Left-handedness in K-type multilevel system in the presence of spontaneously generated coherence

The left-handedness in atomic vapor medium consisting of five energy levels in K-type configuration is studied in this work. The theoretical modeling has been done using density matrix approach in which the spontaneously generated coherence (SGC) is also included. The system shows negative electrical permittivity (ϵ) as well as negative magnetic permeability (μ) and thus displays the negative refractive index (n) for certain values of system parameters in the presence of SGC. The parameters (ϵ, μ, n) quantifying left-handedness in the system become more negative if the SGC is strong. Under the off-resonant conditions these parameters become less negative and the left-handedness of system degrades.