  Optical re-brightenings in the afterglows of some gamma-ray bursts (GRBs) are
unexpected within the framework of the simple external shock model. While it
has been suggested that the central engines of some GRBs are newly born
magnetars, we aim to relate the behaviors of magnetars to the optical
re-brightenings. A newly born magnetar will lose its rotational energy in the
form of Poynting-flux, which may be converted into a wind of electron-positron
pairs through some magnetic dissipation processes. As proposed by Dai (2004),
this wind will catch up with the GRB outflow and a long-lasting reverse shock
would form. By applying this scenario to GRB afterglows, we find that the
reverse shock propagating back into the electron-positron wind can lead to an
observable optical re-brightening and a simultaneous X-ray plateau (or X-ray
shallow decay). In our study, we select four GRBs, i.e., GRB 080413B, GRB
090426, GRB 091029, and GRB 100814A, of which the optical afterglows are well
observed and show clear re-brightenings. We find that they can be well
interpreted. In our scenario, the spin-down timescale of the magnetar should be
slightly smaller than the peak time of the re-brightening, which can provide a
clue to the characteristics of the magnetar.
