  The study of short-duration gamma-ray bursts provides growing evidence that a
good fraction of double neutron star mergers lead to the formation of stable
millisecond magnetars. The launch of Poynting flux by the millisecond magnetars
could leave distinct electromagnetic signatures that reveal the energy
dissipation processes in the magnetar wind. In previous studies (Wang & Dai
2013b; Wang et al. 2015), we assume that the magnetar wind becomes completely
lepton-dominated so that electrons/positrons in the magnetar wind are
accelerated by a diffusive shock. However, theoretical modeling of pulsar wind
nebulae shows that in many cases the magnetic field energy in the pulsar wind
may be strong enough to suppress diffusive shock acceleration. In this paper,
we investigate the reverse shock emission as well as the forward shock emission
with an arbitrary magnetization parameter $\sigma$ of a magnetar wind. We find
that the reverse shock emission strongly depends on $\sigma$, and in
particular, $\sigma \sim 0.3$ leads to the strongest reverse shock emission.
Future observations would be helpful to diagnose the composition of the
magnetar wind.
