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 twolevel 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 frequencydependent dielectric constant is obtained.As an example,the permittivity of (Erx Y1-x)3Al5O12 is calculated numerically in consideration of the transition between 4I15/2and 4F9/2.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.