  Besides light curves and spectra, polarization provides a different powerful
tool of studying the $\gamma-$ray burst (GRB) prompt phase. Compared with the
time-integrated and energy-integrated polarization, time-resolved and
energy-resolved polarization can deliver more physical information about the
emitting region. Here we investigate time-resolved and energy-resolved
polarization of GRB prompt emission using the synchrotron models. We find that
the equal arrival time surface effect is very important in shaping the PD
curves when the physical conditions of emitting region changes violently with
radius. Polarization properties are neither correlated with the spectral lag
nor the peak energy evolution patterns. Polarization properties with a mixed
magnetic field are very similar to those for a corresponding ordered magnetic
field but the former has a smaller polarization degree. The emission at the MeV
peak can be highly polarized for a synchrotron model while it is unpolarized as
predicted by a dissipative photosphere model. Future energy-resolved
polarization observations can distinguish between these two models.
