Saturation of superradiant light scattering from an atomic grating with a large number of atoms

Superradiance has drawn increasing interest, motivated by the development of quantum technology. In general, a large number of atoms are favored for inducing a strong superradiance. However, our analytical and numerical calculations of light scattering from an atomic grating longitudinally pumped by a laser show that when the atom number is small, superradiant light scattering (SLS) is induced, that is, the reflected light intensity is proportional to the square of the atom number, whereas the SLS is saturated with the increase in the atom number. In our calculation, using the coupled-wave theory, we treat the atomic grating as a dynamical photonic crystal and find rich time-dependent optical properties due to collective atomic recoil motion, which is available within research under current experimental condition. Thus, our paper could also spark an investigation of the optical features of tunable photonic crystals in the time domain.