Optical Vortex Dichroism

• Optical vortex dichroism is the differential response of materials to light beams with orbital angular momentum, exposing chirality and anisotropic properties.
• It employs controlled vortex beams to probe selection rules in magnetic, atomic, and chiral systems, achieving significant dichroic contrasts in experiments.
• Enhanced by tight focusing and nonlinear processes, VD offers novel applications in chiral sensing, quantum control, and nanoscale metrology.

Optical vortex dichroism (VD) refers to the differential absorption, scattering, or emission of optical vortex beams—light fields with orbital angular momentum (OAM) $l\in\mathbb{Z}$—depending on the sign of their OAM or its interaction with the spin angular momentum (SAM, $\sigma=\pm1$). Unlike conventional circular dichroism (CD), which probes the response of chiral matter to circular polarization (helicity), VD generalizes this concept to the vorticity of the electromagnetic field, enabling the probing of material chirality, anisotropy, and magnetic order through the structured phase and topological charge of incident light. VD occurs in domains ranging from linear to nonlinear optics, and across atomic, nanoscale, and bulk material platforms.

1. Theoretical Foundations of Vortex Dichroism

The fundamental distinction between CD and VD lies in the conserved angular momentum of the photon. For conventional CD, the selection rules are governed by photon spin (helicity) $\sigma$ and its coupling to chiral structures or magnetic excitations. In VD, the optical field possesses OAM $l$ via azimuthal phase $e^{i l \phi}$, and the total angular momentum (TAM), $j=\sigma+l$, governs the light–matter interaction, as shown for example in AFM resonance absorption in TbFe$_3$(BO$_3$)$_4$ and Ni$_3$TeO$_6$ (Sirenko et al., 2020). The central object of study becomes the differential absorption, scattering, or emission as the sign of $l$ is reversed—holding $\sigma$ fixed—or vice versa.

In the multipole expansion of light–matter interaction, standard electric-dipole (E1) processes are only weakly sensitive to the OAM of the field in isotropic and achiral environments. However, in the presence of chiral matter, anisotropy, magnetic order, or by including longitudinal field corrections ($\propto1/{k w_0}$), the OAM variable mediates new selection rules for dichroic response (Forbes et al., 2021, Forbes et al., 2024).

2. Selection Rules and Physical Mechanisms

2.1. Total Angular Momentum Selection in Magnetic Materials

At antiferromagnetic (AFM) resonances, light absorption is governed by the TAM $j=\sigma+l$. For magnon excitations ($\Delta m=\pm1$), only photons with $j=+1$ or $j=-1$ are absorbed, with the selection rule enforced by the direction and magnitude of the external magnetic field $B$. In the case of higher-order vortex beams ($|l|\geq2$), the OAM dominates over SAM: when $|l|\gg|\sigma|$, the sign of $l$ alone determines which transition branch is active, leading to the regime of pure vortex dichroism (Sirenko et al., 2020).

For atomic systems, higher multipole transitions (e.g., electric quadrupole, $E2$) allow VD even in isotropic, non-chiral atoms. The absorption rate depends on either the OAM or SAM—or their combination—producing dichroism that can approach unity at the vortex center for $E2$ transitions, e.g., in trapped-ion experiments (Afanasev et al., 2017).

2.2. Chiral and Anisotropic Media

In chiral molecules and nanostructures, VD can be mediated via E1–M1 interference in the dipole approximation, provided the longitudinal field components of the vortex are significant. This E1–M1 term is responsible for the handedness sensitivity, allowing the dichroism to persist even in isotropic, tumbling molecular ensembles (e.g., in solution) (Forbes et al., 2021, Forbes et al., 2024).

In anisotropic but achiral media, purely electric-dipole (E1) interactions become sufficient when orientation or ordering is present. The interference between transverse and longitudinal field components results in a linear, first-order OAM-sensitive correction to the absorption rate, reachable with tight optical focusing ($\theta=1/(k w_0)\sim0.1$), and generating measurable VD even in structurally non-chiral samples (Forbes et al., 2024).

2.3. Structured Nanostructures and Nonlinear Regimes

In scattering from nanoscale chiral scatterers (helical ribbons), Method of Moments simulations reveal pronounced VD even for purely OAM beams ($\sigma=0$), emphasizing the geometric coupling between OAM and handed 3D structure. For twist ribbons (planar chirality), only SAM participates in dichroism, confirming the necessity of genuine 3D chirality for OAM-induced VD (Wang et al., 25 Jan 2026).

In nonlinear optics, two-photon absorption (TPA) by chiral molecules with focused vortex beams (nonlinear vortex dichroism, NVD) relies on E1–M1 tensor interference and the interplay of field gradients and molecular orientation. This nonlinear VD exhibits pronounced spatial dependence, polarization orientation sensitivity, and irreducible-tensor selection rules for allowed transitions, expanding the symmetry and information content of traditional chiroptical spectroscopy (Cheeseman et al., 2024).

3. Quantitative Metrics and Experimental Observables

3.1. Contrasts and Dissymmetry Factors

VD is quantified as the normalized difference in absorption or scattering rates (or cross sections) for beams of opposite OAM sign: $$\mathrm{VD} = \frac{P_{+l} - P_{-l}}{P_{+l} + P_{-l}}$$ where $P_{\pm l}$ is the absorbed or scattered power under OAM $l=\pm m$. Experiments show that in AFM resonance spectroscopy, dichroic contrasts $|D|>0.9$ (approaching unity) are achievable for $l$ up to 4, indicating nearly complete suppression of absorption for the “forbidden” OAM (Sirenko et al., 2020). In atomic quadrupole transitions, local dichroism at the vortex core reaches 100% (Afanasev et al., 2017). For plasmonic nanohelices, simulated VD values of $\sim10\%$ for purely OAM-driven cases and nearly 200% when SAM and OAM co-propagate have been reported (Wang et al., 25 Jan 2026).

3.2. Experimental Protocols

Experimental realization of VD involves generating and precisely controlling the OAM degree of freedom using spatial light modulators, spiral phase plates, q-plates, or axicons. Focusing is critical: tight focus ($w_0\sim\lambda$) enhances the longitudinal field and the resulting $\ell$-sensitive dichroism. Polarization must be well-controlled and matched to the sample’s tensor properties or orientation.

Measurement strategies include direct transmission or scattering (for bulk or nanoscale samples), selective monitoring of atomic populations (in BECs or ion traps), or imaging the spatial distribution of absorption in the focal plane (e.g., to resolve the spatially varying sign structure of $\Delta\Gamma(r)$ in chiral molecules) (Sirenko et al., 2020, Mondal et al., 2014, Forbes et al., 2021, Forbes et al., 2024).

Table: Representative VD Contrasts

System	Mechanism	($l, \sigma$)	Max VD	Reference
Ni$_3$TeO$_6$, TbFe$_3$(BO$_3$)$_4$	AFM resonance/magnon	$(\pm 1, 0)$	$0.98$	(Sirenko et al., 2020)
Ion (Ca$^+$) quad. abs.	$E2$ atomic transition	$(m=1, \Lambda)$	$1$ (locally)	(Afanasev et al., 2017)
Helical nano-ribbon	nano-scatterer	$(0, \pm1)$	$\pm10.5\%$	(Wang et al., 25 Jan 2026)
Chiral molecules (soln.)	E1–M1 (chiral)	$(\pm1, 0)$	$\sim$ few \%	(Forbes et al., 2021)
Anisotropic nanorod	E1 (oriented)	$(\pm1)$	$\sim80\%$	(Forbes et al., 2024)

4. Symmetry Principles and Selection Rules

Symmetry considerations govern when and how VD can appear. In systems characterized by anisotropy or partial ordering (such as aligned nanorods or 2D materials), VD is robust and macroscopically observable. In isotropic, achiral media, VD is forbidden for linear in-plane polarization owing to rotational averaging, but survives for chiral and some nonlinear contexts (Forbes et al., 2024, Forbes et al., 2021). In multiphoton and nonlinear harmonic generation processes, group-theoretic selection rules link the symmetry of the particle ($C_{n v}$ or $D_{n h}$), crystalline orientation ($\beta$), harmonic order $q$, and vortex charge $m$ to the possibility and magnitude of VD. The universal rule for nonlinear VD is that it appears if there exist lattice tensor indices $m_\chi^{(1,2)}$ such that $\Delta m_\chi=\nu n\neq 0$, where $n$ is the particle’s rotational order and $\nu$ any integer, and provided the lattice rotation $\beta$ avoids symmetry-saturating values (Nikitina et al., 2024).

In atomic and quantum systems, angular momentum selection rules for the transitions ($\Delta m=\pm l$) extend the paradigm of polarization-driven selection to the spatial topology of the optical field, directly connecting the matter’s quantum numbers to the photon’s OAM (Mondal et al., 2014, Afanasev et al., 2017).

5. Nonlinear Vortex Dichroism: Theory and Signatures

Nonlinear VD (NVD) emerges in two-photon (and higher-order) processes when the spatiotemporal structure of the vortex beam interacts with chiral tensors (E1–M1) of the target molecules (Cheeseman et al., 2024). The NVD signal,

$$\Delta W^{(2)}_x(r,\phi;\ell) = \frac{2N\pi\rho}{60\hbar c^3\epsilon_0^2}\bar I^2g^{(2)}\frac{\ell\gamma(r)}{k^2r}f_{\mathrm{LG}}^4(r)\mathrm{Re}\{ \dots \}$$

explicitly depends on the sign and magnitude of $\ell$ and exhibits strong spatial and polarization dependence. The irreducible tensor structure creates allowed and forbidden channels depending on the molecular point group and electronic structure. NVD enables access to chiral structure information inaccessible to linear or conventional CD methods and can be spatially or polarization-angle resolved for more selective chiroptical spectroscopy.

Key practical features include robustness to molecular tumbling, sensitivity to polarization orientation (rotating the incident polarization axis rigidly rotates the observed NVD lobes), and enhancement under tight focusing ($k w_0\sim 1$), or in high-Q resonant conditions (Cheeseman et al., 2024, Nikitina et al., 2024).

6. Applications and Technological Implications

VD expands the toolkit for probing condensed matter, quantum gases, and nanoscale materials beyond the capabilities of CD.

• Magnetic and Multiferroic Materials: VD enables selective excitation and detection of magnon and phonon modes according to total angular momentum. This facilitates valley-specific and topologically protected excitation schemes (Sirenko et al., 2020).
• Quantum Gases and Matter-Wave Physics: The OAM-resolved optical manipulation and detection of vortices in Bose–Einstein condensates realize minimally destructive, handedness-specific probes of superfluid order (Mondal et al., 2014).
• Chiral Sensing and Spectroscopy: The survival of VD in isotropic liquids allows for chirality sensing of biomolecules or ultrafast discrimination of enantiomers by OAM reversal, even when CD is suppressed (Forbes et al., 2021, Cheeseman et al., 2024).
• Nano-optics and Metrology: VD in oriented nanostructures provides a local, sensitive indicator of sample anisotropy and a direct readout of the OAM content of light, with applications in optical alignment and OAM-characterization (Forbes et al., 2024).
• Nonlinear Photonics: Harnessing nonlinear VD in harmonic generation or multiphoton absorption provides new contrast channels for chiral imaging, molecular fingerprinting, and control over light–matter angular momentum exchange (Nikitina et al., 2024, Cheeseman et al., 2024).
• Nanoscale Chirality Detection: The sensitivity of VD to genuine geometric chirality enables discrimination between planar and three-dimensional chiral nanostructures, with prospects for enantiomer-selective photonics and OAM-enhanced biosensing (Wang et al., 25 Jan 2026).

7. Future Directions and Open Challenges

Research continues into the optimization of VD for practical systems. Key areas include enhancing the magnitude of VD via nanostructure engineering and resonant design, exploring the role of higher OAM and multipolar transitions, understanding the interplay of OAM with other field degrees of freedom (spatiotemporal vortices, vector beams), and realizing ultrafast or quantum-regime probes capitalizing on the topological features of optical vortices.

VD systematically extends chiral and magnetic optical spectroscopy into higher-dimensional parameter spaces, coupling engineered light topology to emergent order and symmetry in matter. This platform enables fundamental studies and emerging applications in nano-optics, quantum control, and molecular discrimination across physics, chemistry, and materials science (Sirenko et al., 2020, Mondal et al., 2014, Forbes et al., 2021, Afanasev et al., 2017, Forbes et al., 2024, Nikitina et al., 2024, Wang et al., 25 Jan 2026, Cheeseman et al., 2024).