  Bound states in the continuum in periodic photonic systems like photonic
crystal slabs are proved to be accompanied by vortex polarization singularities
on the photonic bands in the momentum space. The winding structures of
polarization states not only widen the field of topological physics but also
show great potential that such systems could be applied in polarization
manipulating. In this work, we report the phenomenon that by in-plane inversion
($C_2$) symmetry breaking, pairs of circularly polarized states could spawn
from the eliminated Bound states in the continuum. Along with the appearance of
the circularly polarized states as the two poles of the Poincar\'e sphere
together with linearly polarized states covering the equator, full coverage on
the Poincar\'e sphere could be realized. As an application, ellipticity
modulation of linear polarization is demonstrated in the visible frequency
range. This phenomenon provides new degree of freedom in modulating
polarization.
