Light is an excellent medium for both classical and quantum information transmission due to its speed, manipulability, and abundant degrees of freedom into which to encode information. Recently, space-division multiplexing has gained attention as a means to substantially increase the rate of information transfer by utilizing sets of infinite-dimensional propagation eigenmodes such as the Laguerre-Gaussian "donut" modes. Encoding in these high-dimensional spaces necessitates devices capable of manipulating photonic degrees of freedom with high efficiency. In this work, we demonstrate controlling the optical susceptibility of an atomic sample can be used as powerful tool for manipulating the degrees of freedom of light that pass through the sample. Utilizing this tool, we demonstrate photonic mode conversion between two Laguerre-Gaussian modes of a twisted optical cavity with high efficiency. We spatiotemporally modulate the optical susceptibility of an atomic sample that sits at the cavity waist using an auxiliary Stark-shifting beam, in effect creating a mode-coupling optic that converts modes of orbital angular momentum l = 3 → l = 0. The internal conversion efficiency saturates near unity as a function of the atom number and modulation beam intensity, finding application in topological few-body state preparation, quantum communication, and potential development as a flexible tabletop device.