Centroid shifts of spatiotemporal vortex pulses reflected and refracted on graphene.

The Goos-Hänchen and Imbert-Fedorov shifts are significant wave phenomena, yet the underlying mechanism governing the spatiotemporal vortex pulses reflected and refracted on graphene remains opaque. In this study, we analytically derive the expressions for the centroid shifts of spatiotemporal vortex pulses by applying the Fresnel-Snell formulas to each plane wave in the incident spatiotemporal vortex pulse spectrum. We demonstrate that the longitudinal shifts are correlated with the angular shifts, and thus, both are subject to resonant enhancement in the vicinity of the Brewster angle. It is possible to tune the resonant enhancement of the shifts by modifying the Fermi energy of graphene. An increase in the vortex topological charge results in an enhancement of both the angular and longitudinal shifts while the transverse shifts are reduced. The shifts of the intensity distribution, in accordance with the Goos-Hänchen and Imbert-Fedorov shifts, facilitate experimental measurements. The high frequency in the terahertz region will diminish the resonant enhancement of the spatial shifts of the reflected wavepackets. The analysis presented here can be extended with minimal effort to spatiotemporal vortex pulses reflected and refracted on other two-dimensional atomic crystals.