  Using a fully real-space perspective on high harmonic generation (HHG) in
solids, we examine the relationship between microscopic response, macroscopic
propagation of this response to the far field, and the extremely short
dephasing times routinely used in the theoretical simulations of experimentally
measured solid-state HHG spectra. We find that far field propagation naturally
reduces the contribution to the observed HHG emission from electrons that do
not return to the lattice site where they have been injected into the
conduction band. We then show that extremely short dephasing times routinely
used in microscopic simulations suppress many electron trajectories that
contribute to the far-field spectra, leading to significant distortions of the
true high harmonic response. We show that a real-space based dephasing
mechanism, which preferentially suppresses trajectories which veer too far away
from their original lattice site, yield HHG spectra that faithfully retain
those trajectories that contribute to the far-field spectra while filtering out
those which do not, already at the microscopic level. Our findings emphasize
the similarities between atomic and solid-state HHG by highlighting the
importance of the intensity-dependent phase of HHG emission and address the
longstanding issue regarding the origin of extremely short dephasing times in
solid-state HHG.

Optics