  We study the band structure modulation and spin-Hall effect of a
two-dimensional heavy-hole system with $k^3$-Rashba spin-orbit coupling (RSOC),
irradiated by linearly polarized light. We find that the band structure becomes
anisotropic under the illumination by the light. Most remarkably, a pair of
additional spin-degeneracy points (apart from $\Gamma$ point) emerge in the
energy dispersion, the locations of which are solely determined by the strength
of the amplitude of the incident light. If this degeneracy occurs around the
Fermi level, the spin-Hall conductivity (SHC) exhibits a resonance. Away from
the degeneracy points, the light rotates the average spin polarization. The
possible effects of $k^3$-Dresselhaus spin-orbit coupling are also discussed.
