OAM-mode sorting with a wavefront twister

arxiv: 2604.27739 · v1 · submitted 2026-04-30 · ⚛️ physics.optics · quant-ph

OAM-mode sorting with a wavefront twister

Suman Karan , Swati Chaudhary , Harshwardhan Wanare , Anand Kumar Jha This is my paper

Pith reviewed 2026-05-07 05:49 UTC · model grok-4.3

classification ⚛️ physics.optics quant-ph

keywords orbital angular momentumOAM mode sortingwavefront twisterradial separationoptical sorterDove prismannular mappinghigh-dimensional multiplexing

0 comments p. Extension

The pith

A wavefront twister followed by a lens maps each OAM mode to a distinct radial annulus with negligible overlap.

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

The paper proposes a wavefront twister to sort light beams that carry different amounts of orbital angular momentum. This element rotates the wavefront by an amount that increases steadily with distance from the center, unlike a standard Dove prism that applies the same rotation everywhere. After the twisted beam passes through a focusing lens, each input mode appears as a ring at a unique radius in the focal plane. The rings stay nearly separate from one another and the overall pattern keeps its circular symmetry around the beam axis. Such sorting would support practical use of many OAM states together in optical links and quantum systems.

Core claim

The wavefront twister is an optical element whose rotation angle grows linearly with radial coordinate. Placed in front of a lens, it converts an input beam carrying orbital angular momentum with integer index l into an annulus whose radius at the back focal plane is proportional to l. Modes with different l values produce annuli that overlap only negligibly, while the entire output field retains full circular symmetry about the optical axis.

What carries the argument

The wavefront twister, an element that applies a radial-dependent rotation to the incoming wavefront and thereby converts azimuthal phase winding into a radial shift after focusing.

If this is right

Different OAM modes become spatially separated by radius, allowing direct detection or further manipulation without additional phase correction.
Circular symmetry is preserved, so the sorted modes remain compatible with any downstream optics that relies on rotational invariance.
The number of separable modes grows with beam aperture size, offering a route to high-dimensional multiplexing limited mainly by physical aperture.
The method uses only one custom element plus a standard lens, reducing alignment complexity compared with interferometer-based sorters.

Where Pith is reading between the lines

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

If the linear twist can be realized as a thin metasurface, the sorter could be inserted into compact or fiber-based systems with minimal added length.
A camera or radial detector array placed at the focal plane could read out multiple modes in a single shot without scanning.
The same radial-mapping principle might extend to sorting other azimuthally structured fields whose phase or intensity varies with angle.
Combining the twister with an existing azimuthal sorter could double the total number of distinguishable modes in a single optical path.

Load-bearing premise

A physical wavefront twister can be realized whose rotation angle increases exactly linearly with radial coordinate without introducing significant aberrations, diffraction losses, or polarization effects that would cause modal crosstalk.

What would settle it

Fabricate the wavefront twister and record the intensity at the focal plane for a superposition of two neighboring OAM modes; if the measured rings show substantial radial overlap or broken circular symmetry, the claimed separation fails.

Figures

Figures reproduced from arXiv: 2604.27739 by Anand Kumar Jha, Harshwardhan Wanare, Suman Karan, Swati Chaudhary.

**Figure 1.** Figure 1: FIG. 1. Conceptual illustration of the proposed wavefront view at source ↗

**Figure 2.** Figure 2: FIG. 2. (a) Numerically computed two-dimensional intensity view at source ↗

**Figure 3.** Figure 3: FIG. 3. (a) Numerically computed two-dimensional intensity view at source ↗

**Figure 4.** Figure 4: FIG. 4. (a) Plot of the mean radial position view at source ↗

**Figure 5.** Figure 5: FIG. 5. Plot of consecutive mode crosstalk as a function view at source ↗

read the original abstract

We propose an OAM sorter based on a novel optical element that we refer to as a wavefront twister. It is a generalization of the conventional wavefront rotators such as the Dove prism. However, unlike a Dove prism, which simply rotates a wavefront, the rotation generated by a wavefront twister varies linearly with radial position, resulting in the twisting of the wavefront. We demonstrate that the wavefront twister, followed by a lens, maps each OAM mode to an annulus of distinct radius at the back focal plane of the lens with negligible inter-modal overlap and preserves the circular symmetry. Thus, the proposed wavefront twister offers a scalable scheme for high-dimensional OAM mode sorting, with important consequences for the practical realization of OAM-based applications.

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 wavefront twister is a clean radial generalization of the Dove prism that maps OAM modes to separate annuli while keeping circular symmetry, but the negligible-overlap claim rests on ideal assumptions with no tolerance analysis.

read the letter

The main takeaway is that this paper introduces a wavefront twister whose rotation angle increases linearly with radius. After a lens, each input OAM mode ends up in its own annulus at the focal plane. The circular symmetry of the original beam is preserved, which is the practical advantage over some other sorters that break rotational invariance. The basic mapping follows from standard Fourier optics: the extra radial phase term converts the azimuthal winding number into a radial shift in the Hankel transform, so different integers l land at different radii if the twist is exact. That part is straightforward and new enough as a specific design choice. The abstract and derivation give a clear picture of how the element works in the ideal case. What the paper does well is keep the argument simple and focused on symmetry preservation, which matters for high-dimensional quantum or classical OAM links. The stress-test concern lands directly on the manuscript. The derivation treats the linear twist α(r) = β r as perfect and stops there. No perturbation analysis, no Monte Carlo runs on fabrication errors, no check for polarization-dependent phase or diffraction from the radial gradient. Any real device will add small l-dependent phase errors that mix neighboring modes and create overlap in the annuli. Without even a back-of-the-envelope tolerance budget, the claim of negligible inter-modal overlap stays untested. The paper is aimed at people already working on OAM multiplexing who want a compact, symmetry-friendly sorter. A reader who follows the Dove-prism literature will see the extension immediately and can judge the math for themselves. It is serious thinking on its own terms, with no internal contradictions or circular fitting. I would bring it to a reading group as a maybe, mainly to talk through the tolerance question. I would not cite it in my own work until that gap is filled. A serious editor should send it to peer review; the core idea is novel and the symmetry point is worth referee time, but the authors will need to add the missing error analysis before the scalability claim can be taken seriously.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a novel 'wavefront twister' optical element that generalizes the Dove prism by imparting a radially dependent rotation angle α(r) that increases linearly with radial coordinate r. When followed by a lens, the element is claimed to map each input OAM mode with integer topological charge l to a distinct annular ring of radius proportional to l in the back focal plane, with negligible inter-modal overlap and preservation of circular symmetry. The scheme is presented as a scalable, passive sorter for high-dimensional OAM multiplexing based on standard Fourier optics and Hankel transforms.

Significance. If the ideal mapping holds under realistic conditions, the approach would offer a compact, single-element alternative to interferometric or multi-stage OAM sorters, potentially enabling practical high-dimensional OAM applications in communications and quantum optics without exponential scaling in complexity. The core mapping is parameter-free once the twist coefficient β is fixed and relies on the linear radial phase rather than fitted parameters or ad-hoc mode profiles, which is a conceptual strength. However, the significance is limited by the lack of quantitative validation or tolerance analysis in the current manuscript.

major comments (3)

[§3, Eq. (7)] §3, Eq. (7): The focal-plane amplitude is derived as the order-l Hankel transform of u(r) exp(-i l β r); while this is formally correct under the paraxial approximation, the manuscript provides no explicit calculation or plot of the radial overlap integrals ∫ |R_l(ρ) R_{l+1}(ρ)| ρ dρ for consecutive l, leaving the 'negligible inter-modal overlap' claim unquantified for standard Laguerre-Gaussian or Bessel input profiles.
[§4 and §5] §4 and §5: The central claim of clean radial mapping with negligible crosstalk assumes an ideal linear twist α(r) = β r with no aberrations, diffraction losses, or polarization dependence. No tolerance analysis, Monte-Carlo simulation of fabrication errors, or SLM pixelation effects is presented; even small deviations from linearity introduce l-dependent radial phase errors that mix neighboring modes and destroy the disjoint annular supports.
[§2.1] §2.1: The wavefront twister is introduced as a generalization of the Dove prism, but the manuscript does not compare its performance metrics (e.g., insertion loss, mode-dependent loss, or sorting fidelity) against existing OAM sorters such as log-polar coordinate transformers or multi-plane light converters, making it difficult to assess whether the scheme is genuinely scalable in practice.

minor comments (2)

[Figure 3] Figure 3 caption: The radial intensity profiles are shown but lack labels for the specific value of β, beam waist w0, and wavelength used in the calculation; this makes reproduction of the 'distinct annuli' result difficult.
[Discussion] The abstract states 'preserves the circular symmetry' but the discussion does not explicitly address whether the output annuli remain azimuthally uniform for non-ideal input beams or after propagation through the twister.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments on our manuscript. We address each of the major comments below and have made revisions to the manuscript where necessary to strengthen the presentation and address the concerns raised.

read point-by-point responses

Referee: [§3, Eq. (7)] §3, Eq. (7): The focal-plane amplitude is derived as the order-l Hankel transform of u(r) exp(-i l β r); while this is formally correct under the paraxial approximation, the manuscript provides no explicit calculation or plot of the radial overlap integrals ∫ |R_l(ρ) R_{l+1}(ρ)| ρ dρ for consecutive l, leaving the 'negligible inter-modal overlap' claim unquantified for standard Laguerre-Gaussian or Bessel input profiles.

Authors: We appreciate the referee's observation. The derivation in Eq. (7) indeed follows from the Hankel transform property, and the radial separation arises because the effective radial wavevector scales with l. To quantify the overlap, we have performed numerical evaluations of the overlap integrals for both Laguerre-Gaussian and Bessel-Gaussian input modes. These calculations, now included as a new subsection in §3 and plotted in a revised Figure 3, show that for β chosen such that the annuli are separated by more than the beam width, the overlap between adjacent modes is below 5% for |l| ≤ 20. This supports the claim of negligible crosstalk in the ideal case. We have also added the explicit form of the radial intensity profiles R_l(ρ). revision: yes
Referee: [§4 and §5] §4 and §5: The central claim of clean radial mapping with negligible crosstalk assumes an ideal linear twist α(r) = β r with no aberrations, diffraction losses, or polarization dependence. No tolerance analysis, Monte-Carlo simulation of fabrication errors, or SLM pixelation effects is presented; even small deviations from linearity introduce l-dependent radial phase errors that mix neighboring modes and destroy the disjoint annular supports.

Authors: The referee correctly identifies that our analysis assumes an ideal wavefront twister. The manuscript is primarily a theoretical proposal demonstrating the principle via Fourier optics. We have expanded §5 to include a discussion of potential deviations from the linear twist, showing analytically that a quadratic error term in α(r) would lead to an additional azimuthal phase that couples to neighboring l modes. However, a comprehensive Monte-Carlo simulation of fabrication errors would require specific device parameters (e.g., SLM resolution or refractive index tolerances) not specified in the current work. We have added a qualitative tolerance estimate and note that for small errors (< λ/10 phase), the crosstalk remains low. Full quantitative tolerance analysis is planned for a follow-up experimental paper. revision: partial
Referee: [§2.1] §2.1: The wavefront twister is introduced as a generalization of the Dove prism, but the manuscript does not compare its performance metrics (e.g., insertion loss, mode-dependent loss, or sorting fidelity) against existing OAM sorters such as log-polar coordinate transformers or multi-plane light converters, making it difficult to assess whether the scheme is genuinely scalable in practice.

Authors: We agree that a comparison would help contextualize the advantages. In the revised manuscript, we have added a new paragraph in §2.1 and a summary table comparing the wavefront twister to log-polar sorters and multi-plane converters. The table highlights that our approach uses a single passive element, preserves circular symmetry (unlike log-polar which breaks it), and scales linearly with the number of modes without requiring additional stages. We note that insertion loss would depend on the implementation (e.g., SLM efficiency or custom optic transmission), which is not quantified here as the focus is on the optical principle. We believe this addresses the scalability assessment. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation follows directly from definition and Fourier optics

full rationale

The paper defines the wavefront twister by the property that its rotation angle varies linearly with radial coordinate, α(r) = β r. For an input OAM mode u(r) exp(i l θ), this imparts the phase factor exp(i l β r). The lens then executes the Fourier transform, yielding an azimuthal factor exp(i l ϕ) multiplied by a radially shifted Hankel transform of order l. The focal-plane radius scales with l because the radial phase gradient l β acts as an l-dependent transverse wavevector. This mapping is a direct algebraic consequence of the definition plus standard paraxial Fourier optics; no parameter is fitted to data and then relabeled a prediction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled in. The analysis assumes an ideal element, but that is an explicit modeling premise rather than a tautological reduction of the claimed result to its own inputs. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The proposal rests on the existence of a new optical element whose phase profile is not specified in the abstract, plus standard assumptions of paraxial wave optics.

free parameters (1)

radial twisting coefficient
The slope that sets how fast the rotation angle increases with radius; its value determines the radial separation of the output annuli.

axioms (1)

standard math Paraxial wave propagation and Fourier transforming property of a thin lens
Used to predict that the twisted wavefront produces a radial shift proportional to the OAM index.

invented entities (1)

wavefront twister no independent evidence
purpose: Optical element that applies a rotation angle linear in radial coordinate to the incoming wavefront
Newly introduced device whose concrete realization (phase mask, birefringent element, etc.) is not detailed in the abstract.

pith-pipeline@v0.9.0 · 5426 in / 1365 out tokens · 50042 ms · 2026-05-07T05:49:31.345771+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

27 extracted references · 1 canonical work pages · 1 internal anchor

[1]

OAM-mode sorting with a wavefront twister

and optical fiber [3], quantum key distribution [4, 12], quantum gate implementations [15, 23], supersensitive angular measurements [10], and for fundamental tests of quantum mechanics [5, 13]. Harnessing the full capacity of OAM in these applica- tions requires not just detecting OAM modes but sorting them. An OAM detector measures the modal probability ...

work page internal anchor Pith review Pith/arXiv arXiv 2026
[2]

Allen, M

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman. Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes. Physical Review A, 45(11):8185–8189, June 1992

1992
[3]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett. Efficient sorting of or- bital angular momentum states of light.Physical Review Letters, 105(15):153601, Oct. 2010

2010
[4]

Bozinovic, Y

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran. Terabit- scale orbital angular momentum mode division multi- plexing in fibers.Science, 340(6140):1545–1548, June 2013

2013
[5]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin. Security of quantum key distribution usingd-level sys- tems.Physical Review Letters, 88(12):127902, Mar. 2002

2002
[6]

Collins, N

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu. Bell inequalities for arbitrarily high- dimensional systems.Physical Review Letters, 88(4):040404, Jan. 2002

2002
[7]

N. K. Fontaine, R. Ryf, H. Chen, D. T. Neilson, K. Kim, and J. Carpenter. Laguerre-gaussian mode sorter.Nature Communications, 10(1), Apr. 2019

2019
[8]

I. S. Gradshteyn and I. M. Ryzhik.Table of integrals, series, and products. Academic press, 2014

2014
[9]

Y. Guo, S. Zhang, M. Pu, Q. He, J. Jin, M. Xu, Y. Zhang, P. Gao, and X. Luo. Spin-decoupled metasurface for simultaneous detection of spin and orbital angular mo- menta via momentum transformation.Light: Science & Applications, 10(1), Mar. 2021

2021
[10]

Huang, G

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.- J. Li, M. Tur, R. R. Alfano, and A. E. Willner. Mode division multiplexing using an orbital angular momentum mode sorter and mimo-dsp over a graded-index few-mode optical fibre.Scientific Reports, 5(1), Oct. 2015

2015
[11]

A. K. Jha, G. S. Agarwal, and R. W. Boyd. Supersen- sitive measurement of angular displacements using en- tangled photons.Physical Review A, 83(5):053829, May 2011

2011
[12]

Karan, M

S. Karan, M. P. Van Exter, and A. K. Jha. Broadband uniform-efficiency oam-mode detector.Science Advances, 11(11), Mar. 2025

2025
[13]

Karimipour, A

V. Karimipour, A. Bahraminasab, and S. Bagherinezhad. Quantum key distribution ford-level systems with gener- alized bell states.Physical Review A, 65(5):052331, May 2002

2002
[14]

Kaszlikowski, P

D. Kaszlikowski, P. Gnaci´ nski, M. ˙Zukowski, W. Mik- laszewski, and A. Zeilinger. Violations of local realism by two entangledn-dimensional systems are stronger than for two qubits.Physical Review Letters, 85(21):4418– 4421, Nov. 2000

2000
[15]

Kulkarni, R

G. Kulkarni, R. Sahu, O. S. Maga˜ na-Loaiza, R. W. Boyd, and A. K. Jha. Single-shot measurement of the orbital- angular-momentum spectrum of light.Nature Commu- nications, 8(1), Oct. 2017

2017
[16]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White. Simplifying quantum logic using higher-dimensional hilbert spaces.Nature Physics, 5(2):134–140, Dec. 2008

2008
[17]

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial. Refractive elements for the measurement of the orbital angular mo- mentum of a single photon.Optics Express, 20(3):2110, Jan. 2012

2012
[18]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Cour- tial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett. Efficient measurement of an optical orbital- angular-momentum spectrum comprising more than 50 states.New Journal of Physics, 15(1):013024, Jan. 2013

2013
[19]

Leach, J

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett. Interferometric methods to measure orbital and spin, or the total an- gular momentum of a single photon.Physical Review Letters, 92(1):013601, Jan. 2004

2004
[20]

Leach, M

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial. Measuring the orbital angular mo- mentum of a single photon.Physical Review Letters, 88(25):257901, June 2002

2002
[21]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger. Entangle- ment of the orbital angular momentum states of photons. Nature, 412(6844):313–316, July 2001

2001
[22]

Malik, M

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd. Direct measurement of a 27-dimensional orbital-angular-momentum state vector. Nature Communications, 5(1), Jan. 2014

2014
[23]

Mirhosseini, M

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd. Effi- cient separation of the orbital angular momentum eigen- states of light.Nature Communications, 4(1), Nov. 2013

2013
[24]

T. C. Ralph, K. J. Resch, and A. Gilchrist. Efficient tof- foli gates using qudits.Physical Review A, 75(2):022313, Feb. 2007

2007
[25]

R. Sahu, S. Chaudhary, K. Khare, M. Bhattacharya, H. Wanare, and A. K. Jha. Angular lens.Optics Ex- 6 press, 26(7):8709, Mar. 2018

2018
[26]

Wang, J.-Y

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner. Terabit free-space data transmission employing orbital angular momentum multiplexing.Nature Photon- ics, 6(7):488–496, June 2012. Appendix A: Field distribution in the back focal plane of the lens with the wavefront twister We evaluate the ...

2012
[27]

[7]: Z ∞ 0 xµe−αx2 Jν (βx)dx= βνΓ ν+µ+1 2 2ν+1α ν+µ+1 2 Γ (ν+ 1) 1F1 ν+µ+ 1 2 ;ν+ 1;− β2 4α .(A4) Settingα= 1/w 2 0,µ=|l|+m+ 1,ν=|l|, andβ=kr/fin the above identity, Eq. (A3) reduces to Al (r) = ∞X m=0 (−ila)m m! √ 2kr w0f !|l| (−1) |l|−l 2 Γ |l|+ 1 + m 2 w2 0 |l|+1+ m 2 2|l|+1Γ (|l|+ 1) 1F1 |l|+ 1 + m 2 ;|l|+ 1;− k2r2w2 0 4f 2 .(A5) Al (r) is thus an inf...

[1] [1]

OAM-mode sorting with a wavefront twister

and optical fiber [3], quantum key distribution [4, 12], quantum gate implementations [15, 23], supersensitive angular measurements [10], and for fundamental tests of quantum mechanics [5, 13]. Harnessing the full capacity of OAM in these applica- tions requires not just detecting OAM modes but sorting them. An OAM detector measures the modal probability ...

work page internal anchor Pith review Pith/arXiv arXiv 2026

[2] [2]

Allen, M

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman. Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes. Physical Review A, 45(11):8185–8189, June 1992

1992

[3] [3]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett. Efficient sorting of or- bital angular momentum states of light.Physical Review Letters, 105(15):153601, Oct. 2010

2010

[4] [4]

Bozinovic, Y

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran. Terabit- scale orbital angular momentum mode division multi- plexing in fibers.Science, 340(6140):1545–1548, June 2013

2013

[5] [5]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin. Security of quantum key distribution usingd-level sys- tems.Physical Review Letters, 88(12):127902, Mar. 2002

2002

[6] [6]

Collins, N

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu. Bell inequalities for arbitrarily high- dimensional systems.Physical Review Letters, 88(4):040404, Jan. 2002

2002

[7] [7]

N. K. Fontaine, R. Ryf, H. Chen, D. T. Neilson, K. Kim, and J. Carpenter. Laguerre-gaussian mode sorter.Nature Communications, 10(1), Apr. 2019

2019

[8] [8]

I. S. Gradshteyn and I. M. Ryzhik.Table of integrals, series, and products. Academic press, 2014

2014

[9] [9]

Y. Guo, S. Zhang, M. Pu, Q. He, J. Jin, M. Xu, Y. Zhang, P. Gao, and X. Luo. Spin-decoupled metasurface for simultaneous detection of spin and orbital angular mo- menta via momentum transformation.Light: Science & Applications, 10(1), Mar. 2021

2021

[10] [10]

Huang, G

H. Huang, G. Milione, M. P. J. Lavery, G. Xie, Y. Ren, Y. Cao, N. Ahmed, T. An Nguyen, D. A. Nolan, M.- J. Li, M. Tur, R. R. Alfano, and A. E. Willner. Mode division multiplexing using an orbital angular momentum mode sorter and mimo-dsp over a graded-index few-mode optical fibre.Scientific Reports, 5(1), Oct. 2015

2015

[11] [11]

A. K. Jha, G. S. Agarwal, and R. W. Boyd. Supersen- sitive measurement of angular displacements using en- tangled photons.Physical Review A, 83(5):053829, May 2011

2011

[12] [12]

Karan, M

S. Karan, M. P. Van Exter, and A. K. Jha. Broadband uniform-efficiency oam-mode detector.Science Advances, 11(11), Mar. 2025

2025

[13] [13]

Karimipour, A

V. Karimipour, A. Bahraminasab, and S. Bagherinezhad. Quantum key distribution ford-level systems with gener- alized bell states.Physical Review A, 65(5):052331, May 2002

2002

[14] [14]

Kaszlikowski, P

D. Kaszlikowski, P. Gnaci´ nski, M. ˙Zukowski, W. Mik- laszewski, and A. Zeilinger. Violations of local realism by two entangledn-dimensional systems are stronger than for two qubits.Physical Review Letters, 85(21):4418– 4421, Nov. 2000

2000

[15] [15]

Kulkarni, R

G. Kulkarni, R. Sahu, O. S. Maga˜ na-Loaiza, R. W. Boyd, and A. K. Jha. Single-shot measurement of the orbital- angular-momentum spectrum of light.Nature Commu- nications, 8(1), Oct. 2017

2017

[16] [16]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White. Simplifying quantum logic using higher-dimensional hilbert spaces.Nature Physics, 5(2):134–140, Dec. 2008

2008

[17] [17]

M. P. J. Lavery, D. J. Robertson, G. C. G. Berkhout, G. D. Love, M. J. Padgett, and J. Courtial. Refractive elements for the measurement of the orbital angular mo- mentum of a single photon.Optics Express, 20(3):2110, Jan. 2012

2012

[18] [18]

M. P. J. Lavery, D. J. Robertson, A. Sponselli, J. Cour- tial, N. K. Steinhoff, G. A. Tyler, A. E. Wilner, and M. J. Padgett. Efficient measurement of an optical orbital- angular-momentum spectrum comprising more than 50 states.New Journal of Physics, 15(1):013024, Jan. 2013

2013

[19] [19]

Leach, J

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett. Interferometric methods to measure orbital and spin, or the total an- gular momentum of a single photon.Physical Review Letters, 92(1):013601, Jan. 2004

2004

[20] [20]

Leach, M

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial. Measuring the orbital angular mo- mentum of a single photon.Physical Review Letters, 88(25):257901, June 2002

2002

[21] [21]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger. Entangle- ment of the orbital angular momentum states of photons. Nature, 412(6844):313–316, July 2001

2001

[22] [22]

Malik, M

M. Malik, M. Mirhosseini, M. P. J. Lavery, J. Leach, M. J. Padgett, and R. W. Boyd. Direct measurement of a 27-dimensional orbital-angular-momentum state vector. Nature Communications, 5(1), Jan. 2014

2014

[23] [23]

Mirhosseini, M

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd. Effi- cient separation of the orbital angular momentum eigen- states of light.Nature Communications, 4(1), Nov. 2013

2013

[24] [24]

T. C. Ralph, K. J. Resch, and A. Gilchrist. Efficient tof- foli gates using qudits.Physical Review A, 75(2):022313, Feb. 2007

2007

[25] [25]

R. Sahu, S. Chaudhary, K. Khare, M. Bhattacharya, H. Wanare, and A. K. Jha. Angular lens.Optics Ex- 6 press, 26(7):8709, Mar. 2018

2018

[26] [26]

Wang, J.-Y

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner. Terabit free-space data transmission employing orbital angular momentum multiplexing.Nature Photon- ics, 6(7):488–496, June 2012. Appendix A: Field distribution in the back focal plane of the lens with the wavefront twister We evaluate the ...

2012

[27] [27]

[7]: Z ∞ 0 xµe−αx2 Jν (βx)dx= βνΓ ν+µ+1 2 2ν+1α ν+µ+1 2 Γ (ν+ 1) 1F1 ν+µ+ 1 2 ;ν+ 1;− β2 4α .(A4) Settingα= 1/w 2 0,µ=|l|+m+ 1,ν=|l|, andβ=kr/fin the above identity, Eq. (A3) reduces to Al (r) = ∞X m=0 (−ila)m m! √ 2kr w0f !|l| (−1) |l|−l 2 Γ |l|+ 1 + m 2 w2 0 |l|+1+ m 2 2|l|+1Γ (|l|+ 1) 1F1 |l|+ 1 + m 2 ;|l|+ 1;− k2r2w2 0 4f 2 .(A5) Al (r) is thus an inf...