Optical anisotropy in vertically oriented TiO 2 nanotube arrays.

Nanofabricated optically anisotropic uniaxial thin films with deep submicron feature sizes are emerging as potential platforms for low-loss all-dielectric metamaterials, and for Dyakonov surface wave-based subwavelength optical confinement and guiding at interfaces with isotropic media. In this context, we investigate the optical properties of one such uniaxial platform, namely self-organized titania nanotube arrays (TNTAs) grown by the bottom-up nanofabrication process of electrochemical anodization on silicon wafer substrates, and subsequently annealed at different temperatures, i.e. 500 °C and 750 °C. We performed detailed quantitative analysis of the structure of the TNTAs using x-ray diffraction and Raman spectroscopy, which revealed a measurable phonon confinement in TNTAs annealed at 500 °C. Variable angle spectroscopic ellipsometry was used to investigate the optical anisotropy in two kinds of TNTAs-those constituted by anatase-phase and those containing a mixture of anatase and rutile phases. Both kinds of TNTAs were found to have positive birefringence (Δn) exceeding 0.06 in the spectral region of interest while mixed phase TNTAs exhibited Δn as high as 0.15. The experimentally measured anisotropy in the refractive index of the TNTAs was compared with the predictions of two different effective medium approximations incorporating the uniaxial geometry. The measured value of Δn for TNTAs exceeded that of bulk anatase single crystals, indicating the potential of nanostructured dielectrics to outperform dielectric crystals of the same material with respect to the magnitude of the achievable directional refractive index contrast.