  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.

Atomic Physics