Fano-control of localized and nonlocalized nonlinear response

We investigate the response of nonlinear media interacting with metal nanoparticle-quantum emitter dimers. First, we study the controll of local nonlinear processes taking place in a hot-spot. Fano resonances can control nonlinear response in two ways. (i) A linear Fano resonance can enhance the hot spot field, resulting in an enhanced nonlinear signal. (ii) A nonlinear Fano resonance can enhance the nonlinear signal also without enhancing the hot spot. Here, we utilize the latter one, i.e., case (ii). On a basic analytical model, we obtain the steady state solutions for the linear and nonlinear response. We demonstrate the enhancement and suppression of the second harmonic generation (SHG) process. We also compare our results with the numerical solutions to Maxwell equations via finite difference time domain (FDTD) simulations. Most importantly, we demonstrate the suppression of SHG process by utilizing the FDTD simulations which is predicted by the analytical model. The suppression takes place if the level-spacing of the quantum emitter (QE) is chosen to match the SH frequency, i.e., Weg. Such a phenomenon can be utilized for preventing nonlinear losses. Second, we study the Fano-control of nonlocal processes, i.e., the ones taking place out of the hot spots. The Fano control of local nonlinear processes in the hot spots has already been studied extensively in the literature. Conventional frequency converters, however, operate throughout the crystal body. Thus, here we study the case where the frequency conversion process takes place along the body of a nonlinear crystal. Metal nanoparticle-quantum emitter dimers control the down-conversion process, taking place throughout the crystal body, via introducing interfering conversion paths. Dimers behave as interaction centers. We show that 2 orders of magnitude enhancement is possible at weak interaction strengths, on top of the enhancement due to localization effects. That is, this factor multiplies the enhancement taking place due to the field localization. Our findings also provide a switch mechanism for the nonlinear conversion via voltage tuning the level spacing of QEs.