Hyperbolic-to-hyperbolic transition at exceptional Reststrahlen point in rare-earth oxyorthosilicates.

Anisotropic optical crystals can exhibit a hyperbolic response within the Reststrahlen band (RB) and support directional polaritonic propagations when interacting with light. Most of the reported low-symmetry optical crystals showcase the evolution from hyperbolic to elliptic dispersion topologies, largely owing to their adjacent RBs being either overlapped or separated. Here, we report an exceptional Reststrahlen point (ERP) in rare-earth oxyorthosilicate YSiO, at which two neighboring RBs almost kiss each other. Consequently, we observe the direct hyperbolic-to-hyperbolic topological transition: the hyperbolic branches close and reopen along with the rotating transverse axis (TA). At such ERP, the TA merges to the direction orthogonal to its proximate phonon mode, mainly due to the interplay between these two non-orthogonal phonon modes. We also find that even with the existence of only one single RB, the TA can rotate in-plane. Our findings are prevalent in isostructural rare-earth oxyorthosilicates, such as LuSiO. The universally underlying physics of ERP and its corresponding special class of rare-earth oxyorthosilicates may offer playgrounds for continuously tuning phonon polariton propagation direction, and broadband controlling light dispersion of polaritonic nanodevices.