In a general aspect, optical beams are manipulated. In some cases, an optical device includes an inlet to receive a first beam, and one or more prism pairs. Each prism pair includes one or more birefringent gradients configured to transform the first beam into a second beam. The second beam is associated with a lattice of cells, where each cell includes a first portion and a second portion. The first portion is associated with a first orbital angular momentum (OAM) mode and a first polarization, and the second portion is associated with a second OAM mode and a second polarization.