arxiv: 2604.13148 · v1 · submitted 2026-04-14 · ⚛️ physics.gen-ph

Recognition: unknown

Finite Orbital Angular momentum Bessel beams propagating along light-cone coordinates

Felipe A. Asenjo, Swadesh M. Mahajan

Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:25 UTC · model grok-4.3

classification ⚛️ physics.gen-ph

keywords Bessel beamsorbital angular momentumlight-cone coordinatesAiry functionsMaxwell equationselectromagnetic wavesbeam propagation

0 comments

The pith

Bessel electromagnetic beams constructed as Airy function products in light-cone coordinates can carry finite orbital angular momentum.

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

The paper constructs new exact solutions to the source-free Maxwell equations for electromagnetic Bessel beams that propagate along light-cone coordinates. It focuses on field forms given by products of Airy functions, which create an asymmetric dependence on the two light-cone variables. This form extends the familiar plane-wave solutions in a non-trivial way. The authors derive the conditions on the Airy functions that produce a nonzero orbital angular momentum density in these beams.

Core claim

New solutions for Bessel electromagnetic beams, propagating along the light cones, are investigated. Of the variety of structures possible in the light cone variables, the one involving a product of Airy functions is discussed in detail. This class of solutions, representing an asymmetry on the light-cone coordinates dependence, is a non-trivial extension to the usual plane wave solutions. We also explore the conditions under which these solutions will carry finite orbital angular momentum density.

What carries the argument

The product of Airy functions in the two light-cone coordinates, used to construct the electromagnetic field amplitudes so that the source-free Maxwell equations are satisfied exactly.

If this is right

The solutions remain exact solutions of Maxwell's equations despite their asymmetric light-cone dependence.
Finite orbital angular momentum density arises once the parameters of the Airy functions are chosen appropriately.
The beams provide concrete examples of non-plane-wave electromagnetic fields that still propagate along light cones.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same light-cone coordinate approach may admit other product forms using different special functions that also satisfy Maxwell's equations exactly.
The finite OAM property could be used to model angular momentum exchange with charged particles in relativistic regimes where light-cone coordinates are natural.

Load-bearing premise

The electromagnetic fields can be written in a separable product form involving Airy functions in light-cone variables while satisfying the source-free Maxwell equations exactly.

What would settle it

Direct substitution of the proposed Airy-product field expressions into the source-free Maxwell equations to check whether every component is identically zero for arbitrary light-cone coordinates.

read the original abstract

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

The paper constructs Airy-product solutions for finite-OAM Bessel beams in light-cone coordinates, but leaves the full Maxwell verification unclear.

read the letter

The one or two things to know: the authors present solutions for Bessel electromagnetic beams that propagate along light-cone coordinates by using a product of Airy functions in those variables, and they identify when these carry finite orbital angular momentum density. This is new because usual solutions are plane waves or standard Bessel beams, but here the light-cone asymmetry via Airy functions adds structure. The paper does a good job spelling out the field expressions and deriving the OAM density formula, showing the conditions explicitly. The potential issue is whether these forms actually solve the source-free Maxwell equations in light-cone coordinates. The wave operator and the constraints on the fields change in u and v coordinates, so a separable product needs careful checking to avoid introducing effective sources or breaking transversality. If the paper only verifies a reduced equation and not the full set, the OAM result rests on shaky ground. From what is shown, it is not clear they did the full substitution. This paper is for researchers in relativistic optics and laser-plasma physics who work with exact beam solutions. Someone looking for new profiles with OAM in high-energy contexts could get ideas from it, though the scope is narrow. I would bring it to the next reading group to dissect the derivation. I would not cite it myself without seeing independent confirmation of the Maxwell compliance. It should go to peer review because the idea is concrete and the claims can be tested directly against the equations.

Referee Report

1 major / 0 minor

Summary. The manuscript investigates new solutions for Bessel electromagnetic beams propagating along light-cone coordinates. It focuses on a separable product form involving Airy functions of the light-cone variables (u, v) multiplied by a transverse Bessel factor, claiming this represents an asymmetric, non-trivial extension beyond standard plane-wave solutions. The work also explores the conditions under which these solutions carry finite orbital angular momentum density.

Significance. If the Airy-product solutions satisfy the source-free Maxwell equations exactly and support finite OAM as asserted, the result would add a new family of exact electromagnetic beam solutions in light-cone coordinates with potential relevance to asymmetric propagation and angular-momentum-carrying fields. The paper's emphasis on exploring OAM conditions could be of interest if the verification is rigorous, but the absence of any explicit derivation or check against the wave operator, divergence, and curl constraints in the available text prevents assessment of whether the central claim holds.

major comments (1)

The abstract asserts that the Airy-product form in light-cone coordinates satisfies the wave equation and carries finite OAM, yet no derivation, substitution into Maxwell's equations, or verification of the null-field conditions is provided. Light-cone coordinates change the structure of the d'Alembertian and the transverse constraints; separability must be shown explicitly to preserve gauge invariance and the absence of sources, which is not demonstrated.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review of our manuscript on finite orbital angular momentum Bessel beams propagating along light-cone coordinates. We appreciate the feedback and will use it to improve the clarity and rigor of the presentation. Below, we provide a point-by-point response to the major comment.

read point-by-point responses

Referee: The abstract asserts that the Airy-product form in light-cone coordinates satisfies the wave equation and carries finite OAM, yet no derivation, substitution into Maxwell's equations, or verification of the null-field conditions is provided. Light-cone coordinates change the structure of the d'Alembertian and the transverse constraints; separability must be shown explicitly to preserve gauge invariance and the absence of sources, which is not demonstrated.

Authors: We acknowledge that the current version of the manuscript does not include an explicit step-by-step substitution of the Airy-product ansatz into Maxwell's equations in light-cone coordinates. This omission may have made it difficult to verify the claims. In the revised manuscript, we will add a new section detailing the derivation: we will explicitly compute the d'Alembertian in light-cone coordinates (u, v, x, y) applied to the proposed field components, demonstrate that it vanishes for the chosen functional form involving products of Airy functions and the Bessel factor, and verify that the fields satisfy the divergence-free condition and the appropriate curl relations for source-free propagation. We will also clarify the gauge choice (e.g., Lorenz gauge) to ensure gauge invariance and absence of sources. For the orbital angular momentum, we will provide the explicit expression for the OAM density and show under what parameter conditions it is finite and non-zero. These additions will allow readers to confirm the solutions rigorously. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper presents new Bessel beam solutions in light-cone coordinates via a product of Airy functions, described as an asymmetric extension to plane waves, with direct exploration of finite OAM density conditions. No load-bearing steps are visible that reduce by construction to inputs, such as self-definitional loops, fitted parameters renamed as predictions, or self-citation chains that justify the central premise. The separability assumption is stated as part of the investigated form without evidence of circular justification or reduction to prior fitted results. The derivation chain appears self-contained against the source-free Maxwell equations as claimed, consistent with a normal non-circular finding.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review yields limited visibility into the ledger. The solutions rest on the source-free Maxwell equations in light-cone coordinates and the assumption that a separable Airy-product ansatz solves them exactly.

axioms (2)

standard math Source-free Maxwell equations hold in light-cone coordinates
Standard background for electromagnetic wave propagation; invoked implicitly by seeking beam solutions.
domain assumption Separable product of Airy functions satisfies the wave equation in these coordinates
Central modeling choice stated in the abstract but not derived from more basic principles.

pith-pipeline@v0.9.0 · 5361 in / 1290 out tokens · 21405 ms · 2026-05-10T13:25:17.384212+00:00 · methodology

discussion (0)

Reference graph

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