Light scattering from a periodically modulated two dimensional electron gas with partially filled Landau levels

We study light scattering from a periodically modulated two dimensional electron gas in a perpendicular magnetic field. If a subband is partially filled, the imaginary part of the dielectric function as a function of frequency contains additional discontinuities to the case of completely filled subbands. The positions of the discontinuities may be determined from the partial filling factor and the height of the discontinuity can be directly related to the modulation potential. The light scattering cross section contains a new peak which is absent for integer filling.