Revealing a mode interplay that controls second harmonic radiation in gold nanoantennas

In this work, we investigate the generation of second harmonic light by gold nanorods and demonstrate that the collected nonlinear intensity depends upon a phase interplay between different modes available in the nanostructure. By recording the backward and forward emitted second harmonic signals from nanorods with various lengths, we find that the maximum nonlinear signal emitted in the forward and backward directions is not obtained for the same nanorod length. We confirm the experimental results with the help of full-wave computations done with a surface integral equation method. These observations are explained by the multipolar nature of the second harmonic emission, which emphasizes the role played by the relative phase between the second harmonic modes. Our findings are of a particular importance for the design of plasmonic nanostructures with controllable nonlinear emission and nonlinear plasmonic sensors as well as for the coherent control of harmonic generations in plasmonic nanostructures.