Surface and bulk contributions to the second-order nonlinear optical response of a gold film

We use two-beam second-harmonic generation to separate the surface (electric dipole origin) and bulk (magnetic dipole and electric quadrupole origin) contributions to the second-order nonlinear optical response of an isotropic gold film. The bulk response is unambiguously observed and explained by momentum damping of electrons in a free-electron model. Although bulk effects could be enhanced by inhomogeneous local fields in metal nanostructures and have been used to model second-harmonic generation from metamaterials [Y. Zeng et al., Phys. Rev. B 79, 235109 (2009)], we find that surface effects dominate the nonlinearity. Our quantitative results for the surface and bulk parameters set the baseline for future descriptions of the second-order response of nanostructured metals.

Figure 1

(Color online) Two-beam second-harmonic generation. (a) Surface geometry where two fundamental beams $\mathbf{a}$ and $\mathbf{b}$ intersect at a gold film and the second-harmonic signal $\mathbf{E}$ generated jointly by the two beams is detected in reflection. (b) Experimental setup: BS, beam splitter; M, mirror; P, polarizer; QWP, zero-order quarter-wave plate; VP, variable-angle polarizer; and PMT, photomultiplier tube. A prism in the path of the control beam adjusts its delay and synchronizes the pulse with that of the probe beam.

Figure 2

(Color online) The second-harmonic intensity as a function of the rotation angle of QWP. (a) $\left(-45°,s\right)$ signal fitted to surface-only models (dashed lines) based on external and internal fields and a model with both surface and bulk contributions (black solid line). (b) The black dots, red squares, green up-pointing triangles, and blue down-pointing triangles are the data for $\left(-45°,s\right)$, $\left(-45°,p\right)$, $\left(p,-45°\right)$, and $\left(s,-45°\right)$, respectively. The lines correspond to a simultaneous fit of all data to a model with both surface and bulk contributions.