Second harmonic generation by periodically-structured metal surfaces

Abstract

We present an approach to calculating second harmonic generation from periodically-structured metal surfaces. It requires the numerical solution of Maxwell's equations at both the first and second harmonic, but the electronic response to these fields is treated by a parametrization scheme developed earlier. Several model systems are considered, including metal patches of various shapes or holes in a metal film. Detailed calculations using the finite-difference time-domain method lead to predictions of the frequency dependence of second harmonic generation for different diffracted beams and polarizations. There is more spectral structure than what is evident in the linear reflection or transmission.

Linearly polarized second harmonic generation microscopy reveals chirality

“…The presence of this very sharp resonance near 800 nm suggests that the second harmonic light is most likely generated from the regions of high charge accumulation or in the places of strong field-enhancement due to the lightning-rod effect. Its sensitivity to chirality can then be attributed to enantiomerically sensitive plasmon modes, which were already observed in linear optics [30], and which could be related to the SHG response through recent theoretical studies [31][32][33].…”

The role of chiral local field enhancements below the resolution limit of Second Harmonic Generation microscopy

“…Additionally, the plasmonic mechanisms themselves, such as coupling between the charge oscillations, can be studied in the SHG enhanced signal [32][33][34][35]. Moreover, the enhanced SHG brings insight into new optical and magneto-optical [36] properties, and has lead to the development of several theoretical models [37][38][39][40][41][42]. In the study of chiral metallic nanostructures, we have seen that the SHG signal contains contributions from the chirality, the electro-magnetic properties and the geometry at the nanoscale; it is therefore important to understand which contributions are dominant.…”

Modal analysis method to describe weak nonlinear effects in metamaterials

“…u † m,e |X u 1,o u 1,o . This requires a full understanding of the SH mechanism 46,53,57,60 . Before discussing these results we note that there are general features of SHG from metallic nanostructures that indicate which mode will dominate.…”

“…where X is an operator whose form is determined by the particular form of the nonlinearity, and can encompass different nonlinear mechanisms presented in 46,53,57,60 . For example, for the hydrodynamic model (see below) X is a differential operator given by the last three terms of Eq.…”