  We propose a four-level cascade-type atomic system in which two reverse
four-wave mixing (FWM) processes can coexist via optical transitions in
distinct pathways. This enables the generation of high- or low-frequency vortex
beams on demand and facilitates spatial phase modulation of the vortex beam
intensity distribution. The two reverse FWM processes can yield the
sum-frequency vortex beam with high frequency and the difference-frequency
vortex beam with low frequency, corresponding to frequency up-conversion and
down-conversion, respectively. The closed-loop configuration's phase
sensitivity allows for asymmetric phase modulation of the spatial distributions
of the two output vortex beams. Additionally, increasing the phase enables
spatial rotation of the output beams. Our proposed scheme holds promise for
potential applications in quantum nonlinear optics and vortex exchange.
