Non Instantaneous Second Harmonic Generation in Gold Nanoparticles

Nonlinear metamaterials have revolutionized nonlinear optics in recent years, allowing unprecedented capabilities that could not be achieved with natural nonlinear materials. In this respect, metasurfaces, the 2D form of metamatetials, has exhibited nonlinear response up to 3 order of magnitude stronger than conventional nonlinear crystals. In addition, their sensitivity allows for unique capabilities in sensing and material classification of molecular structures such as DNA. Also, a complete theoretical description, based on the nonlinear scattering theory, has been found suitable to describe the geometrical contribution of nanostructures[NS] to their nonlinear response. Yet, till now, only the instantaneous nonlinear response has been investigated in a comprehensive theory, not capturing the full response which includes resonant behavior in addition to a non-instantaneous response found through their resonant linewidth.

Here, we show, for the first time to our knowledge, coherent control measurements of nonlinear second harmonic generation[SHG] in resonant non-instantaneous media. In particular, we investigated gold split ring resonators with localized surface plasmonic resonances [LSPR] found in 1400-1600 nm. We experimentally demonstrate a clear indication of their resonant and non-instantaneous behavior manifested by varying intensity and coherently controlling a degenerate pump-probe SHG process. We also develop a theoretical framework capturing non-instantaneous resonant phenomena which captures resonant effects as well as deviations from the conventional SHG intensity usually proportional to the square of the fundamental frequency intensity.

These newly captured phenomena are a substantial step in understanding the temporal dependence of nonlinearities in gold NS’s, which we believe will allow development novel sensing methods incorporating temporal figure prints in material identification through use of coherent control nonlinear spectroscopy. Newly designed meta-surfaces, could be used to observe temporal finger prints in chemical and biological materials such as DNA or photosystem proteins.