An analytical method to study the magneto-optical effects of a graphene sheet embedded between two magneto-optical media

•We develop a transfer matrix method to calculate the MO responses of graphene.•In general formalism, the graphene sheet is embedded between two MO media.•We analytically and numerically evaluated the obtained transfer matrix method.•A graphene sheet at the interface of air and InAs layer is considered for numerical calculations. This paper represents a developed theoretical model for studying the magneto-optical (MO) effects of reflected light from the interface of two semi-infinite MO materials with a graphene sheet between them. For this purpose, we have developed a 4 by 4 transfer matrix method, and we have evaluated this method analytically and numerically. Our model can be used to investigate the MO responses of the structures such as MO and MO, dielectric and MO, and dielectric and dielectric materials interface with a graphene sheet between them. The intensity reflection coefficient (IR), Kerr rotation angle (θK), and ellipticity (ηK) from these structures can be calculated using this method. We have analytically evaluated our model by comparing with few previous works of other authors. However, for numerical evaluation, we have considered a graphene sheet lied on the interface of air and InAs (S1 structure) under an external magnetic field in the THz frequency region. The MO responses of the S1 structure have been investigated and compared with other two structures responses, one is semi-infinite InAs layer (S2 structure), and the other one is a graphene sheet on SiC substrate (S3 structure). The effects of applied magnetic field strength and ambient temperature on the MO responses of these three structures have been investigated.