  The homochirality of biological molecules on the Earth is a long-standing
mystery regarding the origin of life. Circularly polarized ultraviolet (UV)
light could induce the enantiomeric excess of biological molecules in the
interstellar medium, leading to the homochirality on the earth. By performing
3D radiation transfer simulations with multiple scattering processes in
interstellar dusty slabs, we study the generation of circular polarization (CP)
of ultraviolet light at Lyman $\alpha$ ($\lambda = 0.1216~{\rm \mu m}$) as well
as in the near-infrared (NIR, $\lambda = 2.14~{\rm \mu m}$) wavelengths. Our
simulations show that the distributions of CP exhibit a symmetric quadrupole
pattern, regardless of wavelength and viewing angle. The CP degree of scattered
light from a dusty slab composed of aligned grains is $\sim 15$ percent for
Ly$\alpha$ and $\sim 3$ percent at NIR wavelengths in the case of oblate grains
with an MRN size distribution. We find that the CP degree of Ly$\alpha$ is well
correlated with that in the NIR regardless of viewing angles, whilst being a
factor of $\sim 5$ higher. Thus, high CP of Ly$\alpha$ is expected in sites
where NIR CP is detected. We suggest that such circularly polarized Ly$\alpha$
may initiate the enantiomeric excess of biological molecules in space.
