. We model our data to extract the relevant optical (refractive index, absorption coefficient, penetration length) electronic (Fermi velocity) and electrical (carrier density, mobility) properties of the different graphene samples.