  In the presence of a (time-dependent) macroscopic electric field the electron
dynamics of dielectrics cannot be described by the time-dependent density only.
We present a real-time formalism that has the density and the macroscopic
polarization P as key quantities. We show that a simple local function of P
already captures long-range correlation in linear and nonlinear optical
response functions. Specifically, after detailing the numerical implementation,
we examine the optical absorption, the second- and third-harmonic generation of
bulk Si, GaAs, AlAs and CdTe at different level of approximation. We highlight
links with ultranonlocal exchange-correlation functional approximations
proposed within linear response time-dependent density functional theory
framework.
