Second-harmonic generation from asymmetric nanostructures

The optics of media with dimensions small compared to the optical wavelength is characterized by distinctive phenomena such as optical field confinement and structural resonances. With a strong focus in research on the linear optical processes of nanostructures and colloids, the nonlinear optical properties have remained comparably unexplored. The nonlinear response, however, differs fundamentally due to its high symmetry selectivity. This can be explored, e.g., in second-harmonic generation (SHG), to probe different source polarizations which sensitively depend on dimensions and overall symmetry of the nanostructures.

In second-harmonic generation (SHG) and sum-frequency generation (SFG) both local surface dipolar and higher-order nonlocal bulk terms contribute to the overall second-order source polarization. Their separation has been a long standing problem in surface nonlinear optics because of the fundamental importance for proper signal assignment.

We demonstrated that on the nanoscale the independent emission of the different nonlinear source polarizations (nonlinear Rayleigh scattering) allows the distinct observation of local surface and nonlocal bulk contributions for partially asymmetric nanostructures. This is readily possible for appropriate selection of polarization and detection directions:

Second-harmonic generation from individual nanoscopic metal tips. As a partially asymmetric nanostructure the tips allow for the distinction of otherwise inseparable local surface Ploc(2) and nonlocal bulk Pnon-loc(2)SH source polarizations via their different polarization characteristics for emission.

Unique for asymmetric nanostructures are configurations without any mirror plane such as this crossed sagittalin → sagittalout configuration. Here, simply by selecting the detection polarization parallel or perpendicular to the tip axis, emission from the bulk or surface term, respectively, can be selected:

Second-harmonic polarization dependence for a Au-tip with radius r ∼ 20 nm and sagittal pump illumination and orthogonal sagittal SHG detection. For p-polarized detection, SHG is dominated by the local dipole allowed pinpout-contribution. In contrast, for s-polarized detection only the nonlocal, bulk polarization contributes.

The table summarizes the SH-intensities and their assignment to the respective source terms for this configuration:

Directional and polarization symmetry selection rules for SHG for asymmetric nanostructures for sagittal-pump -- sagittal-SHG detection configuration. Numbers refer to relative intensities observed in the experiment for Au tips.

We take advantage of these results for simultaneous probing of the changes in the bulk and surface response of nanoparticles during molecular adsorption. In addition, the symmetry properties of the tip-sample configuration are used for s-SNOM SHG imaging.

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Ultrafast electron dynamics of single metal nanostructures

Here, we study the phase decoherence of individual free standing gold nanotips by second-harmonic interferometric two-pulse correlation spectroscopy using sub-10 fs Ti:S fundamental excitation. In sagittal excitation and 90° SHG scattering detection this gives access to the pure local surface SHG response associated with the axial plasmon resonance of the structure.

Response theory model for the electric field of driving laser pulse and resonant particle plasmon response.

The coherent dynamics observed can be described by a plasmon resonant one-photon transition with a dephasing time T2 ~3-5 fs with the range depending on tip geometry. A model deconvolution of different individual contributions to the coherent optical response observed and the driving field transient is obtained by integrating the coupled differential equations describing the system evolution derived from the optical Bloch equations for a three level system.

Schematic of possible excitation and relaxation pathways for two-pulse coherent excitation: Two-photon interband transition between d and sp band of Au, and surface plasmon excitation.

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