FEM Solutions To Maxwell's Equations

Near Field Optics of Resonant Scattering by
Particulate Systems

Roger H. French

DuPont Co., Central Research
Wilmington Delaware USA
and
University of Pennsylvania, Materials Science Department
Philadelphia Pennsylvania USA

Particulate dispersions of ceramic particles in polymers can achieve dramatic optical effects which form the basis of pigmentary, opacifying, and photonic effects in paints, paper, plastics, and photonic materials. These effects arise due to the strong resonant coupling of the radiation wavelength and the similarly sized microstructural features in dispersions with high optical contrast. Mie theory, an analytical solution to Maxwell’s equations, can treat the resonant scattering of a single isotropic sphere, but particulate dispersions have large numbers of optically interacting, arbitrarily shaped, and optically anisotropic particles, and their behavior is not represented in Mie theory’s single scattering perspective. In realistic particulate dispersions of highly resonant particles, the optical interactions of the particles plays a critical role in the behavior of the system. At low particle volume concentrations (PVC), for instance below 3 vol.% TiO₂ in resin, multiple scattering approximations (whereby the particles are considered single scatters and their far field scattering can be summed as intensities) can apply and give rise to both scattering and diffraction. Most practical applications are at higher PVCs and the particles exhibit dependent scattering; they are interacting in the near field and a full treatment of optics is required.

Using computational optics and employing a time-domain finite element method, we determine the near field optics and light scattering properties of complex particulate microstructures in the strong coupling regime. The scattering properties of isolated quinacridone red, and optically anisotropic, morphological, titania particles demonstrate the non-intuitive nature of resonant scattering. The dramatic changes in scattering by particulate agglomerates highlight the critical role of near field optical interactions in these systems. Crowding of pigment particles at concentrations above a few volume percent shows that the near-field optical interactions change rapidly with increasing particle separation and extend to separations of 3-4 light wavelengths. The roles of resonant coupling, multiple scattering, and dependent scattering can be seen from comparison of computation and experimental results for crowded particulate dispersions of TiO₂ and quinacridone. These systems also show the effects of multiple particles to produce increased back scattering, and the role of optical absorption on setting the effective optical path length in the dispersion.