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In this letter we have proposed a four-level graphene monolayer system for identifying the topological charge of Laguerre–Gaussian light. Here, we have shown that due to the four-wave mixing mechanism in the monolayer graphene system, a weak signal beam can be generated due to quantum coherence and interference effect. We have discussed the spatially dependent linear absorption spectrums of the weak probe and new generated signal beams via quantum mechanical density matrix formalism. We have found that by numbering the spot areas of the probe and signal beams, one can realize the topological charge of the Laguerre–Gaussian beam interacts by monolayer graphene system. Moreover, we have realized that for some topological charge the new generated signal beam can be amplified in the graphene system.

In this paper, we study the tunneling induced optical bistability (OB) in a quantum dot (QD)-metallic nanoparticle (MNP) hybrid system via surface plasmon effects. We realized that in the presence of the tunneling effect, OB arises when the probe light is parallel to the major axis of the hybrid system. We realized the threshold of OB can be controlled by controlling the distance parameter between the QD and MNP. For appropriate distance between the QD and MNP, we find that optical multistability (OM) appears in the system. We find that the threshold of OM can be adjusted when we consider the radius effect of the MNP, respectively.

In this letter, we have studied the optical lateral shifts of transmitted and reflected lights in a defect structure doped by a single layer of graphene nanostructure. For adapting the optical features of the lateral shifts, we have first studied the refractive index properties of the defect layer. We have studied the conditions for achieving the negative and positive refractive index of the graphene monolayer system. After that, we have discussed the optical lateral shifts of the reflected and transmitted light beams when the refractive index of the graphene nanostructure become positive or negative, respectively. We have found that the enhanced lateral shifts for reflected and transmitted lights may be possible for a positive refractive index. For the negative refractive index, we have realized that simultaneous negative or positive lateral shifts are possible for the reflected and transmitted light beams. In our proposed scheme, the lateral shifts at the fixed incident angle are possible only by tuning the optical parameters without needing to change the cavity structure.

In this paper, we have discussed the spatial dependence of linear and nonlinear optical properties of infrared laser pulse in a single-layer graphene system. We have proposed two scenarios for adjusting the linear and nonlinear optical properties of the medium. In the first assumption, the graphene system interacts by an elliptical polarized optical vortex light and we adjust the linear and nonlinear properties via ellipticity and vorticity parameters. We found that the enhanced nonlinear coefficient was obtained with reduced linear absorption. In the second assumption, we assumed that two composite optical vortex lights interact with graphene layer. In this case the linear and nonlinear optical properties can be controlled via orbital angular momentum (OAM) of the applied lights. Here, we have shown that by adjusting the azimuthal angle of the composite vortex light, the spatial control of linear and nonlinear properties is possible. We found that in some regions of space the probe absorption vanishes and enhanced the nonlinear coefficient accompanied with optical transparency. Our results may be useful applications in future in all-optical system devices in nanostructures.