Graphene exhibits excellent electronic and optical properties, which has been proposed as an advanced material for new generation of electronic and optical devices. We develop a detailed theoretical mode to investigate the optical properties of graphene-wafer systems. The photon-excited carriers and emission are obtained based on the mass-balance equation and the charge number conservation equation, which are derived from Boltzmann equation. The analytical results of photon excited carrier density and photon emission coefficient are achieved self-consistently in terahertz radiation fields. It is found that the photon excited carrier density increases with doped electron density or temperature decreasing. The higher the doped electron density and the lower the temperature, the larger the photon emission coefficient is. The optical emission increases with doped electron density increasing, and the optical emission increases with temperature decreasing. It shows that photon-excited carriers and emission of graphene can be effectively tuned by gate voltage. These theoretical results can be used to understand the relevant experimental findings. This theoretical study can benefit the applications in advanced optoelectronic devices based on graphene, especially terahertz devices.