Not yet reviewed by Pith; the record is open.

One of the major difficulties in realizing a high-dimensional frequency converter for conventional optical vortex (COV) stems from the difference in ring diameter of COV modes with different topological charge numbers l. Here, we implement a high-dimensional frequency convertor for perfect optical vortex (POV) modes with invariant size through the four-wave mixing (FWM) process by utilizing Bessel-Gaussian beams instead of Laguerre-Gaussian beams. The measured conversion efficiency from 1530 nm to 795 nm is independent of l at least in subspace of {-6,...,6}, and the achieved conversion fidelities for two-dimensional (2D) superposed POV states exceed 97%. We further realize the frequency conversion of 3D, 5D and 7D superposition states with fidelities as high as 96.70%, 89.16% and 88.68%, respectively. The reported scheme is implemented in hot atomic vapor, it's also compatible with the cold atomic system and may find applications in high-capacity and long-distance quantum communication.