Complex Doppler effect in left-handed metamaterials
  The Doppler shift is investigated in one-dimensional system with moving source. Theoretical findings are confirmed in numerical simulations of optical and acoustical waves propagation in simple metamaterial model, showing the reversed shift and the existence of multiple frequency modes. The properties of these waves are discussed. The effect of absorption on the phenomenon is outlined. 
David Ziemkiewicz, Sylwia Zieli\'nska-Raczy\'nska
physics.optics physics.class-ph physics.comp-ph