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

## TL;DR

This paper theoretically investigates how second-harmonic generation in plasmonic and dielectric nanostructures couples spin and orbital angular momenta, revealing mechanisms for enhancement and conservation laws relevant to nanophotonics.

## Contribution

It introduces a comprehensive theoretical framework for nonlinear spin-orbital angular momentum coupling in nanostructures, including a general conservation law and comparison of dielectric and plasmonic systems.

## Key findings

- Comparable second-harmonic conversion efficiency in dielectric and plasmonic nanostructures with resonances.
- Mechanisms for second-harmonic enhancement in chiral clusters are identified.
- Dielectric nanostructures are more suitable for experimental studies due to lower losses.

## Abstract

We present a theoretical study of the characteristics of the nonlinear spin-orbital angular momentum coupling induced by second-harmonic generation in plasmonic and dielectric nanostructures made of centrosymmetric materials. In particular, the connection between the phase singularities and polarization helicities in the longitudinal components of the fundamental and second-harmonic optical fields and the scatterer symmetry properties are discussed. By in-depth comparison between the interaction of structured optical beams with plasmonic and dielectric nanostructures, we have found that all-dielectric and plasmonic nanostructures that exhibit magnetic and electric resonances have comparable second-harmonic conversion efficiency. In addition, mechanisms for second-harmonic enhancement for single and chiral clusters of scatterers are unveiled and the relationships between the content of optical angular momentum of the incident optical beams and the enhancement of nonlinear light scattering is discussed. In particular, we formulate a general angular momenta conservation law for the nonlinear spin-orbital angular momentum interaction, which includes the quasi-angular-momentum of chiral structures with different-order rotational symmetry. As a key conclusion of our study relevant to nanophotonics, we argue that all-dielectric nanostructures provide a more suitable platform to investigate experimentally the nonlinear interaction between spin and orbital angular momenta, as compared to plasmonic ones, chiefly due to their narrower resonance peaks, lower intrinsic losses, and higher sustainable optical power.