  We present a detailed theoretical study of light scattering off superfluid
trapped Fermi gas of atoms at zero temperature. We apply Nambu-Gorkov formalism
of superconductivity to calculate the response function of superfluid gas due
to stimulated light scattering taking into account the final state
interactions. The polarization of light has been shown to play a significant
role in response of Cooper-pairs in the presence of a magnetic field.
Particularly important is a scheme of polarization-selective light scattering
by either spin-component of the Cooper-pairs leading to the single-particle
excitations of one spin-component only. These excitations have a threshold of
$2\Delta$ where $\Delta$ is the superfluid gap energy. Furthermore,
polarization-selective light scattering allows for unequal energy and momentum
transfer to the two partner atoms of a Cooper-pair. In the regime of low energy
($<< 2\Delta$) and low momentum ($<2\Delta/(\hbar v_F)$, $v_F$ being the Fermi
velocity) transfer, a small difference in momentum transfers to the two
spin-components may be useful in exciting Bogoliubov-Anderson phonon mode. We
present detailed results on the dynamic structure factor (DSF) deduced from the
response function making use of generalized fluctuation-dissipation theorem.
Model calculations using local density approximation for trapped superfluid
Fermi gas shows that when the energy transfer is less than $2\Delta_0$, where
$\Delta_0$ refers to the gap at the trap center, DSF as a function of energy
transfer has reduced gradient compared to that of normal Fermi gas.
