Bulk contribution in surface sum-frequency spectroscopy (with H. Held, X. Wei and Y. R. Shen)

Symmetry argument rules that sum frequency generation (SFG) is forbidden in a medium with an inversion center but allowed at a surface or interface where the inversion symmetry is necessarily broken. Therefore, SFG (or SHG) is highly surface-specific, and in recent years has been developed into a most powerful and versatile surface probe. In a typical surface SFG experiment, two input laser beams at frequencies w₁  and w₂  overlap at a surface or interface to generate a sum-frequency output in both reflection and transmission directions. By scanning w₂  over molecular vibrational modes, one can obtain a surface vibrational spectrum which contains important information regarding the surface molecular structure.

But the sum frequency signal from an centrosymmetric medium can also be generated due to higher-order nonlinear effects in its bulk. The latter include non-local electric dipole, magnetic dipole and electric quadrupole contributions. Since the true surface signal comes from just a few monolayers, its magnitude can be comparable with that of the higher-order effects. It is therefore important to be able to separate the surface and bulk contributions or at least to be able to estimate the relative magnitude of the two. During the year I have spent at Berkeley, we have performed systematic theoretical and experimental investigation of the potential effect of the bulk contributions on reconstructing the surface structure.

While in general, the bulk contribution can be identified in a transmission geometry due to an enlarged coherence length, there exists a term which behaves similarly to the surface and is not separable from the latter in experiments that allow no modification to the surface structure. We have studied the nature of this term and found it to be related to ambiguity in separating the surface and the bulk. Dependent on the choice of the molecular reference frame, the same molecule can be attributed either to the bulk of to the surface; the surface structure cannot be specified without indicating what reference frame is chosen.

We found that the problem of bulk contribution can in general be resolved by combining transmission measurements with the use of additional (yet very reasonable) theoretical assumptions and developed practical recipes of dealing with major bulk contributions.

[Paper]