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Orbital Optical Chirality in Structured Light

Updated 8 July 2026
  • Orbital optical chirality is defined as the handedness of a field’s spatial phase twist in vortex beams, distinct from spin-induced circular polarization.
  • It arises from nonparaxial effects and the contribution of longitudinal fields, enabling observable phenomena like vortex dichroism and chiroptical interactions.
  • Measurement strategies, including helical dichroism and focused field analysis, reveal its practical applications in nanophotonics and quantum materials.

Orbital optical chirality denotes the handedness associated with the orbital structure of an electromagnetic field, rather than solely with its spin or circular polarization. In this usage, chirality is encoded by the spatial phase twist of vortex modes, typically through the azimuthal factor eiϕe^{i\ell\phi}, where the sign of the topological charge sets clockwise versus counter-clockwise orbital winding. Across recent work, this notion appears in several closely related forms: as an orbital contribution to optical chirality density, as OAM-dependent differential absorption or reflection, as chirality-selective lasing and near-to-far-field OAM conversion, and as an angular-momentum-resolved probe of geometric chirality in quantum materials (Forbes et al., 2021, Forbes et al., 2023, Wang et al., 25 Jun 2025).

1. Definitions and field-theoretic foundations

The orbital degree of freedom enters most directly through the generator of azimuthal rotations,

L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},

whose cylindrical eigenfunctions carry the phase factor eilϕe^{il\phi}. In the vortex-mode language used for structured light, the sign of ll directly encodes the handedness of the orbital field twist, while l|l| fixes the phase winding and the OAM per photon (Wang et al., 25 Jun 2025).

Optical chirality density is a local pseudoscalar quantity. A standard instantaneous definition is

C(r,t)=ε02E(r,t) ⁣ ⁣[×E(r,t)]+μ02H(r,t) ⁣ ⁣[×H(r,t)],C(\mathbf r,t)=\frac{\varepsilon_0}{2}\,\mathbf E(\mathbf r,t)\!\cdot\![\nabla\times\mathbf E(\mathbf r,t)] +\frac{\mu_0}{2}\,\mathbf H(\mathbf r,t)\!\cdot\![\nabla\times\mathbf H(\mathbf r,t)],

and, for monochromatic fields, one often uses a time-averaged form such as

Cˉ(r)=ε0ω2 ⁣[E(r) ⁣ ⁣B(r)].\bar C(\mathbf r)=\frac{\varepsilon_0\omega}{2}\,\Im\!\bigl[\mathbf E^*(\mathbf r)\!\cdot\!\mathbf B(\mathbf r)\bigr].

These quantities measure the handedness of the local electromagnetic field and, in one formulation, its ability to drive electric-dipole–magnetic-dipole transitions in chiral matter (Forbes et al., 2021, Forbes et al., 2023).

Within paraxial beam theory, optical chirality can be separated into polarization-associated and orbital-associated parts,

C=Cpol+Corb.C=C_{\rm pol}+C_{\rm orb}.

For beams propagating along z^\hat z, the orbital term arises from longitudinal fields and transverse spatial derivatives; one convenient expression is

Corb(r,t)12ω0c0{Ez(xEyyEx)+Bz(xByyBx)}.C_{\rm orb}(r,t)\simeq \frac{1}{2\omega_0 c_0} \left\{ E_z(\partial_xE_y-\partial_yE_x)+B_z(\partial_xB_y-\partial_yB_x) \right\}.

This decomposition makes explicit that orbital chirality is not simply the presence of OAM as an abstract mode label; it is tied to how longitudinal components and in-plane vorticity enter the full Maxwell field (Neufeld et al., 2017).

A recurring consequence is that purely transverse paraxial beams with negligible L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},0 have L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},1, whereas tightly focused or exact nonparaxial solutions can support a distinctly orbital contribution to optical chirality. This suggests that “orbital optical chirality” is best understood not as a single invariant attached to all OAM beams, but as a regime-dependent property of the full field structure.

2. Nonparaxiality, longitudinal fields, and spin–orbit coupling

The central technical issue is that orbital chirality becomes physically active when one goes beyond a strictly transverse paraxial model. For Laguerre–Gaussian light, the leading paraxial field is transverse, but the first-order longitudinal correction,

L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},2

is precisely the term identified as crucial for vortex dichroism. In high-NA focusing, paraxial theory is insufficient and vectorial Debye theory is required to describe the focal field (Forbes et al., 2021, Ni et al., 2018).

A closely related result appears for tightly focused Bessel vortex beams. Using the Lax-series expansion up to second order in the smallness parameter L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},3, the focal-plane optical chirality density acquires terms absent in paraxial theory and depends explicitly on the topological charge L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},4, the polarization ellipticity L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},5, and the degree of polarization L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},6. In that formulation, the paraxial term proportional to L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},7 vanishes unless both L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},8 and L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},9, but the nonparaxial corrections survive even for linear input eilϕe^{il\phi}0 or unpolarized input eilϕe^{il\phi}1. The result is a richly structured chirality landscape with alternating sign regions, ringed spatial profiles, and explicit eilϕe^{il\phi}2-dependence through eilϕe^{il\phi}3 and eilϕe^{il\phi}4 (Forbes et al., 2023).

An extreme version of the same mechanism was developed for superpositions of co-propagating Bessel beams with eilϕe^{il\phi}5. At the beam center, all transverse field components vanish while the longitudinal components survive, so that only eilϕe^{il\phi}6 and eilϕe^{il\phi}7 contribute to the local chirality density. In that configuration, the ratio eilϕe^{il\phi}8 can be made arbitrarily large by destructive interference in the energy density while keeping eilϕe^{il\phi}9 finite. The novelty is that enhanced optical chirality is then produced by longitudinal fields rather than by the usual transverse circular polarization (Rosales-Guzmán et al., 2012).

Spin–orbit coupling remains important even in explicitly orbital settings. In a focused-reflected beam, the spin-orbit interaction generates spatially non-uniform polarization across the beam cross-section because orthogonal field components are superposed with polarization-dependent interface reflection coefficients. Polarization filtering then converts a ll0 or ll1 charge vortex into two ll2 or ll3 vortices, depending on the input circular polarization, and the resulting optical vortex trajectory depends on input spin, vortex charge, and the reflecting surface characteristics. In the reported quartz-crystal experiment, that trajectory was used to quantify both the sign and the magnitude of the chiral parameter (Baishya et al., 2024).

3. Chiroptical interactions, dichroism, and competing mechanisms

The most direct operational definition of orbital optical chirality is often differential response under opposite vortex handedness. By analogy with circular dichroism, helical dichroism is defined as

ll4

where ll5 are reflectances under illumination by opposite OAM charges. In tightly focused illumination of chiral meso-structures, the reported HD reached ll6 for left-handed structures and ll7 for right-handed structures, while an achiral cylinder gave ll8 for all ll9. The peak shifted with structure diameter in a manner consistent with the focused-ring scaling l|l|0, and the spectra were unchanged under linear, left-circular, or right-circular input polarization, indicating a purely orbital effect in that regime (Ni et al., 2018).

At the microscopic level, the mechanism is more subtle. In the multipolar Hamiltonian,

l|l|1

different approximations lead to different symmetry conclusions. In a paraxial QED analysis of Laguerre–Gaussian absorption, OAM-sensitive discrimination in a freely propagating beam is tied to electric-dipole–electric-quadrupole or electric-quadrupole–electric-quadrupole terms, with a characteristic dependence on the product l|l|2. That framework also distinguishes sharply between 2D and 3D chirality and shows that some 3D-chiral contributions disappear under full orientational averaging (Forbes et al., 2018).

A later treatment that retained longitudinal fields reached a different conclusion for nonparaxial vortex modes. There, both oriented and randomly oriented chiral particles absorb photons from twisted beams at different rates depending on whether the vortex twists to the right or to the left through an electric-dipole–magnetic-dipole coupling scheme. The resulting vortex dichroism survives orientational averaging because the longitudinal field components permit OAM transfer even during dipole interactions, and no electric quadrupole is required in that mechanism (Forbes et al., 2021).

These two lines of analysis are not simply redundant. A plausible implication is that the question “does OAM directly couple to chirality?” has no single answer independent of beam model, focusing, and symmetry class. In strictly paraxial transverse optics, OAM sensitivity is strongly constrained. Once longitudinal fields, tight focusing, interfaces, or structured matter are included, orbital handedness can become an experimentally resolvable chiroptical variable.

4. Measurement strategies and experimental implementations

Several distinct observables have been used to operationalize orbital optical chirality. They differ in whether the measured quantity is a field property, a material response, or a dynamical consequence of chiral light–matter coupling.

Platform Observable Reported outcome
Chiral meso-structures Helical dichroism l|l|3 from reflectance l|l|4; sign flips with structural handedness
Quartz crystal in focused-reflected geometry Optical vortex trajectory Quantifies sign and magnitude of the chiral parameter
Single trapped chiral microsphere Orbital period l|l|5 Sensitivity l|l|6; at least one order of magnitude better precision than similar existing approaches
l|l|7-symmetric moiré material OAM-resolved dc photocurrent l|l|8 Intrinsic chirality in l|l|9; strain activates C(r,t)=ε02E(r,t) ⁣ ⁣[×E(r,t)]+μ02H(r,t) ⁣ ⁣[×H(r,t)],C(\mathbf r,t)=\frac{\varepsilon_0}{2}\,\mathbf E(\mathbf r,t)\!\cdot\![\nabla\times\mathbf E(\mathbf r,t)] +\frac{\mu_0}{2}\,\mathbf H(\mathbf r,t)\!\cdot\![\nabla\times\mathbf H(\mathbf r,t)],0

In mesoscale reflection measurements, scale matching is decisive: the focused vortex ring radius must overlap the chiral structure diameter. Under that condition, differential reflectance between C(r,t)=ε02E(r,t) ⁣ ⁣[×E(r,t)]+μ02H(r,t) ⁣ ⁣[×H(r,t)],C(\mathbf r,t)=\frac{\varepsilon_0}{2}\,\mathbf E(\mathbf r,t)\!\cdot\![\nabla\times\mathbf E(\mathbf r,t)] +\frac{\mu_0}{2}\,\mathbf H(\mathbf r,t)\!\cdot\![\nabla\times\mathbf H(\mathbf r,t)],1 and C(r,t)=ε02E(r,t) ⁣ ⁣[×E(r,t)]+μ02H(r,t) ⁣ ⁣[×H(r,t)],C(\mathbf r,t)=\frac{\varepsilon_0}{2}\,\mathbf E(\mathbf r,t)\!\cdot\![\nabla\times\mathbf E(\mathbf r,t)] +\frac{\mu_0}{2}\,\mathbf H(\mathbf r,t)\!\cdot\![\nabla\times\mathbf H(\mathbf r,t)],2 becomes large and robust, and opposite handedness of the structure reverses the sign of the response (Ni et al., 2018).

In optical tweezers, a different observable emerges. For a chiral sphere trapped in the ring of a focused vortex beam, the steady-state orbital period is

C(r,t)=ε02E(r,t) ⁣ ⁣[×E(r,t)]+μ02H(r,t) ⁣ ⁣[×H(r,t)],C(\mathbf r,t)=\frac{\varepsilon_0}{2}\,\mathbf E(\mathbf r,t)\!\cdot\![\nabla\times\mathbf E(\mathbf r,t)] +\frac{\mu_0}{2}\,\mathbf H(\mathbf r,t)\!\cdot\![\nabla\times\mathbf H(\mathbf r,t)],3

with equilibrium position set by the Mie–Debye force and C(r,t)=ε02E(r,t) ⁣ ⁣[×E(r,t)]+μ02H(r,t) ⁣ ⁣[×H(r,t)],C(\mathbf r,t)=\frac{\varepsilon_0}{2}\,\mathbf E(\mathbf r,t)\!\cdot\![\nabla\times\mathbf E(\mathbf r,t)] +\frac{\mu_0}{2}\,\mathbf H(\mathbf r,t)\!\cdot\![\nabla\times\mathbf H(\mathbf r,t)],4 including the Faxén correction near a coverslip. Because both C(r,t)=ε02E(r,t) ⁣ ⁣[×E(r,t)]+μ02H(r,t) ⁣ ⁣[×H(r,t)],C(\mathbf r,t)=\frac{\varepsilon_0}{2}\,\mathbf E(\mathbf r,t)\!\cdot\![\nabla\times\mathbf E(\mathbf r,t)] +\frac{\mu_0}{2}\,\mathbf H(\mathbf r,t)\!\cdot\![\nabla\times\mathbf H(\mathbf r,t)],5 and C(r,t)=ε02E(r,t) ⁣ ⁣[×E(r,t)]+μ02H(r,t) ⁣ ⁣[×H(r,t)],C(\mathbf r,t)=\frac{\varepsilon_0}{2}\,\mathbf E(\mathbf r,t)\!\cdot\![\nabla\times\mathbf E(\mathbf r,t)] +\frac{\mu_0}{2}\,\mathbf H(\mathbf r,t)\!\cdot\![\nabla\times\mathbf H(\mathbf r,t)],6 depend smoothly on the chirality index C(r,t)=ε02E(r,t) ⁣ ⁣[×E(r,t)]+μ02H(r,t) ⁣ ⁣[×H(r,t)],C(\mathbf r,t)=\frac{\varepsilon_0}{2}\,\mathbf E(\mathbf r,t)\!\cdot\![\nabla\times\mathbf E(\mathbf r,t)] +\frac{\mu_0}{2}\,\mathbf H(\mathbf r,t)\!\cdot\![\nabla\times\mathbf H(\mathbf r,t)],7, the period shifts approximately linearly with C(r,t)=ε02E(r,t) ⁣ ⁣[×E(r,t)]+μ02H(r,t) ⁣ ⁣[×H(r,t)],C(\mathbf r,t)=\frac{\varepsilon_0}{2}\,\mathbf E(\mathbf r,t)\!\cdot\![\nabla\times\mathbf E(\mathbf r,t)] +\frac{\mu_0}{2}\,\mathbf H(\mathbf r,t)\!\cdot\![\nabla\times\mathbf H(\mathbf r,t)],8, enabling extraction of C(r,t)=ε02E(r,t) ⁣ ⁣[×E(r,t)]+μ02H(r,t) ⁣ ⁣[×H(r,t)],C(\mathbf r,t)=\frac{\varepsilon_0}{2}\,\mathbf E(\mathbf r,t)\!\cdot\![\nabla\times\mathbf E(\mathbf r,t)] +\frac{\mu_0}{2}\,\mathbf H(\mathbf r,t)\!\cdot\![\nabla\times\mathbf H(\mathbf r,t)],9 from timing data. For Cˉ(r)=ε0ω2 ⁣[E(r) ⁣ ⁣B(r)].\bar C(\mathbf r)=\frac{\varepsilon_0\omega}{2}\,\Im\!\bigl[\mathbf E^*(\mathbf r)\!\cdot\!\mathbf B(\mathbf r)\bigr].0 and Cˉ(r)=ε0ω2 ⁣[E(r) ⁣ ⁣B(r)].\bar C(\mathbf r)=\frac{\varepsilon_0\omega}{2}\,\Im\!\bigl[\mathbf E^*(\mathbf r)\!\cdot\!\mathbf B(\mathbf r)\bigr].1–5, the reported values were Cˉ(r)=ε0ω2 ⁣[E(r) ⁣ ⁣B(r)].\bar C(\mathbf r)=\frac{\varepsilon_0\omega}{2}\,\Im\!\bigl[\mathbf E^*(\mathbf r)\!\cdot\!\mathbf B(\mathbf r)\bigr].2–200 ms, Cˉ(r)=ε0ω2 ⁣[E(r) ⁣ ⁣B(r)].\bar C(\mathbf r)=\frac{\varepsilon_0\omega}{2}\,\Im\!\bigl[\mathbf E^*(\mathbf r)\!\cdot\!\mathbf B(\mathbf r)\bigr].3–3 sCˉ(r)=ε0ω2 ⁣[E(r) ⁣ ⁣B(r)].\bar C(\mathbf r)=\frac{\varepsilon_0\omega}{2}\,\Im\!\bigl[\mathbf E^*(\mathbf r)\!\cdot\!\mathbf B(\mathbf r)\bigr].4, and Cˉ(r)=ε0ω2 ⁣[E(r) ⁣ ⁣B(r)].\bar C(\mathbf r)=\frac{\varepsilon_0\omega}{2}\,\Im\!\bigl[\mathbf E^*(\mathbf r)\!\cdot\!\mathbf B(\mathbf r)\bigr].5 for relative timing error Cˉ(r)=ε0ω2 ⁣[E(r) ⁣ ⁣B(r)].\bar C(\mathbf r)=\frac{\varepsilon_0\omega}{2}\,\Im\!\bigl[\mathbf E^*(\mathbf r)\!\cdot\!\mathbf B(\mathbf r)\bigr].6 (Diniz et al., 2024).

In quantum materials, orbital chirality can be isolated by symmetry-resolved nonlinear optics. For two interfering vortex beams with OAM difference Cˉ(r)=ε0ω2 ⁣[E(r) ⁣ ⁣B(r)].\bar C(\mathbf r)=\frac{\varepsilon_0\omega}{2}\,\Im\!\bigl[\mathbf E^*(\mathbf r)\!\cdot\!\mathbf B(\mathbf r)\bigr].7, the dc photocurrent decomposes into OAM channels Cˉ(r)=ε0ω2 ⁣[E(r) ⁣ ⁣B(r)].\bar C(\mathbf r)=\frac{\varepsilon_0\omega}{2}\,\Im\!\bigl[\mathbf E^*(\mathbf r)\!\cdot\!\mathbf B(\mathbf r)\bigr].8. In a moiré material with unbroken Cˉ(r)=ε0ω2 ⁣[E(r) ⁣ ⁣B(r)].\bar C(\mathbf r)=\frac{\varepsilon_0\omega}{2}\,\Im\!\bigl[\mathbf E^*(\mathbf r)\!\cdot\!\mathbf B(\mathbf r)\bigr].9 symmetry, only C=Cpol+Corb.C=C_{\rm pol}+C_{\rm orb}.0 channels survive, and the lowest nontrivial intrinsic contribution appears in the C=Cpol+Corb.C=C_{\rm pol}+C_{\rm orb}.1 channel of the helicity-dependent dc photocurrent. Uniaxial strain introduces an C=Cpol+Corb.C=C_{\rm pol}+C_{\rm orb}.2 harmonic and activates a C=Cpol+Corb.C=C_{\rm pol}+C_{\rm orb}.3 channel. Experimentally, driving the relative phase as C=Cpol+Corb.C=C_{\rm pol}+C_{\rm orb}.4 places each OAM channel at harmonic C=Cpol+Corb.C=C_{\rm pol}+C_{\rm orb}.5, so lock-in detection at C=Cpol+Corb.C=C_{\rm pol}+C_{\rm orb}.6 isolates the intrinsic chiral current while C=Cpol+Corb.C=C_{\rm pol}+C_{\rm orb}.7 tracks the strain-induced contribution. Typical responsivities C=Cpol+Corb.C=C_{\rm pol}+C_{\rm orb}.8–20 mA/W at C=Cpol+Corb.C=C_{\rm pol}+C_{\rm orb}.9 mW imply ideal single-domain currents of z^\hat z0–20 z^\hat z1A, and after beam-waist and domain-disorder reductions, a few-nA local photocurrent remains within reach (Yokoshi et al., 15 Jun 2026).

At the nanophotonic interface, chiral near fields can also be converted into far-field OAM. Spiral grooves milled on both sides of a thin suspended gold membrane launch plasmonic vortices with charge z^\hat z2, the central aperture enforces strict mode-matching selection rules, and the transmitted far-field OAM follows summation rules determined by the input and output spiral pitches together with aperture cutoff. In this setting, orbital chirality is generated in the near field and then re-radiated as a tailored far-field vortex (Gorodetski et al., 2013).

5. Active generation of orbital-chiral light

Orbital optical chirality is not only probed; it can be generated and tuned directly in active photonic devices. One route uses a microring Fabry–Pérot cavity with an uneven photon potential produced by a small tilt between the mirrors. The field is expanded as

z^\hat z3

and the pump position controls the relative gain of the clockwise and counterclockwise components. The resulting dissymmetry factor can be tuned continuously from z^\hat z4 to z^\hat z5, corresponding to fully negative- or positive-helicity OAM emission. In that platform, high-order vortices were demonstrated up to z^\hat z6, and multi-vortex emission was realized in both spatial and temporal domains (Qiao et al., 2022).

A distinct mechanism was demonstrated in twisted bilayer metasurfaces. There, two individually achiral semiconductor membrane metasurfaces are bonded with a twist angle z^\hat z7 and gap z^\hat z8 nm to form a chiral Moiré supercell. Gain-guided collective guided resonances in the two layers are coupled by a non-Hermitian four-mode Hamiltonian acting on clockwise and counterclockwise states in both membranes. Exceptional points occur when interlayer and intralayer couplings cancel, and at the exceptional point z^\hat z9 the eigenvector

Corb(r,t)12ω0c0{Ez(xEyyEx)+Bz(xByyBx)}.C_{\rm orb}(r,t)\simeq \frac{1}{2\omega_0 c_0} \left\{ E_z(\partial_xE_y-\partial_yE_x)+B_z(\partial_xB_y-\partial_yB_x) \right\}.0

is purely CW in both layers. Near that point, one mode acquires a net gain advantage and dominates lasing, producing single-mode intrinsically chiral emission (Wang et al., 25 Jun 2025).

The experimental signatures in the twisted bilayer system are explicitly orbital. The lasing threshold was Corb(r,t)12ω0c0{Ez(xEyyEx)+Bz(xByyBx)}.C_{\rm orb}(r,t)\simeq \frac{1}{2\omega_0 c_0} \left\{ E_z(\partial_xE_y-\partial_yE_x)+B_z(\partial_xB_y-\partial_yB_x) \right\}.1 kW/cmCorb(r,t)12ω0c0{Ez(xEyyEx)+Bz(xByyBx)}.C_{\rm orb}(r,t)\simeq \frac{1}{2\omega_0 c_0} \left\{ E_z(\partial_xE_y-\partial_yE_x)+B_z(\partial_xB_y-\partial_yB_x) \right\}.2, the single-mode emission could be tuned over a 250 nm band from 1430 nm to 1680 nm by adjusting pump locus and power, and self-interference gave fork fringes with Corb(r,t)12ω0c0{Ez(xEyyEx)+Bz(xByyBx)}.C_{\rm orb}(r,t)\simeq \frac{1}{2\omega_0 c_0} \left\{ E_z(\partial_xE_y-\partial_yE_x)+B_z(\partial_xB_y-\partial_yB_x) \right\}.3 and fixed handedness set by the bilayer chirality. Polarization-resolved imaging and fringe-contrast fitting yielded a CW:CCW amplitude ratio of approximately Corb(r,t)12ω0c0{Ez(xEyyEx)+Bz(xByyBx)}.C_{\rm orb}(r,t)\simeq \frac{1}{2\omega_0 c_0} \left\{ E_z(\partial_xE_y-\partial_yE_x)+B_z(\partial_xB_y-\partial_yB_x) \right\}.4, corresponding to Corb(r,t)12ω0c0{Ez(xEyyEx)+Bz(xByyBx)}.C_{\rm orb}(r,t)\simeq \frac{1}{2\omega_0 c_0} \left\{ E_z(\partial_xE_y-\partial_yE_x)+B_z(\partial_xB_y-\partial_yB_x) \right\}.5–0.5 and operation near, but not exactly at, the exceptional point (Wang et al., 25 Jun 2025).

Taken together, these devices show that orbital chirality can be engineered through gain asymmetry, non-Hermitian mode coupling, or near-field geometric chirality. This suggests that orbital optical chirality has become not only a diagnostic observable but also a design variable in integrated photonics.

6. Orbital chirality in matter, symmetry selection, and conceptual boundaries

The idea of orbital chirality extends beyond the optical field itself into electronic structure. In chiral crystals such as CoSi, circular-dichroism ARPES reveals a momentum-dependent orbital-angular-momentum texture with monopole-like orbital-momentum locking that depends on crystal handedness. The intrinsic chiral circular dichroism is defined as

Corb(r,t)12ω0c0{Ez(xEyyEx)+Bz(xByyBx)}.C_{\rm orb}(r,t)\simeq \frac{1}{2\omega_0 c_0} \left\{ E_z(\partial_xE_y-\partial_yE_x)+B_z(\partial_xB_y-\partial_yB_x) \right\}.6

and functions as an enantiomer-resolved probe of chiral electron states. In that context, the optical observable does not measure the chirality of a free-space vortex beam, but rather the handedness of orbital electronic states selected by circularly polarized light (Brinkman et al., 2024).

A broader theoretical framework relates structural chirality to electronic chirality through orbital–momentum locking. In a chiral lattice, a symmetry-allowed coupling

Corb(r,t)12ω0c0{Ez(xEyyEx)+Bz(xByyBx)}.C_{\rm orb}(r,t)\simeq \frac{1}{2\omega_0 c_0} \left\{ E_z(\partial_xE_y-\partial_yE_x)+B_z(\partial_xB_y-\partial_yB_x) \right\}.7

produces Corb(r,t)12ω0c0{Ez(xEyyEx)+Bz(xByyBx)}.C_{\rm orb}(r,t)\simeq \frac{1}{2\omega_0 c_0} \left\{ E_z(\partial_xE_y-\partial_yE_x)+B_z(\partial_xB_y-\partial_yB_x) \right\}.8 and a sign structure Corb(r,t)12ω0c0{Ez(xEyyEx)+Bz(xByyBx)}.C_{\rm orb}(r,t)\simeq \frac{1}{2\omega_0 c_0} \left\{ E_z(\partial_xE_y-\partial_yE_x)+B_z(\partial_xB_y-\partial_yB_x) \right\}.9. Within that picture, current-induced orbital polarization underlies not only anomalous circularly polarized light emission but also chirality-induced spin selectivity and electric magnetochiral anisotropy. This does not collapse optical and electronic chirality into one quantity, but it shows that orbital angular momentum provides a common symmetry channel across them (Yan, 2023).

The moiré proposal sharpens this symmetry viewpoint further. There, intrinsic loop-current chirality is encoded in a L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},00-selected angular harmonic of the Berry curvature and is optically isolated by the OAM difference L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},01 of interfering vortex beams. The same triangular geometry appears in both the loop phase L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},02 and the L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},03 Berry-curvature harmonic L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},04, and unbroken L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},05 forces the intrinsic response into the L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},06 channel. When L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},07 is broken, other L^z=iϕ,\hat L_z=-\,i\hbar\,\frac{\partial}{\partial \phi},08 channels appear in precise correspondence with the perturbation’s angular harmonic (Yokoshi et al., 15 Jun 2026).

Several misconceptions follow from conflating these regimes. Orbital optical chirality is not identical to circular polarization, since linearly polarized or even unpolarized tightly focused vortex beams can possess nonzero optical chirality density through nonparaxial corrections (Forbes et al., 2023). It is not guaranteed by OAM alone in a strictly paraxial description, since some orbital-sensitive effects require quadrupolar couplings or spin–orbit terms (Forbes et al., 2018). Nor is it restricted to the field in empty space: it can reside in near fields, emitted laser modes, electronic orbital textures, symmetry-resolved photocurrents, or optomechanical observables such as an orbital period. The literature therefore supports a precise but plural usage: orbital optical chirality refers to chiral phenomena in which orbital angular momentum, spatial phase twist, or orbital-mode asymmetry is the operative handed degree of freedom.

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