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Spin-dependent properties of optical modes guided by adiabatic trapping potentials in photonic Dirac metasurfaces

Nature Nanotechnology volume 18, pages 875–881 (2023)Cite this article

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Abstract

The Dirac-like dispersion in photonic systems makes it possible to mimic the dispersion of relativistic spin-1/2 particles, which led to the development of the concept of photonic topological insulators. Despite recent demonstrations of various topological photonic phases, the full potential offered by Dirac photonic systems, specifically their ability to emulate the spin degree of freedom—referred to as pseudo-spin—beyond topological boundary modes has remained underexplored. Here we demonstrate that photonic Dirac metasurfaces with smooth one-dimensional trapping gauge potentials serve as effective waveguides with modes carrying pseudo-spin. We show that spatially varying gauge potentials act unevenly on the two pseudo-spins due to their different field distributions, which enables control of guided modes by their spin, a property that is unattainable with conventional optical waveguides. Silicon nanophotonic metasurfaces are used to experimentally confirm the properties of these guided modes and reveal their distinct spin-dependent radiative character; modes of opposite pseudo-spin exhibit disparate radiative lifetimes and couple differently to incident light. The spin-dependent field distributions and radiative lifetimes of their guided modes indicate that photonic Dirac metasurfaces could be used for spin-multiplexing, controlling the characteristics of optical guided modes, and tuning light–matter interactions with photonic pseudo-spins.

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Fig. 1: Spin-full guiding potentials generated by spatially variable mass terms.
Fig. 2: First-principles design of a spin-full waveguide and non-Hermitian spin Hall effect.
Fig. 3: Experimental results evidencing pseudo-spin-polarized transport and non-Hermitian spin Hall effect in the Dirac meta-waveguide.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Qiao, W. et al. Toward scalable flexible nanomanufacturing for photonic structures and devices. Adv. Mater. 28, 10353–10380 (2016).

    Article  CAS  Google Scholar 

  2. Li, C. et al. Dielectric metasurfaces: from wavefront shaping to quantum platforms. Prog. Surf. Sci. 95, 100584 (2020).

    Article  CAS  Google Scholar 

  3. Plotnik, Y. et al. Observation of unconventional edge states in ‘photonic graphene’. Nat. Mater. 13, 57–62 (2014).

    Article  CAS  Google Scholar 

  4. Bliokh, K. Y. Weak antilocalization of ultrarelativistic fermions. Phys. Lett. A 344, 127–130 (2005).

    Article  CAS  Google Scholar 

  5. Morozov, S. V. et al. Strong suppression of weak localization in graphene. Phys. Rev. Lett. 97, 016801 (2006).

    Article  CAS  Google Scholar 

  6. Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photonics 8, 821–829 (2014).

    Article  CAS  Google Scholar 

  7. Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).

    Article  CAS  Google Scholar 

  8. Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nat. Phys. 7, 907–912 (2011).

    Article  CAS  Google Scholar 

  9. Cheng, X. et al. Robust reconfigurable electromagnetic pathways within a photonic topological insulator. Nat. Mater. 15, 542–548 (2016).

    Article  CAS  Google Scholar 

  10. Khanikaev, A. B. & Shvets, G. Two-dimensional topological photonics. Nat. Photonics 11, 763–773 (2017).

    Article  CAS  Google Scholar 

  11. Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).

    Article  CAS  Google Scholar 

  12. Slobozhanyuk, A. et al. Three-dimensional all-dielectric photonic topological insulator. Nat. Photonics 11, 130–136 (2017).

    Article  CAS  Google Scholar 

  13. Yang, Y. et al. Realization of a three-dimensional photonic topological insulator. Nature 565, 622–626 (2019).

    Article  CAS  Google Scholar 

  14. Szameit, A., Rechtsman, M. C., Bahat-Treidel, O. & Segev, M. PT-symmetry in honeycomb photonic lattices. Phys. Rev. A 84, 021806R (2011).

    Article  Google Scholar 

  15. Zhen, B. et al. Spawning rings of exceptional points out of Dirac cones. Nature 525, 354–358 (2015).

    Article  CAS  Google Scholar 

  16. Leykam, D., Bliokh, K. Y., Huang, C., Chong, Y. D. & Nori, F. Edge modes, degeneracies, and topological numbers in non-Hermitian systems. Phys. Rev. Lett. 118, 040401 (2017).

    Article  Google Scholar 

  17. Liu, T. et al. Second-order topological phases in non-Hermitian systems. Phys. Rev. Lett. 122, 076801 (2019).

    Article  CAS  Google Scholar 

  18. Liu, Y. G. N., Jung, P. S., Parto, M., Christodoulides, D. N. & Khajavikhan, M. Gain-induced topological response via tailored long-range interactions. Nat. Phys. 17, 704–709 (2021).

    Article  CAS  Google Scholar 

  19. Xia, S. et al. Nonlinear tuning of PT symmetry and non-Hermitian topological states. Science 372, 72–76 (2021).

    Article  CAS  Google Scholar 

  20. Parto, M., Liu, Y. G. N., Bahari, B., Khajavikhan, M. & Christodoulides, D. N. Non-Hermitian and topological photonics: optics at an exceptional point. Nanophotonics 10, 403–423 (2020).

    Article  Google Scholar 

  21. Lumer, Y., Plotnik, Y., Rechtsman, M. C. & Segev, M. Self-localized states in photonic topological insulators. Phys. Rev. Lett. 111, 243905 (2013).

    Article  Google Scholar 

  22. Hadad, Y., Khanikaev, A. B. & Alù, A. Self-induced topological transitions and edge states supported by nonlinear staggered potentials. Phys. Rev. B 93, 55112 (2016).

    Article  Google Scholar 

  23. Leykam, D. & Chong, Y. D. Edge solitons in nonlinear-photonic topological insulators. Phys. Rev. Lett. 117, 143901 (2016).

    Article  Google Scholar 

  24. Hadad, Y., Soric, J. C., Khanikaev, A. B. & Alú, A. Self-induced topological protection in nonlinear circuit arrays. Nat. Electron. 1, 178–182 (2018).

    Article  Google Scholar 

  25. D’Aguanno, G. et al. Nonlinear topological transitions over a metasurface. Phys. Rev. B 100, 214310 (2019).

    Article  Google Scholar 

  26. Smirnova, D., Leykam, D., Chong, Y. & Kivshar, Y. Nonlinear topological photonics. Appl. Phys. Rev. 7, 021306 (2020).

    Article  CAS  Google Scholar 

  27. Maczewsky, L. J. et al. Nonlinearity-induced photonic topological insulator. Science 370, 701–704 (2020).

    Article  CAS  Google Scholar 

  28. Gao, F. et al. Topologically protected refraction of robust kink states in valley photonic crystals. Nat. Phys. 14, 140–144 (2018).

    Article  CAS  Google Scholar 

  29. Liu, J. W. et al. Valley photonic crystals. Adv. Phys. X 6, 1905546 (2021).

    Google Scholar 

  30. Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).

    Article  CAS  Google Scholar 

  31. Raghu, S. & Haldane, F. D. M. Analogs of quantum-Hall-effect edge states in photonic crystals. Phys. Rev. A 78, 033834 (2008).

    Article  Google Scholar 

  32. Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).

    Article  CAS  Google Scholar 

  33. Khanikaev, A. B. et al. Photonic topological insulators. Nat. Mater. 12, 233–239 (2013).

    Article  CAS  Google Scholar 

  34. Silveirinha, M. G. Bulk-edge correspondence for topological photonic continua. Phys. Rev. B 94, 205105 (2016).

    Article  Google Scholar 

  35. Bisharat, D. J. & Sievenpiper, D. F. Electromagnetic-dual metasurfaces for topological states along a 1D interface. Laser Photonics Rev. 13, 1900126 (2019).

    Article  CAS  Google Scholar 

  36. Wu, L. H. & Hu, X. Scheme for achieving a topological photonic crystal by using dielectric material. Phys. Rev. Lett. 114, 223901 (2015).

    Article  Google Scholar 

  37. Barik, S., Miyake, H., Degottardi, W., Waks, E. & Hafezi, M. Two-dimensionally confined topological edge states in photonic crystals. New J. Phys. 18, 113013 (2016).

    Article  Google Scholar 

  38. Barik, S. et al. A topological quantum optics interface. Science 359, 666–668 (2018).

    Article  CAS  Google Scholar 

  39. Gorlach, M. A. et al. Far-field probing of leaky topological states in all-dielectric metasurfaces. Nat. Commun. 9, 909 (2018).

    Article  Google Scholar 

  40. Mei, J., Chen, Z. & Wu, Y. Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals. Sci. Rep. 6, 32752 (2016).

    Article  CAS  Google Scholar 

  41. Smirnova, D. et al. Third-harmonic generation in photonic topological metasurfaces. Phys. Rev. Lett. 123, 103901 (2019).

    Article  CAS  Google Scholar 

  42. Tworzydło, J., Groth, C. W. & Beenakker, C. W. J. Finite difference method for transport properties of massless Dirac fermions. Phys. Rev. B 78, 235438 (2008).

    Article  Google Scholar 

  43. Hernández, A. R. & Lewenkopf, C. H. Finite-difference method for transport of two-dimensional massless Dirac fermions in a ribbon geometry. Phys. Rev. B 86, 155439 (2012).

    Article  Google Scholar 

  44. Landau, L. D. and Lifschitz, E. M. Quantum Mechanics: Non-relativistic Theory (Pergamon, 1977).

  45. Parappurath, N., Alpeggiani, F., Kuipers, L. & Verhagen, E. Direct observation of topological edge states in silicon photonic crystals: spin, dispersion, and chiral routing. Sci. Adv. 6, eaaw4137 (2020).

    Article  CAS  Google Scholar 

  46. Liu, W. et al. Generation of helical topological exciton–polaritons. Science 370, 600–604 (2020).

    Article  CAS  Google Scholar 

  47. Li, M. et al. Experimental observation of topological Z2 exciton–polaritons in transition metal dichalcogenide monolayers. Nat. Commun. 12, 4425 (2021).

    Article  CAS  Google Scholar 

  48. Guddala, S. et al. Topological phonon–polariton funneling in midinfrared metasurfaces. Science 374, 225–227 (2021).

    Article  CAS  Google Scholar 

  49. Bliokh, K. Y., Dressel, J. & Nori, F. Conservation of the spin and orbital angular momenta in electromagnetism. New J. Phys. 16, 093037 (2014).

    Article  Google Scholar 

  50. Bliokh, K. Y. et al. Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems. Opt. Express 19, 26132 (2011).

    Article  Google Scholar 

  51. De Paz, M. B., Vergniory, M. G., Bercioux, D., Garciá-Etxarri, A. & Bradlyn, B. Engineering fragile topology in photonic crystals: topological quantum chemistry of light. Phys. Rev. Res. 1, 032005 (2019).

    Article  Google Scholar 

  52. De Paz, M. B. et al. Energy density as a probe of band representations in photonic crystals. J. Phys. Condens. Matter 34, 314002 (2022).

    Article  Google Scholar 

  53. Xiao, B. et al. Exciting reflectionless unidirectional edge modes in a reciprocal photonic topological insulator medium. Phys. Rev. B 94, 195427 (2016).

    Article  Google Scholar 

  54. Slobozhanyuk, A. et al. Near-field imaging of spin-locked edge states in all-dielectric topological metasurfaces. Appl. Phys. Lett. 114, 031103 (2019).

    Article  Google Scholar 

  55. Li, Y. et al. Mode-selective single-dipole excitation and controlled routing of guided waves in a multi-mode topological waveguide. Appl. Phys. Lett. 120, 221702 (2022).

    Article  CAS  Google Scholar 

  56. Shalaev, M. I., Walasik, W., Tsukernik, A., Xu, Y. & Litchinitser, N. M. Robust topologically protected transport in photonic crystals at telecommunication wavelengths. Nat. Nanotechnol. 14, 31–34 (2019).

    Article  CAS  Google Scholar 

  57. Collins, M. J., Zhang, F., Bojko, R., Chrostowski, L. & Rechtsman, M. C. Integrated optical Dirac physics via inversion symmetry breaking. Phys. Rev. A 94, 063827 (2016).

    Article  Google Scholar 

  58. Zeng, Y. et al. Electrically pumped topological laser with valley edge modes. Nature 578, 246–250 (2020).

    Article  CAS  Google Scholar 

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Acknowledgements

The work was supported by the Office of Naval Research (ONR) award N00014-21-1-2092 (A.B.K.), the National Science Foundation (NSF) grant DMR-1809915 (A.B.K.) and the Simons Collaboration on Extreme Wave Phenomena (A.B.K.). D.S. acknowledges support from the Australian Research Council (DE190100430). J.A. and M.A. thank AFRL/RW Emerging Technologies for their support. Fabrication of samples for this work was performed at the Nanofabrication Facility at the Advanced Science Research Center at The Graduate Center of the City University of New York.

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Author notes

  1. These authors contributed equally: Svetlana Kiriushechkina, Anton Vakulenko, Daria Smirnova.

Authors and Affiliations

  1. Electrical Engineering and Physics, The City College of New York, New York, NY, USA

    Svetlana Kiriushechkina, Anton Vakulenko, Sriram Guddala, Yuma Kawaguchi, Filipp Komissarenko & Alexander B. Khanikaev

  2. ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Research School of Physics, The Australian National University, Canberra, ACT, Australia

    Daria Smirnova

  3. Air Force Research Laboratory, Munitions Directorate, Eglin AFB, Eglin, FL, USA

    Monica Allen & Jeffery Allen

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  1. Svetlana Kiriushechkina
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Contributions

A.B.K. conceived the research. D.S. performed theoretical calculations. S.K. and A.V. performed first-principles simulations, fabrication of samples and optical characterization, including real-space imaging and angle-resolved reflectivity measurements. A.V., S.G. and F.K. assembled the experimental set-up. A.B.K., M.A. and J.A. guided and supervised the project. All authors contributed to discussion of the results and manuscript preparation.

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Correspondence to Alexander B. Khanikaev.

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Kiriushechkina, S., Vakulenko, A., Smirnova, D. et al. Spin-dependent properties of optical modes guided by adiabatic trapping potentials in photonic Dirac metasurfaces. Nat. Nanotechnol. 18, 875–881 (2023). https://doi.org/10.1038/s41565-023-01380-9

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