In this study, the Optical conductivity of substitutionary doped graphene is
investigated in presence of the Rashba spin orbit coupling (RSOC). Calculations have been performed within the coherent potential approximation (CPA) beyond the Dirac cone approximation. Results of the current
study demonstrate that the optical conductivity is increased by increasing
the RSOC strength. Meanwhile it was observed that the anisotropy of the
band energy results in a considerable anisotropic optical conductivity (AOC)
in monolayer graphene. The sign and magnitude of this anisotropic conductivity was shown to be controlled by the external field frequency. It was also shown that the Rashba interaction results in electron-hole asymmetry
in monolayer graphene.