  The central engine and jet composition of gamma-ray bursts (GRBs) remain
mysterious. Here we suggest that observations on polarization evolution of
early optical afterglows may shed light on these questions. We first study the
dynamics of a reverse shock and a forward shock that are generated during the
interaction of a relativistic jet and its ambient medium. The jet is likely
magnetized with a globally large-scale magnetic field from the central engine.
The existence of the reverse shock requires that the magnetization degree of
the jet should not be high ($\sigma\leq 1$), so that the jet is mainly composed
of baryons and leptons. We then calculate the light curve and polarization
evolution of an early optical afterglow, and find that when the polarization
position angle changes by $90^\circ$ during the early afterglow, the
polarization degree is zero for a toroidal magnetic field but is very likely to
be non-zero for an aligned magnetic field. This result would be expected to
provide a probe for the central engine of GRBs, because an aligned field
configuration could originate from a magnetar central engine and a toroidal
field configuration could be produced from a black hole via the
Blandford-Znajek mechanism. Finally, for such two kinds of magnetic field
configurations, we fit the observed data of the early optical afterglow of GRB
120308A equally well.
