Calculations of Linear and Nonlinear Optical Properties of Ionic Crystal Surfaces and Fullerenes
Electronic and optical properties of ionic crystal surfaces and fullerenes have been studied by means of cluster calculations based on the Local Density Approximation (LDA) method using a numerical LCAO approach.
The calculations for the bulk, stoichiometric and non-stoichiometric (111) surfaces of the divalent ionic crystals, CaF2 and BaF2, were based on the construction of an appropriate cluster of Ba++/Ca++ and F- ions representing a local environment of the specific system. Such a cluster of ions was then embedded in an external potential to treat the long range Coulomb interaction correctly. Calculations performed for stoichiometric surfaces give an electronic structure similar to the bulk, while calculations performed for non-stoichiometric clusters show the existence of occupied surface states in the upper half of the band gap. The prediction of these types of occupied surface states was used in the interpretation of experimental observations concerning photoemission and laser-induced desorption from the (111) surface of BaF2 .
The phenomenological theory of second harmonic generation, SHG, at surfaces was used to explain observed polarization and azimuthal dependencies on these types of materials. The dispersion of the second order polarizability g(2)(-2w,w,w) of a cluster in the surface environment was also calculated. Assuming a non-stoichiometric surface composition, as indicated by experiments, the calculated difference in dispersion of g(2)(-2w,w,w) between CaF2 and BaF2 might explain the large difference in SHG intensity from surfaces of these compounds.
The recent interest in the nonlinear optical properties of fullerenes, especially Buckminsterfullerene, C60, motivated me to evaluate the electronic contribution to the linear and nonlinear polarizabilities for this molecule using LDA wavefunctions and transition moments. The induced dipole moment was calculated using an external static field term in the Hamiltonian. By repeating such calculations for different field strengths, the static linear and nonlinear polarizabilities of C60 have been evaluated. To approximately treat the dynamic polarizabilities, the static field results were used to determine an effective interaction parameter in a simplified Random Phase Approximation (RPA) approach. After inclusion of broadening and Lorentz local field factors, the dispersion of the linear dielectric function for films of C60 is well described. The screened static non-resonant third order nonlinear polarizability calculated for a free C60 molecule was found to agree with other theoretical calculations. The available experimental values, however, are about two orders of magnitude larger. In fact, they are in the range of the calculated values for the free response. To investigate the effect of screening, the dispersion for the free and screened third order nonlinear polarizabilities appropriate for third harmonic generation (THG), degenerate four wave mixing (DFWM) and electric field induced second harmonic generation (EFISH) experiments have been evaluated.