Polarized induced phase grating in a quantized four-level graphene monolayer system

We discuss the electromagnetically induced grating (EIG) and electromagnetically induced phase grating (EIPG) in a four-level quantized graphene monolayer system. By using the density matrix technique and perturbation theory, we first obtain the self-Kerr nonlinear susceptibility of the graphene system; afterwards, we study the amplitude and phase modulations of the probe light. We discovered that the EIG and EIPG can be found by controlling the elliptically polarized coupling fields that interact with the monolayer graphene system. Owing to the phase modulation of the transmitted light beam, we recognized that the probe strength can also additionally switch from zeroth-order to high-order diffraction. Moreover, we found that the diffraction performance of the grating may be adjusted through tuning the polarization of the coupling light.