Pith. sign in

REVIEW 2 major objections 5 minor 1 cited by

Exploiting the combined dynamic and geometric phases for optical vortex beam generation using metasurfaces

T0 review · 2 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A metasurface can generate the same optical vortex while tuning its polarization sensitivity by splitting the phase into dynamic and geometric parts.

desk verdict A useful hybrid-phase metasurface demonstration whose central decomposition has a removable but awkward singularity for the circular-polarization case it showcases. read the letter →

arxiv 2412.05121 v1 pith:QX6BTRI6 submitted 2024-12-06 physics.optics physics.app-ph

Jialong Cui , Chen Qing , Lishuang Feng , Dengke Zhang This is my paper · ORCID
classification physics.opticsphysics.app-ph
keywords opticalvortexmetasurfacePancharatnam-Berryphasedynamicorbitalangularmomentumpolarizationcontrolnanofinhybrid
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

Metasurfaces can imprint a phase shift on light in two separable ways: a dynamic phase that is polarization-independent and a Pancharatnam-Berry geometric phase that depends on the polarization state. This paper argues that the two can be deliberately combined in a single nanofin array so that the total orbital-angular-momentum charge of a generated vortex is the sum of a dynamical and a geometrical contribution. The payoff would be that the same vortex beam can be produced by many different structural layouts, with the device's sensitivity to incident polarization tuned continuously by choosing how much of the phase gradient is dynamic and how much geometric. The authors demonstrate this with four eight-sector metasurfaces that all produce a charge-1 vortex: a pure-dynamic, a pure-geometric, and two hybrid designs, and they show experimentally that the hybrids interpolate between polarization-blind and polarization-selective behavior.

What carries the argument

The central object is the phase decomposition $\psi_{a\to b} = \psi_D + \psi_{\mathrm{PB}}$ for a lossless nanofin metasurface, expressed through the Jones matrix of a rotated birefringent unit (Eq. (3)) with dynamic phase $\psi_D = (\phi_x+\phi_y)/2$ and birefringent phase difference $\psi_B = \phi_x-\phi_y$. The geometric contribution $\psi_{\mathrm{PB}}$ is controlled by the rotation angle $\psi_R$ and the input polarization through the Stokes-vector term $\arg(Q\cdot A)$. This decomposition is load-bearing because it converts the azimuthal phase gradient $\partial\psi_{a\to b}/\partial\phi$ into a sum of a dynamic and a geometric gradient, so the designer can apportion the topological charge between the two mechanisms and select nanofin dimensions and orientations from RCWA-computed phase maps to realize each chosen split.

What would settle it

Project the fabricated vortex beam onto OAM eigenmodes (or analyze fork interferograms) and compare the fraction of power in charge +1 with the value predicted from the RCWA unit-cell phases; if the local-response assumption fails, the vortex purity will fall short, and the discrepancy should worsen when the number of azimuthal sectors is reduced.

Watch

Extended reading notes

Core claim

The paper's central claim is that the total phase shift from input polarization $|a\rangle$ to output polarization $|b\rangle$ decomposes as $\psi_{a\to b} = \psi_D + \psi_{\mathrm{PB}}$, where $\psi_D$ is the dynamic phase and $\psi_{\mathrm{PB}}$ is the Pancharatnam-Berry geometric phase. From this decomposition the authors derive that the total orbital-angular-momentum charge generated by an azimuthally varying metasurface splits as $C_{\mathrm{Tot}} = C_D + C_{\mathrm{PB}}$, a sum of a dynamical contribution proportional to $\partial\psi_D/\partial\phi$ and a geometrical contribution proportional to $\partial\psi_{\mathrm{PB}}/\partial\phi$. They then build two hybrid designs: HD-xLP reproduces a pure-dynamic vortex for x-polarized input while introducing polarization filtering, and HG-LCP reproduces a pure-geometric vortex for left-circularly-polarized input while damping the chirality reversal seen in the pure-geometric design. The experiments confirm that identical scalar vortex beams can be generated by pure and hybrid designs, with measurably different dependence on the incident polarization state.

Load-bearing premise

The design assumes that the phase response computed for an infinite periodic nanofin array (RCWA) holds for every unit inside the fabricated eight-sector metasurface, so inter-sector coupling and fabrication deviations could corrupt the designed spiral phase profile.

Editorial extensions

If this is right

  • Because the total OAM charge is the sum of a dynamic and a geometric contribution, the same charge-1 vortex can be produced by multiple distinct nanofin layouts, relaxing the constraints on structure and material choice.
  • The polarization response of a vortex-generating metasurface can be tuned continuously by changing how the azimuthal phase gradient is split between dynamic and geometric parts.
  • Hybrid designs can act as polarization filters: HD-xLP produces a vortex for x-polarized input but a plane wave for y-polarized input.
  • The dynamic contribution can damp the chirality reversal of a pure geometric design, so HG-LCP keeps a well-defined vortex for LCP input without the same sensitivity to opposite chirality.
  • Higher-order vortices should be reachable by increasing the number of sectors and the phase gradient, with no fundamental change in the hybrid design rule.

Reading between the lines

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

  • [Editorial inference] The same phase-splitting principle could be used for other azimuthally or spatially varying phase profiles, such as polarization-controlled holograms or lenses, not only vortices.
  • [Editorial inference] If the RCWA local-response assumption is the limiting factor, the hybrid approach may offer a test bed: comparing many-sector versus few-sector versions quantifies inter-sector coupling.
  • [Editorial inference] The continuous tunability of polarization sensitivity suggests a design rule for devices whose response to polarization must be matched to a channel, e.g., minimizing or maximizing spin-orbit conversion.
  • [Editorial inference] The paper's measured OAM charge as a function of input polarization could be compared with the analytic formula to extract the actual dynamic/geometric split, offering a metrology method for fabricated phase profiles.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The manuscript proposes that the total phase shift produced by a metasurface can be decomposed into a dynamic phase and a Pancharatnam-Berry (PB) geometric phase, so that the total orbital angular momentum (OAM) charge of a generated vortex beam splits into a dynamical contribution and a geometrical contribution. On this basis, the authors design four metasurface configurations—two pure-dynamic/pure-geometric and two hybrid variants—to generate scalar vortex beams with OAM charge 1 for x-polarized and left-circularly-polarized (LCP) input light. They fabricate samples and measure interference patterns with a Mach-Zehnder interferometer, reporting that hybrid designs generate the same vortex as the pure designs while providing tunable polarization sensitivity.

Significance. If the phase decomposition can be made rigorous for the circular-polarization cases, the paper offers a useful design concept: hybrid dynamic-and-geometric phase metasurfaces can generate specified vortex beams while controlling the polarization response, which is relevant for polarization-tunable devices. The strength of the paper is its experimental demonstration of four designs with interference patterns consistent with OAM charge 1 for the intended input polarizations, and the clear qualitative demonstration that the hybrid designs interpolate between polarization-independent and polarization-selective behavior. However, the central theoretical formula used for the geometric phase is undefined for the very LCP-to-RCP transformation that two of the four demonstrated designs rely on, so the theoretical foundation of the central claim requires repair.

major comments (2)
  1. [II.A, Eq. (2); II.B pure-geometric design] Equation (2) is not defined for the LCP-to-RCP transformations used in the PG-LCP and HG-LCP designs. For LCP input the Stokes vector is A=(0,0,1); for the linear eigenstate |q1⟩ at rotation angle ψR the Stokes vector is Q=(cos 2ψR, sin 2ψR, 0), so Q·A=0 and ψqa=arg(Q·A) is undefined. Moreover, since the output is RCP, ⟨a|b⟩=0 and ψa→b in Eq. (1) is undefined. The text nonetheless presents Eq. (1) and Eq. (2) as a general decomposition and uses them to claim CTot=CD+CPB. This central claim is therefore not supported for the demonstrated circular-polarization cases. Please provide a regularized or limiting definition of Eq. (2), or replace the general claim with the explicit Jones-matrix calculation for the circular case: for ψB=π the output acquires the phase ψD+π/2+2ψR, so the OAM charge is ∂ψD/∂ϕ+2∂ψR/∂ϕ. The paper should also state the domain of validity of Eq. (2). The deduction is deferred to the Supporting Information, which is not available in the reviewed manuscript, so the issue cannot be resolved elsewhere.
  2. [II.A, Eq. (1); II.C design and simulation] The derivation of the decomposition assumes a lossless conversion, since ψD=arg(µ1µ2)/2 is stated to hold 'for a lossless conversion' and Eq. (3) uses unitary eigenstructure. In the actual designs, units are selected only for high transmittance (Section II.C), and the RCWA maps in Fig. 3 include finite transmittance. The paper should quantify the effect of residual amplitude imbalance and non-unitary eigenvalues on the designed phase profile and on the claim that the pure and hybrid designs generate identical vortex beams. Without such quantification, the equality between pure and hybrid designs is only approximate, even though the measured fork patterns are consistent with OAM charge 1.
minor comments (5)
  1. [Section II.C/Fig. 5(c-d)] The 'average OAM charge' plotted in Figs. 5(c) and 5(d) is not defined in the text; please state how this quantity is computed from the measured or simulated interference patterns.
  2. [Section II.A] The notation uses 'A' both for the Stokes vector of the input state and, implicitly, for the input polarization state vector; please use a distinct symbol for at least one of these to avoid ambiguity.
  3. [Fig. 4 caption] The caption contains a repeated sentence about a displacement between the centers of the two beams; please edit the caption to remove the duplication.
  4. [Throughout] There are typographical errors such as 'thex(y)-polarized' in Section II.B, 'an uniform' in Section II.C, and 'Specially,' in Section II.B; a careful proofreading pass is recommended.
  5. [Section II.B] The statement that for the pure-geometric design 'we can derive a relationship where ψa→b=2ψR' is stated without derivation; please include the derivation or a reference, especially because Eq. (2) as written does not apply to that case.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the phase decomposition and OAM-charge partition follow from the stated Jones-matrix/Pancharatnam relations, and the four vortex designs are independently verified by measured interference patterns.

full rationale

The central relation psi_a->b = psi_D + psi_PB (Eq. 1) is presented as a Pancharatnam-connection decomposition, with Eq. (2) giving psi_PB explicitly in terms of the eigenphase difference psi_- and the Stokes overlap Q.A. The partition of the total OAM charge as C_Tot = C_D + C_PB follows by taking azimuthal gradients of Eq. (1), so it is a mathematical consequence of the stated decomposition rather than a parameter fitted to the measured vortex data. The four metasurface designs (PD-xLP, HD-xLP, PG-LCP, HG-LCP) are constructed by choosing nanofin dimensions and orientations from RCWA maps to realize prescribed {psi_D, psi_B, psi_R} sector sets; the resulting vortices are then checked by simulated and experimental interference patterns, so the vortex outputs are not used to fit the phase inputs. Refs. [30,31] are same-author citations supporting the C_Tot = C_D + C_PB terminology, but the main text also supplies Eqs. (1)-(2), and the experimental fork-pattern measurements provide independent confirmation, so the self-citations are not load-bearing in a circular way. One genuine but non-circular weakness: Eq. (2) contains psi_qa = arg(Q.A), which is undefined when Q.A = 0, exactly the LCP-to-RCP case used in the PG-LCP and HG-LCP designs, and the paper defers the detailed deduction to unavailable Supporting Information. Therefore the in-text formula cannot directly justify psi_a->b = 2psi_R for those designs; however, this is a derivation gap or singularity, not an equivalence-by-construction or a fitted-input-renamed-as-prediction, so the circularity score remains 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The central claim rests on standard Jones calculus, an approximate lossless assumption, the Pancharatnam-Berry phase formula, and the RCWA local-response assumption. The only hand-chosen numbers are the per-sector phase targets and the sector count for the demonstrations, not fitted constants in the theory.

free parameters (2)
  • Eight-sector phase targets = Eight discrete sets of {psi_D, psi_B, psi_R}; exact W,L values from RCWA maps are not tabulated
    Chosen by hand to realize OAM charge 1 and the intended polarization response; these are implementation choices, not fitted theory constants.
  • Sector discretization = 8 sectors
    Arbitrary sampling of the spiral phase profile; changing the sector count changes vortex fidelity and maximum achievable charge.
assumptions (4)
  • standard math Jones matrix model for a rotated birefringent nanofin
    Used to derive Eq. (3); assumes the metasurface unit behaves as a local waveplate with two orthogonal eigen-polarizations.
  • domain assumption Lossless or high-transmittance approximation
    The phase decomposition psi_D = arg(mu1*mu2)/2 and the unitary Jones matrix require negligible loss; the paper selects high-transmittance units but does not quantify residual loss.
  • domain assumption Pancharatnam-Berry phase formula, Eq. (2)
    Central formula for the geometric phase contribution, quoting the Pancharatnam connection; the derivation is deferred to the Supporting Information.
  • domain assumption RCWA periodic-array result represents local response
    The design database is built from periodic-array simulations and then applied to finite eight-sector devices; no direct near-field or inter-sector coupling validation is provided.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Exploiting the combined dynamic and geometric phases for optical vortex beam generation using metasurfaces." pith.science (2026). https://pith.science/paper/QX6BTRI6

@misc{pith2026241205121,
  author       = {Pith},
  title        = {Pith review of: Exploiting the combined dynamic and geometric phases for optical vortex beam generation using metasurfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QX6BTRI6}},
  note         = {Machine review of arXiv:2412.05121}
}
read the original abstract

The generation of optical vortex beams is pivotal for a myriad of applications, encompassing optical tweezing, optical communications, and quantum information, among others. The metasurface-based approach has realized significant advancements in vortex production, utilizing either dynamic or geometric phases. The dynamic design exhibits indifference to the polarization state of incident light, while the geometric design is inextricably tied to it. In the study, we put forth the proposition that combining dynamic and geometric phases could unlock the potential of metasurface design in generating optical vortices. A hybrid design that harnesses the combined dynamic and geometric phases can attain the same objective while offering tunable functional control over the polarization of light. We establish a correlation between the structural parameters of metasurface and the topological charge of the resulting vortices. The experimental results fully demonstrate the design's flexibility and its effective control over the polarization constraints of incident light. Our research uncovers the capacity for vortex generation through the manipulation of hybrid phases introduced by metasurfaces, indicating significant potential for the design of optical devices and the future advancement of innovative optical applications.

Figures

Figures reproduced from arXiv: 2412.05121 by the authors.

Figure 1
Figure 1. Optical vortex beams generated using metasurfaces. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Phase shifts and configurations of metasurface. (a) Phase shifts from [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Basic optical features of uniform metasurfaces. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Four distinct metasurface configurations are engineered to produce optical vortex beams. Metasurfaces utilizing (a) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Fabricated metasurfaces and measurement setups. (a) Scanning electron microscope (SEM) images of the fabricated [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Measured interference patterns for optical vortex [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

Discussion (0). Continue with ORCID to comment.

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. Thermal atoms facilitate intensity clipping between vectorial dual-beam generated by a single metasurface chip

    physics.optics 2024-12 conditional novelty 6.0 of 10

    A single metasurface generates two vector beams, and hot atomic vapor lets the control beam reshape the signal beam's intensity pattern.

Reference graph

Works this paper leans on

38 extracted references · 37 canonical work pages · cited by 1 Pith paper

  1. [1]

    The gra- dient of geometric phase is accomplished by rotating the uniform nano-units, which have ψB(ϕ) =π, to different angles ψR(ϕ) within each sector

    The pure-geometric design, denoted as PG-LCP, is illustrated for converting a LCP planewave into a vortex beam with the opposite polarization chirality. The gra- dient of geometric phase is accomplished by rotating the uniform nano-units, which have ψB(ϕ) =π, to different angles ψR(ϕ) within each sector. For comparison, the hybrid design, denoted as HG-LC...

    work page

  2. [2]

    This methodology for vortex beam generation epitomizes the pure-geometric design approach

    and arg (Q· A) as prescribed by equation (2). This methodology for vortex beam generation epitomizes the pure-geometric design approach. In practice, the total phase gradient can be actualized by concurrently modulating ψD and ψPB along ϕ, integrating the dynamical and geometrical contributions. This approach, which amalgamates both phase components, can ...

    work page

  3. [3]

    R., O’Holleran, K

    Dennis, M. R., O’Holleran, K. & Padgett, M. J. Singular optics: Optical vortices and polarization singularities. Prog. Opt. 53, 293–363 (2009)

    work page 2009

  4. [4]

    Shen, Y. et al. Optical vortices 30 years on: OAM manip- ulation from topological charge to multiple singularities. Light: Sci. Appl. 8, 90 (2019)

    work page 2019

  5. [5]

    Molina-Terriza, G., Torres, J. P. & Torner, L. Twisted photons. Nat. Phys. 3, 305–310 (2007)

    work page 2007

  6. [6]

    & Padgett, M

    Franke-Arnold, S., Allen, L. & Padgett, M. J. Advances in optical angular momentum. Laser Photonics Rev. 2, 299–313 (2008)

    work page 2008

  7. [7]

    Bliokh, K. Y. & Nori, F. Transverse and longitudinal angular momenta of light. Phys. Rep. 592, 1–38 (2015)

    work page 2015

  8. [8]

    Yao, A. M. & Padgett, M. J. Orbital angular momentum: origins, behavior and applications. Adv. Opt. Photonics 3, 161 (2011)

    work page 2011

Show all 38 references
  1. [9]

    Miao, P. et al. Orbital angular momentum microlaser. Science 353, 464–467 (2016)

    2016

  2. [10]

    Zhang, Z. et al. Tunable topological charge vortex micro- laser. Science 368, 760–763 (2020). 9

    2020

  3. [11]

    Wang, X. et al. Recent advances on optical vortex gener- ation. Nanophotonics 7, 1533–1556 (2018)

    2018

  4. [12]

    Yu, N. et al. Light propagation with phase discontinuities: Generalized laws of reflection and refraction. Science 334, 333–337 (2011)

    2011

  5. [13]

    Meinzer, N., Barnes, W. L. & Hooper, I. R. Plasmonic meta-atoms and metasurfaces. Nat. Photonics 8, 889–898 (2014)

    2014

  6. [14]

    M., Arbabi, E., Arbabi, A

    Kamali, S. M., Arbabi, E., Arbabi, A. & Faraon, A. A review of dielectric optical metasurfaces for wavefront control. Nanophotonics 7, 1041–1068 (2018)

    2018

  7. [15]

    & Capasso, F

    Yu, N. & Capasso, F. Flat optics with designer metasur- faces. Nat. Mater. 13, 139–150 (2014)

    2014

  8. [16]

    Overvig, A. C. et al. Dielectric metasurfaces for complete and independent control of the optical amplitude and phase. Light: Sci. Appl. 8 (2019)

    2019

  9. [17]

    & Yang, Y

    Bai, Y., Lv, H., Fu, X. & Yang, Y. Vortex beam: genera- tion and detection of orbital angular momentum [invited]. Chin. Opt. Lett. 20, 012601 (2022)

    2022

  10. [18]

    & Yang, X

    Zhang, Y., Liu, W., Gao, J. & Yang, X. Generating fo- cused 3D perfect vortex beams by plasmonic metasurfaces. Adv. Opt. Mater. 6 (2018)

    2018

  11. [19]

    Wang, D. et al. High-efficiency metadevices for bifunc- tional generations of vectorial optical fields. Nanophoton- ics 10, 685–695 (2020)

    2020

  12. [20]

    Guo, Y. et al. Classical and generalized geometric phase in electromagnetic metasurfaces. Photonics Insights 1, R03 (2022)

    2022

  13. [21]

    The adiabatic phase and pancharatnam’s phase for polarized light

    Berry, M. The adiabatic phase and pancharatnam’s phase for polarized light. J. Mod. Opt. 34, 1401–1407 (1987)

    1987

  14. [22]

    Guti´ errez-Vega, J. C. Pancharatnam-berry phase of opti- cal systems. Opt. Lett. 36, 1143 (2011)

    2011

  15. [23]

    Khorasaninejad, M. et al. Polarization-insensitive metal- enses at visible wavelengths. Nano Lett. 16, 7229–7234 (2016)

    2016

  16. [24]

    Y., Rodr´ ıguez-Fortu˜ no, F

    Bliokh, K. Y., Rodr´ ıguez-Fortu˜ no, F. J., Nori, F. & Zayats, A. V. Spin-orbit interactions of light. Nat. Photonics 9, 796–808 (2015)

    2015

  17. [25]

    C., Ambrosio, A., Rubin, N

    Devlin, R. C., Ambrosio, A., Rubin, N. A., Mueller, J. P. B. & Capasso, F. Arbitrary spin-to-orbital angular momentum conversion of light. Science 358, 896–901 (2017)

    2017

  18. [26]

    & Paparo, D

    Marrucci, L., Manzo, C. & Paparo, D. Optical spin-to- orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. 96, 163905 (2006)

    2006

  19. [27]

    & Faraon, A

    Arbabi, A., Horie, Y., Bagheri, M. & Faraon, A. Di- electric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission. Nat. Nanotechnol. 10, 937–943 (2015)

    2015

  20. [28]

    A., Devlin, R

    Balthasar Mueller, J., Rubin, N. A., Devlin, R. C., Groever, B. & Capasso, F. Metasurface polarization optics: Independent phase control of arbitrary orthogo- nal states of polarization. Phys. Rev. Lett. 118, 113901 (2017)

    2017

  21. [29]

    Zhang, S. et al. Dynamic display of full-stokes vectorial holography based on metasurfaces. ACS Photonics 8, 1746–1753 (2021)

    2021

  22. [30]

    Wang, Z. et al. Bifunctional manipulation of terahertz waves with high-efficiency transmissive dielectric metasur- faces. Adv. Sci. 10 (2022)

    2022

  23. [31]

    L., Albero, J

    Mart´ ınez-Fuentes, J. L., Albero, J. & Moreno, I. Analysis of optical polarization modulation systems through the pancharatnam connection. Opt. Commun. 285, 393–401 (2012)

    2012

  24. [32]

    & Huang, Y

    Zhang, D., Feng, X. & Huang, Y. Orbital angular momen- tum induced by nonabsorbing optical elements through space-variant polarization-state manipulations. Phys. Rev. A 98, 043845 (2018)

    2018

  25. [33]

    & Huang, Y

    Zhang, D., Feng, X., Cui, K., Liu, F. & Huang, Y. Identi- fying orbital angular momentum of vectorial vortices with pancharatnam phase and stokes parameters. Sci. Rep. 5, 11982 (2015)

    2015

  26. [34]

    Sun, J. et al. Spinning light on the nanoscale. Nano Lett. 14, 2726–2729 (2014)

    2014

  27. [35]

    & Sha, W

    Chen, M., Jiang, L. & Sha, W. Orbital angular momen- tum generation and detection by geometric-phase based metasurfaces. Appl. Sci. 8, 362 (2018)

    2018

  28. [36]

    Huo, P. et al. Photonic spin-multiplexing metasurface for switchable spiral phase contrast imaging. Nano Lett. 20, 2791–2798 (2020)

    2020

  29. [37]

    Karimi, E. et al. Generating optical orbital angular mo- mentum at visible wavelengths using a plasmonic meta- surface. Light: Sci. Appl. 3, e167–e167 (2014)

    2014

  30. [38]

    Liu, G.-G. et al. Measurement of the topological charge and index of vortex vector optical fields with a space- variant half-wave plate. Opt. Lett. 43, 823 (2018)

    2018

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.