Light Propagation in Strongly Scattering, Random Colloidal Films: The Role of the Packing Geometry

We study the propagation of light through randomly packed films of micron-sized spheres. Dried films consist of strongly scattering core-shell particles mixed with polymer spheres, which are then dissolved to tune the number of contacts, $Z$, among the remaining scatterers. The transport mean free path $l^{*}$ is measured from the width of the coherent backscattering cone; $l^{*}=2.1\mu \mathrm{m}$ when $Z\sim 4–5$, but increases twofold (scattering weakens) in a film with $Z\sim 9–10$. The results contradict the standard diffusive transport model, but are explained by accounting for optical coupling of contacting spheres.

Figure 1

Schematic of coherent backscattering setup. A beam splitter allows sample illumination and detection of the backscattered light by the Si photodiode. The inset schematically shows the samples studied here. Dissolving the PMMA spheres allows us to tune $Z$, the coordination of the remaining ZnS-PS scatterers.

Figure 2

Backscattered intensity from films of ZnS-PS and PMMA spheres. The solid symbols show results of the binary films with $f=0.40$ and 1. The open symbols show the same samples after the PMMA spheres were dissolved. Data are plotted as $\ln \{[I(\theta )-I_b]/A\}$ vs ($\theta -{\theta }_0$) so that the slope is proportional to $l^{*}$. (Inset) $I(\theta )$ for the sample with $f=0.40$ after the PMMA were dissolved. The curve shows the result of a fit convolved with the angular resolution.

Figure 3

Measured $l^{*}$ vs the number fraction of strongly scattering ZnS-PS spheres, $f$ (a) Transport mean free path, $l^{*}$, measured in mixtures of ZnS-PS spheres (1000 nm-PS-core-80 nm-ZnS-shell) and PMMA spheres (1080 nm diameter). (b) Measured $l^{*}$ in mixtures of ZnS-PS and PMMA spheres with cross-linking polymer added (●). The open circles (○) show $l^{*}$ of the same films after the PMMA spheres were dissolved, leaving only the ZnS-PS spheres. The solid curve shows the prediction of the standard scattering theory, while the dashed curve shows the prediction of the modified theory discussed in the text.