Efficient method for the numerical extraction of Bergman’s spectral density function

Abstract

Effective properties of random particulate media are key to better understand their electromagnetic characteristics. For that purpose, many effective medium theories were developed. In this work, Bergman’s theory of homogenisation is explored. The core of this theory is its spectral density function (SDF), which contains the contribution of the mixture internal geometry on the effective properties. Here, we extract it with a standard but time-consuming homogenisation procedure, and a novel one, much faster. The two homogenisation methods plus the two extracted SDFs are then compared using a practical example showcasing excellent agreement between them.