Reflection of two-dimensional surface polaritons by metallic nano-plates on atomically thin crystals

Owning to their unusual optical properties, such as electrical tunability and strong spatial confinement, two-dimensional surface polaritons (2DSPs) hold great promise for deep sub-wavelength manipulation of light in a reduced low-dimensional space. Control of 2DSPs is possible by using their interaction with a boundary between two media, similar to how light behaves in three-dimensional (3D) space. The understanding of the interaction in the 2D case is still in its early stages, unlike the 3D case, as in-depth investigations are only available in a few cases including the interaction of 2DSPs with structured 2D crystals. Here, we extend the scope of our understanding to the interaction of 2DSPs with metallic nano-plates on 2D crystals, focusing on the reflection of 2DSPs. Through our rigorous model, we reveal that, for strongly confined 2DSPs having much larger momentum than free space photons, the interaction results in almost total internal reflection of 2DSPs as the radiative coupling of the 2DSPs to free space is negligible. We also find that the reflection involves an anomalous phase shift dependent on the thickness of the nano-plate, due to the temporary storing of electromagnetic energy in the evanescent waves induced near the edge of the nano-plate. Our theory predicts that the phase shift saturates to an anomalous value, 0.885π, as the nano-plate becomes thicker. Our work provides a detailed understanding of how to manipulate the 2DSPs by using one of the simplest nanostructures, essential for the further development of nanostructure-integrated low-dimensional devices for polariton optics.