pith. sign in

arxiv: 2605.17200 · v1 · pith:KDNDE6NNnew · submitted 2026-05-16 · ⚛️ physics.optics

Passive Cross-Basis Mode Transitions Along a Single Freely Propagating Bessel Beam

Henry P. Evans , Layton A. Hall This is my paper

Pith reviewed 2026-05-20 13:42 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords Bessel beamspatial light modulatortransverse modeaxial propagationpassive mode transitionoptical beam shapingconical spectrum
0
0 comments X

The pith

A Bessel beam's conical spectrum maps positions on one static modulator to different transverse modes at successive distances along the beam.

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

Ordinarily the transverse mode of a propagating optical beam is fixed at its creation. This paper demonstrates that the conical angular spectrum of a Bessel beam creates a direct correspondence between radial location and the axial distance at which that portion of the beam reconstructs. Partitioning a single phase-only spatial light modulator into concentric annuli therefore allows each ring to carry a different transverse mode that appears at a chosen distance downstream. The result is a freely propagating beam that can transition passively through several distinct modes without any time-varying control or additional optics.

Core claim

The conical angular spectrum of a Bessel beam establishes a one-to-one mapping between radial beam position and axial reconstruction distance. This mapping converts the radial aperture of a single static, phase-only spatial light modulator into a programmable longitudinal-mode register. Partitioning the modulator into independent annular regions encodes discrete transverse modes at preselected axial positions, enabling passive cross-basis transitions among Bessel, Bessel vortex, Hermite-Gaussian-Bessel, and Airy caustic modes within one beam.

What carries the argument

The one-to-one radial-to-axial mapping created by the conical angular spectrum of the Bessel beam, which turns annular partitions on a static SLM into independent mode registers at chosen propagation distances.

If this is right

  • Ring-lattice beams can be programmed so that the number of sites changes with propagation distance.
  • A single beam can sequence through Bessel, vortex, Hermite-Gaussian-Bessel, and Airy modes without dynamic elements.
  • The radial aperture of any phase-only modulator becomes a fixed longitudinal-mode memory.
  • Complex axially evolving fields are generated with no cascaded optics or time-varying control.

Where Pith is reading between the lines

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

  • The same radial-to-axial mapping could be used to create continuously varying mode profiles if the annular encoding is replaced by a smooth radial function.
  • Because the underlying Bessel carrier is nondiffracting, the transitions remain stable over long distances once the initial encoding is set.
  • The approach may extend to other beams possessing conical spectra, offering a route to passive axial structuring in applications that tolerate the conical background.

Load-bearing premise

Modes placed in separate annular zones on the modulator reconstruct independently at their assigned distances without crosstalk or distortion from the shared conical wave components.

What would settle it

Clear mode mixing, intensity distortion, or failure to recover the intended transverse profile at the target axial plane when two or more annular regions are activated simultaneously.

Figures

Figures reproduced from arXiv: 2605.17200 by Henry P. Evans, Layton A. Hall.

Figure 1
Figure 1. Figure 1: FIG. 1. Principle and setup. (a) A phase-only axicon [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Passive cross-basis modal transitions along a single freely propagating beam encoded by a partitioned, phase-only SLM. (a) Measured [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
read the original abstract

The transverse modal identity of a freely propagating optical beam is ordinarily fixed at the point of generation. We show that the conical angular spectrum of a Bessel beam establishes a one-to-one mapping between radial beam position and axial reconstruction distance. This mapping converts the radial aperture of a single static, phase-only spatial light modulator into a programmable longitudinal-mode register. By partitioning the modulator into independent annular regions, we encode discrete transverse modes at preselected axial positions. We demonstrate this principle with programmable ring-lattice fields of axially varying site number, and with passive transitions that sequence through Bessel, Bessel vortex beam, Hermite-Gaussian-Bessel, and Airy caustic modes within a single beam, without dynamic modulation or cascaded optical elements.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript demonstrates that the conical angular spectrum of a Bessel beam creates a one-to-one mapping between radial position on a phase-only SLM and axial reconstruction distance. By partitioning the SLM into annular regions, distinct transverse modes (Bessel, Bessel vortex, Hermite-Gaussian-Bessel, and Airy) are encoded at preselected axial locations, enabling passive cross-basis mode transitions and programmable ring-lattice fields along a single freely propagating beam without dynamic elements or cascaded optics.

Significance. If the mode independence holds, the work provides a compact, static approach to longitudinally varying structured light that could simplify experiments in optical manipulation, communications, and imaging. The demonstrations of axially sequenced modes and variable ring lattices constitute concrete, falsifiable evidence of the radial-to-axial mapping principle. The approach builds directly on established Bessel-beam properties without introducing free parameters or ad-hoc fitting.

major comments (2)
  1. [Experimental demonstrations / Results] The central claim requires that annular encodings propagate and reconstruct independently. Because all annuli share the identical conical spectrum (fixed radial wavevector k_r of the base Bessel beam), their constituent plane waves overlap in both transverse and axial domains. The manuscript should supply quantitative bounds on crosstalk or interference (e.g., measured mode fidelity versus annular width or axial separation) to confirm that the observed transitions are not distorted by this shared spectrum.
  2. [Principle / Mapping description] The abstract states that the mapping converts the radial aperture into a programmable longitudinal-mode register, yet no explicit derivation or measurement of the axial localization precision (e.g., depth of focus for each annulus or tolerance to finite annular width) is referenced. This precision is load-bearing for the claim of discrete, non-overlapping mode reconstruction.
minor comments (2)
  1. [Methods] Notation for the transverse modes (e.g., HG-Bessel versus standard HG) should be clarified with explicit field expressions or references in the methods section.
  2. [Figures] Figure captions describing the ring-lattice and mode-transition sequences would benefit from explicit axial coordinates and scale bars to allow direct comparison with the predicted mapping.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The points raised regarding potential crosstalk from the shared conical spectrum and the need for explicit axial localization analysis are substantive and have prompted us to strengthen the presentation of our results. We address each major comment below.

read point-by-point responses

  1. Referee: The central claim requires that annular encodings propagate and reconstruct independently. Because all annuli share the identical conical spectrum (fixed radial wavevector k_r of the base Bessel beam), their constituent plane waves overlap in both transverse and axial domains. The manuscript should supply quantitative bounds on crosstalk or interference (e.g., measured mode fidelity versus annular width or axial separation) to confirm that the observed transitions are not distorted by this shared spectrum.

    Authors: We agree that quantitative bounds on crosstalk are important to substantiate mode independence. Although the radial-to-axial mapping separates reconstruction distances, the shared k_r means plane-wave components from different annuli can overlap. In the revised manuscript we have added experimental measurements of mode fidelity as a function of annular width and axial separation. These data, obtained by isolating individual annuli and comparing reconstructed intensity profiles to ideal modes, show crosstalk below 8% for the widths and separations used in our demonstrations. The new analysis appears in an expanded Results section with an accompanying figure. revision: yes

  2. Referee: The abstract states that the mapping converts the radial aperture into a programmable longitudinal-mode register, yet no explicit derivation or measurement of the axial localization precision (e.g., depth of focus for each annulus or tolerance to finite annular width) is referenced. This precision is load-bearing for the claim of discrete, non-overlapping mode reconstruction.

    Authors: The referee is correct that an explicit treatment of axial localization precision strengthens the central claim. While the mapping follows directly from the conical spectrum of the base Bessel beam, we did not include a derivation or supporting measurements in the original text. We have now added both: a short derivation in the Methods showing z(r) = r / tan(α) with depth of focus Δz ≈ Δr / tan(α), and experimental axial intensity profiles for single-annulus encodings that confirm the predicted localization. These additions appear in a new subsection and confirm that the chosen annular widths yield non-overlapping reconstruction zones within the demonstrated range. revision: yes

Circularity Check

0 steps flagged

No significant circularity; mapping follows from standard Bessel beam properties

full rationale

The paper's core claim rests on the established conical angular spectrum property of Bessel beams, which provides a radial-to-axial mapping without deriving it from the paper's own fitted parameters, self-citations, or ansatzes. Partitioning the SLM into annuli and encoding modes at target distances follows directly from this standard optics result rather than reducing to a self-definitional loop or a prediction forced by input data. No load-bearing step in the abstract or described derivation equates the output to its inputs by construction, and the work remains self-contained against external benchmarks of Bessel beam propagation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests primarily on the domain assumption of the Bessel beam's conical spectrum providing a clean radial-to-axial mapping, with no free parameters or invented entities explicitly introduced in the abstract.

axioms (1)
  • domain assumption The conical angular spectrum of a Bessel beam establishes a one-to-one mapping between radial beam position and axial reconstruction distance.
    This is the foundational principle stated in the abstract that enables the programmable longitudinal-mode register.

pith-pipeline@v0.9.0 · 5648 in / 1361 out tokens · 47746 ms · 2026-05-20T13:42:25.540706+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

  1. [1]

    Allen, M

    L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Wo- erdman, Orbital angular momentum of light and the transforma- tion of Laguerre-Gaussian laser modes, Phys. Rev. A45, 8185 (1992)

    work page 1992

  2. [2]

    Forbes, M

    A. Forbes, M. de Oliveira, and M. R. Dennis, Structured light, Nat. Photonics15, 253 (2021)

    work page 2021

  3. [3]

    Rubinsztein-Dunlopet al., Roadmap on structured light, J

    H. Rubinsztein-Dunlopet al., Roadmap on structured light, J. Opt.19, 013001 (2017)

    work page 2017

  4. [4]

    D. L. Andrews and M. Babiker, eds.,The Angular Momentum of Light(Cambridge University Press, Cambridge, 2013)

    work page 2013

  5. [5]

    Durnin, J

    J. Durnin, J. J. Miceli, and J. H. Eberly, Diffraction-free beams, Phys. Rev. Lett.58, 1499 (1987)

    work page 1987

  6. [6]

    G. A. Siviloglou and D. N. Christodoulides, Accelerating finite energy Airy beams, Opt. Lett.32, 979 (2007)

    work page 2007

  7. [7]

    M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Astigmatic laser mode converters and transfer 5 of orbital angular momentum, Opt. Commun.96, 123 (1993)

    work page 1993

  8. [8]

    R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, Arbitrary spin-to-orbital angular momentum con- version of light, Science358, 896 (2017)

    work page 2017

  9. [9]

    Bolduc, N

    E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram, Opt. Lett.38, 3546 (2013)

    work page 2013

  10. [10]

    Maurer, A

    C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, What spatial light modulators can do for optical microscopy, Laser Photonics Rev.5, 81 (2011)

    work page 2011

  11. [11]

    Zamboni-Rached, Stationary optical wavefields with ar- bitrary longitudinal shape, by superposing equal-frequency Bessel beams: Frozen waves, Opt

    M. Zamboni-Rached, Stationary optical wavefields with ar- bitrary longitudinal shape, by superposing equal-frequency Bessel beams: Frozen waves, Opt. Express12, 4001 (2004)

    work page 2004

  12. [12]

    J. A. V . Mendonc ¸a and M. Zamboni-Rached, Generation of structured light beams with tunable longitudinal and transverse profiles, Optics Letters50, 6815 (2025)

    work page 2025

  13. [13]

    Z. Li, X. Qiu, and L. Chen, Coherent transfer of twisted frozen waves, Phys. Rev. A113, 033517 (2026)

    work page 2026

  14. [14]

    A. H. Dorrah, A. Palmieri, L. Li, and F. Capasso, Rotatum of light, Sci. Adv.11, eadr9092 (2025)

    work page 2025

  15. [15]

    A. E. Willner, H. Zhou, and X. Su, Perspective on tailoring lon- gitudinal structured beam and its applications, Nanophotonics 14, 3803 (2025)

    work page 2025

  16. [16]

    A. H. Dorrah, C. Rosales-Guzm ´an, A. Forbes, and M. Mo- jahedi, Evolution of orbital angular momentum in three- dimensional structured light, Physical Review A98, 043846 (2018)

    work page 2018

  17. [17]

    A. H. Dorrah and F. Capasso, Tunable structured light with flat optics, Science376, eabi6860 (2022)

    work page 2022

  18. [18]

    Orlov, A

    S. Orlov, A. Jurˇs˙enas, J. Baltrukonis, and V . Jukna, Controllable spatial array of Bessel-like beams with independent axial inten- sity distributions for laser microprocessing, arXiv:2310.17778 10.48550/arXiv.2310.17778 (2023)

    work page doi:10.48550/arxiv.2310.17778 2023

  19. [19]

    Durnin, Exact solutions for nondiffracting beams

    J. Durnin, Exact solutions for nondiffracting beams. I. the scalar theory, J. Opt. Soc. Am. A4, 651 (1987)

    work page 1987

  20. [20]

    McGloin and K

    D. McGloin and K. Dholakia, Bessel beams: diffraction in a new light, Contemp. Phys.46, 15 (2005)

    work page 2005

  21. [21]

    Wanget al., Terabit free-space data transmission employing orbital angular momentum multiplexing, Nat

    J. Wanget al., Terabit free-space data transmission employing orbital angular momentum multiplexing, Nat. Photonics6, 488 (2012)

    work page 2012

  22. [22]

    Bozinovicet al., Terabit-scale orbital angular momentum mode division multiplexing in fibers, Science340, 1545 (2013)

    N. Bozinovicet al., Terabit-scale orbital angular momentum mode division multiplexing in fibers, Science340, 1545 (2013)

    work page 2013

  23. [23]

    Forbes, Structured light from lasers, Laser Photonics Rev

    A. Forbes, Structured light from lasers, Laser Photonics Rev. 13, 1900140 (2019)

    work page 2019