Abnormal Dielectric Response in an Optical Range Based on Electronic Transition in Rare-Earth-Ion-Doped Crystals

A new scheme to realize an abnormal dielectric response at optical wavelength is developed on the basis of two-level electronic transition of rare-earth ion doped crystals. Based on the semi-classical theory and the Judd–Ofelt theory, the electric dipole transition under a weak field is analyzed, and a general expression for the frequency-dependent dielectric constant is obtained. As an example, the permittivity of (Er_xY_1−x)₃Al₅O₁₂ is calculated numerically in consideration of the transition between ⁴I_15/2and ⁴F_9/2. An optimized dielectric property with a negative real part and low absorption is achieved. This proposes a new mechanism for building extraordinary electromagnetic media at optical frequencies by using a quantum process.