Effective optical properties of highly ordered mesoporous thin films

This paper expands our previous numerical studies predicting the optical properties of highly ordered mesoporous thin films from two-dimensional (2D) nanostructures with cylindrical pores to three-dimensional (3D) structures with spherical pores. Simple, face centered, and body centered cubic lattices of spherical pores and hexagonal lattice of cylindrical pores were considered along with various pore diameters and porosities. The transmittance and reflectance were numerically computed by solving 3D Maxwell's equations for transverse electric and transverse magnetic polarized waves normally incident on the mesoporous thin films. The effective optical properties of the films were determined by an inverse method. Reflectance of 3D cubic mesoporous thin films was found to be independent of polarization, pore diameter, and film morphology and depended only on film thickness and porosity. By contrast, reflectance of 2D hexagonal mesoporous films with cylindrical pores depended on pore shape and polarization. The unpolarized reflectance of 2D hexagonal mesoporous films with cylindrical pores was identical to that of 3D cubic mesoporous films with the same porosity and thickness. The effective refractive and absorption indices of 3D films show good agreement with predictions by the 3D Maxwell-Garnett and nonsymmetric Bruggeman effective medium approximations, respectively.