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Light’s intensity pattern does not always reveal how its energy moves. In a partially coherent beam, correlations between different points can encode transverse energy-flow structure that is invisible in an intensity image. Separately, a 2025 experiment found that topological signatures in particular entangled orbital-angular-momentum states remained largely unchanged under modeled noise that included photon loss. These are two distinct results: one describes flow in classical structured beams; the other tracks topology in noisy quantum states.
Why an intensity image can hide how light flows
An intensity image shows where the average optical energy is concentrated. It does not, by itself, specify the direction or pattern of transverse energy transport. As Martínez-Herrero and Sanz put it in their 2026 preprint, “The intensity fixes where the averaged optical energy is located, but not how it moves.”
For partially coherent light, the cross-spectral density (CSD) describes correlations between pairs of spatial points. Its diagonal contains the intensity; information away from the diagonal includes phase correlations that can encode transverse momentum and transport. The preprint uses this information to define a generalized transverse flux and an effective velocity, obtained by dividing that flux by intensity. Integrating the velocity field gives streamlines that represent optical energy flow.
These streamlines are not paths traced by material particles, nor do they mean that individual photons have been followed along the curves. They are a way to represent the organization of energy flow in the beam. The authors characterize that organization using streamlines and quantities such as circulation Γ, vorticity Ω and accumulated angular displacement Θ. Their formulation is for quasi-monochromatic, partially coherent paraxial fields and reduces to the familiar coherent description in the single-mode limit. The work is a preprint, not a peer-reviewed experimental demonstration: Martínez-Herrero and Sanz, “Hidden transverse-flow topology in partially coherent structured light” (2026).
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How the same intensity can conceal different flow patterns
The preprint’s examples show why looking only at brightness can be misleading. Two beams can share an intensity profile yet have different coherence structure and, as a result, different transverse flow.
Twisted Gaussian Schell-model beams
In this example, the intensity can remain a circular Gaussian even though the coherence phase produces distributed rotational flow. The authors describe the azimuthal velocity as proportional to radius, with nonzero vorticity. The rotation is therefore a feature of the inferred flow field, not a swirl that must appear in the beam’s brightness pattern.
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Laguerre–Christoffel–Darboux beams
Sources with identical intensity profiles can have different angular coherence structures. In the paper’s single-charge case, the resulting streamlines spiral and the circulation is nonzero. In the balanced opposite-charge case, azimuthal flux cancels and the streamlines are radial. The contrast is a concrete example of why the intensity profile alone cannot uniquely determine transport.
The proposed way to recover such trajectories is to use the complex second-order coherence function. The paper says this reconstruction is possible in principle; it does not establish a completed experimental measurement of these example trajectories or specify a validated instrument and measurement procedure.
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What “energy leaks away” means in the separate quantum result
Photon loss belongs to a different result from the beam-flow examples. In a 2025 peer-reviewed study, de Mello Koch and colleagues examined entangled orbital-angular-momentum (OAM) states under noise models that include photon loss. They report that the states’ measured topological spectra remained largely unchanged relative to the initial experimental spectrum in the cases analyzed, even as the noise model degraded state purity.
The paper describes high-dimensional OAM-entangled states reaching 48-dimensional topological manifolds, with signatures of more than 17,000 topological numbers. Those figures refer to the study’s topological analysis; they do not mean 17,000 devices or applications. The resilience claim is limited to the particular states, observables and modeled noise conditions studied. It is not a general guarantee that topology survives arbitrary loss, and it is not evidence that the partially coherent beam-flow patterns above were tested under photon loss. See de Mello Koch et al., “Revealing the topological nature of entangled orbital angular momentum states of light” (Nature Communications, 2025).
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How the two findings differ
| Question | Partially coherent beam-flow preprint | Entangled OAM-state study |
|---|---|---|
| What system is studied? | Quasi-monochromatic, partially coherent paraxial structured beams. | Entangled photons in orbital-angular-momentum states. |
| What information reveals topology? | Correlations and phase in the cross-spectral density, used to construct a transverse flux and velocity field. | A reconstructed quantum-state topological spectrum. |
| What does “loss” refer to? | The paper’s beam-flow examples do not establish a photon-loss test. | Modeled noise includes photon loss and degrades state purity; the reported spectrum remains largely unchanged in the cases analyzed. |
| What is the evidence level? | A 2026 preprint presenting a formulation and analytical examples. | A peer-reviewed 2025 experimental report on OAM-entangled states and modeled noise. |
What the results do—and do not—show
- An intensity pattern is not a complete description of transverse transport in partially coherent light; off-diagonal coherence can carry flow information.
- Different flow organizations, including spiral and radial streamlines, can be associated with identical intensity profiles in the preprint’s examples.
- The quantum study offers a distinct, bounded result: selected topological spectra in particular entangled OAM states were largely stable under the modeled noise conditions, including photon loss.
- Neither result establishes how much energy is typically lost in practical optical systems, how common these effects are in deployed systems, or that any topology is universally protected against loss.
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