A beat wave approach to harmonic generation in chiral media

Abstract: We extend the beat-wave framework for laser harmonic generation - where spectra form regular lattices in Fourier space - to the nonlinear response of isotropic chiral media driven by locally chiral light. We represent the enantio-sensitive response of the medium by a chiral zero-frequency (DC) mode derived from the transverse spin density induced by structured or focused fields. Beating between this DC mode and the driving electromagnetic modes yields alternating chiral and achiral contributions on a regular harmonic lattice. We derive a general criterion for when chiral and achiral pathways overlap at the same harmonic and generate enantio-sensitive interference that survives spatial or angular integration (global chirality), versus when enantio-sensitivity remains confined to spatially varying patterns (local chirality). We apply the criterion to published configurations of synthetic chiral light, including OAM-carrying bicircular fields and crossed multicolour beams, and show that it reproduces and clarifies their reported global-chirality and beam-bending regimes.