| We present results of ultrafast second-harmonic generation spectroscopy of GaN/Al{dollar}rmsb2Osb3{dollar} samples. We develop a formalism to calculate the nonlinear response of thin nonlinear films excited by an ultrashort laser source (Ti:Al{dollar}rmsb2Osb3),{dollar} and we use this formalism to extract {dollar}chisbsp{lcub}zxx{rcub}{lcub}(2){rcub}(omega=2omegasb{lcub}o{rcub}){dollar} and {dollar}chisbsp{lcub}xzx{rcub}{lcub}(2){rcub}(omega=2omegasb{lcub}o{rcub}){dollar} from our SHG measurements over a two photon energy range of 2.6-3.4 eV. By comparing spectra from several samples, we find a weak sub-band gap enhancement of {dollar}chisbsp{lcub}zxx{rcub}{lcub}(2){rcub}(omega=2omegasb{lcub}o{rcub}){dollar} at a two photon energy of 2.80 eV that is not present in {dollar}chisbsp{lcub}xzx{rcub}{lcub}(2){rcub}(omega=2omegasb{lcub}o{rcub}).{dollar} This enhancement is independent of the carrier concentration, intentional doping, and presence of the "yellow luminescence band" defects. This feature may result from a three photon process involving a midgap defect state. We analyze three photon processes that include a defect state with group theory and demonstrate that several processes contribute to {dollar}chisbsp{lcub}zxx{rcub}{lcub}(2){rcub}(omega=2omegasb{lcub}o{rcub}){dollar} but not to {dollar}chisbsp{lcub}xzx{rcub}{lcub}(2){rcub}(omega=2omegasb{lcub}o{rcub}).{dollar} In addition, we determined sample orientational miscuts by rotational SHG, and we found that these miscuts do not generate strain induced interface states. We determined a Sellmeier dispersion relationship for the index of refraction of GaN by a novel light transmission method, and we report on photoluminescence of our GaN/Al{dollar}rmsb2Osb3{dollar} samples.; In a second project we have designed and built a nonlinear optical microscope. We have used the new tool to perform preliminary investigations of the nonlinear optical properties of carbon nanoropes. We suggest that nonlinear optical microscopy is a potentially useful technique for analyzing carbon nanotube symmetry, as well as in studies of other heterogeneities. Finally, we place an upper limit on the dominant second order hyperpolarizability, {dollar}alphasbsp{lcub}zzz{rcub}{lcub}(2){rcub},{dollar} of carbon nanotubes based on our nonlinear optical microscopy measurements. |
