Drude-Lorentz Model for Dispersion in Dielectrics

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Drude and Lorentz (ca. 1900) developed a classical theory to account for the complex index of refraction and dielectric constant of materials, as well as their variations with the frequency of light. The model is based on treating electrons as damped harmonically bound particles subject to external electric fields. A highly simplified version of the model is given in this Demonstration, with results limited to a qualitative level. Still, the phenomena of normal and anomalous dispersion and their relation to the absorption of radiation can be quite reasonably accounted for. The classical parameters of the theory transform simply to their quantum analogs, so that the results remain valid in modern theories of materials science.


Usually the dielectric constant increases slowly with frequency—normal dispersion. However, in the neighborhood of an atomic transition the material exhibits anomalous dispersion, in which the dielectric constant decreases sharply with frequency, accompanied by absorption of light.

In this Demonstration, you can vary the parameters and . A checkbox highlights the region of anomalous dispersion.


Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA



In the more accurate quantum theory of dispersion, the frequency is replaced by a sum over several atomic transition frequencies and the damping parameters are determined by excited-state lifetimes.

The real and imaginary parts of the susceptibility are connected by the Kramers–Kronig relations: and , where signifies the Cauchy principal value of the integral.


[1] L. Rosenfeld, Theory of Electrons, New York: Dover Publications, 1965, pp. 68 ff.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.