  We investigate the effect of the jet's immediate surroundings on the
non-thermal synchrotron emission and its polarization properties. The ambient
medium is equipped with a turbulent magnetic field, which is compressed and
amplified by the jets as they progress. This leads to high polarization at the
forward shock surface. The randomness in the magnetic polarities of the
external fields in the shocked ambient medium (SAM) results in vector
cancellation of the polarized components from the jet, thereby causing
depolarization of the radiation from the cocoon. We find that due to the slow
decay of the fields in the SAM, such depolarization by the fields with large
correlation lengths is more prominent when compared to the small-scale fields.
Also, the low-power jets, which have magnetic fields comparable in strength to
those in the SAM, are more severely affected by the SAM's depolarizing effect,
than the high-power ones. The turbulent backflows in the cocoon, as well as the
shearing of fields near the contact discontinuity, strengthen the poloidal
component in the jet. This causes internal depolarization due to the
cancellation of the orthogonally polarized components along the Line of Sight
as the field transitions from ordered toroidal to poloidal. The synchrotron
maps display high-emission filaments in the cocoon with magnetic fields aligned
along them. The kink instability leads to the wiggling motion of the jet's
spine, resulting in hotspot complexes in low-power sources.
