Nonlocal current-response theory of structured-light dichroism

Akihito Kato; Nobuhiko Yokoshi

arxiv: 2604.10001 · v1 · submitted 2026-04-11 · ⚛️ physics.optics · cond-mat.other

Nonlocal current-response theory of structured-light dichroism

Akihito Kato , Nobuhiko Yokoshi This is my paper

Pith reviewed 2026-05-10 16:48 UTC · model grok-4.3

classification ⚛️ physics.optics cond-mat.other

keywords nonlocal current responsestructured light dichroismoptical vortex beamsminimal-coupling Hamiltonianhelicity-odd projectionsorbital angular momentum selection rules

0 comments

The pith

Absorption in structured light is a bilinear functional of the vector potential and a nonlocal current response kernel.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper starts from the minimal-coupling Hamiltonian and writes optical absorption as a bilinear expression involving the electromagnetic vector potential and the nonlocal current response of the matter system. This form applies directly to inhomogeneous fields such as optical vortex beams. Dichroic signals appear as the parts of the response kernel that reverse sign when the helicity of the light is flipped. The kernel is then separated into symmetry, tensorial, and mode-space parts, which produces selection rules for orbital angular momentum in both single and mixed helical modes. Local phenomena such as spatial dispersion and optical chirality are recovered as limiting cases when the kernel is expanded to first order in field gradients.

Core claim

Starting from the minimal-coupling Hamiltonian, absorption is expressed as a bilinear functional of the electromagnetic vector potential and the nonlocal current response. This provides a general description of light-matter coupling in optical vortex beams and other inhomogeneous fields. Dichroic signals are identified as helicity-odd projections of the nonlocal response kernel, which is resolved into symmetry, tensorial, and mode-space sectors. For single helical modes the theory supplies diagonal orbital-angular-momentum-resolved contributions together with selection rules; for mixed modes interference terms give access to off-diagonal coherence.

What carries the argument

The nonlocal current response kernel, which encodes the light-matter interaction and is decomposed into symmetry, tensorial, and mode-space sectors to isolate helicity-odd dichroic contributions.

Load-bearing premise

The nonlocal current response kernel can be defined and decomposed directly from the minimal-coupling Hamiltonian for arbitrary inhomogeneous fields without additional uncontrolled approximations.

What would settle it

Measure the helicity-dependent difference in absorption for a single helical vortex beam and check whether the observed dichroism matches the predicted helicity-odd projection of the kernel while the even part remains unchanged.

read the original abstract

We develop a microscopic theory of optical absorption and structured-light dichroism in a nonlocal minimal-coupling framework. Starting from the minimal-coupling Hamiltonian, we express absorption as a bilinear functional of the electromagnetic vector potential and the nonlocal current response, providing a general description of light--matter coupling in optical vortex beams and other inhomogeneous fields. Dichroic signals are identified as helicity-odd projections of the nonlocal response kernel, and the response is resolved into symmetry, tensorial, and mode-space sectors. For single helical modes, the theory yields diagonal OAM-resolved contributions together with the corresponding selection rules and symmetry constraints. For mixed modes, interference between distinct OAM components provides access to off-diagonal coherence of the nonlocal kernel, with a tensor structure determined by the polarization composition of the field. The theory also clarifies how local structures associated with symmetric spatial dispersion, optical chirality, and tensorial anisotropy emerge as gradient-level manifestations of the underlying nonlocal response.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper builds a reliable nonlocal framework for dichroism in structured light by resolving OAM modes and their interferences from the minimal-coupling Hamiltonian.

read the letter

The main takeaway is that this paper constructs a nonlocal current-response framework for structured-light dichroism that starts from the minimal-coupling Hamiltonian and handles both pure and mixed orbital angular momentum modes without introducing extra approximations. It does well by providing explicit expressions for diagonal OAM-resolved absorption contributions in single helical modes, along with the associated selection rules and symmetry constraints. For mixed modes, it identifies how interference terms reveal off-diagonal elements of the nonlocal kernel, with the tensor structure tied to the field's polarization. The clarification that local phenomena like optical chirality and tensorial anisotropy appear as gradient expansions of the nonlocal kernel is a helpful way to connect to existing local-response literature. The derivations rely on standard first-order time-dependent perturbation theory, so the bilinear functional form for absorption and the helicity-odd projection for dichroism follow directly from the symmetry properties of the kernel. The decomposition into symmetry, tensorial, and mode-space sectors is a valid re-basing that applies generally to linear response in inhomogeneous fields. No load-bearing assumptions beyond linear response are needed, which keeps the argument sound. One soft spot is that the presentation stays at the formal level, with no specific material calculations or direct comparisons to experimental data on vortex-beam dichroism. This makes it harder to gauge the practical advantage over local theories in quantitative terms right away. The citation pattern is appropriate and does not rely on self-references for the core results. This paper is for theorists working on light-matter interactions in condensed matter or optics, especially those dealing with chiral structured light or nonlocal effects. A reader who wants a systematic way to treat inhomogeneous electromagnetic fields in absorption processes will find the organization useful. It deserves a serious referee because the framework is logically tight and extends prior approaches in a controlled manner. I recommend sending it out for peer review.

Referee Report

0 major / 3 minor

Summary. The manuscript develops a microscopic theory of optical absorption and structured-light dichroism in a nonlocal minimal-coupling framework. Starting from the minimal-coupling Hamiltonian, absorption is expressed as a bilinear functional of the electromagnetic vector potential and the nonlocal current response kernel. Dichroic signals are identified as helicity-odd projections of the kernel, which is decomposed into symmetry, tensorial, and mode-space sectors. For single helical modes the theory yields diagonal OAM-resolved contributions and selection rules; for mixed modes, interference terms access off-diagonal coherences whose tensor structure follows from the field's polarization. Local structures (symmetric spatial dispersion, optical chirality, anisotropy) are recovered as gradient-level manifestations of the underlying nonlocal kernel.

Significance. If the derivations hold, the work supplies a first-principles, parameter-free re-expression of absorption for spatially inhomogeneous fields that directly incorporates orbital angular momentum and helicity without local approximations. The symmetry-based identification of dichroism as the helicity-odd part of the kernel and the sector decomposition are general and should apply to any linear-response current kernel. The explicit treatment of mixed OAM modes and the emergence of local limits from the nonlocal starting point are concrete strengths that could guide both analytic calculations and numerical implementations for vortex-beam spectroscopy.

minor comments (3)

The abstract and introduction refer to 'the nonlocal current response kernel' without an early equation number; adding a forward reference to its definition (presumably in §2 or §3) would improve readability for readers who wish to trace the bilinear functional immediately.
In the discussion of mixed-mode interference, the tensor structure arising from polarization composition is stated but not illustrated with an explicit 2×2 or 3×3 matrix example for a concrete pair of OAM values; a short worked example would clarify how off-diagonal kernel elements enter the observable.
The manuscript should state the precise conditions under which the linear-response assumption remains valid for tightly focused vortex beams (e.g., intensity thresholds or focal-spot size relative to the material coherence length).

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our manuscript, including the emphasis on the nonlocal minimal-coupling framework, helicity-odd projections for dichroism, OAM-resolved selection rules, and the recovery of local limits. The recommendation for minor revision is noted. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained from minimal-coupling Hamiltonian

full rationale

The paper starts from the standard minimal-coupling Hamiltonian and uses first-order time-dependent perturbation theory to express absorption as a bilinear functional of the vector potential A and the nonlocal current response kernel. This definition of the kernel and its decomposition into symmetry/tensorial/mode-space sectors is a direct consequence of linear response without fitted parameters or self-citations. Helicity-odd projections for dichroism follow from symmetry properties of the kernel (time-reversal/parity). For single and mixed OAM modes, the diagonal/off-diagonal contributions and selection rules are derived from the same framework. No load-bearing step reduces by construction to an input or prior self-citation; the approach remains valid for inhomogeneous fields under standard linear-response assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The theory rests on the standard minimal-coupling Hamiltonian as the starting point and introduces the nonlocal current response kernel as the primary new object without independent falsifiable evidence supplied in the abstract.

axioms (1)

standard math Minimal-coupling Hamiltonian provides the complete starting point for light-matter interaction in this context.
Invoked explicitly as the foundation for expressing absorption.

invented entities (1)

nonlocal current response kernel no independent evidence
purpose: To express absorption and dichroism in inhomogeneous fields and resolve into symmetry and mode sectors.
Defined as the central object of the theory; no external falsifiable handle is given in the abstract.

pith-pipeline@v0.9.0 · 5455 in / 1349 out tokens · 42951 ms · 2026-05-10T16:48:31.285074+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages · 1 internal anchor

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The present the- ory also provides a natural starting point for nonlinear structured-light spectroscopy

probe a genuinely nonlinear regime. The present the- ory also provides a natural starting point for nonlinear structured-light spectroscopy. In particular, the distinc- tion developed here between diagonal and oﬀ-diagonal mode-space channels carries over naturally to higher- order response. We intend the comparison here to be qualitative. The present anal...

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L. Ye, J. R. Rouxel, S. Asban, B. R¨ osner, and S. Mukamel, Probing Molecular Chirality by Orbital- Angular-Momentum-Carrying X-ray Pulses, J. Chem. Theory Comput. 15, 4180–4186 (2019)

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Jiang, Y

X. Jiang, Y. Nam, J. R. Rouxel, H. Yong, and S. Mukamel, Time-resolved enantiomer-exchange probed by using the orbital angular momentum of X-ray light, Chem. Sci. 14, 11067–11075 (2023)

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[29]

Cheng, L

C. Cheng, L. Rao, J. Ye, X. Zhao, Z. Che, W. Liu, J. Wang, and L. Shi, Navigating optical skyrmions—from historical origins to applications: tutorial, Adv. Opt. Photon. 18, 1–104 (2026)

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D. M. Lipkin, Existence of a new conservation law in elec - tromagnetic theory, J. Math. Phys. 5, 696–700 (1964)

work page 1964
[31]

Tang and A

Y. Tang and A. E. Cohen, Optical chirality and its inter- action with matter, Phys. Rev. Lett. 104, 163901 (2010)

work page 2010
[32]

Beyond optical chirality density: tensor-based description of electromagnetic chirality

I. Smagin and S. Dyakov, Beyond optical chirality den- sity: tensor-based description of electromagnetic chiral - ity, arXiv:2603.14071 (2026)

work page internal anchor Pith review Pith/arXiv arXiv 2026
[33]

Kato and N

A. Kato and N. Yokoshi, Description of molecular chiral - ity and its analysis with high harmonic generation, Phys. Rev. B 110, 085308 (2024)

work page 2024

[1] [1]

The present the- ory also provides a natural starting point for nonlinear structured-light spectroscopy

probe a genuinely nonlinear regime. The present the- ory also provides a natural starting point for nonlinear structured-light spectroscopy. In particular, the distinc- tion developed here between diagonal and oﬀ-diagonal mode-space channels carries over naturally to higher- order response. We intend the comparison here to be qualitative. The present anal...

work page

[2] [2]

Allen, M

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes, Phys. Rev. A 45, 8185 (1992)

work page 1992

[3] [3]

Rodger and B

A. Rodger and B. Nord´ en, Circular Dichroism and Linear Dichroism: A Textbook on Polarized-Light Spectroscopy (Oxford University Press, Oxford, 1997)

work page 1997

[4] [4]

Berova, K

N. Berova, K. Nakanishi, and R. W. Woody, Circu- 8 lar Dichroism: Principles and Applications (Wiley-VCH, New York, 2000)

work page 2000

[5] [5]

L. D. Barron, Molecular Light Scattering and Optical Ac- tivity, 2nd ed. (Cambridge University Press, Cambridge, England, 2004)

work page 2004

[6] [6]

L¨ oﬄer, D

W. L¨ oﬄer, D. J. Broer, and J. P. Woerdman, Circular dichroism of cholesteric polymers and the orbital angular momentum of light, Phys. Rev. A 83, 065801 (2011)

work page 2011

[7] [7]

Brullot, M

W. Brullot, M. K. Vanbel, T. Swusten, and T. Verbiest, Resolving enantiomers using the optical angular momen- tum of twisted light, Sci. Adv. 2, e1501349 (2016)

work page 2016

[8] [8]

K. A. Forbes and G. A. Jones, Optical vortex dichroism in chiral particles, Phys. Rev. A 103, 053515 (2021)

work page 2021

[9] [9]

K. A. Forbes and D. L. Andrews, Orbital angular mo- mentum of twisted light: Chirality and optical activity, J. Phys. Photonics 3, 022007 (2021)

work page 2021

[10] [10]

Hashiyada, A

S. Hashiyada, A. Wu, and Y. Y. Tanaka, Unveiling or- bital optical chirality through multipolar chiral light– matter interaction, Optica 13, 353 (2026)

work page 2026

[11] [11]

Jain, J.-L

A. Jain, J.-L. B´ egin, and R. Bhardwaj, HD in enan- tiomeric solutions, J. Chem. Phys. 159, 014504 (2023)

work page 2023

[12] [12]

K. A. Forbes and D. Green, Topological-charge- dependent dichroism and birefringence of optical vortices , Laser Photon. Rev. 18, 2400109 (2024)

work page 2024

[13] [13]

A. Jain, H. Northﬁeld, E. Karimi, P. Berini, and R. Bhardwaj, Selective and Tunable Absorption of Twisted Light in Achiral and Chiral Plasmonic Metasurfaces, ACS Nano 18, 27383 (2024)

work page 2024

[14] [14]

J. Ni, S. Liu, G. Hu, Y. Hu, Z. Lao, J. Li, Q. Zhang, D. Wu, S. Dong, J. Chu, and C.-W. Qiu, Giant HD of Sin- gle Chiral Nanostructures with Photonic Orbital Angular Momentum, ACS Nano 15, 2893 (2021)

work page 2021

[15] [15]

B´ egin, A

J.-L. B´ egin, A. Jain, A. Parks, F. Hufnagel, P. Corkum, E. Karimi, T. Brabec, and R. Bhardwaj, Nonlinear HD in chiral and achiral molecules, Nat. Photon. 17, 82 (2023)

work page 2023

[16] [16]

Cheeseman and K

L. Cheeseman and K. A. Forbes, Nonlinear Vortex Dichroism in Chiral Molecules, Adv. Opt. Mater. 13, 2402151 (2025)

work page 2025

[17] [17]

Marrucci, C

L. Marrucci, C. Manzo, and D. Paparo, Optical spin-to- orbital angular momentum conversion in inhomogeneous anisotropic media, Phys. Rev. Lett. 96, 163905 (2006)

work page 2006

[18] [18]

Y. Zhao, J. S. Edgar, G. D. M. Jeﬀries, D. McGloin, and D. T. Chiu, Spin-to-orbital angular momentum conver- sion in a strongly focused optical beam, Phys. Rev. Lett. 99, 073901 (2007)

work page 2007

[19] [19]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Angular momenta and spin-orbit interaction of nonparaxial light in free space, Phys. Rev. A 82, 063825 (2010)

work page 2010

[20] [20]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Has- man, Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems, Opt. Express 19, 26132 (2011)

work page 2011

[21] [21]

N. H. List, J. Kauczor, T. Saue, H. J. A. Jensen, and P. Norman, Beyond the electric-dipole approximation: A formulation and implementation of molecular response theory for the description of absorption of electromag- netic ﬁeld radiation, J. Chem. Phys. 142, 244111 (2015)

work page 2015

[22] [22]

N. O. Foglia, S. Komorovsk´ y, F. H. Ruud, F. Neese, and D. Maganas, Going beyond the electric-dipole ap- proximation in the calculation of absorption and (mag- netic) circular dichroism spectra including scalar rela- tivistic and spin-orbit coupling eﬀects, J. Chem. Phys. 157, 084120 (2022)

work page 2022

[23] [23]

F. P. Bonaf´ e, E. I. Albar, S. T. Ohlmann, V. P. Koshel- eva, C. M. Bustamante, F. Troisi, A. Rubio, and H. Ap- pel, Full minimal coupling Maxwell-TDDFT: An ab initio framework for light-matter interaction beyond the dipole approximation, Phys. Rev. B 111, 085114 (2025)

work page 2025

[24] [24]

Lazzeretti, Frequency-dependent current density t en- sors as density functions of dynamic polarizabilities, J

P. Lazzeretti, Frequency-dependent current density t en- sors as density functions of dynamic polarizabilities, J. Chem. Phys. 150, 184117 (2019)

work page 2019

[25] [25]

Mukamel, Principles of Nonlinear Optical Spec- troscopy (Oxford University Press, New York, 1995)

S. Mukamel, Principles of Nonlinear Optical Spec- troscopy (Oxford University Press, New York, 1995)

work page 1995

[26] [26]

V. Y. Chernyak, P. Saurabh, and S. Mukamel, Non-linear non-local molecular electrodynamics with nano-optical ﬁelds, J. Chem. Phys. 143, 164107 (2015)

work page 2015

[27] [27]

L. Ye, J. R. Rouxel, S. Asban, B. R¨ osner, and S. Mukamel, Probing Molecular Chirality by Orbital- Angular-Momentum-Carrying X-ray Pulses, J. Chem. Theory Comput. 15, 4180–4186 (2019)

work page 2019

[28] [28]

Jiang, Y

X. Jiang, Y. Nam, J. R. Rouxel, H. Yong, and S. Mukamel, Time-resolved enantiomer-exchange probed by using the orbital angular momentum of X-ray light, Chem. Sci. 14, 11067–11075 (2023)

work page 2023

[29] [29]

Cheng, L

C. Cheng, L. Rao, J. Ye, X. Zhao, Z. Che, W. Liu, J. Wang, and L. Shi, Navigating optical skyrmions—from historical origins to applications: tutorial, Adv. Opt. Photon. 18, 1–104 (2026)

work page 2026

[30] [30]

D. M. Lipkin, Existence of a new conservation law in elec - tromagnetic theory, J. Math. Phys. 5, 696–700 (1964)

work page 1964

[31] [31]

Tang and A

Y. Tang and A. E. Cohen, Optical chirality and its inter- action with matter, Phys. Rev. Lett. 104, 163901 (2010)

work page 2010

[32] [32]

Beyond optical chirality density: tensor-based description of electromagnetic chirality

I. Smagin and S. Dyakov, Beyond optical chirality den- sity: tensor-based description of electromagnetic chiral - ity, arXiv:2603.14071 (2026)

work page internal anchor Pith review Pith/arXiv arXiv 2026

[33] [33]

Kato and N

A. Kato and N. Yokoshi, Description of molecular chiral - ity and its analysis with high harmonic generation, Phys. Rev. B 110, 085308 (2024)

work page 2024