Spectral, tensor, and ab initio theoretical analysis of optical second harmonic generation from the rutile TiO2(110) and (001) faces

We give an overview of our recent experimental study on the optical second harmonic (SH) response of the rutile TiO2(110) and (001) faces, and the analysis of these results by phenomenological electromagnetic theory using nonlinear susceptibility tensors and by ab initio theory using the self-consistent full potential linearized augmented plane-wave (FLAPW) method within the local-density approximation. Since bulk rutile TiO2 has a uniaxial crystal structure of symmetry D4h14, the nonlinear optical response of its surface and bulk showed remarkable anisotropy. The TiO2(110) face exhibited stronger reflected SH response when the incident electric field was directed parallel than perpendicular to the [001] axis, while the TiO2(001) face exhibited relatively isotropic SH response. The anisotropy of the SH intensity patterns depended remarkably on the incident photon energy and the polarization combination. By using a phenomenological electromagnetic theory, we performed a simultaneous analysis of the SH intensity patterns from the (110) and (001) faces as a function of the sample rotation angle around its surface normal. As a result we could separate the contributions from the surface second-order and bulk higher-order nonlinear susceptibilities. We also found that the SH intensity spectra as a function of the SH photon energy depended strongly on the sample rotation angle and the polarization combination of the fundamental and SH light. The onset of the SH resonance of the TiO2(110) face was located at 2ℎω ∼3.4 eV when the induced nonlinear polarization was perpendicular to the surface. It was located at 2ℎω ∼3.2 eV when the induced nonlinear polarization is parallel to the [001] direction in the surface plane. These onset energies were higher than the onset energy of the bulk linear absorption at 3.0 eV. On the other hand, the onset energy of the SH resonance of the (001) face was found at 2ℎω ∼3.0 eV. A discussion is given on the physical meaning of the observed SH intensity spectra. Furthermore, an ab initio calculation of the nonlinear optical response from the TiO2(110) surface using the FLAPW method was performed. The calculated results agreed very well with the experimental SH intensity patterns and spectra. We found both from the phenomenological and ab initio calculation that the main SH response from the TiO2(110) surface originated from the Ti-O-Ti-O- zigzag chains on the TiO2(110) surface