  Approximating the frequency dispersion of the permittivity of materials with
simple analytical functions is of fundamental importance for understanding and
modeling their optical properties. Quite generally, the permittivity can be
treated in the complex frequency plane as an analytic function having a
countable number of simple poles which determine the dispersion of the
permittivity, with the pole weights corresponding to generalized conductivities
of the medium at these resonances. The resulting Drude-Lorentz model separates
the poles at frequencies with zero real part (Ohm's law and Drude poles) from
poles with finite real part (Lorentz poles). To find the parameters of such an
analytic function, we minimize the error weighted deviation between the model
and measured values of the permittivity. We show examples of such optimizations
for various semiconductors (Si, GaAs and Ge), for different frequency ranges
and up to five pairs of Lorentz poles accounted for in the model.
