  We formulate a theory of bulk optical current for a periodically driven
system, which accounts for the mixing of external drive and laser field
frequencies and, therefore, the broadening of the harmonic spectrum compared to
the undriven system. We express the current in terms of Floquet-Bloch bands and
their non-adiabatic Berry connection and curvature. Using this expression, we
relate spatio-temporal symmetries of the driven model to selection rules for
current harmonics. We illustrate the application of this theory by studying
high harmonic generation in the periodically driven Su-Schrieffer-Heeger model.
In the high frequency and low field amplitude limit, we find analytical
expressions for current harmonics. We also calculate the current numerically
beyond the high frequency limit and verify that when the drive breaks a
temporal symmetry, harmonics forbidden in the undriven model become available.
Moreover, we find significant enhancement in higher harmonics when the system
is driven, even for low field amplitudes. Our work offers a unified Floquet
approach to nonlinear optical properties of solids, which is useful for
realistic calculations of high harmonic spectra of electronic systems subject
to multiple periodic drives.
