Second-order nonlocal shifts of scattered wave-packets: What can be measured by Goos–Hänchen and Imbert–Fedorov effects?

The scattering of wavepackets with arbitrary energy dispersion on surfaces has been analyzed. Expanding up to second order in scattering shifts, it is found that besides the known Goos–Hänchen or Imbert–Fedorov spatial offset, as well as the Wigner delay time, new momentum and frequency shifts appear. Furthermore, the width of the scattered wave packet becomes modified as well, which can lead to a shrinking of pulses by multiple scattering. For a model of dielectric material characterized by a longitudinal and transverse dielectric function the shifts are calculated analytically. From the Goos–Hänchen and Imbert–Fedorov shifts one can access the longitudinal and transversal dielectric function. Perfectly aligned crystal symmetry axes with respect to scattering beam shows no Imbert–Fedorov effect. It is found that the Goos–Hänchen and Imbert–Fedorov effect are absent for homogeneous materials. Oppositely it is found that the Wigner delay time and the shrinking of the temporal pulse width allows to access the dielectric function independent on the beam geometry.