Multiplication of the orbital angular momentum of phonon polaritons via sublinear dispersion

Optical vortices (OVs) promise to greatly enhance optical information capacity via orbital angular momentum (OAM) multiplexing. The need for on-chip integration of OAM technologies has prompted research into subwavelength-confined polaritonic OVs. However, the topological order imprinted by the structure used for the transduction from free-space beams to surface polaritons is inherently fixed after fabrication. Here, we overcome this limitation via dispersion-driven topological charge multiplication. We switch the OV topological charge within a small $\sim 3 \%$ frequency range by leveraging the strong sublinear dispersion of low-loss surface phonon polaritons (SPhP) on silicon carbide membranes. Applying the Huygens principle we quantitatively evaluate the topological order of the experimental OVs detected by near-field imaging. We further explore the deuterogenic effect, which predicts the coexistence of multiple topological charges in higher-order polaritonic OVs. Our work demonstrates a viable method to manipulate the topological charge of polaritonic OVs, paving the way for the exploration of novel OAM-enabled light-matter interactions at mid-infrared frequencies.