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Cited by 184Topological Materials and PhenomenaOrbital Angular Momentum in OpticsQuantum Mechanics and Non-Hermitian Physics

Unveiling pseudospin and angular momentum in photonic graphene

Open access
Song, Daohong, Paltoglou, Vassilis, Liu, Sheng, Zhu, Yi, Gallardo, Daniel, Tang, Liqin, Xu, Jingjun, Ablowitz, Mark +2 more·2015·Nature Communications
DOI 10.1038/ncomms7272
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Abstract

Pseudospin, an additional degree of freedom inherent in graphene, plays a key role in understanding many fundamental phenomena such as the anomalous quantum Hall effect, electron chirality and Klein paradox. Unlike the electron spin, the pseudospin was traditionally considered as an unmeasurable quantity, immune to Stern-Gerlach-type experiments. Recently, however, it has been suggested that graphene pseudospin is a real angular momentum that might manifest itself as an observable quantity, but so far direct tests of such a momentum remained unfruitful. Here, by selective excitation of two sublattices of an artificial photonic graphene, we demonstrate pseudospin-mediated vortex generation and topological charge flipping in otherwise uniform optical beams with Bloch momentum traversing through the Dirac points. Corroborated by numerical solutions of the linear massless Dirac-Weyl equation, we show that pseudospin can turn into orbital angular momentum completely, thus upholding the belief that pseudospin is not merely for theoretical elegance but rather physically measurable. Artificial photonic graphene, a honeycomb array of evanescently coupled waveguides, has proven to be a useful tool for investigating graphene physics in various optical settings. Here, Song et al.demonstrate pseudospin-mediated vortex generation and topological charge flipping in otherwise uniform optical beams.

AI snapshot

Written from the paper’s full text.

TL;DR

Using a photonic honeycomb lattice, the authors selectively excite one of the two sublattices and observe a singly charged optical vortex appear in a beam that initially had no phase singularity, with the vortex charge reversing when the other sublattice is excited. Numerical and analytical treatment of the massless Dirac–Weyl equation indicates that the initial pseudospin is fully converted into orbital angular momentum, making the sublattice degree of freedom experimentally accessible.

Key findings

  • In three-beam excitation, exciting only sublattice A or only B produced similar conical-diffraction output intensities but opposite singly charged vortices in interferograms; no integer vortex appeared when both sublattices were excited or when a single triangular lattice replaced the honeycomb lattice.
  • Two-beam excitation at two Dirac points generated a new spectral component at the third Dirac point via Bragg reflection; its far-field pattern showed opposite vortex singularities depending on whether A or B was excited.
  • Dirac-equation analysis with total AM \(J=L+S\) showed initial pseudospin converts completely to orbital AM (\(\langle S\rangle_i = \langle L\rangle_f\)); for \(m=1\), A excitation gives B a \(+1\) charge and B excitation gives A a \(-1\) charge. Experimental lattice: index change about \(1.5\times10^{-4}\), lattice constant about \(7\,\mu\text{m}\), propagation \(2\,\text{cm}\); simulations used \(7\,\mu\text{m}\) spacing, \(2\times10^{-4}\) index modulation, and \(20\,\text{mm}\) propagation.
  • The effect occurred at the same K valley in an unstrained honeycomb lattice, so no pseudomagnetic field or valley-dependent Berry curvature was involved; no difference was seen when the same sublattice was excited from different valley sets.

Methods

  • Photonic graphene was made by optical induction in a photorefractive nonlinear crystal using a 488 nm argon-ion laser; the writing beam was ordinarily polarized and the probe extraordinarily polarized, with an amplitude mask producing either triangular or honeycomb interference patterns.
  • Probing used three interfering beams aimed at three Dirac points or two interfering beams aimed at two Dirac points; output intensity and phase were monitored via interferograms with an inclined reference plane wave, and the Brillouin-zone spectrum was measured with incoherent light.
  • Theory and numerics used the paraxial Schrödinger equation, a tight-binding reduction to the linear massless Dirac–Weyl equation, a total-AM decomposition \(J=L+S\), numerical propagation, and asymptotic steepest-descent/stationary-phase calculations.

Limitations

  • The paper does not state a dedicated limitations section. It explicitly notes that the probe intensity/polarization was chosen to avoid nonlinear self-action, that no pseudomagnetic field was involved, and that no valley-dependent difference was observed.
  • Evident from the text: the demonstration is tied to a specific photorefractive optical-induction platform (488 nm, about \(7\,\mu\text{m}\) lattice constant, about \(2\,\text{cm}\) propagation in experiment; \(20\,\text{mm}\) in simulation), so generality to other platforms is not tested here.
  • Evident: pseudospin is inferred from the generated vortex/AM and interferograms plus Dirac-equation modeling rather than from a direct Stern–Gerlach-type measurement; the text itself frames pseudospin as traditionally considered unmeasurable by magnetic fields.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1038/ncomms7272

Cites

45 of 45 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

6 of 11 cited sources checked · 3 supported · 0 flagged · accuracy not yet measured

  • Premisecitation

    Photonic graphene, a honeycomb array of evanescently coupled waveguides, is a useful tool for investigating graphene physics in various optical settings.

    “In particular, photonic graphene (a honeycomb array of evanescently coupled waveguides 14 ) has proven to be a useful tool for investigating graphene physics in various optical settings [15][16][17][18][19][20][21][22][23] .”
    Quote in the paperSubstantial claim2 of 3 sources checked
    • cites [14] Peleg, O. et al. Conical diffraction and gap solitons in honeycomb photonic lattices. Phys. Rev. Lett. 98, 103901 (2007). source
    • cites [15] Sepkhanov, R. A., Bazaliy, Y. B. & Beenakker, C. W. J. Extremal transmission at the Dirac point of a photonic band structure. Phys. Rev. A 75, 063813 (2007). source
    • cites [16] Ochiai, T. & Onoda, M. Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states. Phys. Rev. B 80, 155103 (2009). source
    • Rests on an assumption: Photonic lattices offer control over initial conditions and allow monitoring the actual wavefunction including phase, enabling direct observation of graphene wave dynamics in regimes not accessible in natural graphene.
  • Premisecitation

    Unlike electron spin, pseudospin is not detectable by any magnetic field even if it corresponds to an angular momentum.

    “This is simply because that, unlike the electron spin, the pseudospin is not detectable by any magnetic field even if it corresponds to an angular momentum (AM) 25,26 .”
    • Also stated in: § Abstract · hedged
      “Unlike the electron spin, the pseudospin was traditionally considered as an unmeasurable quantity, immune to Stern-Gerlach-type experiments.”
    Quote in the paperSubstantial claim2 of 2 sources checked
    • cites [25] Mecklenburg, M. & Regan, B. C. Spin and the Honeycomb Lattice: Lessons from Graphene. Phys. Rev. Lett. 106, 116803 (2011). source

      The paper identifies graphene pseudospin with real angular momentum (p. 3) and describes its coupling to photon polarization (p. 4). It does not say that pseudospin is undetectable by any magnetic field; its comparison with a magnetic dipole’s motion is a formal analogy, not a statement about magnetic-field detection. (LLM, conf=0.87)

      Experimental — accuracy not yet measured
    • cites [26] Trushin, M. & Schliemann, J. Pseudospin in optical and transport properties of graphene. Phys. Rev. Lett. 107, 156801 (2011). source

      On p. 1, the paper says graphene pseudospin does not directly interact with an external magnetic field, precluding Stern–Gerlach-type detection; it discusses angular momentum only as a formal interpretation. The claim's assertion that pseudospin is not detectable by any magnetic field is broader than the paper's qualified statement about direct interaction. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
  • Interpretationcitation

    The observed pseudospin angular momentum does not result from the valley-dependent nonzero Berry curvature at the K and K' valleys.

    “The observed pseudospin AM does not result from the valleydependent nonzero Berry curvature at the K and K 0 valleys 34 .”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [34] Xiao, D., Yao, W. & Niu, Q. Valley-contrasting physics in graphene: magnetic moment and topological transport. Phys. Rev. Lett. 99, 236809 (2007). source

      The discussion on p. 2 relates Berry curvature to the valley orbital magnetic moment, and Fig. 3 on p. 4 reports opposite Berry-curvature signs in the two valleys. Our copy does not discuss an observed pseudospin angular momentum or establish that it does not result from that curvature. (LLM, conf=0.82)

      Experimental — accuracy not yet measured
  • Findingown data

    The topological charge of the generated vortex flips when the excitation of the probe beam moves from one sublattice to the other.

    “Moreover, the topological charge of the generated vortex flips as the excitation of the probe beam moves from one sublatttice to another.”
    Quote in the paperSubstantial claim
  • Findingown data

    Numerical solutions of the linear massless Dirac-Weyl equation corroborate that pseudospin can turn into orbital angular momentum completely.

    “Corroborated by numerical solutions of the linear massless Dirac-Weyl equation, we show that pseudospin can turn into orbital angular momentum completely, thus upholding the belief that pseudospin is not merely for theoretical elegance but rather physically measurable.”
    Quote in the paperSubstantial claim
  • May combine two claims. 7
  • Classified as probably not a substantial claim. 1

  • May combine two claims.

    Findingcitation

    The vortex generation and topological charge flipping is achieved by exciting the two sublattices at the same K valley in a uniform, non-strained HCL, so no pseudomagnetic field is involved.

    “We note that our vortex generation and topological charge flipping is achieved by exciting the two sublattices at the same K valley (see Fig. 3) in a uniform (non-strained) HCL, thus no pseudomagnetic field is involved 22 .”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [22] Rechtsman, M. C. et al. Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures. Nat. Photon. 7, 153–158 (2013). source

  • May combine two claims.

    Findingown data

    In both settings, a global singly charged vortex is created, with opposite topological charges.

    “In both cases, a global singly charged vortex is created, as identified by a fork bifurcation in the central fringes, although the topological charges are opposite (Fig. 2d,h).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    When both sublattices A and B are simultaneously excited, or when the HCL is replaced by a single triangular lattice, no integer vortex is generated.

    “In addition, when both sublattices A and B are simultaneously excited or when the HCL is replaced by a single triangular lattice, no integer vortex is generated.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In experiment, interferograms indicate that a singly charged optical vortex is created in each case, and the topological charge is flipped when excitation shifts from sublattice A to B.

    “However, the interferograms obtained with an inclined reference plane wave indicate that not only is a singly charged optical vortex created in each case, but also the topological charge is flipped (opposite fringe bifurcation) when the excitation shifts from sublattice A to B (Fig. 3d,h).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Although the output intensity of the probe beam displays a similar conical diffraction pattern in both settings, their phase structure is dramatically different.

    “Surprisingly, although the output intensity of the probe beam displays a similar conical diffraction pattern 14,28 as shown in Fig. 2c,g, their phase structure as monitored from interferograms is dramatically different.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [14] Peleg, O. et al. Conical diffraction and gap solitons in honeycomb photonic lattices. Phys. Rev. Lett. 98, 103901 (2007). source
    • cites [28] Hamilton, W. R. Third supplement to an essay on the theory of systems of rays. Trans. R. Irish Acad. 17, 1–144 (1837).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S4 (based).

    Study design and conductnone given

    The intensity and polarization of all beams are chosen such that there is no nonlinear self-action of the probe beam.

    “Note that the intensity/polarization of all beams is chosen such that there is no nonlinear self-action of the probe beam.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    The total angular momentum of the system J would not be conserved if pseudospin is ignored, because the orbital angular momentum itself in the HCL is not conserved.

    “Before closing, we emphasize that the total AM of the system J would not be conserved but should we ignore the pseudospin, simply because the orbital AM itself in the HCL is not conserved.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The results indicate that pseudospin is a real angular momentum, observable and measurable.

    “Our results indicate clearly that the pseudospin is of real AM, observable and measurable.”
    Quote in the paperSubstantial claim
8 of 8

  • The paper relies on this without support.

    Direct tests of graphene pseudospin as an observable angular momentum had remained unfruitful before this study.

    “but so far direct tests of such a momentum remained unfruitful.”

  • The paper relies on this without support.

    Photonic lattices offer control over initial conditions and allow monitoring the actual wavefunction including phase, enabling direct observation of graphene wave dynamics in regimes not accessible in natural graphene.

    “As photonic lattices offer exquisite control over initial conditions and allow for monitoring the actual wavefunction (including phase), it is possible to directly observe graphene wave dynamics using classical light waves in regimes not accessible in natural graphene.”
2 of 2

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • If one excites only a single sublattice at either K-valleys or K'-valleys, the output is also circularly symmetric.

    “If one excites only a single sublattice at either K -valleys or K ′ -valleys, the output is also circularly symmetric [57].”

    From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [57]

    The three-beam excitation section reports similar conical-diffraction output patterns when either sublattice is excited. The Discussion says that exciting the same sublattice from the two sets of valleys produced no observed difference. Our copy does not explicitly establish that those outputs are circularly symmetric. (LLM, conf=0.78)

    Experimental — accuracy not yet measured

  • Understanding and development of optical spin-orbit interactions, photonic pseudospins, and valley degrees of freedom have offered new knobs for manipulation of light in photonic structures.

    “However, the understanding and development of optical spinorbit interactions [56], photonic pseudospins [57], and valley degrees of freedom[58-65] have offered us new knobs that can be used for manipulation of light in photonic structures, in analogy with parallel advances in electric systems.”

    From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [57]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • The initially empty sublattice is described as remaining empty

    Minor

    The first statement sets the other spinor component to zero at an unspecified propagation distance z, but the later statement says that component is generated during propagation. If the zero condition is intended only for the input plane, it needs z = 0.

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. Hamilton, W. R. Third supplement to an essay on the theory of systems of rays. Trans. R. Irish Acad. 17, 1–144 (1837).

Cited by

Sorted by citations

Related

Authors
Song, D., Paltoglou, V., Liu, S., Zhu, Y., Gallardo, D., Tang, L., Xu, J., Ablowitz, M., Efremidis, N. K., & Chen, Z.
Affiliations
  • Nankai University (CN)
  • University of Crete (GR)
  • Northwestern Polytechnical University (CN)
  • Tsinghua University (CN)
  • San Francisco State University (US)
  • University of Colorado Boulder (US)
Corresponding author
  • Xu, Jingjun
  • Chen, Zhigang
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2015-02-17
Volume
6
Issue
1
Pages
6272-6272
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/ncomms7272
OpenAlex
W2105621925
Cited by
183
References
41
Citations by year
2026: 6 · 2025: 15 · 2024: 25 · 2023: 17 · 2022: 18 · 2021: 17 · 2020: 23 · 2019: 10 · 2018: 17 · 2017: 7 · 2016: 19 · 2015: 8 · 2014: 1
FWCI
8.63
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Communications (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (1404510, 1125935)
  • Higher Education Discipline Innovation Project (B07013, IRT0149, No. B07013)
  • Division of Chemistry (CHE-1125935)
  • European Social Fund
  • Air Force Office of Scientific Research
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
Keywords
pseudospin, photonic graphene, orbital angular momentum, Dirac point, vortex formation, Dirac-Weyl equation, evanescently coupled waveguides

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