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The Center for Bright Beams, A National Science Foundation Science and Technology Center

1D Quantum Simulations of Electron Rescattering with Metallic Nanoblade

A focused view of the electron probability density in space over time. The electron begins at its ground state in the metal towards the left. As the external field is applied, the electron may be excited and/or tunnel out of the metal. Once outside the metal, it may propagate and either return to the metal or escape permanently. Various energy bands may be seen just from this image from the different slopes of electron probability density bunches. This simulation was performed using a 20 GV/m peak enhanced field at 800 nm. Note that the snippet shown here is only a piece of the full simulation—neither spatial nor temporal boundaries are included.

We find that the semi-infinite Jellium slab with surface atomic core, alongside an initial single electron groundstate anchored to that atom, is a sufficient model for obtaining qualitatively accurate spectra without including space-charge effects. However, this model yields final electron yields that differ from similar experiments for nanostructure photocathodes. Our near-future next steps to close this gap are to include space-charge effects and to use a delocalized electron initial state in a finite Jellium slab.

Electron rescattering has been well studied and simulated for cases with ponderomotive energies of the quasi-free electrons, derived from laser–gas and laser–surface interactions, lower than 50 eV. However, with advents in longer wavelengths and laser field enhancement metallic surfaces, previous simulations no longer suffice to describe more recent strong field and high yield experiments. We present a brief introduction to and some of the theoretical and empirical background of electron rescattering emissions from a metal. We set upon using the Jellium potential with a shielded atomic surface potential to model the metal. We then explore how the electron energy spectra are obtained in the quantum simulation, which is performed using a custom computationally intensive time-dependent Schrödinger equation solver via the Crank–Nicolson method. Finally, we discuss the results of the simulation and examine the effects of the incident laser’s wavelength, peak electric field strength, and field penetration on electron spectra and yields. Future simulations will investigate a more accurate density functional theory metallic model with a system of several non-interacting electrons. Eventually, we will move to a full time-dependent density functional theory approach.

Applications and Relation to CBB Goals:

Our continuing progress of modeling metallic nanostructures interacting with intense enhanced laser fields will ultimately lead us to the ability to fine-tune our experimental setup. Parameters that may be optimized to achieve CBB’s goal of higher electron yields and lower mean transverse energy include blade array spacing, metallic layer thickness, material choices, edge radius, laser pulse length, and more.


J. Mann, G. Lawler, and J. Rosenzweig, “1D Quantum Simulations of Electron Rescattering with Metallic Nanoblades,” Instruments, vol. 3, no. 4, p. 59, Dec. 2019, doi: 10.3390/instruments3040059. Available. [Online]