A multiple reflection model for the investigation of infrared transmission of a graphene/substrate system

We develop a multiple reflection model (MRM) for the examination of infrared transmission properties of a graphene/substrate system. The incident angle and the multiple reflection beams in the substrate with finite thickness are taken into consideration. The model can be applied to predict the optical responses of graphene/substrate systems or to extract the real part of the optical conductance of graphene from the experimental measurement. As an example, we calculate the relative transmittance of graphene/quartz and graphene/sapphire systemsby using MRM and provide an experimental verification in the near-infrared range. The measured results show good agreement with the calculated ones. Our method can be easily extended to accurately and non-invasively identify the layer numbers of other 2D materials, and assess the quality of them.