Transverse Optical Properties of the Eu³⁺:Y₂SiO₅ Crystal in Electromagnetically Induced Transparency

According to density matrix equations of the interaction between light and matter, the expression for the susceptibility of the Eu³⁺:Y₂SiO₅ crystal is obtained. When the control field is a Gaussian beam, we investigate and analyze the influence of probe detuning, the Rabi frequency of the control field and the laser line width on the transverse optical properties. We also analyze the influence of the dope-ion concentration on electromagnetically induced transparency (EIT). The analysis result indicates that the transmission is not a monotonic function of the dope-ion concentration. Based on the influences of various parameters on the transverse optical properties, we choose the appropriate parameters to realize the desired EIT and gradient refractive index, which has applications in focusing and imaging.