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We employ structured light for the second-harmonic generation fromsubwavelength AlGaAs nanoparticles that support both electric and magneticmultipolar Mie resonances. The vectorial structure of the pump beam allowsaddressing selectively Mie-resonant modes and control the strength of thegenerated nonlinear fields. We observe experimentally the enhancement of thesecond-harmonic generation for the azimuthally polarized vector beams nearmagnetic dipole resonance, and match our observations with the numericaldecomposion of the Mie-type multipoles for the fundamental and generatedsecond-harmonic fields

Enhanced second-harmonic generation with structured light in AlGaAs nanoparticles governed by magnetic response