  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.
