3 case of tuned coupling field ( Δ$_{c}$ = 0 ) are For simplicity, from this point on, it is assumed that the Rabi frequencies (Ω$_{c}$ and Ω$_{p}$) are real numbers, the spontaneous decay rates are the same for all levels, i.e. γ$_{21}$ = γ$_{31}$ = γ , and other parameters are normalized to the spontaneous decay rate γ . In the following, using the derived expression for susceptibility χ , in terms of given system parameters, the response of the atomic system to the applied coherent and incoherent fields is studied. It has to say that the main interest is in dispersion and absorption properties of the probe field around zero de- tuning, Δ$_{p}$ = 0. and respectively, where For r$_{2}$ = 0, equations 6 and 7 are used to draw the plot contours of Fig.3a and Fig.3b, respectively. In Fig.3a, the superluminal regions are colored and the subluminal region is left white. In addition, the separating contours ( n$_{g}$ − 1 = 0) are plotted with red-solid lines. In this figure the contour lines for ( n$_{g}$ − 1) = − 30 , − 20 , − 10, and − 3 are plotted in black-dashed style. Fig.3b illustrates the absorption property of the medium, χ $^{′′}$. In this figure the absorptive and amplifying regions are separated by the contour line of χ ′′ = 0 (red-solid line) and the darkness of the colored regions is a measure of their absorption or amplification magnitude for the probe field. Therefore First the familiar effect of the coupling field in absence of the indirect incoherent pumps ( r$_{1}$ = r$_{2}$ = 0) is men- tioned. In this case due to application of the coupling field, the absorption line for probe field splits into two absorption lines and consequently the slope of dispersion changes from negative to positive. In Fig.2 the real (a) and imaginary (b) parts of the susceptibility are plotted versus the probe field detuning. It shows that increasing the value of the Rabi frequency, Ω$_{c}$, leads to the ap- pearance of a transparent region between the absorption lines around zero detuning, Δ$_{p}$ = 0, which is an EIT sit- uation proportional to lossless subluminal light propaga- tion. For the next step, while the strength of the second indirect incoherent pump is zero ( r$_{2}$ = 0 ), the effects of driving transition | 1 〉 ↔ | 2 〉 by the coupling field and populating level | 3 〉 is investigated. To get a rough view of this condition, it will be useful to draw some contour plots for n$_{g}$ − 1 and χ $^{′′}$, via the coupling Rabi frequency, Ω$_{c}$ , and the first indirect incoherent pump strength, r$_{1}$ , while r$_{2}$ and Δ$_{p}$ are zero. Using Eqs.(5) and adjusting scale arbitrarily by letting N℘ 2 13 ε $_{0}$ℏ = 1 and 2 πω$_{p}$ = 10 $^{2}$γ , the explicit expressions for n$_{g}$ − 1 and χ ′′ in terms of Ω$_{c}$, r$_{1}$ , and r$_{2}$ at zero probe field detuning (Δ$_{p}$ = 0) are A = 2Ω 2 c + r$_{2}$ + r$_{1}$ + 1 , B = ( r$_{2}$ + r$_{1}$ + 1) 2 + 4( r$_{1}$ + 2)Ω 2 $_{c}$. χ ′′ = 4 ( r$_{2}$ − 2 r$_{1}$ + 1) Ω 2 c AB − 2( r$_{1}$ − 1)( r$_{2}$ + r$_{1}$ + 1) AB , (7) n$_{g}$ − 1 = 10 $^{2}$γ A $^{2}$B { 4( r$_{1}$ − 1)( r$_{2}$ + r$_{1}$ + 1) − 4 ( r$_{1}$ ( r$_{1}$ − 5) + r$_{2}$ + 2 r$_{1}$r$_{2}$ + r 2 ) Ω 2 c − 16( r$_{1}$ − 1)Ω 4 c } , (6) ρ$_{11}$ = ( 1 + r$_{1}$ γ$_{31}$ + 2 | Ω$_{c}$ | 2 + Γ$_{21}$ r$_{2}$ Γ$_{21}$ γ$_{21}$ + 2 | Ω$_{c}$ | 2 ) − 1 (5a) ρ$_{22}$ = ( 2 | Ω$_{c}$ | 2 + Γ$_{21}$ r$_{2}$ Γ$_{21}$ γ$_{21}$ + 2 | Ω$_{c}$ | 2 ) ρ$_{11}$ (5b) ρ$_{33}$ = r$_{1}$ γ$_{31}$ ρ$_{11}$ (5c) ρ$_{21}$ = i Ω ∗ c Γ$_{21}$ ( ρ$_{11}$ − ρ$_{22}$ ) (5d) ρ$_{31}$ = i Ω ∗ p (Γ$_{31}$ − i Δ$_{p}$) + | Ω$_{c}$ | 2 (Γ 32 − i Δ$_{p}$) × { ( ρ$_{11}$ − ρ$_{33}$ ) − | Ω$_{c}$ | 2 Γ$_{21}$(Γ$_{32}$ − i Δ$_{p}$) ( ρ$_{11}$ − ρ$_{22}$ ) } . (5e) FIG. 3: Contour plots for n$_{g}$ − 1 = 0 (red-solid lines), − 30, − 20, − 10, and − 3 (black-dashed lines) (a) and χ ′′ = 0 (red- solid line), − 0 . 15, − 0 . 11, − 0 . 07, − 0 . 03, − 0 . 012, and − 0 . 005 (black-dashed lines) (b) via Ω c and r$_{1}$ . The common param- eters are γ = 1, r$_{2}$ = 0, Δ c = 0, and Δ p = 0.