Dispersion Theory, Sum Rules, and Their Application to the Analysis of Optical Data

Abstract

The basic optical properties of solids, despite being greatly diverse are strictly limited by nature. These limitations take the form of sum rules and dispersion relations that reflect the physical laws governing the dynamics of matter and its interaction with light. The sum rules provide a useful means of testing optical measurements, particularly wide-range composite data, both against theoretical constraints and independently measured quantities. This chapter introduces sum rules with emphasis on the underlying physics and applications. Besides giving insight into the mathematical structure of the optical functions, the various sum rules also provide a means of relating different physical properties without model fits to spectra and are valuable as self-consistency tests. In the case of anisotropic media or symmetry-breaking external fields, the individual dielectric tensor elements should be treated separately. The best-known optical sum rule is the f sum rule, which can be written in a variety of forms useful in optical analysis.