Electromagnetically induced left-handedness by both coherent and incoherent fields

We propose a scheme of electromagnetically induced left-handedness in a dense atomic vapor medium. By applying an incoherent pump field to manipulate the populations in atomic levels, and a strong coherent field to create quantum coherence, the magnetic part of the probe field can be amplified instead of strong absorption as usual materials. The system has negative permittivity and permeability simultaneously with transparent propagation of the electric part of the probe field. It is shown that the pumping rate of incoherent field, the intensity and frequency detuning of the coherent field, exert effects on the properties of the negative refractive index of left-handed material.

Figure 1

The energy scheme of a four-level atomic system interacting with a coherent ${\Omega }_c$ and an incoherent pumps $\Lambda$ and a probe field ${\Omega }_p$.

Figure 2

(Color online) The real (top figure) and imaginary (bottom figure) parts of the relative electric permittivity ${\epsilon }_r$ and magnetic permeability ${\mu }_r$ of the system as a function of probe frequency detuning ${\Delta }_p$.

Figure 3

(Color online) Frequency dependence of the real and imaginary parts of the relative refractive index.