Role of incoherent pumping and Er³⁺ ion concentration on subluminal and superluminal light propagation in Er³⁺-doped YAG crystal

We study the absorption-dispersion process and group index of weak probe field in a four-level Er³⁺:YAG crystal. We find that the Er³⁺ ion concentration and incoherent pumping field can influence the absorption-dispersion process and group index of weak probe field. Moreover, our results show that Er³⁺ ion concentration plays a major role in lasing without inversion and absorption with inversion.