  In the Poynting Flux dominated outflow (the initial ratio of the
electromagnetic energy flux to the particle energy flux $\sigma_0\gg1$) model
for Gamma-ray bursts, nearly half of the internally dissipated magnetic energy
is converted into the prompt $\gamma-$ray energy emission and the rest is
converted into the kinetic energy of the outflow. Consequently, at the end of
the $\gamma-$ray burst, $\sigma$ decreases significantly ($\sigma\sim 1$ or
even smaller). We numerically investigate the very early reverse shock emission
powered by such mildly magnetized outflows interacting with medium--uniform
interstellar medium (ISM) or stellar wind (WIND). We show that for
$\sigma\sim0.05-1$ and typical parameters of Gamma-ray bursts, both the
ISM-ejecta interaction and the WIND-ejecta interaction can power very strong
optical emission ($m_{\rm R}\sim 10-12{\rm th}$ magnitude or even brighter).
Similar to the very early afterglow powered by the non-magnetized ejecta
interacting with the external medium, the main difference between the
ISM-ejecta interaction case and the WIND-ejecta interaction case is that,
before the reverse shock crosses the ejecta, the R-band emission flux increases
rapidly for the former, but for the latter it increases only slightly. (The
abstract has been shortened). We suggest that the linear polarization detection
of the early multi-wavelength afterglow is highly needed to see whether the
outflows powering GRBs are magnetized or not.
