Wigner time delays and Goos-Hänchen shifts of 2D quantum vortices scattered by potential barriers

Abstract: We consider reflection and transmission of 2D quantum wavepackets with phase vortices (also known in optics as spatiotemporal vortex pulses) at potential step-like, delta-function, and rectangular barriers. The presence of a vortex significantly modifies the Wigner time delays and Goos-H\"{a}nchen shifts, previously studied for Gaussian-like wavepackets. In particular, the scattered wavepackets undergo non-zero time delays and lateral shifts even for purely real scattering coefficients, when the standard Wigner and Artmann formulae vanish. We derive analytical expressions for the vortex-induced times delays and spatial shifts of 2D vortices and verify these with numerical calculations of the Schr\"{o}dinger equation. The time delays and shifts are resonantly enhanced in the vicinity of the critical-angle incidence for a step-like potential and near transmission resonances for a rectangular barrier.