Second-order nonlocal shifts of scattered wave-packets: What can be measured by Goos-H\"anchen and Imbert-Fedorov effects ?

TL;DR

This paper analyzes second-order scattering shifts of wavepackets, revealing new momentum and frequency shifts, and shows how these effects can be used to probe dielectric properties and pulse modifications during scattering.

Contribution

It introduces second-order scattering shifts including new momentum and frequency effects, and demonstrates how these can be used to measure dielectric functions and pulse modifications.

Findings

New momentum and frequency shifts appear at second order.

Goos-H"anchen and Imbert-Fedorov effects depend on material symmetry.

Wigner delay time and pulse shrinking provide dielectric information regardless of beam geometry.

Abstract

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-H\"anchen 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-H\"anchen 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-H\"anchen 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.