{"id":"5dd00a24-344a-4fc6-9eca-001622b0e3d4","arxiv_id":"2501.13246","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The authors demonstrate programmable 3D toroidal beams with arbitrary OAM orientation delivered through a multimode fiber using transmission-matrix-based wavefront shaping.","lead":"This paper experimentally generates programmable three-dimensional toroidal light beams, with chosen polarization and tilted orbital angular momentum, and sends them through a multimode fiber. The method combines a wavelength-selective switch, a mode sorter, and measured fiber transmission matrices to shape 90 spatial and polarization modes.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Fidelity is measured only against T·T†·E_target, the same transmission matrix used to compute the input, so a flawed or incomplete T would still yield high overlap; no quantitative comparison to the ideal toroidal target is reported.","rationale":"The concern is load-bearing because every quantitative fidelity claim in the paper (|O|^2 = 79–83%) is computed against E_out,expected, which is derived from the same T used to compute the input. If T is approximately unitary, this is fine; if not, E_out,expected is not the target. The reader identified the related issue of TM validity and drift; our concern is the circularity of the validation even assuming a stable, complete T. The paper does show 'Ideal target' images, so a direct numerical comparison is feasible and would settle the point. Independent support: the method is a standard transmission-matrix predistortion, and the apparatus is sophisticated; the issue is not feasibility but evidence. The appropriate verdict remains conditional: the central result is plausible but the reported fidelity metric does not yet establish the stated 'arbitrary' control. No change from the reader's conditional verdict is needed; the same missing test is the key.","tokens_in":12382,"tokens_out":4758,"duration_ms":55274,"concrete_test":"Compute the squared overlap |O|^2 between the experimentally measured field E_out,measured(t,x,y) and the ideal target E_out,target(t,x,y) defined in Methods 4.4 (before any transmission-matrix projection), over the same delay window used in Eq. 13, for the beams in Fig. 3 and Fig. 4g. Also compute |O|^2 between E_out,expected and E_out,target. If the measured-to-ideal overlap is much lower than the reported measured-to-expected overlap, the claim of high-fidelity arbitrary toroidal generation is not established and the paper should be revised to report the achievable fidelity to the intended target.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is complete experimental control of arbitrary 3D OAM toroidal beams. The load-bearing validation is the overlap integral in Eq. 13, which compares the measured output E_out,measured to E_out,expected = T(λ)T†(λ) E_out,target (Eq. 10). The input was computed from the same measured T(λ) via Eq. 9: E_inject = T† E_target. This makes the fidelity metric self-referential: E_out,expected is not the ideal toroid unless T is unitary. For a square but non-unitary T (mode-dependent loss, incomplete mode basis, imperfect calibration), T T† is a non-trivial filter, so E_out,expected can differ substantially from E_out,target. If T is wrong or incomplete, both the injected field and the reference field inherit the same error, and the reported |O|^2 ≈ 0.8 can be high while the generated beam deviates from the intended toroid. The paper plots an 'Ideal target' but reports no quantitative overlap between the measured field and that target. The demonstrated orientations also cover only a few discrete angles, not the full 'any 3D spatiotemporal axis' claimed, although that is secondary. The missing test is therefore whether the measured output actually resembles the ideal toroidal beam, not merely the forward-model prediction.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":12655,"tokens_out":6089,"duration_ms":66069,"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":[{"comment":"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.","section":"§2.3, §4.6, §4.7, Eqs. (10) and (13)"},{"comment":"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.","section":"§2.3, Fig. 4, and §1"},{"comment":"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.","section":"§4.1.3 and Methods 4.6"}],"minor_comments":[{"comment":"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).","section":"Eqs. (3)–(4)"},{"comment":"There is a duplicated word: 'through the the spectrally-resolved TM' should read 'through the spectrally-resolved TM'.","section":"§4.6, text before Eq. (10)"},{"comment":"Please give the numerical values of R, r, and the temporal window used for each figure so that the aspect-ratio claim is reproducible.","section":"§4.2 and Fig. 3"},{"comment":"The phrase '45-degree polarized' should be clarified as a linear polarization at 45° to avoid ambiguity with circular or other polarization states.","section":"§2.3"},{"comment":"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.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"The core technical work appears sound and significant, but the fidelity metric is the central issue: it compares the measured field to a forward-model prediction built from the same transmission matrix used for generation. I would be willing to accept a revision that adds a direct overlap with the ideal toroidal target, reports the singular-value behavior of T, and tempers the 'arbitrary/complete' claims to match the demonstrated parameter range. I do not see signs of misconduct or intent to mislead; the issue is a benchmark-design problem that is fixable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's what you should know: this is a genuinely new experimental capability—programmable, polarization-resolved toroidal beams with tilted OAM delivered through a 90-mode multimode fiber—and the hardware work is impressive. The catch is that the headline fidelity numbers (79–83% overlap) are partially self-referential, so treat them as evidence of control over the fiber, not yet as proof that the output matches the ideal toroid.\n\nWhat's actually new and good: The authors combine a wavelength-selective switch and a multi-plane light converter to shape 25,000 spatiotemporal/polarization degrees of freedom, and they use a measured transmission matrix to precompensate for the fiber. They convincingly demonstrate horizontal, vertical, and 45-degree polarization states; poloidal and toroidal phase wraps; rotations about x, y, and an off-axis 3D direction; and they show the output after 5 m of fiber. That is a real step beyond free-space toroidal beams and STOVs with fixed orientation. The figures are clear and the Methods are detailed enough for reproduction; the data are not deposited though, only 'available on reasonable request'.\n\nWhere it's soft: The overlap integral in Eq. 13 compares the measured field to E_out,expected = T T† E_target, using the same measured T that generated the input. If T is incomplete or has mode-dependent loss, T T† can distort the field while still being 'expected.' So a high overlap with the expected field does not guarantee the output resembles the ideal toroid. The paper plots the 'Ideal target' and the simulated field side by side, but it never reports the overlap between the measured and ideal target. That missing number is the key validation. Minor points: the claim of arbitrary 3D OAM orientation rests on a few discrete angles (one off-axis case), and there are no error bars or repeatability measurements.\n\nOn balance, the central result is likely correct—the generated beams look like toroids and the system clearly has the claimed control. But the validation needs an independent check: decompose the measured field against the ideal target, or validate with a separately measured transmission matrix.\n\nWho this is for: anyone working on structured light, fiber delivery, or optical manipulation. It deserves a serious referee, not a desk reject. I'd ask the authors to add the ideal-target overlap and a repeatability measurement before publication.","headline":"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.","tokens_in":13206,"tokens_out":2854,"would_cite":false,"duration_ms":25768,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["toroidal beams","orbital angular momentum","multimode fiber","transmission matrix","spatiotemporal beam shaping","wavelength-selective switch","polarization control","optical manipulation"],"falsifier":"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.","tokens_in":12184,"feed_emoji":"🍩","tokens_out":5197,"duration_ms":46941,"temperature":0.7,"pith_summary":"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.","feed_headline":"Toroidal light beams get arbitrary 3D OAM orientation through a fiber","feed_subtitle":"One transmission-matrix measurement calibrates 25,000 degrees of freedom to steer OAM about any axis.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Provides the apparatus for arbitrary vector spatiotemporal beam generation on which this work builds.","marker":"[2]"},{"why":"The MPLC mode sorter that maps SLM spots to Hermite-Gaussian modes.","marker":"[45]"},{"why":"Transmission matrix measurement approach used to characterize the fiber.","marker":"[48]"},{"why":"Multispectral transmission matrix and the conjugate-transpose predistortion method used to compute the input field.","marker":"[49]"},{"why":"Polarization-resolved characterization of a multimode fiber, basis for measuring the TM in both polarizations.","marker":"[46]"},{"why":"First experimental realization of toroidal vortices of light, the target structure this paper generalizes.","marker":"[12]"}],"fun_headline_variants":["Single transmission matrix shapes arbitrary 3D toroidal beams in fiber","Toroidal beams get full 3D OAM control via multimode fiber","25,000 programmable degrees of freedom sculpt 3D toroidal beams","Fiber-delivered toroidal beams with arbitrary 3D orientation and OAM"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Single transmission matrix shapes arbitrary 3D toroidal beams in fiber","Toroidal beams get full 3D OAM control via multimode fiber","25,000 programmable degrees of freedom sculpt 3D toroidal beams","Fiber-delivered toroidal beams with arbitrary 3D orientation and OAM"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000811,"raw_usage":{"total_tokens":3597,"prompt_tokens":1024,"completion_tokens":2573,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":640,"completion_tokens_details":{"reasoning_tokens":2492}},"tokens_in":640,"tokens_out":2573,"duration_ms":20418,"temperature":1.0,"reasoning_tokens":2492,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T16:19:30.243666+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the apparatus for arbitrary vector spatiotemporal beam generation on which this work builds."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The MPLC mode sorter that maps SLM spots to Hermite-Gaussian modes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Transmission matrix measurement approach used to characterize the fiber."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Multispectral transmission matrix and the conjugate-transpose predistortion method used to compute the input field."},{"cited_title":"& Carpenter, J","cited_arxiv_id":null,"evidence_quote":"Polarization-resolved characterization of a multimode fiber, basis for measuring the TM in both polarizations."},{"cited_title":"& Zhan, Q","cited_arxiv_id":null,"evidence_quote":"First experimental realization of toroidal vortices of light, the target structure this paper generalizes."}],"review_version":1}