Abstract
We construct a four-level system where a metastable state is included in an <TEX>$Er^{3＋}$</TEX> Doped Yttrium aluminum garnet (YAG) crystal. Because of the action of the coherent field, the traditional light amplification with inversion can be exhibited with remarkable variation. As a result, we propose a method to achieve the gain equalization by atomic coherence. At the same time, we find that the high index of refraction accompanied by vanishing absorption can also be reached in this model. We also find that a higher index of refraction with zero absorption can be easily obtained when the coherent field is off resonance.
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