  There is increasing evidence that massive stars may exhibit an enhanced mass
loss shortly before their termination explosion. Some of them also indicate the
enhancement of their circumstellar matter (CSM) is not spherically symmetric.
Supernova (SN) interacting with aspherical CSM could induce special
polarization signals from multiple radiation components that deviate from
spherical symmetry. We investigate the time-evolution of the continuum
polarization induced by the SN ejecta interacting with a disk/torus-like CSM.
Our calculation suggests that the interaction between the SN ejecta and an
immediate disk-like CSM with a thin, homogenous density structure would produce
a high continuum polarization, which may reach a peak level of $\sim$15\%. The
interplay between the evolving geometry of the emitting regions and the
time-variant flux ratio between the polar ejecta and the equatorial CSM
interaction may produce a double-peaked feature in the polarization time
sequence. A similar trend of the time evolution of the polarization is also
found for a radially extended CSM disk that exhibits a wind-like density
structure, with an overall relatively lower level of continuum polarization
($<2.5\%$) during the interaction process. We also identify a non-uniform
temperature distribution along the radial direction of the CSM disk, which
yields a strong wavelength dependence of the continuum polarization. These
signatures provide a unique geometric diagnostic to explore the interaction
process and the associated extreme mass loss of the progenitors of interacting
transients.
