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We present a theoretical study of the characteristics of the nonlinearspin-orbital angular momentum coupling induced by second-harmonic generation inplasmonic and dielectric nanostructures made of centrosymmetric materials. Inparticular, the connection between the phase singularities and polarizationhelicities in the longitudinal components of the fundamental andsecond-harmonic optical fields and the scatterer symmetry properties arediscussed. By in-depth comparison between the interaction of structured opticalbeams with plasmonic and dielectric nanostructures, we have found thatall-dielectric and plasmonic nanostructures that exhibit magnetic and electricresonances have comparable second-harmonic conversion efficiency. In addition,mechanisms for second-harmonic enhancement for single and chiral clusters ofscatterers are unveiled and the relationships between the content of opticalangular momentum of the incident optical beams and the enhancement of nonlinearlight scattering is discussed. In particular, we formulate a general angularmomenta conservation law for the nonlinear spin-orbital angular momentuminteraction, which includes the quasi-angular-momentum of chiral structureswith different-order rotational symmetry. As a key conclusion of our studyrelevant to nanophotonics, we argue that all-dielectric nanostructures providea more suitable platform to investigate experimentally the nonlinearinteraction between spin and orbital angular momenta, as compared to plasmonicones, chiefly due to their narrower resonance peaks, lower intrinsic losses,and higher sustainable optical power.

Mixing of spin and orbital angular momenta via second-harmonic generation in plasmonic and dielectric chiral nanostructures