The missing ingredient in effective-medium theories: Standard deviations

Craig F. Bohren, Xuerong Xiao, Akhlesh Lakhtakia

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Effective-medium theories for electromagnetic constitutive parameters of particulate composite materials are theories of averages. Standard deviations are absent because of the lack of rigorous theories. But ensemble averages and standard deviations can be calculated from a rigorous theory of reflection by planar multilayers. Average reflectivities at all angles of incidence and two orthogonal polarization states for a multilayer composed of two kinds of electrically thin layers agree well with reflectivities for a single layer with the same overall thickness and a volume-weighted average of the relative permittivities of these two components. But the relative standard deviation can be appreciable depending on the angle of incidence and the polarization state of the incident illumination, and increases with increasing difference between the constitutive parameters of the two layers. This suggests that average constitutive parameters obtained from effective-medium theories do not have uniform validity for all calculations in which they might be used.

Original languageEnglish (US)
Article number713521
Pages (from-to)1312-1315
Number of pages4
JournalJournal of Modern Optics
Issue number15
StatePublished - Sep 10 2012

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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