Experimental intensity analysis of second harmonic generation at the Cu(110) surface

We have analyzed second harmonic generation (SHG) intensities from Cu(110) at fundamental wavelengths λ=1064 nm and between λ=650 and 540 nm. Experimentally the light incidence direction was chosen along the two inequivalent mirror planes of the surface lattice unit cell, and the linear polarizations of both input (fundamental) and output (frequency-doubled) radiation could be varied independently. At λ=1064 nm the relative sizes of the different components of the second-order susceptibility tensor are as follows: |χzzz|=2490, |χyzy|=139 and |χzyy|=33.7. The remaining elements are below detection threshold: |χxzx|<3 and |χzxx|<3. This analysis is based on the use of Fresnel coefficients and bulk optical constants. The results indicate that SHG is dominated by transitions induced by the z-components of the incident electric field. However, the situation is completely different in the intensity maximum (λ=600 nm) of a resonant intersurface band transition occurring around the Ȳ-point of the surface Brillouin zone: now SHG is dominated by the zyy tensor component, which exceeds both yzy and zzz, while again |χzxx| and |χxzx| are negligible. All available data, including temperature-dependent SHG studies of different authors, clearly show that contributions of electronic surface states to SHG intensities may be significant or even dominant. Therefore, a detailed quantitative understanding is a necessary condition for any analysis of adsorbate-induced SHG signals, since adsorbates can modify the surface electronic properties considerably. Our results furthermore indicate that the use of isotropic Fresnel coefficients to model the SHG-active electric fields is inadequate for a complete quantitative analysis.