5 FIG. 7: (a) The group index, ( n$_{g}$ − 1), versus r$_{1}$ for the parameters r$_{2}$ = 0 . 0, Ω c = 1 . 0 (solid), 1 . 7 (dashed), 4 . 0 (dot- dashed), and 6 . 0 (dotted). (b) The group index against Ω c for the parameters r$_{2}$ = 0 . 0, r$_{1}$ = 1 . 5 (solid), 2 . 0 (dashed), 3 . 0 (dot-dashed), and 5 . 0 (dotted). (c) The group index versus r$_{1}$ while r$_{2}$ = r$_{2}$ ( r$_{1}$, Ω c ) defined in Eq. (8) for the parameters Ω c = 0 . 5 (solid), 0 . 75 (dashed), 1 . 0 (dot-dashed), and 1 . 7 (dotted). Other common parameters are γ = 1 and Δ c = Δ p = 0. FIG. 6: Real (a) and imaginary (b) parts of susceptibility versus probe field detuning for the parameters γ = 1, r$_{1}$ = 1 . 5, Ω c = 1 . 69, r$_{2}$ = 0 (solid), 1 . 0 (dashed), and 2 . 43 (dot-dashed). positive to negative. On the other hand, the steepest anomalous slope of dispersion occurs when 2 < Ω$_{c}$ < 3 and a strong enough indirect incoherent pump, popu- lates level | 3 〉 . Fig.5 is presented to see how an increase in r$_{1}$ causes the gain deeps to become more distinguish- able and consequently the anomalous slope of dispersion become steeper. In Fig.5a for r$_{1}$ = 1 . 2 (solid line) the slope of dispersion around zero probe field detuning is positive. With increasing the indirect incoherent pump rate to r$_{1}$ = 1 . 5 (dashed lines), the slope of dispersion becomes zero and it is negative for r$_{1}$ = 3 . 0 (dash dotted lines). In Fig.5b, the probe field absorption curves are plotted. It shows that the subluminal and superluminal light propagation around zero probe detuning is accom- panied by a considerable gain. It is time to investigate the optical response of the medium to populating level | 2 〉 while the transition | 1 〉 ↔ | 3 〉 is driven by the coher- ent field, and the population between levels | 1 〉 and | 3 〉 is inverted due to the indirect incoherent pump with a rate r$_{1}$ > γ . In Fig.6, the real (a) and imaginary (b) parts of χ are plotted versus probe field detuning. The common parameters are Ω$_{c}$ = 1 . 69 γ , and r$_{1}$ = 1 . 5 γ . The first plots (solid lines), corresponding to r$_{2}$ = 0, are pre- sented for comparison only. They show that the slope of dispersion is almost zero around zero probe field de- tuning and there is a considerable amount of gain due to the partly combined gain deeps. By populating level | 2 〉 with rate r$_{2}$ = γ , (dashed lines), the slope of dispersion becomes negative around Δ$_{p}$ = 0. The absorption curve varies according to the probe field detuning, so that the maximum reduction in gain occurs around zero probe field detuning, while beyond Δ$_{p}$ = ± Ω$_{c}$ γ , the gain in- creases slightly. By increasing the value of r$_{2}$ to 2 . 43 γ 1 2 3 4 5 6 7 8 9 10 GLYPH<Minus> 30 GLYPH<Minus> 20 GLYPH<Minus> 10 0 10 20 30 r$_{1}$ n g GLYPH<Minus> 1 1 2 3 4 5 6 7 8 9 10 GLYPH<Minus> 30 GLYPH<Minus> 20 GLYPH<Minus> 10 0 10 20 30 GLYPH<CapOmega>$_{c}$ n g GLYPH<Minus> 1 1 2 3 4 5 6 GLYPH<Minus> 30 GLYPH<Minus> 20 GLYPH<Minus> 10 0 r$_{1}$ n g GLYPH<Minus> 1 a b c GLYPH<Minus> 6 GLYPH<Minus> 4 GLYPH<Minus> 2 0 2 4 6 GLYPH<Minus> 0.05 0.00 0.05 GLYPH<CapDelta>$_{p}$ Re GLYPH<LParen1> Χ GLYPH<RParen1> GLYPH<Minus> 6 GLYPH<Minus> 4 GLYPH<Minus> 2 0 2 4 6 GLYPH<Minus> 0.08 GLYPH<Minus> 0.06 GLYPH<Minus> 0.04 GLYPH<Minus> 0.02 0.00 GLYPH<CapDelta>$_{p}$ Im GLYPH<LParen1> Χ GLYPH<RParen1> a b