  The formation of black hole-neutron star (BH-NS) or BH-BH systems may be
accompanied with special supernova (SN) signals, due to the accretion feedback
from the companion BH. The additional heating, which is mainly attributed to
the Blandford-Payne mechanism, would disrupt the isotropic nature of the
luminosity distribution on the surface of the SN ejecta, leading to the
appearance of polarization. Here we develop a three dimensional (3D) Monte
Carlo polarization simulation code (MCPSC) to conduct simulations for these
special SNe. We find that the maximum polarization level of approximately \sim
2 occurs at the peak time of SN emission in the "close-binary" scenario, while
in the "faraway-binary" case, maximum polarization (i.e. \sim 0.7) is observed
at a considerably later time than the peak of the SN. The magnitude of
polarization is dependent on the degree of unevenness in the luminosity
distribution and the angle between the line of sight and the equatorial
direction. When considering the geometric distortion of supernova ejecta at the
same time, the magnitude of polarization may either increase (for a oblate
ellipsoidal shape) or decrease (for a prolate ellipsoidal shape). The
polarization signatures represent a promising auxiliary instrument to
facilitate the identification of the companion-fed SNe. Moreover, by comparing
the event rate of these special SNe with the event rate density of LIGO-Virgo
detected BH-NS/BH systems could further help to distinguish the BH-NS/BH
formation channel.
