Pith. sign in

REVIEW 2 major objections 5 minor 54 references

Zigzag edge states in polariton honeycombs lock elliptical polarization to propagation direction via TE–TM coupling, enabling helicity-controlled edge lasing without magnetic fields.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · grok-4.5

2026-07-11 22:43 UTC pith:ZRZGD4TR

load-bearing objection Clean Stokes maps and helicity-controlled edge lasing in polariton honeycombs; the ‘solely evanescent’ claim is slightly oversold because residual edge strain is unquantified, but the data still stand. the 2 major comments →

arxiv 2607.03961 v1 pith:ZRZGD4TR submitted 2026-07-04 cond-mat.mes-hall physics.optics

Spin-momentum locking of polariton edge states in honeycomb lattices

Andrea Herrero Otermin , Nicola Carlon Zambon , Dheerendra Singh , Neha Bhoria , Rimi Banerjee , Christian Mayer , Simon Betzold , Siddhartha Dam
show 5 more authors
Monika Emmerling Sven H\"ofling Luis Vi\~na Subhaskar Mandal Carlos Ant\'on-Solanas
This is my paper
classification cond-mat.mes-hall physics.optics PACS 71.36.+c42.50.Tx78.67.Pt
keywords spin-momentum lockingexciton-polaritonhoneycomb latticezigzag edge statesTE-TM splittingpolariton lasingphotonic spin-orbit coupling
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper shows that the same TE–TM birefringence that leaves bulk polariton modes linearly polarized forces zigzag edge states to become elliptically polarized, with the handedness locked to the direction of travel. Because the edge wavefunction decays into the bulk, one momentum component is imaginary; that complex wavevector, together with the effective spin–orbit field of the cavity mirrors, produces a finite circular-polarization component S3 that flips sign when the edge state reverses. The authors measure this spin–momentum locking by full Stokes polarimetry on both a gapless honeycomb and a stretched honeycomb that opens a photonic gap. In the gapped lattice, spin-polarized non-resonant pumping selectively amplifies one of the two counter-propagating edge modes, so that the lasing beam itself can be steered left or right simply by changing the pump helicity. The result supplies an all-optical route to unidirectional polariton transport that does not require external magnets or broken time-reversal symmetry.

Core claim

Zigzag edge states of a polariton honeycomb lattice acquire an intrinsic elliptical polarization whose handedness is locked to group velocity, arising solely from the interplay of the cavity TE–TM field with the imaginary transverse wavevector of the exponentially localized mode; the same locking survives in a stretched honeycomb supporting a band gap and permits helicity-selective edge-state lasing.

What carries the argument

The TE–TM effective magnetic field (Ωx ∝ −∂x^{2} + ∂y^{2}, Ωy ∝ −2∂x∂y) evaluated on a complex edge wavevector ky → iλy, which yields a circular polarization S3 ∝ 2λy kx/(kx^{2} + λy^{2}) that reverses with kx.

Load-bearing premise

Any residual strain or linear-polarization splitting at the zigzag interface is small enough that the observed elliptical texture can be attributed entirely to the complex-wavevector mechanism.

What would settle it

Measure the linear Stokes parameters S1 and S2 of the same zigzag edge states under linearly polarized excitation; if a large residual linear dichroism appears that dominates the circular component S3, the pure-evanescent origin of the locking is ruled out.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Spin-selective optical gain can route polariton edge emission left or right without magnets or synthetic gauge fields.
  • The same locking is expected for any exponentially localized photonic edge mode once TE–TM (or analogous) birefringence is present.
  • In a gapped stretched honeycomb the edge modes can be lasing-isolated from the bulk continuum, enabling directional polariton lasers.
  • Time-resolved experiments could track the ultrafast build-up of the spin texture and the propagation of spin-polarized wave packets along the edge.

Where Pith is reading between the lines

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

  • Because triangular honeycomb domains are bounded entirely by zigzag edges, the same mechanism should allow spin-locked circulation around sharp corners without additional engineering.
  • The reversed group-velocity sign observed in the stretched lattice suggests that longer-range hoppings and TE–TM spin-flip terms can be deliberately tuned to flip the locking direction on demand.
  • If residual interface strain can be mapped and suppressed more systematically, the |S3| value itself becomes a direct experimental readout of the edge decay constant λy.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The manuscript reports experimental observation of spin-momentum locking (SML) for zigzag edge states (ZES) in GaAs-based exciton-polariton honeycomb lattices. TE–TM splitting of the microcavity provides an effective photonic spin–orbit coupling. Bulk Bloch modes remain linearly polarized by inversion symmetry, while exponentially localized ZES acquire elliptical polarization whose handedness is locked to propagation direction (S3 ∝ 2λ y kx/(kx^{2}+λ y^{2}), opposite for ±kx). Full Stokes polarimetry in energy–momentum and real space demonstrates this texture in a gapless honeycomb lattice under linear and circular non-resonant pumping. The effect persists in a Kekulé-distorted (stretched) honeycomb that opens a photonic gap isolating the edge modes; above a clear lasing threshold, spin-selective gain then enables helicity-controlled selective lasing of either chiral edge state without external magnetic fields. Supporting Gross–Pitaevskii simulations and a minimal edge-state model are provided.

Significance. If residual interface strain is negligible, the work cleanly isolates a universal mechanism—transverse spin of complex-wavevector edge modes under TE–TM coupling—from topology per se, and shows that the same texture survives gap opening and can be exploited for all-optical, magnetic-field-free directional edge lasing. This is a concrete advance over earlier polariton honeycomb edge-state experiments (where strain obscured the polarization texture) and supplies a practical route to ultrafast spin-controlled unidirectional polariton transport. The combination of energy–momentum Stokes maps, real-space directionality under circular pumps, power-dependent threshold and linewidth collapse, and matching simulations constitutes a solid experimental package for a specialized condensed-matter/photonics journal.

major comments (2)
  1. Introduction and Results (comparison with Milićević et al. 2015): the central attribution that the observed |S3|≈0.4 and the reversed group-velocity sign arise “solely from their evanescent character” under TE–TM coupling rests on the claim that residual interface strain (or other linear-polarization splitting at the zigzag boundary) is negligible. Prior work is explicitly said to have been obscured by such strain, yet the manuscript provides no edge-resolved S1/S2 maps, linear-dichroism spectra, or quantitative bound on residual birefringence at the edge. Without that control, a weaker strain-induced linear dichroism could still contribute to the measured circular texture and could renormalize the longer-range hoppings that set the group-velocity sign. A short quantification (or an explicit upper bound extracted from existing Stokes data) is load-bearing for the “solely” claim and shoul
  2. Results, stretched-lattice section and associated SI tight-binding analysis: the observed reversal of SML directionality (and of ZES group velocity) relative to the regular honeycomb is attributed to competition between spin-conserving hoppings and TE–TM-induced spin-flip terms. Because the zigzag band is intrinsically flat, its dispersion is set by microscopic parameters that are fitted rather than independently measured. The Gross–Pitaevskii simulations reproduce the sign only after those hoppings are chosen. A clearer statement of which parameters are fixed by bulk dispersion alone versus which are adjusted to match the edge, together with a brief sensitivity check, would strengthen the claim that the reversal is a genuine microscopic consequence rather than a fitting choice.
minor comments (5)
  1. Figure 1 caption and body text: panels (b)–(d) are referenced inconsistently (band structure vs. TE–TM field texture). Align the caption labels with the in-text citations.
  2. Equation (2) and surrounding text: the proportionality for S3 is given without stating the overall normalization or the precise definition of the Stokes parameter used experimentally; a one-line clarification would help readers compare theory and data.
  3. Figure 4(a): the elliptical spot is said to cover “approximately four edge pillars” in the text and “six pillars” in the caption; reconcile the numbers.
  4. Supplementary Information is cited for the effective edge model, Gross–Pitaevskii details, and the tight-binding analysis of the velocity reversal; ensuring these sections are complete and self-contained will be important for reproducibility.
  5. A few typographical inconsistencies appear (e.g., “latticedistortion”, missing spaces around equals signs in Va=Vb). A light copy-edit pass would improve readability.

Circularity Check

0 steps flagged

No significant circularity: SML formula is a direct substitution into the standard TE-TM Hamiltonian; experiment and corroborative simulations are independent of any fitted definition of the target.

full rationale

The paper's central theoretical step is the substitution ky o i heta y into the well-known TE-TM Hamiltonian (Eq. 1), which immediately yields the quoted S3 o 2 heta y kx/(kx^{2} + heta y^{2}) with opposite sign under kx o -kx. This is a first-principles calculation from Maxwell constraints on evanescent waves (citing Mechelen & Jacob and Kavokin et al.), not a definition or fit of the observed polarization. Hopping parameters t, t' are extracted from bulk dispersion solely for sample characterization and for initializing Gross-Pitaevskii simulations that reproduce (but do not force) the measured SML texture and group-velocity reversal. Selective lasing under circular pumping is an experimental observation enabled by the gap, not a prediction derived from a self-referential ansatz. Self-citations (e.g., prior chirality-control and polariton-lattice papers by overlapping authors) supply context and experimental technique but are not load-bearing for the SML derivation or the claim that the effect arises from the complex wavevector. Residual-strain concerns affect correctness, not circularity. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The load-bearing physics is standard: TE–TM birefringence of planar microcavities, complex wavevector of edge-localized modes, and spin-selective nonresonant gain. Free parameters are characterization fits (hoppings, Rabi splitting, thresholds), not knobs that define SML into existence. No new particles or forces are postulated; SML is imported from known electromagnetism and applied to this lattice.

free parameters (5)
  • nearest-neighbor hopping t = 0.39 meV
    Fitted from bulk dispersion along K–Γ–K′; used to characterize the lattice, not to define SML.
  • next-nearest-neighbor hopping t′ = 0.06 meV
    Fitted from dispersion; sets finite ZES group velocity and chiral-symmetry breaking of the edge band.
  • vacuum Rabi splitting ħΩ_R = ≈8.4 meV
    From independent avoided-crossing measurement; places the system in strong coupling.
  • lattice overlap parameters Va, Vb = 0.8/0.8 and 0.9/0.7
    Engineered center-to-center separations (regular: 0.8/0.8; stretched: 0.9/0.7) that set gap size and edge dispersion; design choices, not post-hoc fits to S3.
  • edge-lasing threshold P_th = 21.5 mW
    Measured power at nonlinear intensity rise and linewidth collapse; characterizes the nonlinear regime.
axioms (5)
  • domain assumption Microcavity TE–TM splitting is equivalent to the effective in-plane field H_TE-TM ∝ Ωx σx + Ωy σy with the double-winding texture in k-space.
    Standard polariton spin–orbit model (Kavokin et al., Sala et al.); invoked in Introduction and Eq. (1).
  • domain assumption Exponentially localized edge modes have imaginary transverse wavevector and therefore carry transverse spin locked to propagation direction (universal SML of evanescent waves).
    Taken from Mechelen & Jacob (Optica 2016) and applied to ZES; central interpretive axiom.
  • domain assumption Nonresonant circular pumping partially spin-polarizes the exciton reservoir and preferentially feeds co-circular polariton modes.
    Used to explain selective amplification and lasing under σ± pumps; standard in polariton spin literature.
  • domain assumption Linearized mean-field Gross–Pitaevskii dynamics adequately reproduce linear-regime PL maps under localized circular excitation.
    Simulations in Figs. 2(f,g) and SI; not used as sole proof of SML.
  • domain assumption Kekulé-type stretch (Va ≠ Vb) opens a bulk gap while preserving edge-localized states inside the gap.
    From Wu & Hu topological photonic crystal scheme; confirmed by measured bulk and edge dispersions.

pith-pipeline@v1.1.0-grok45 · 15804 in / 3615 out tokens · 37088 ms · 2026-07-11T22:43:05.261661+00:00 · methodology

0 comments
read the original abstract

Transverse-electric/Transverse-magnetic splitting in dielectric-mirror microcavities introduces an effective spin-orbit coupling for photons. While the bulk states remain linearly polarized, for exponentially localized edge states in a photonic lattice, this coupling induces elliptical polarization whose handedness is locked to the propagation direction, analogous to the transverse spin of evanescent electromagnetic waves. We reveal spin-momentum locking through Stokes polarimetry of zigzag edge states in a honeycomb exciton-polariton lattice. The effect persists in a stretched honeycomb supporting a photonic bandgap, where spin-polarized carrier injection enables selective lasing of either chiral edge states. Our results provide a route toward ultrafast spin-controlled unidirectional propagation in polariton systems without external magnetic fields.

Figures

Figures reproduced from arXiv: 2607.03961 by Andrea Herrero Otermin, Carlos Ant\'on-Solanas, Christian Mayer, Dheerendra Singh, Luis Vi\~na, Monika Emmerling, Neha Bhoria, Nicola Carlon Zambon, Rimi Banerjee, Siddhartha Dam, Simon Betzold, Subhaskar Mandal, Sven H\"ofling.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (d), reveals that spin-momentum locking persists in the stretched lattice. Interestingly, its sign is reversed relative to the normal honeycomb lattice [ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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

54 extracted references · 1 linked inside Pith

  1. [1]

    F. D. M. Haldane and S. Raghu, Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry, Physical Review Letters100, 013904 (2008)

    2008

  2. [2]

    Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Observation of unidirectional backscattering-immune topological electromagnetic states, Nature461, 772–775 (2009)

    2009

  3. [3]

    H. Zhao, X. Qiao, T. Wu, B. Midya, S. Longhi, and L. Feng, Non-hermitian topological light steering, Science 365, 1163 (2019)

    2019

  4. [4]

    Bahari, A

    B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, Nonreciprocal lasing in topological cavities of arbitrary geometries, Science358, 636 (2017)

    2017

  5. [5]

    St-Jean, V

    P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T.Ozawa, L.LeGratiet, I.Sagnes, J.Bloch,andA.Amo, Lasing in topological edge states of a one-dimensional lat- tice, Nature Photonics11, 651 (2017)

    2017

  6. [6]

    M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science359, eaar4005 (2018)

    2018

  7. [7]

    J.-H. Choi, W. E. Hayenga, Y. G. N. Liu, M. Parto, B. Bahari, D. N. Christodoulides, and M. Khajavikhan, Room temperature electrically pumped topological insu- lator lasers, Nature Communications12, 3434 (2021)

    2021

  8. [8]

    Dikopoltsev, T

    A. Dikopoltsev, T. H. Harder, E. Lustig, O. A. Egorov, J. Beierlein, A. Wolf, Y. Lumer, M. Emmerling, C. Schneider, S. Höfling, M. Segev, and S. Klembt, Topo- logical insulator vertical-cavity laser array, Science373, 1514 (2021)

    2021

  9. [9]

    Mittal, V

    S. Mittal, V. V. Orre, D. Leykam, Y. Chong, and M. Hafezi, Photonic Anomalous Quantum Hall Effect, Physical Review Letters123, 043201 (2019)

    2019

  10. [10]

    Chénier, B

    A. Chénier, B. d’Aligny, F. Pellerin, P.-E. Blanchard, T. Ozawa, I. Carusotto, and P. St-Jean, Quantized hall drift in a frequency-encoded photonic chern insulator, Phys. Rev. X16, 011020 (2026). 6

    2026

  11. [11]

    Roberts, B

    N. Roberts, B. Salter, J. Binysh, P. J. Mosley, and A. Souslov, Twisted optical fibres as photonic topolog- ical insulators, Nature Photonics20, 324–331 (2026)

    2026

  12. [12]

    Schine, A

    N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Si- mon, Synthetic Landau levels for photons, Nature534, 671 (2016)

    2016

  13. [13]

    L. W. Clark, N. Schine, C. Baum, N. Jia, and J. Si- mon, Observation of Laughlin states made of light, Na- ture582, 41 (2020)

    2020

  14. [14]

    Wang, F.-M

    C. Wang, F.-M. Liu, M.-C. Chen, H. Chen, X.-H. Zhao, C. Ying, Z.-X. Shang, J.-W. Wang, Y.-H. Huo, C.-Z. Peng, X. Zhu, C.-Y. Lu, and J.-W. Pan, Realization of fractional quantum Hall state with interacting photons, Science384, 579 (2024)

    2024

  15. [15]

    C. L. Kane and E. J. Mele,Z2 Topological Order and the Quantum Spin Hall Effect, Physical Review Letters95, 146802 (2005)

    2005

  16. [16]

    C. L. Kane and E. J. Mele, Quantum Spin Hall Effect in Graphene, Physical Review Letters95, 226801 (2005)

    2005

  17. [17]

    B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Quantum spin hall effect and topological phase transition in hgte quantum wells, Science314, 1757–1761 (2006)

    2006

  18. [18]

    L. Lu, J. D. Joannopoulos, and M. Soljačić, Topological photonics, Nature Photonics8, 821–829 (2014)

    2014

  19. [19]

    Wu and X

    L.-H. Wu and X. Hu, Scheme for achieving a topologi- cal photonic crystal by using dielectric material, Physical Review Letters114, 223901 (2015)

    2015

  20. [20]

    Ozawa, H

    T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zil- berberg, and I. Carusotto, Topological photonics, Re- views of Modern Physics91, 015006 (2019)

    2019

  21. [21]

    Arora, T

    S. Arora, T. Bauer, R. Barczyk, E. Verhagen, and L. Kuipers, Direct quantification of topological protec- tion in symmetry-protected photonic edge states at tele- com wavelengths, Light: Science & Applications10, 9 (2021)

    2021

  22. [22]

    C. A. Rosiek, G. Arregui, A. Vladimirova, M. Albrecht- sen, B. Vosoughi Lahijani, R. E. Christiansen, and S. Sto- bbe, Observation of strong backscattering in valley-hall photonic topological interface modes, Nature Photonics 17, 386–392 (2023)

    2023

  23. [23]

    S. Xu, Y. Wang, and R. Agarwal, Absence of topological protection of the interface states inZ2 photonic crystals, Physical Review Letters131, 053802 (2023)

    2023

  24. [24]

    Lévêque, Y

    G. Lévêque, Y. Pennec, P. Szriftgiser, A. Amo, and A. Martínez, Scattering-matrix approach for a quanti- tative evaluation of the topological protection in valley photoniccrystals,PhysicalReviewA108,043505(2023)

    2023

  25. [25]

    A. B. Khanikaev, S. Hossein Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Photonic topological insulators, Nature Materials12, 233–239 (2012)

    2012

  26. [26]

    Hafezi, S

    M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Tay- lor, Imaging topological edge states in silicon photonics, Nature Photonics7, 1001–1005 (2013)

    2013

  27. [27]

    Yang, Z.-K

    Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, and R.- M. Ma, Spin-momentum-locked edge mode for topologi- cal vortex lasing, Phys. Rev. Lett.125, 013903 (2020)

    2020

  28. [28]

    H. Ando, T. Sogawa, and H. Gotoh, Photon-spin con- trolled lasing oscillation in surface-emitting lasers, Appl. Phys. Lett.73, 566 (1998)

    1998

  29. [29]

    F.-K. Hsu, W. Xie, Y.-S. Lee, S.-D. Lin, and C.-W. Lai, Ultrafast spin-polarized lasing in a highly photoexcited semiconductor microcavity at room temperature, Phys. Rev. B91, 195312 (2015)

    2015

  30. [30]

    Carlon Zambon, P

    N. Carlon Zambon, P. St-Jean, M. Milićević, A. Lemaître, A. Harouri, L. Le Gratiet, O. Bleu, D. D. Solnyshkov, G. Malpuech, I. Sagnes, S. Ravets, A. Amo, and J. Bloch, Optically controlling the emission chirality of microlasers, Nature Photonics13, 283 (2019)

    2019

  31. [31]

    Widmann, J

    S. Widmann, J. Bellmann, J. Düreth, S. Dam, C. G. Mayer, P. Gagel, S. Betzold, M. Emmerling, S. Man- dal, R. Banerjee, T. C. H. Liew, R. Thomale, S. Höfling, and S. Klembt, Artificial gauge fields and dimensions in a polariton hofstadter ladder (2025), arXiv:2506.13521 [cond-mat.mes-hall]

    Pith/arXiv arXiv 2025

  32. [32]

    T. V. Mechelen and Z. Jacob, Universal spin-momentum locking of evanescent waves, Optica3, 118 (2016)

    2016

  33. [33]

    P. Shi, L. Du, C. Li, A. V. Zayats, and X. Yuan, Trans- verse spin dynamics in structured electromagnetic guided waves, Proceedings of the National Academy of Sciences 118, e2018816118 (2021)

    2021

  34. [34]

    Hosten and P

    O. Hosten and P. Kwiat, Observation of the Spin Hall Effect of Light via Weak Measurements, Science319, 787 (2008)

    2008

  35. [35]

    Parappurath, F

    N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Ver- hagen, Direct observation of topological edge states in sil- icon photonic crystals: Spin, dispersion, and chiral rout- ing, Science Advances6, eaaw4137 (2020)

    2020

  36. [36]

    Carusotto and C

    I. Carusotto and C. Ciuti, Quantum fluids of light, Rev. Mod. Phys.85, 299 (2013)

    2013

  37. [37]

    Kusudo, N

    K. Kusudo, N. Y. Kim, A. Löffler, S. Höfling, A. Forchel, andY.Yamamoto,Stochasticformationofpolaritoncon- densates in two degenerate orbital states, Physical Re- view B87, 214503 (2013)

    2013

  38. [38]

    Klembt, T

    S. Klembt, T. H. Harder, O. A. Egorov, K. Winkler, R. Ge, M. A. Bandres, M. Emmerling, L. Worschech, T. C. H. Liew, M. Segev, C. Schneider, and S. Höfling, Exciton-polariton topological insulator, Nature562, 552–556 (2018)

    2018

  39. [39]

    Jacqmin, I

    T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaître, J. Bloch, and A. Amo, Direct observation of dirac cones and a flatband in a honeycomb lattice for polaritons, Physical Review Letters112, 116402 (2014)

    2014

  40. [40]

    Kavokin, G

    A. Kavokin, G. Malpuech, and M. Glazov, Optical Spin Hall Effect, Physical Review Letters95, 136601 (2005)

    2005

  41. [41]

    Leyder, M

    C. Leyder, M. Romanelli, J. P. Karr, E. Giacobino, T. C. H. Liew, M. M. Glazov, A. V. Kavokin, G. Malpuech, and A. Bramati, Observation of the op- tical spin Hall effect, Nature Physics3, 628 (2007)

    2007

  42. [42]

    Kammann, T

    E. Kammann, T. C. H. Liew, H. Ohadi, P. Cilibrizzi, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, A. V. Ka- vokin, and P. G. Lagoudakis, Nonlinear optical spin hall effect and long-range spin transport in polariton lasers, Physical Review Letters109, 036404 (2012)

    2012

  43. [43]

    V. G. Sala, D. D. Solnyshkov, I. Carusotto, T. Jacqmin, A. Lemaître, H. Terças, A. Nalitov, M. Abbarchi, E. Ga- lopin, I. Sagnes, J. Bloch, G. Malpuech, and A. Amo, Spin-orbit coupling for photons and polaritons in mi- crostructures, Phys. Rev. X5, 011034 (2015)

    2015

  44. [44]

    C. E. Whittaker, T. Dowling, A. V. Nalitov, A. V. Yulin, B. Royall, E. Clarke, M. S. Skolnick, I. A. Shelykh, and D. N. Krizhanovskii, Optical analogue of dresselhaus spin–orbit interaction in photonic graphene, Nature Pho- tonics15, 193–196 (2020)

    2020

  45. [45]

    Milićević, T

    M. Milićević, T. Ozawa, P. Andreakou, I. Carusotto, T. Jacqmin, E. Galopin, A. Lemaître, L. Le Gratiet, 7 I. Sagnes, J. Bloch, and A. Amo, Edge states in polariton honeycomb lattices, 2D Materials2, 034012 (2015)

    2015

  46. [46]

    Weisbuch, M

    C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Observation of the coupled exciton-photon mode split- ting in a semiconductor quantum microcavity, Phys. Rev. Lett.69, 3314 (1992)

    1992

  47. [47]

    See Supplementary Information for additional details

  48. [48]

    Michaelis de Vasconcellos, A

    S. Michaelis de Vasconcellos, A. Calvar, A. Dousse, J. Suffczyński, N. Dupuis, A. Lemaître, I. Sagnes, J. Bloch, P. Voisin, and P. Senellart, Spatial, spectral, and polarization properties of coupled micropillar cavi- ties, Applied Physics Letters99, 101103 (2011)

    2011

  49. [49]

    Houdré, C

    R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, Measurement of cavity- polariton dispersion curve from angle-resolved photo- luminescence experiments, Physical Review Letters73, 2043–2046 (1994)

    2043

  50. [50]

    Z. P. Wang, Q. B. Li, Q. Tan, Z. J. Huang, and J. H. Shi, Method of measuring the practical retardance and judgingthefastorslowaxisofaquarter-waveplate,Mea- surement39, 729–735 (2006)

    2006

  51. [51]

    Mangussi, M

    F. Mangussi, M. Milićević, I. Sagnes, L. L. Gratiet, A. Harouri, A. Lemaître, J. Bloch, A. Amo, and G. Usaj, Multi-orbitaltightbindingmodelforcavity-polaritonlat- tices, Journal of Physics: Condensed Matter32, 315402 (2020)

    2020

  52. [52]

    Lindemann, G

    M. Lindemann, G. Xu, T. Pusch, R. Michalzik, M. R. Hofmann, I. Žutić, and N. C. Gerhardt, Ultrafast spin- lasers, Nature568, 212–215 (2019)

    2019

  53. [53]

    Klaas, O

    M. Klaas, O. A. Egorov, T. C. H. Liew, A. Nalitov, V. Marković, H. Suchomel, T. H. Harder, S. Betzold, E. A. Ostrovskaya, A. Kavokin, S. Klembt, S. Höfling, and C. Schneider, Nonresonant spin selection methods and polarization control in exciton-polariton conden- sates, Physical Review B99, 115303 (2019)

    2019

  54. [54]

    B. Real, N. C. Zambon, P. St-Jean, I. Sagnes, A. Lemaître, A. Harouri, S. Ravets, J. Bloch, and A. Amo, Chiralemission inducedbyoptical zeemaneffect in polariton micropillars, Phys. Rev. Research3, 043161 (2021)

    2021