The manipulated left-handedness in a rare-earth-ion-doped optical fiber by the incoherent pumping field

The left-handedness was demonstrated by the simulation with a three-level quantum system in an Er3+-dopped ZrF4-BaF2-LaF3-AlF3-NaF (ZBLAFN) optical fiber. And the left-handedness can be regulated by the incoherent pumping field. Our scheme may provide a solid candidate other than the coherent atomic vapor for left-handedness, and may extend the application of the rare-earth-ion-doped optical fiber in metamaterials and of the incoherent pumping light field in quantum optics.