6 rate r$_{2}$ = r$_{2}$ ( r$_{1}$, Ω$_{c}$) defined in Eq.(8). It shows that even for Ω$_{c}$ < 1 the probe pulse can propagate superluminally while the medium is transparent, if proper values for r$_{1}$ and r$_{2}$ are chosen. (dashed-dotted lines) the region of anomalous dispersion becomes wider and its negative slope increases in abso- lute value. The absorption curve undergoes variations similar to those of the previous case ( r$_{2}$ = γ ). The value of the gain for the latter case ( r$_{2}$ = 2 . 43 γ ) vanishes at Δ$_{p}$ = 0. The proper value of r$_{2}$ resulting in zero gain around Δ$_{p}$ = 0 can be obtained by: In conclusion, we have controlled the dispersion and the absorption of a weak probe field in a three-level V- type atomic system. By application of indirect incoher- ent pump fields the effect of populating upper levels on optical properties of the atomic medium in presence of a strong coherent pump field has been investigated and it has been found that linear positive or negative transpar- ent dispersion could occur between the doublet absorp- tion or gain lines, respectively. Then the absorption free superluminal light propagation has been established in this system. Fig.7 displays the effect of incoherent and coherent pump fields on the group index. Fig.7a shows the group index versus indirect incoherent pump rate r$_{1}$ for Ω$_{c}$ = 1 . 0 (solid), 1 . 7 (dashed), 4 . 0 (dot-dashed), 6 . 0 (dotted), while r$_{2}$ = 0 . 0. Fig.7b displays group index versus co- herent pump field, Ω$_{c}$, for r$_{1}$ = 1 . 5 (solid), 2 . 0 (dashed), 3 . 0 (dash-dotted), and 5 . 0 (dotted), while r$_{2}$ = 0. In Fig.7c, the group index is plotted as a function of r$_{1}$ for Ω$_{c}$ = 0 . 5 (solid), 0 . 7 (dashed), 1 . 0 (dot-dashed), and 1 . 7 (dotted) while the second indirect incoherent pump has III. CONCLUSION r$_{2}$ ( r$_{1}$, Ω$_{c}$) = r 2 1 + 4 r$_{1}$ Ω 2 c − 2Ω 2 c − 1 − r$_{1}$ + 2Ω 2 c + 1 . (8) (Springer, New York, 1996) p. 91. [1] L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, Na- ture (London) 397 (1999) 594. [2] M. O. Scully, Nature (London) 426 (2003) 616; M. O. Scully, M. S. Zubairy, Science 301 (2003) 181. [3] M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, Science 301 (2003) 200; M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, Phys. Rev. Lett. 90 (2003) 113903. [4] D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, M. D. Lukin, Phys. Rev. Lett. 86 (2001) 783; M. Bajcsy, A. S. Zibrov, M. D. Lukin, Nature (London) 426 (2003) 638. [5] L. J. Wang, A. Kuzmich, A. Dogariu, Nature (London) 406 (2000) 277; A. Dogariu, A. Kuzmich, L. J. Wang, Phys. Rev. A 63 (2001) 053806. [6] A. Lezama, S. Barreiro, A. M. Akulshin, Phys. Rev. A 59 (1999) 4732; A. V. Taichenachev, A. M. Tumaikin, V. I. Yudin, Phys. Rev. A 61 (1999) 011802 (R). [7] S. E. Harris, Phys. Today 50 (1997) 36. [8] M. Xiao, Y. Q. Li, S. Z. Jin, J. Gea-Banacloche, Phys. Rev. Lett. 74 (1995) 666. [9] Lord Rayleigh, Phil. Mag. XLVIII, 151 (1899). [10] L. Brillouim, Wave propagation and Group Velocity (Academic Press, New York, 1960). [11] M. Born and E. Wolf, Principles of Optics (Cambridge Uni. Press, Cambridge, 1997, 7th ed.). [12] L. D. Landau and E. Lifshitz, Electrodynamics of Con- tinuous Media (Pergamon, Oxford, 1960) P. 286. [13] Md. A. I. Talukder, Y. Amagishi and M. Tomita, Phys. Rev. Lett. 86 (2001) 3546. [14] Y. Shimizu, N. Shiokawa, N. Yamamoto, M. Kozuma, T. Kuga, L. Deng, and E. W. Hagley, Phys. Rev. Lett. 89 (2002) 233001. [15] R. Y. Chiao, in Amazing Light, a Volume Dedicated to C. H. Townes on His Eightieth Birthday, Ed. R. Y. Chiao, [32] G. S. Agarwal, T. Nath Dey, S. Menon, Phys. Rev. A 64 (2001) 053809. [16] R. Y. Chiao, Phys. Rev. A 48 (1993) R34. [17] E. L. Bolda, R. Y. Chiao, and J. C. Garrisson, Phys. Rev. A 48 (1993) 3890. [18] A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49 (1994) 2071. [19] M. W. Mitchell and R. Y. Chiao, Am. J. Phys. 66 (1998) 14. [20] E. L. Bolda, J. C. Garrison, and R. Y. Chiao, Phys. Rev. A 49 (1994) 2938. [21] R. Y. Chiao and A. Steinberg, in Progress in Optics, Ed. E. Wolf (Elsevier, Amsterdam, 1997), P. 345. [22] A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Phys. Rev. Lett. 71 (1993) 708. [23] M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, Opt. Commu. 87 (1992) 109. [24] M. Mahmoudi, M. Sahrai, H. Tajalli, Phys. Lett. A 357 (2006) 66. [25] M. Mahmoudi, J. Evers, Phys. Rev. A 74 (2006) 063827. [26] J. Qian, H. Zhang, J. Opt. Soc. Am. B 21 (2004) 1364. [27] M. Mahmoudi, S.Worya Rabiei, L. Ebrahimi Zohravi, and M. Sahrai, Opt Commun. 281 (2008) 4681. [28] Y. Zeng, D. Han, Y. Bai, W. Chen, H. Cao, H. Lu, Phys. Lett. A 373 (2009) 3591-3593. [29] D. Bullock, J. Evers, C. H. Keitel, Phys. Lett. A 307 (2003) 8-12. [30] M. Mahmoudi, S. W. Rabiei, L. Safari, M. Sahrai, Laser Phys. Vol. 19 No. 7 (2009) 1428-1433. [31] M. O. Scully, M. S. Zubairy, Quantum Optic, Cambridge University Press, London, 1997.