Abstract
<title>Abstract</title> <p>Orbital angular momentum (OAM) has enabled linear chiroptical discrimination, but its potential to probe nonlinear optical responses in chiral nanoparticles remains largely untapped. Here we introduce the vortex offset technique, employing asymmetric Laguerre–Gaussian beams with a controlled phase-singularity displacement δ, to drive two-photon luminescence from individual twisted gold nanorods. Breaking the cylindrical symmetry of conventional vortex beams generates a crescent-shaped intensity profile that selectively couples to chiral nanostructures, yielding single-particle chiral sensitivity 10^5-fold greater than conventional circular dichroism (CD). We further define momentum dichroism that captures the combined effect of spin and orbital angular momentum in twophoton absorption. We discover a δ-dependent coupling parameter q that governs angular momentum transfer, a new observable capturing combined spin and orbital angular momentum effects in two-photon absorption. Opposite momentum-dichroism trends for left- and right-handed enantiomers enable unambiguous chirality identification. This work transforms structured light from a passive probe into an active participant in angular momentum exchange at the nanoscale – and does so in the nonlinear regime, achieving single-particle chiral sensitivity that outperforms both conventional CD and symmetric OAM methods.</p>