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Interest in the optical properties of plasmonic nanoparticles embedded in transparent polymers is expanding due to
potential uses in sustainability, biomedicine, and manufacturing. Geometric optics of polydimethylsiloxane (PDMS)
thin films containing uniformly or asymmetrically distributed polydisperse reduced gold nanoparticles (AuNPs) or
uniformly distributed monodisperse solution synthesized AuNPs were recently evaluated using a compact linear
algebraic sum. Algebraic calculation of geometric transmission, reflection, and attenuation for AuNP-PDMS films
provides a simple, workable alternative to effective medium approximations, computationally expensive methods, and
fitting of experimental data. Generally, transmission and reflection increased with AuNP isotropy and particle density, as
displayed on a novel ternary diagram. Irregular AuNP morphology and size distribution caused optical attenuation from
polydisperse films to increase in proportion to log10 increases in gold content, resulting in lower attenuation per gold
mass when compared to monodisperse AuNPs. Uniform monodisperse AuNP-PDMS films attenuated light in proportion
to gold content, with films attenuating 0.15 fractional units per 0.1 mass-percent AuNPs. Thin layers of concentrated
AuNPs attenuated light more efficiently. A 25 micron thick layer of 1.2 mass-percent AuNPs attenuated 0.5 fractional
units, the same number as a 130 micron thick 0.6 mass-percent film. Measured optical responses from asymmetric
AuNP-PDMS films with an adjacent back-reflector and pairs of uniformly distributed films were predictable within 0.04
units of linear algebraic estimates based on geometric optics. This approach allows for the summative optical responses
of a sequence of 2D elements comprising a 3D assembly to be analyzed.
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