  In this work, we discuss the connections between pseudo spin, real spin of
electrons in material and spin polarization of photo-emitted electrons out of
material. By investigating these three spin textures for Bi$_2$Se$_3$ and
SmB$_6$ compounds, we find that the spin orientation of photo-electrons for
SmB$_6$ has different correspondence to pseudo spin and real spin compare to
Bi$_2$Se$_3$, due to the different symmetry properties of the photo-emission
matrix between initial and final states. We calculate the spin polarization and
circular dichroism spectra of photo-emitted electrons for both compounds, which
can be detected by spin-resolved and circular dichroism angle resolved
photo-emission spectroscopy experiment.
