Nonlinear parametric generation of optical vortices and their propagation in graphene quantum dots

In this paper, we investigate the propagation of optical vortices carrying orbital angular momentum in a coherently prepared graphene quantum dot (GQD) system. Using the Maxwell-Bloch equations and assuming weak light-matter interaction, we examine two key scenarios. The first scenario involves the transfer of optical vortices through nonlinear parametric process, starting with one vortex beam absent and then generated during its interaction with the GQD system. We analyze how various system parameters affect vortex conversion efficiency and the matching of optical vortices. Our results reveal that vortex conversion efficiency is significantly influenced by detuning and incoherent pumping, with notable efficiency and steady-state intensity achieved when these parameters are properly manipulated. In the second scenario, where both vortex beams are initially present, we explore their propagation within the GQD medium. In particular, we observe that when both beams are resonant and incoherent pumping is applied, they quickly stabilize and perfectly match over short propagation distances. Conversely, when both beams are nonresonant, they exhibit oscillatory decay in intensity, preventing them from achieving a steady-state match and leading to absorption by the GQD medium. This study enhances our understanding of vortex beam dynamics in GQD systems and provides insights into optimizing vortex beam transfer for high-dimensional quantum information processing applications.