The missing ingredient in effective-medium theories: Standard deviations

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.Comment: 12 pages (accepted for publication in Journal of Modern Optics

The role of angular momentum in the construction of electromagnetic multipolar fields

Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic fields, the multipolar solutions do not share a standard derivation or notation. As a result, expressions originating from different derivations can be difficult to compare. Some of the derivations of the multipolar solutions do not explicitly show their relation to the angular momentum operators, thus hiding important properties of these solutions. In this article, the relation between two of the most common derivations of this set of solutions is explicitly shown and their relation to the angular momentum operators is exposed.Comment: 13 pages, 2 figure