Optimizing the Drude-Lorentz model for material permittivity: Method, program, and examples for gold, silver, and copper

Approximating the frequency dispersion of the permittivity of materials with simple analytical functions is of fundamental importance for understanding and modeling the optical response of materials and resulting structures. In the generalized Drude-Lorentz model, the permittivity is described in the complex frequency plane by a number of simple poles having complex weights, which is a physically relevant and mathematically simple approach: By construction, it respects causality, represents physical resonances of the material, and can be implemented easily in numerical simulations. We report here an efficient method of optimizing the fit of measured data with the Drude-Lorentz model having an arbitrary number of poles. We show examples of such optimizations for gold, silver, and copper, for different frequency ranges and up to four pairs of Lorentz poles taken into account. We also provide a program implementing the method for general use.