Effect of concentration of Er³⁺ ions on ultra-large index of refraction via atomic coherence in Er³⁺: YAG crystal

A four-level system is proposed to produce large index of refraction accompanied by vanishing absorption in the Er^3+-doped yttrium aluminium garnet (YAG) crystal. It is found that the high index of refraction with zero absorption can be provided by adjusting the incoherent pumping, the coherent field, as well as the concentration of Er^3+ ions in the crystal. Furthermore, the value of the incoherent pump to achieve the high index of refraction with zero absorption is greatly changed with increasing the concentration of Er^3+ ions in the crystal. This indicates that the effect of concentration on the high index of refraction with zero absorption cannot be neglected.