46 research outputs found
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