Goos-Hänchen Shift and Even-Odd Peak Oscillations in Edge-Reflections of Surface Polaritons in Atomically Thin Crystals

Two-dimensional surface polaritons (2DSPs), such as graphene plasmons, exhibit various unusual properties, including electrical tunability and strong spatial confinement with high Q-factor, which can enable tunable photonic devices for deep subwavelength light manipulations. Reflection of plasmons at the graphene's edge plays a critical role in the manipulation of 2DSP and enables their direct visualization in near-field infrared microscopy. However, a quantitative understanding of the edge-reflections, including reflection phases and diffraction effects, has remained elusive. Here, we show theoretically and experimentally that edge-reflection of 2DSP exhibits unusual behaviors due to the presence of the evanescent waves, including an anomalous Goos-Hänchen phase shift as in total internal reflections and an unexpected even-odd peak amplitude oscillation from the wave diffraction at the edge. Our theory is not only valid for plasmons in graphene but also for other 2D polaritons, such as phonon polaritons in ultrathin boron nitride flakes and exciton polariton in two-dimensional semiconductors.