Modulation of electron wave packets by scattering on time-harmonic potentials

TL;DR

This paper develops a comprehensive 3D quantum scattering theory for electron wave packets interacting with time-periodic potentials, crucial for advancing low-energy ultrafast electron microscopy and understanding wave packet modulation.

Contribution

It introduces a rigorous 3D quantum scattering framework mapping dynamics into Floquet space, connecting modulation to multi-channel scattering, and evaluates scattering amplitudes with exact and approximate methods.

Findings

Wave packet modulation generates energy sidebands.

Modulation strength depends on transverse focusing.

The theory highlights the importance of 3D effects in electron-wave interactions.

Abstract

The coherent interaction between free electrons and optical near-fields enables the active modulation of electron wave packets, a mechanism central to photon-induced near-field electron microscopy (PINEM). While existing theories effectively describe these interactions at high kinetic energies, the growing interest in low-energy ultrafast electron microscopy demands frameworks that explicitly account for finite wave packet geometries and recoil effects. In this paper, we develop a rigorous 3D quantum scattering theory for electron wave packets interacting with time-periodic potentials, capturing the case of optical near-field interaction. By mapping the time-dependent dynamics into an extended Floquet space, we formally connect the modulation process to time-independent multi-channel scattering. We evaluate the resulting scattering amplitudes using both an exact R-matrix approach and a multi-channel eikonal approximation. The latter analytical approach recovers PINEM-like probabilities weighted by the wave packet's transverse profile. Application of the theory to an oscillating potential demonstrates the generation of distinct energy sidebands, revealing that the modulation strength is sensitive to the transverse focusing of the incident electron pulse, underlining the importance of a fully 3D treatment.