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Light guiding by artificial gauge fields

Abstract

Artificial gauge fields enable uncharged particles to behave as if affected by external fields. Generated by geometry or modulation, artificial gauge fields are instrumental in realizing topological physics in photonics, cold atoms and acoustics. Here, we experimentally demonstrate waveguiding by artificial gauge fields. We construct artificial gauge fields by using waveguide arrays with non-trivial trajectories. Tilting the arrays results in gauge fields that are different in the core and cladding, shifting their dispersion curves, thereby confining the light to the core. In a more advanced setting, we demonstrate waveguiding in a medium with the same gauge and dispersion everywhere, where the only difference between the core and the cladding is a phase shift in the dynamics of the gauge fields, which facilitates waveguiding via bound states in the continuum. Waveguiding and bound states in the continuum via artificial gauge fields relate to a plethora of systems, ranging from photonics and microwaves to cold atoms and acoustics.

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Fig. 1: Waveguiding of light by artificial gauge fields in tilted arrays.
Fig. 2: Experimental results displaying waveguiding by artificial gauge fields in tilted arrays.
Fig. 3: Waveguiding of light by phase-shifted but otherwise identical artificial gauge fields.
Fig. 4: Experimental results displaying waveguiding by phase-shifted artificial gauge fields.
Fig. 5: Experimental results displaying phase-shifted gauge guiding in sinusoidal arrays.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

References

  1. Snyder, A. W. & Love, J. Optical Waveguide Theory (Springer, 1983).

  2. Yeh, P. & Yariv, A. Bragg reflection waveguides. Opt. Commun. 19, 427–430 (1976).

    Article  ADS  Google Scholar 

  3. Ibanescu, M., Fink, Y., Fan, S., Thomas, E. L. & Joannopoulos, J. D. An all-dielectric coaxial waveguide. Science 289, 415–419 (2000).

    Article  ADS  Google Scholar 

  4. Russell, P. Photonic crystal fibers. Science 299, 358–362 (2003).

    Article  ADS  Google Scholar 

  5. Knight, J. C. Photonic crystal fibres. Nature 424, 847–851 (2003).

    Article  ADS  Google Scholar 

  6. Joannopoulos, J. D., Johnson, S. G., Winn, J. N. & Meade, R. D. Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 2008).

  7. Yariv, A., Xu, Y., Lee, R. K. & Scherer, A. Coupled-resonator optical waveguide: a proposal and analysis. Opt. Lett. 24, 711–713 (1999).

    Article  ADS  Google Scholar 

  8. Cohen, O., Freedman, B., Fleischer, J. W., Segev, M. & Christodoulides, D. N. Grating-mediated waveguiding. Phys. Rev. Lett. 93, 103902 (2004).

    Article  ADS  Google Scholar 

  9. Alberucci, A., Marrucci, L. & Assanto, G. Light confinement via periodic modulation of the refractive index. New J. Phys. 15, 083013 (2013).

    Article  ADS  Google Scholar 

  10. Slussarenko, S. et al. Guiding light via geometric phases. Nat. Photon. 10, 571–575 (2016).

    Article  ADS  Google Scholar 

  11. Lin, Q. & Fan, S. Light guiding by effective gauge field for photons. Phys. Rev. X 4, 031031 (2014).

    Google Scholar 

  12. Madison, K. W., Chevy, F., Wohlleben, W. & Dalibard, J. Vortex formation in a stirred Bose–Einstein condensate. Phys. Rev. Lett. 84, 806–809 (2000).

    Article  ADS  Google Scholar 

  13. Lin, Y.-J., Compton, R. L., Jiménez-García, K., Porto, J. V. & Spielman, I. B. Synthetic magnetic fields for ultracold neutral atoms. Nature 462, 628–632 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).

    Article  ADS  Google Scholar 

  16. Lustig, E. et al. Photonic topological insulator in synthetic dimensions. Nature https://doi.org/10.1038/s41586-019-0943-7 (2019).

  17. Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014).

    Article  ADS  Google Scholar 

  18. Aidelsburger, M. et al. Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nat. Phys. 11, 162–166 (2014).

    Article  Google Scholar 

  19. Schmidt, M., Kessler, S., Peano, V., Painter, O. & Marquardt, F. Optomechanical creation of magnetic fields for photons on a lattice. Optica 2, 635–641 (2015).

    Article  Google Scholar 

  20. Xiao, M., Chen, W.-J., He, W.-Y. & Chan, C. T. Synthetic gauge flux and Weyl points in acoustic systems. Nat. Phys. 11, 920–924 (2015).

    Article  Google Scholar 

  21. Fleury, R., Khanikaev, A. B. & Alù, A. Floquet topological insulators for sound. Nat. Commun. 7, 11744 (2016).

    Article  ADS  Google Scholar 

  22. Süsstrunk, R. & Huber, S. D. Observation of phononic helical edge states in a mechanical topological insulator. Science 349, 47–50 (2015).

    Article  ADS  Google Scholar 

  23. Nash, L. M. et al. Topological mechanics of gyroscopic metamaterials. Proc. Natl Acad. Sci. USA 112, 14495–14500 (2015).

    Article  ADS  Google Scholar 

  24. Umucalılar, R. O. & Carusotto, I. Artificial gauge field for photons in coupled cavity arrays. Phys. Rev. A 84, 043804 (2011).

    Article  ADS  Google Scholar 

  25. 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  Google Scholar 

  26. Fang, K., Yu, Z. & Fan, S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nat. Photon. 6, 782–787 (2012).

    Article  ADS  Google Scholar 

  27. Longhi, S. Effective magnetic fields for photons in waveguide and coupled resonator lattices. Opt. Lett. 38, 3570–3573 (2013).

    Article  ADS  Google Scholar 

  28. Rechtsman, M. C. et al. Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures. Nat. Photon. 7, 153–158 (2013).

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

    Article  ADS  Google Scholar 

  30. Dunlap, D. H. & Kenkre, V. M. Dynamic localization of a charged particle moving under the influence of an electric field. Phys. Rev. B 34, 3625–3633 (1986).

    Article  ADS  Google Scholar 

  31. Longhi, S. et al. Observation of dynamic localization in periodically curved waveguide arrays. Phys. Rev. Lett. 96, 243901 (2006).

    Article  ADS  Google Scholar 

  32. Garanovich, I. L. et al. Diffraction control in periodically curved two-dimensional waveguide arrays. Opt. Express 15, 9737–9747 (2007).

    Article  ADS  Google Scholar 

  33. Szameit, A. et al. Polychromatic dynamic localization in curved photonic lattices. Nat. Phys. 5, 271–275 (2009).

    Article  Google Scholar 

  34. Szameit, A. et al. Observation of two-dimensional dynamic localization of light. Phys. Rev. Lett. 104, 223903 (2010).

    Article  ADS  Google Scholar 

  35. Li, E., Eggleton, B. J., Fang, K. & Fan, S. Photonic Aharonov–Bohm effect in photon–phonon interactions. Nat. Commun. 5, 3225 (2014).

    Article  ADS  Google Scholar 

  36. Tzuang, L. D., Fang, K., Nussenzveig, P., Fan, S. & Lipson, M. Non-reciprocal phase shift induced by an effective magnetic flux for light. Nat. Photon. 8, 701–705 (2014).

    Article  ADS  Google Scholar 

  37. Fang, K. & Fan, S. Controlling the flow of light using the inhomogeneous effective gauge field that emerges from dynamic modulation. Phys. Rev. Lett. 111, 203901 (2013).

    Article  ADS  Google Scholar 

  38. Yuan, L., Shi, Y. & Fan, S. Photonic gauge potential in a system with a synthetic frequency dimension. Opt. Lett. 41, 741–744 (2016).

    Google Scholar 

  39. Harari, G. et al. Topological insulator laser: theory. Science 359, eaar4003 (2018).

    Article  Google Scholar 

  40. Bandres, M. A. et al. Topological insulator laser: experiments. Science 359, eaar4005 (2018).

    Article  Google Scholar 

  41. Plotnik, Y. et al. Experimental observation of optical bound states in the continuum. Phys. Rev. Lett. 107, 183901 (2011).

    Article  ADS  Google Scholar 

  42. Hsu, C. W. et al. Observation of trapped light within the radiation continuum. Nature 499, 188–191 (2013).

    Article  ADS  Google Scholar 

  43. Longhi, S. & Valle, G. D. Floquet bound states in the continuum. Sci. Rep. 3, 2219 (2013).

    Article  Google Scholar 

  44. Hsu, C. W., Zhen, B., Stone, A. D., Joannopoulos, J. D. & Soljačić, M. Bound states in the continuum. Nat. Rev. Mater. 1, 16048 (2016).

    Article  ADS  Google Scholar 

  45. Zhen, B., Hsu, C. W., Lu, L., Stone, A. D. & Soljačić, M. Topological nature of optical bound states in the continuum. Phys. Rev. Lett. 113, 257401 (2014).

    Article  ADS  Google Scholar 

  46. Lederer, F. et al. Discrete solitons in optics. Phys. Rep. 463, 1–126 (2008).

    Article  ADS  Google Scholar 

  47. Plotnik, Y. et al. Analogue of Rashba pseudo-spin–orbit coupling in photonic lattices by gauge field engineering. Phys. Rev. B 94, 020301(R) (2016).

    Article  ADS  Google Scholar 

  48. Mazor, Y., Hadad, Y. & Steinberg, B. Z. Planar one-way guiding in periodic particle arrays with asymmetric unit cell and general group-symmetry considerations. Phys. Rev. B 92, 125129 (2015).

    Article  ADS  Google Scholar 

  49. El-Ganainy, R. & Levy, M. Optical isolation in topological-edge-state photonic arrays. Opt. Lett. 40, 5275–5278 (2015).

    Article  ADS  Google Scholar 

  50. Szameit, A. & Nolte, S. Discrete optics in femtosecond-laser-written photonic structures. J. Phys. B At. Mol. Opt. Phys. 43, 163001 (2010).

    Article  ADS  Google Scholar 

  51. Heinrich, M. et al. Supersymmetric mode converters. Nat. Commun. 5, 3698 (2014).

    Article  Google Scholar 

  52. Tenenbaum Katan, Y. & Podolsky, D. Generation and manipulation of localized modes in Floquet topological insulators. Phys. Rev. B 88, 224106 (2013).

    Article  ADS  Google Scholar 

  53. Tenenbaum Katan, Y. & Podolsky, D. Modulated Floquet topological insulators. Phys. Rev. Lett. 110, 016802 (2013).

    Article  ADS  Google Scholar 

  54. Moiseyev, N. Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling. Phys. Rep. 302, 212–293 (1998).

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the German–Israeli DIP Program (grant no. BL 574/13-1), the United States Air Force Office of Scientific Research, the Deutsche Forschungsgemeinschaft (grants nos. SZ 276/9-1, SZ 276/19-1 and SZ 276/20-1) and an Advanced Grant from the European Research Council. The authors thank C. Otto for preparing the high-quality fused-silica samples used in all experiments presented here.

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All authors contributed significantly to this work.

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Correspondence to Mordechai Segev.

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Supplementary information

Supplementary Information

This file contains more information on the work, Supplementary Figures and descriptions of Supplementary Videos 1–3.

Supplementary Video 1

Movie of the experimentally measured profiles of the guiding behaviour of the array as a function of the kx momentum for waveguiding by artificial gauge fields in tilted arrays (Fig. 2a–c).

Supplementary Video 2

Movie of the experimentally measured profiles of the guiding behaviour of the array as a function of the kx momentum for waveguiding by artificial gauge fields in tilted arrays (Fig. 2d–f).

Supplementary Video 3

Movie of the experimentally measured profiles of the guiding behaviour of the array as a function of the kx momentum for waveguiding by phase-shifted artificial gauge fields (Fig. 4).

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Lumer, Y., Bandres, M.A., Heinrich, M. et al. Light guiding by artificial gauge fields. Nat. Photonics 13, 339–345 (2019). https://doi.org/10.1038/s41566-019-0370-1

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