Experimental example of isotropic surface second-harmonic generation: dc-sputtered air-exposed aluminum thin films

We have determined the amplitudes and relative phases of the allowed components of the effective surface second-harmonic susceptibility, χ⁽²⁾, for a set of air-exposed dc-sputtered Al thin films. The second-harmonic intensity and polarization state was measured as a function of linear input polarization state and azimuthal orientation of the sample using a Ti:sapphire laser at 810 nm. The films are found to be optically isotropic with respect to azimuthal rotation angle, consistent with an isotropic χ⁽²⁾ with seven elements in three families. Using measured linear optical properties, the elements of χ⁽²⁾ were determined from the data. In terms of the dimensionless parameters $a, b,$ and d [J. Rudnick and E. A. Stern, Phys. Rev. B 4, 4274 (1971)], we find |a|=2.30±0.72, in rough agreement with previous measurements of the surface current perpendicular to the surface on oxidized Al surface, |b|=0.013±0.004 for the surface current parallel to the surface, and |d|=0.009±0.002 for the bulk contribution. The relative phases of a and b with respect to d are found to be (-0.4±6)^∘ and (63±12)^∘, respectively. The measurement indicates a large discrepancy between measured values and the universal theoretical expectation that b=-1 and $d=1.$