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Plasmonic nanoantennas provide unprecedented opportunities to concentrate light fields in subwavelength-sized volumes.By placing a nonlinear dielectric nanoparticle in such a hot spot,one can hope to take advantage of beth the field enhancement provided by nanoantennas and the large,nonlinear optical susceptibility of dielectric nanoparticles.To test this concept,we combine gold gap nanoantennas with second-order,nonlinear zinc sulfide nanoparticles,and perform second harmonic generation (SHG) spectroscopy onthe combined hybrid dielectric/plasmonic nanoantennas as well as on the individual constituents.We find that SHG from the bare gold nanoantennas,even though it should be forbidden due to symmetry reasons,is several orders of magnitude larger than that of the bare zinc sulfide nanoparticles.Even stronger second harmonic signals are generated by the hybrid dielectric/plasmonic nanoantennas.Control experiments with nanoantennas containing linear lanthanum fluoride nanoparticles reveal;however,that the increased SHG efficiency of the hybrid dielectric/plasmonic nanoantennas does not depend on the nonlinear optical susceptibility of the dielectric nanoparticles but is an effect of the modification of the dielectric environment.The combination of a hybrid dielectric/plasmonic nanoantenna,which is only resonant for the incoming pump light field,with a second nanoantenna,which is resonant for the generated second harmonic light,allows for a further increase in the efficiency of SHG.As the second nanoantenna mediates the coupling of the second harmonic light to the far field,this double-resonant approach also provides us with control over the polarization of the generated light.