Analytical approximations for the higher energy structure in strong field ionization with inhomogeneous electric fields

TL;DR

This paper provides analytical formulas and scaling laws to describe and tune the higher energy structure in strong field ionization caused by inhomogeneous electric fields, aiding experimental optimization.

Contribution

It introduces a closed-form analytical approximation and a tuning scheme for the higher energy structure in inhomogeneous fields, advancing understanding and control.

Findings

Derived a simple scaling law for HES peak location.

Provided an analytical scheme to tune the HES peak width.

Facilitated optimization of nanostructure parameters for HES creation.

Abstract

Recently, the emergence of a higher energy structure (HES) due to a spatial inhomogeneity in the laser electric field, as is typically found close to a nano tip, was reported in Phys.~Rev. Letter {\bf 119}, 053204 (2017). For practical applications, such as the characterization of near-fields or the creation of localized sources of monoenergetic electron beams with tunable energies, further insight into the nature of this higher energy structure is needed. Here, we give a closed form analytical approximation to describe the movement of the electron in the inhomogeneous electric field. In particular, we derive a simple scaling law for the location of the HES peak and give a scheme to analytically tune the width of the peak, both of which will prove useful in optimizing the nanostructure size or geometry for creating the HES in experimental settings.