  We investigate the microscopic properties of the nonlinear optical response
of crystalline solids within Floquet theory, and demonstrate that
optically-induced microscopic charge distributions display complex spatial
structure and nontrivial properties. Their spatial symmetry and temporal
behavior are governed by crystal symmetries. We find that even when a
macroscopic optical response of a crystal is forbidden, the microscopic optical
response can, in fact, be nonzero. In such a case, the optically-induced charge
redistribution can be considerable, even though the corresponding Fourier
component of the time-dependent dipole moment per unit cell vanishes. We
develop a method that makes it possible to completely reconstruct the
microscopic optically-induced charge distributions by means of
subcycle-resolved x-ray-optical wave mixing. We also show how, within this
framework, the direction of the instantaneous microscopic optically-induced
electron current flow can be revealed.
