  We have proposed an arbitrary vector beam (VB) generation scheme in a thin
disk-shaped quantum dot (QD) medium considering phonon interaction. The QD
biexciton system exhibits interplay between first and third-order nonlinear
susceptibility between two orthogonal circular polarisation transitions. Three
QD transitions are coupled with one applied weak and two strong control orbital
angular momentum (OAM) carrying fields. Therefore, the applied field
experiences absorption, and a new field with the desired OAM is generated via
four-wave mixing (FWM). These two orthogonal field superpositions produce VB at
the QD medium end. We have also demonstrated the polarization rotation of a VB
by changing only the relative control field phase. Additionally, we have
analyzed the effect of temperature on the VB generation.
