Orbital angular momentum control of third-harmonic generation and vortex dichroism in isotropic media

Abstract

Structured light carrying orbital angular momentum enables new regimes of nonlinear light-matter interaction. Here we develop a molecular quantum electrodynamics description of third-harmonic generation (THG) driven by focused Laguerre-Gaussian beams in isotropic molecular media. We show that the nonparaxial longitudinal field components of a tightly focused beam permit THG with circularly polarized excitation in an isotropic fluid, a process forbidden for plane waves and paraxial beams. Within the electric-dipole approximation, the resulting emission is independent of the sign of the vortex charge. Including electric-magnetic dipole interference introduces a chiral contribution to the nonlinear response, giving rise to third-harmonic vortex dichroism (THVD). The emitted intensity then acquires a component linear in the topological charge \(\ell\), reversing sign with either the wavefront handedness or molecular chirality. Numerical modelling reveals corresponding spatial asymmetries in the harmonic field. These results establish both an allowed pathway for circularly polarized THG in isotropic fluids and the first chiroptical analogue of THG in such media, identifying orbital angular momentum as a new control parameter for nonlinear chiral spectroscopy.

Figures (6)

• Figure 1: Four topologically distinct time-ordered Feynman diagrams describing THG required in the sum over all pathways. Time flows vertically. The intermediate states are denoted as $|r\rangle$, $|s\rangle$, and $|t\rangle$. Each photon is labelled using Latin indices, $i$, $j$, $k$, and $l$, additionally, they have an associated wave vector, $\textbf{k}$, and polarization constant, $\eta$.
• Figure 2: Third-harmonic intensity distributions computed from Eq. (\ref{['eq:intensityAnswer']}) for varying $\ell$, $p$, and $\theta$. Each panel is normalized to its own maximum, with $\lambda = w_0$ throughout. Increasing $\ell$ broadens the ring structure, while increasing $p$ introduces additional radial nodes. The intensity is asymmetric, with enhanced lobes aligned along the input polarization direction, and the overall pattern rotates with $\theta$.
• Figure 3: Spatial intensity distributions along the direction of propagation for THG when $\ell=2$ and $p=0$, for an input beam with $\lambda=w_0$, and $x$-polarized incident and emission photons. The plots are normalized to the maximum of (e).
• Figure 4: Intensity of third-harmonic generation for circularly polarized input (phase distributions shown in insets). (a,b) For a Gaussian input ($\ell=0$), the generated harmonic carries a vortex of charge $\ell=\pm2$, with the sign set by the input helicity $\sigma$, consistent with angular momentum conservation. (c,d) For circularly polarized vortex beams, spin-orbit interaction emerges: parallel spin and OAM ($\sigma\ell>0$) produce a single-ring structure, whereas antiparallel spin and OAM ($\sigma\ell<0$) yield a distinct intensity profile. All panels are individually normalized, with $\lambda = w_0$.
• Figure 5: Spatial distribution of the THVD signal computed from Eq. (\ref{['eq:THVD_lin_final_general']}) for varying $\ell$ and $\theta$. The sign of the distribution reverses with the handedness of $\ell$ and rotates with $\theta$. In all cases the spatially integrated signal is non-zero, with the effect becoming more pronounced for larger $\ell$. All panels are individually normalized, with $\lambda = w_0$.