Fano enhancement of unlocalized nonlinear optical processes

Field localization boosts nonlinear optical processes at the hot spots of metal nanostructures. Fano resonances can further enhance these "local" processes taking place at the hot spots. However, in conventional nonlinear materials, the frequency conversion takes place along the entire crystal body. That is, the conversion process is "unlocalized." The path interference (Fano resonance) schemes developed for localized processes become useless in such materials. Here, we develop Fano enhancement schemes for unlocalized nonlinear optical processes. We show that three-orders-of-magnitude Fano enhancement multiplies the enhancements achieved via field-trapping techniques, e.g., in epsilon-near-zero materials. We demonstrate the phenomenon both analytically and using numerical solutions of Maxwell's equations. The agreement between the two solutions is impressive. We observe that the interference scheme for unlocalized processes is richer than that for the local processes. The method can be employed for any kind of nonlinear optical conversion. Moreover, Fano enhancement can be continuously controlled by an applied voltage.