Theory of anomalous phase shift in the reflection of graphene surface plasmons by metallic nano-plates

Due to its distinct optical characteristics, such as electrical adjustability and robust spatial confinement, graphene surface plasmons (GSPs) possess significant potential for controlling light within a compressed two-dimensional ( 2D) domain at extremely small sub-wavelength scales. While the interaction of light with materials in three-dimensional (3D) space is well-established, our comprehension of 2D plasmons is still nascent, primarily explored in limited scenarios, such as the interaction of GSPs with structured graphene like nano-gaps. This investigation expands our insights by exploring how GSPs interact with metallic nano-plates, specifically focusing on GSP reflection phase shift. By developing a rigorous model, we show that highly confined GSPs, with significantly larger momentum than free space photons, undergo nearly complete internal reflection associated with an anomalous phase shift of 0.885 pi in the reflection. Our findings contribute a comprehensive understanding of manipulating GSPs using a straightforward nanostructure. This knowledge is essential for advancing nanostructure-integrated low-dimensional devices and 2D nanophotonics.