Modeling the Bulk and Nanometric Dielectric Functions of Au and Ag

In this work, we model the dielectric functions of gold (Au) and silver (Ag) which are typically used in photonics and plasmonics. The modeling has been performed on Au and Ag in bulk and in nanometric states. The dielectric function is presented as a complex number with a real part and an imaginary part. First, we will model the experimental measurements of the dielectric constant as a function of the pulsation ω by appropriate mathematical functions in an explicit way. In the second part we will highlight the contributions to the dielectric constant value due to intraband and interband electronic transitions. In the last part of this work we model the dielectric constant of these metals in the nanometric state using several complex theoretical models such as the Drude Lorentz theory, the Drude two-point critical model, and the Drude three-point critical model. We shall comment on which model fits the experimental dielectric function best over a range of pulsation.