Controlling steady-state second harmonic signal via linear and nonlinear Fano resonances

Nonlinear signal even from a single molecule becomes visible at hot spots of plasmonic nanoparticles. In these structures, Fano resonances can control the nonlinear response in two ways. \textit{(i)} A linear Fano resonance can enhance the hot spot field, resulting enhanced nonlinear signal. \textit{(ii)} A nonlinear Fano resonance can enhance the nonlinear signal without enhancing the hot spot. In this study, we compare the enhancement of second harmonic signal at the steady-state obtained via these two methods. Since we are interested in the steady-state signal, we adapt a linear enhancement which works at the steady-state. This is different than the dark-hot resonances that appears in the transparency window due to enhanced plasmon lifetime.