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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., Comment: 16 pages, 7 figures

We develop the theory of optical beam shifts (both Goos–Hänchen and Imbert–Fedorov) for the case of near-normal incidence, when the incident angle becomes comparable with the angular beam divergence. The developed theory uncovers the unified origin of the anomalous beam shift enhancement via the geometric Berry phase singularity. Particularly, we predict the large Goos–Hänchen shift occurring for small incidence angles. We also propose a simple experimental scheme involving a quarter-wave q-plate that allows us to observe the giant transverse and longitudinal, spatial and angular beam shifts simultaneously. Finally, we analyze the relevant beam parameters, polarization structure, and intensity profiles of the shifted transmitted beam. Our results can find applications in spin–orbit photonics, polarization optics, sensing applications, and quantum weak measurements.

Higher-order topological insulators (HOTIs) have attracted much attention in photonics due to the tightly localized disorder-robust corner and hinge states. Here, we reveal an unconventional HOTI phase with vanishing dipole and quadrupole polarizations. This phase arises in the array of evanescently coupled waveguides hosting degenerate $s$- and $d$-type orbital modes arranged in a square lattice with four waveguides in the unit cell. As we prove, the degeneracy of the modes with the different symmetry gives rise to the nontrivial topological properties rendering the system equivalent to the two copies of anisotropic two-dimensional Su-Schrieffer-Heeger model rotated by 90$^\circ$ with respect to each other and based on $s\pm d$ hybridized orbitals. Our results introduce a route to tailor higher-order band topology leveraging both crystalline symmetries and accidental degeneracies of the different orbital modes., Comment: 13 pages, 9 figures

Transverse (Hall-effect) and Goos--H\"{a}nchen shifts of light beams reflected/refracted at planar interfaces are important wave phenomena, which can be significantly modified and enhanced by the presence of intrinsic orbital angular momentum (OAM) in the beam. Recently, optical spatiotemporal vortex pulses (STVPs) carrying a purely transverse intrinsic OAM were predicted theoretically and generated experimentally. Here we consider the reflection and refraction of such pulses at a planar isotropic interface. We find theoretically and confirm numerically novel types of the OAM-dependent transverse and longitudinal pulse shifts. Remarkably, the longitudinal shifts can be regarded as time delays, which appear, in contrast to the well-known Wigner time delay, without temporal dispersion of the reflection/refraction coefficients. Such time delays allow one to realize OAM-controlled slow (subluminal) and fast (superluminal) pulse propagation without medium dispersion. These results can have important implications in various problems involving scattering of localized vortex states carrying transverse OAM., Comment: 7 pages, 4 figures, to appear in Nanophotonics