Goos-Hanchen and Imbert-Fedorov shifts of vortex beams at air-left-handed-material interfaces

In this paper, we present a systematic study of beam shifts and angular momenta of paraxial vortex beams at air-left-handed-material (LHM) interfaces. It is shown that, compared to their counterparts at air-right-handed-material (RHM) interfaces, the spatial Goos-Hanchen (GH) and Imbert-Fedorov (IF) shifts remain the same, while the angular GH and IF shifts are reversed at air-LHM interfaces. The spatial and angular shifts of paraxial vortex beams have their respective origins in transverse angular momenta and transverse linear momenta. The spatial GH and IF shifts remain unreversed as a result of both reversions of transverse angular momenta and z-component linear momentum, while the angular GH and IF shifts are reversed because the z-component linear momentum is reversed and the transverse linear momenta are unreversed at air-LHM interfaces. In addition, we perform a quantitative analysis on spin-orbit angular momentum conversion and orbit-orbit angular momentum conversion, which further helps us understand the essence of vortex beam shifts at air-LHM interfaces and their fundamental distinctions from those at air-RHM interfaces.