A beat wave approach to harmonic generation in chiral media

TL;DR

This paper extends the beat-wave framework to analyze harmonic generation in isotropic chiral media driven by structured light, revealing conditions for enantio-sensitive interference and global versus local chirality effects.

Contribution

It introduces a general criterion for when chiral and achiral pathways overlap, explaining enantio-sensitive interference in harmonic generation in chiral media.

Findings

Reproduces and clarifies global-chirality regimes in synthetic chiral light configurations.

Identifies conditions for enantio-sensitive interference to survive spatial or angular integration.

Provides a unified framework for understanding harmonic generation in chiral media with structured light.

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.