Dispersion and anisotropy of the optical second-harmonic response of single-crystal Al surfaces

Abstract

We have performed tests of recent theories for the surface second-harmonic (SH) response of a jellium metal by measuring the dispersion characteristics of SH generation from atomically clean Al(111), Al(110), and Al(100) surfaces. This has been done for wavelengths between 565 and 860 nm, by using a picosecond-pulse dye-laser beam incident at angles of 22.5°, 45°, and 67.5°. In all cases, only p-polarized SH light generated by p-polarized incident light was observed. Absolute magnitudes were obtained by normalizing the SH response to that of a quartz plate. Contrary to expectations for a jellium metal, the Al(110) and Al(111) faces each yielded an anisotropic SH response, the intensity varying as the specimens were rotated about their surface normals. The relative magnitude of the anisotropic component increased with increasing wavelength and decreasing angle of incidence. By studying the variation of the SH intensity with temperature and oxygen exposure, we conclude that the anisotropic component is not due to intrinsic electronic effects but rather to the always-present atomic steps on the surface. We thereafter show that the isotropic component of the SH response can be identified with the flat ideally terminated surface. For all three surfaces, the characteristics of the isotropic SH response, in terms of magnitude and wavelength dependence, agree best with the recent results of calculations by Liebsch and Schaich [Phys. Rev. B 40, 5401 (1989)] employing the local-density approximation to calculate the ground-state electron distribution and the random-phase approximation to evaluate the SH response. The only significant deviation from this agreement is observed for Al(100) near 820 nm where an increasing SH response with increasing wavelength is attributed to a surface-state resonance.