Introduction

Virtually every natural and artificial material encountered in our environment is optically nonuniform on scales appreciably larger than molecular. The atmosphere is a mixture of several gases, submicroscopic aerosol particles of varying composition, and larger cloud particles. Sands and soils typically consist of many different kinds and sizes of mineral particles separated by air or water. Living things are made of cells, which themselves are internally inhomogeneous and are organized into larger structures, such as leaves, skin, or hair. Paint consists of white scatterers, typically TiO2 particles, held together by a binder containing the dye that gives the material its color.

These examples show that if we wish to interpret the electromagnetic radiation that reaches us from our surroundings quantitatively, it is necessary to consider the propagation of light through nonuniform media. Except in a few artificially simple cases, the exact solution of this class of problems is not possible today, even with the help of modern high-speed computers. Hence, we must resort to approximate methods whose underlying assumptions and degrees of validity must be judged by the accuracy with which they describe and predict observations.

Effective-medium theories

One such type of approximation is known as an effective-medium theory, which attempts to describe the electromagnetic behavior of a geometrically complex medium by a uniform dielectric constant that is a weighted average of the dielectric constants of all the constituents.