Dynamics of matter-wave and optical fields in superradiant scattering   from Bose-Einstein condensates
  We study superradiant scattering off Bose-Einstein condensates by solving the semiclassical Maxwell-Schroedinger equations describing the coupled dynamics of matter-wave and optical fields. Taking the spatial dependence of these fields along the condensate axis into account, we are able to reproduce and explain many of the characteristic features observed in the experiments of Inouye et al. [Science 285, 571 (1999)] and Schneble et al. [Science 300, 475 (2003)], such as the shape of the atomic side-mode distributions for forward and backward scattering, the spatial asymmetry between forward and backward side modes, and the depletion of the condensate center observed for forward scattering. 
O. Zobay, Georgios M. Nikolopoulos