Doppler effects in a left-handed material: a first-principle theoretical   study
  The Doppler effects for the reflected wave from a moving media are systemically analyzed in this paper. The theoretical formula for the Doppler shift in the left-handed material, which is described by Drude's dispersion model, is presented. This formula is examined by first-principles numerical experiments, which are in agreement with the theoretical results. 
Sanshui Xiao, Min Qiu