Antihyperbolic surface waves on hyperbolic metasurfaces

Hyperbolic metasurfaces exhibit the ability to support surface waves with hyperbolic isofrequency contours (i.e., hyperbolic eigenmodes), offering an exceptional platform for enhancing light-matter interactions. In addition to hyperbolic eigenmodes, hyperbolic metasurfaces can also support the propagation of surface-wave eigenmodes with an antihyperbolic isofrequency contour (i.e., antihyperbolic eigenmodes). In this work, we explore the lesser-known antihyperbolic eigenmodes, highlighting their unique polarization properties compared to hyperbolic eigenmodes. We find that the antihyperbolic eigenmodes at the vertices of the antihyperbolic isofrequency contour and the hyperbolic eigenmodes at the vertices of the hyperbolic isofrequency contour could have purely linear but opposite polarizations. Moreover, we reveal that the manipulation of metasurface's surface conductivity can provide a feasible route to realize the polarization conversion between these linearly polarized antihyperbolic and hyperbolic eigenmodes. That is, the s-polarized antihyperbolic eigenmodes would be changed to p-polarized ones, while the p-polarized hyperbolic eigenmodes are changed to s-polarized ones. These findings offer a pathway to selectively excite either hyperbolic or antihyperbolic eigenmodes, enabling control over subwavelength light propagation. Our results provide insights into polarization manipulation and potential applications in nano-optics and photonic devices.