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Spatiotemporal toroidal light beams with arbitrary polarization and orientation through a multimode fiber

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper experimentally demonstrates complete control of 3D toroidal light beams — including polarization, aspect ratio, and the 3D orientation of their orbital angular momentum — delivered after propagation through a 90-mode multimode…

desk verdict A real experimental advance in programmable toroidal beams through a multimode fiber, but the fidelity metric is self-referential—ask for the measured-versus-ideal overlap before trusting the numbers. read the letter →

arxiv 2501.13246 v2 pith:THZDENBI submitted 2025-01-22 physics.optics

Andrew V. Komonen , Nicolas K. Fontaine , Martin Plöschner , Marcos Maestre Morote , David T. Neilson , Joel Carpenter , Mickael Mounaix This is my paper · ORCID
classification physics.optics
keywords toroidalbeamsorbitalangularmomentummultimodefibertransmissionmatrixspatiotemporalbeamshapingwavelength-selectiveswitchpolarizationcontrolopticalmanipulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper reports the first experimental system that generates toroidal (donut-shaped) optical beams with independent control of their 3D geometry, polarization, and the orientation of their orbital angular momentum (OAM) axis, and delivers them through a multimode fiber supporting 90 modes. The key step is to measure a spectrally resolved transmission matrix of the fiber once, then compute the input field that, after propagation, becomes the desired toroidal beam. The authors demonstrate beams with poloidal and toroidal phase wraps, rotations about the x-axis, y-axis, and arbitrary 3D axes, and horizontal, vertical, and 45-degree polarizations, with squared overlap between measured and simulated fields around 80%. If the claim holds, optical tweezing, metrology, and light-matter interactions that require a directed optical torque could be performed in locations that are otherwise hard to access, such as inside scattering biological tissue.

What carries the argument

The load-bearing element is the spectrally resolved transmission matrix $T(\lambda)$ of the fiber, which linearly maps the 90 input modes (45 Hermite-Gaussian spatial modes per polarization) to the 90 output modes at each wavelength. Propagating the target field backward through this matrix with the conjugate-transpose operator $T^\dagger$ produces an input field that pre-compensates for modal dispersion and mode coupling in the fiber. A wavelength-selective switch with a spatial light modulator provides about 25,000 programmable spatiotemporal and polarization degrees of freedom, and a multi-plane light conversion device maps the SLM spots to the Hermite-Gaussian basis. The torus geometry and its tilt are encoded analytically through the parametric equations and rotation matrices.

What would settle it

Regenerate a toroidal beam with the same target but after deliberately perturbing the fiber (e.g., a small bend or a few degrees of temperature change) and compare the measured output with the expected output; if the squared overlap drops well below the ~80% level, the single-calibration assumption fails for dynamic operation. A second check is to generate a target whose ideal field contains significant power outside the 45-mode-per-polarization basis and measure whether the output still matches the ideal toroid rather than merely the projected version.

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Extended reading notes

Core claim

The central discovery is that a single spectrally-resolved transmission matrix $T(\lambda)$ of a multimode fiber, measured by launching each of 45 Hermite-Gaussian modes per polarization across around 290 spectral components, is sufficient to generate arbitrary polarization-resolved 3D toroidal beams at the fiber output. The input field is computed as $\vec{E}_{\text{inject}} = T^\dagger \vec{E}_{\text{out,target}}$, and the expected output is $\vec{E}_{\text{out,expected}} = T T^\dagger \vec{E}_{\text{out,target}}$; the measured outputs match these expectations with $|O|^2$ between 79% and 83%. The torus is defined by parametric equations in $(x,y,t)$, sliced into 20 temporal cross sections, each decomposed into 45 Hermite-Gaussian modes, and the OAM axis is set by analytically rotating the torus before computing the required input. This yields complete control over the toroidal geometry (major and minor radii), polarization, and the direction of the OAM singularity in 3D, without moving any optical component between configurations.

Load-bearing premise

The single transmission matrix measurement stays valid and complete for all later, more complex beams — the fiber must not drift, heat, bend, or change polarization between calibration and generation, and the 45 Hermite-Gaussian modes per polarization must capture all light that actually propagates.

Editorial extensions

If this is right

  • Toroidal beams carrying OAM along any 3D spatiotemporal axis can be generated by reprogramming the SLM hologram, with no physical realignment, enabling dynamic reorientation of the optical torque.
  • Because the beam is created at the output of a multimode fiber, these customizable optical forces and torques can be applied in hard-to-access locations such as deep inside scattering biological tissues.
  • The same apparatus and workflow extend to other 3D spatiotemporal light structures, such as optical hopfions, by changing only the phase encoding.
  • The 79–83% squared overlaps between measured and numerically propagated fields demonstrate phase-sensitive fidelity of the generation method.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The reported figure of merit compares the measured field with $T T^\dagger \vec{E}_{\text{target}}$, not with the ideal target itself; for a lossy or ill-conditioned fiber, high agreement with this expected field could coexist with lower fidelity to the intended toroid. An overlap against the ideal target would test this directly.
  • The single-calibration assumption implies that practical deployments would need periodic recalibration or real-time feedback to cope with fiber drift, bending, or thermal fluctuations.
  • The 15 GHz spectral resolution and 4.4 THz bandwidth set a limit on the temporal features of the toroid; shorter pulses or sharper spatiotemporal structures would require higher spectral resolution or broader bandwidth.
  • Combining this beam delivery with existing wavefront-shaping microscopy could allow targeted optical manipulation of single particles inside scattering media, but damage thresholds and delivery efficiency at high pulse energies are not addressed here.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper reports the experimental generation of three-dimensional spatiotemporal toroidal beams delivered through a multimode fiber supporting 90 spatial/polarization modes. The generation chain is: define the torus analytically (Eq. 1), slice it into 20 temporal cross sections, decompose into 45 Hermite-Gaussian modes per polarization, measure a spectrally resolved transmission matrix T(λ) of the fiber (Eq. 8), compute the predistorted input E_inject = T† E_target (Eq. 9), display a phase-only hologram computed with a modified Gerchberg-Saxton algorithm, and characterize the output with swept-wavelength off-axis digital holography. The authors demonstrate horizontally, vertically, and 45-degree polarized toroidal beams, rotations about the x- and y-axes at a few discrete angles, one off-axis orientation, and report squared-overlap values between 79% and 83% between the measured field and a numerically propagated reference field E_out,expected = T T† E_target (Eq. 10, Eq. 13). The central claim is complete programmable control of high-dimensional, polarization-resolved, arbitrarily oriented 3D OAM toroidal beams.

Significance. If the central claim is validated, this is a significant advance: it would be the first demonstration of programmable toroidal beams delivered through a multimode fiber, with independent control of polarization, torus geometry, and OAM orientation. The technical apparatus is strong: full spectrally resolved 90-mode transmission-matrix characterization, polarization-diverse WSS-plus-MPLC synthesis, and direct spatiotemporal field measurement by swept-wavelength digital holography. The reported overlap values are high. However, the load-bearing validation is weakened because the reference for the overlap is not the ideal toroidal field but the forward-model prediction T T† E_target computed from the same transmission matrix used to design the input; the paper also makes strong 'arbitrary' and 'complete' claims supported by only a few discrete demonstrations. With a direct comparison to the ideal target and a tempering of the claims, the contribution would be appropriate for a high-impact journal.

major comments (3)
  1. [§2.3, §4.6, §4.7, Eqs. (10) and (13)] The reported fidelity metric is self-referential. Eq. (10) defines the expected output as E_out,expected = T(λ)T†(λ) E_out,target, using the same measured transmission matrix T that is used in Eq. (9) to compute the injected field. The overlap in Eq. (13) therefore measures agreement with the forward model, not agreement with the ideal toroidal beam defined by Eq. (1). If T is non-unitary—because of mode-dependent loss, an incomplete 45-mode-per-polarization basis, or calibration drift—the operator T T† acts as a non-trivial filter, and a measured field can show high overlap with T T† E_target while deviating substantially from E_target. The manuscript never reports the overlap between the measured field and the ideal target, nor the overlap between E_out,expected and E_out,target. Please report these quantities directly and characterize T through its singular-value spectrum, condition number, or effective rank so the reader can assess how much of the 79–83% fidelity reflects actual toroid quality rather than self-consistency with the calibration.
  2. [§2.3, Fig. 4, and §1] The central claims of 'complete experimental control' and 'arbitrary 3D spatiotemporal axis' are not fully supported by the presented data. Fig. 4 demonstrates only three discrete rotation angles about the x-axis, three about the y-axis, and a single off-axis orientation, while Fig. 3 uses a single aspect ratio R/r and a single topological charge. Independent control of the aspect ratio is claimed in the Introduction but not demonstrated quantitatively. Either add a systematic validation (for example, fidelity versus orientation angle and versus R/r, or versus topological charge), or rephrase the claims from 'complete/arbitrary' to 'programmable' over the explicitly demonstrated parameter range.
  3. [§4.1.3 and Methods 4.6] The rotation formalism is only written out for rotation about the x-axis (Eqs. 5–6). Since the paper claims arbitrary 3D orientation, the general rotation matrix or Euler-angle construction used for the off-axis beam in Fig. 4g should be stated explicitly. In addition, large tilt angles can map the torus to a larger temporal extent than the original 2r range; the manuscript should specify the values of R and r used in Figs. 3–4 and confirm that the finite 4.5 ps delay window does not clip the tilted toroids.
minor comments (5)
  1. [Eqs. (3)–(4)] The phase definitions use tan without specifying two-argument atan2 or branch unwrapping; please clarify how u and v are extracted unambiguously over [0, 2π).
  2. [§4.6, text before Eq. (10)] There is a duplicated word: 'through the the spectrally-resolved TM' should read 'through the spectrally-resolved TM'.
  3. [§4.2 and Fig. 3] Please give the numerical values of R, r, and the temporal window used for each figure so that the aspect-ratio claim is reproducible.
  4. [§2.3] The phrase '45-degree polarized' should be clarified as a linear polarization at 45° to avoid ambiguity with circular or other polarization states.
  5. [Data availability] For a methods-heavy experimental paper, depositing the measured fields and reconstruction code in a public repository would strengthen reproducibility; 'available on reasonable request' is weak.

Circularity Check

1 steps flagged · score 6.0 of 10

Fidelity is measured against the same transmission matrix used to compute the input; the validation reduces to a self-consistency check.

  1. fitted input called prediction [Results 2.3; Methods 4.4 Eq. 9, Methods 4.6 Eq. 10, and Eq. 13]
    "To assess the experimental results, we calculate the overlap integral O between the experimentally measured field E_out,measured and the numerically propagated field E_out,expected. ... E_inject(λ) = T†(λ) E_out,target(λ) ... E_out,expected(λ) = T(λ) E_inject(λ) = T(λ)T†(λ) E_out,target(λ)"

    The input field used to drive the fiber is computed from the measured transmission matrix T via Eq. 9. The reference field against which the measured output is scored is then defined in Eq. 10 as T T† applied to the ideal target, i.e. the forward prediction of the same measured T. The overlap integral O in Eq. 13 therefore measures agreement between the measured field and the model's own prediction, not agreement with the ideal toroidal beam. If T is non-unitary, modal-incomplete, or contains calibration errors, the reference field T T† E_target differs from E_target, yet the metric can remain high because both the injected field and the reference inherit the same error.

full rationale

The only substantial circularity is in the validation metric: Eq. 9 computes the predistorted input with T†, Eq. 10 defines the expected output as T T† times the target, and Eq. 13 scores the measured beam against that expected output. This makes the reported fidelities consistency checks of the linear model rather than direct tests of generation of the ideal torus. No independent measure of T's unitarity or mode completeness is given, and no overlap with the ideal target (Eq. 1/2) is reported. Other potential concerns—e.g. that only rotations about x and y are shown before claiming arbitrary 3D axes, or that self-citations [2,49] describe the apparatus and T† method—are not circularity: the cited prior work is independent experimental/technical support, and the generalization from x/y rotations to arbitrary axes is a scope/evidence issue, not a definitional reduction. The target definition (Eq. 1), phase encoding, and Gerchberg-Saxton hologram calculation are self-contained. Overall, one load-bearing 'prediction' (the expected output) reduces to the same measured matrix used to build the input, so a partial circularity score of 6 is appropriate.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The central capability rests on the measured transmission matrix, the completeness of the mode basis, and the stability of the fiber. The free parameters are user-selected target geometry and charge values, not fitted constants. The main unstated dependency is that the 90-mode HG basis captures all relevant degrees of freedom, and that the transmission matrix remains valid between calibration and generation.

free parameters (4)
  • Major torus radius R = not specified numerically in text
    User-chosen target geometry parameter. The claim of arbitrary aspect ratio R/r depends on choosing R freely; it is not fitted to data.
  • Minor torus radius r = not specified numerically in text
    User-chosen target geometry parameter, controlling tube thickness and hole size. Not fitted to data.
  • Tilt angle theta = examples: -60, 30, 90, -45, 45 degrees
    User-chosen orientation angles for the torus and OAM. The claim of arbitrary orientation rests on setting these angles freely; only a discrete set is demonstrated.
  • Topological charge l = 1
    All demonstrated beams use one unit of phase winding. Higher or negative charges are not shown, despite the broader language of arbitrary toroidal structure.
assumptions (4)
  • domain assumption The multimode fiber is a linear, time-invariant system over the duration of the transmission matrix measurement and the subsequent beam generation.
    Invoked in Methods 4.3 and Eq. 8. If the fiber drifts, moves, or changes temperature between calibration and generation, the predistortion becomes invalid.
  • domain assumption The 45 Hermite-Gaussian modes per polarization form a complete basis for the light propagating in the 50-micrometer core, 90-mode fiber.
    Invoked in Methods 4.3 and 4.4. If significant energy couples to modes outside this basis, the measured T is a truncated description and E_out,expected can differ from the true physical output.
  • domain assumption Discrete sampling with 20 temporal slices and about 226 fs resolution adequately represents the continuous 3D toroidal field.
    Used in Results 2.1 and Fig. 1 to slice the torus into 2D cross sections. Undersampling would hide phase or intensity features of the torus.
  • domain assumption Swept-wavelength off-axis digital holography yields accurate complex-field measurements at each wavelength and polarization.
    Invoked in Methods 4.3. Errors in phase retrieval or camera synchronization would propagate into both T and the measured output, inflating the overlap.

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Cite this review

Pith. "Pith review of Spatiotemporal toroidal light beams with arbitrary polarization and orientation through a multimode fiber." pith.science (2026). https://pith.science/paper/THZDENBI

@misc{pith2026250113246,
  author       = {Pith},
  title        = {Pith review of: Spatiotemporal toroidal light beams with arbitrary polarization and orientation through a multimode fiber},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/THZDENBI}},
  note         = {Machine review of arXiv:2501.13246}
}
read the original abstract

Optical toroidal beams, with donut-shaped intensity profiles and orbital angular momentum (OAM), are promising for applications such as optical manipulation, metrology, and advanced light-matter interactions. However, practical implementations are limited by challenges in controlling their full 3D geometry and the orientation of their OAM. In this paper, we experimentally demonstrate high-dimensional, polarization-resolved, programmable 3D spatiotemporal toroidal beams with arbitrary 3D geometry. The beams are delivered after propagation through an optical multimode fiber (MMF) that supports 90 spatial/polarization modes. However, if desired, this system can also deliver these beams directly into free space as well. Our approach leverages 25,000 programmable spatiotemporal and polarization degrees of freedom to achieve precise manipulation of the amplitude, phase, polarization and temporal properties of toroidal beams. These beams feature highly customizable 3D geometries, allowing independent control of their aspect ratio and orientation. We further demonstrate the generation of beams with arbitrary OAM orientation, with beam rotations about any 3D spatiotemporal axis. These beams are delivered through an MMF which enables their transport deep into scattering materials and into otherwise hard-to-access regions which could include biological tissues. Hence, this device could enable the application of completely customizable optical manipulations, including rotations, deep within these materials.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Programmable spatiotemporal OAM optical toroidal beams with completely tunable properties

    physics.optics 2025-06 conditional novelty 6.0 of 10

    A multimode-fiber-based system generates toroidal optical beams with independently tunable temporal duration, aspect ratio, and OAM charge up to |l|=13.

Reference graph

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