We propose an effective-medium theory for random aggregates of small spherical particles that accounts for the finite size of the embedding volume. The technique is based on the identification of the first two orders of the Born series within a finite volume for the coherent field and the effective field. Although the convergence of the Born series requires a finite volume, the effective constants that are derived through this identification are shown to admit of a large-scale limit. With this approach we recover successively, and in a simple manner, some classical homogenization formulas: the Maxwell Garnett mixing rule, the effective-field approximation, and a finite-size correction to the quasi-crystalline approximation (QCA). The last formula is shown to coincide with the usual low-frequency QCA in the limit of large volumes, while bringing substantial improvements when the dimension of the embedding medium is of the order of the probing wavelength. An application to composite spheres is discussed.
© 2006 Optical Society of America
Original Manuscript: May 27, 2005
Manuscript Accepted: July 19, 2005
Vol. 1, Iss. 3 Virtual Journal for Biomedical Optics
Charles-Antoine Guérin, Pierre Mallet, and Anne Sentenac, "Effective-medium theory for finite-size aggregates," J. Opt. Soc. Am. A 23, 349-358 (2006)