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Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures


Magnetic effects at optical frequencies are notoriously weak, so magneto-optical devices must be large to create a sufficient effect. In graphene, it has been shown that inhomogeneous strains can induce ‘pseudomagnetic fields’ that behave in a similar manner to real ones. Here, we show experimentally and theoretically that it is possible to induce such a field at optical frequencies in a photonic lattice. To our knowledge, this is the first realization of a pseudomagnetic field in optics. The field yields ‘photonic Landau levels’ separated by bandgaps in the spatial spectrum of the structured dielectric lattice. The gaps between these highly degenerate levels lead to transverse optical confinement. The use of strain allows for the exploration of magnetic-like effects in a non-resonant way that would be otherwise inaccessible in optics. It also suggests the possibility that aperiodic photonic-crystal structures can achieve greater field enhancement and slow-light effects than periodic structures via high density of states at the Landau levels. Generalizing these concepts to systems beyond optics, such as matter waves in optical potentials, offers new intriguing physics that is fundamentally different from that in purely periodic structures.

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Figure 1: Description of honeycomb photonic lattice and band structure.
Figure 2: Effect of strain on the eigenvalue spectrum of the honeycomb photonic lattice.
Figure 3: Experimental and simulation results for increasing strain.
Figure 4: Effect of a defect waveguide on beam confinement.


  1. 1

    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).

    ADS  Article  Google Scholar 

  2. 2

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

    ADS  Article  Google Scholar 

  3. 3

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

    ADS  Article  Google Scholar 

  4. 4

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

    ADS  Article  Google Scholar 

  5. 5

    Cai, W. & Shalaev, V. Optical Metamaterials: Fundamentals and Applications (Springer, 2009).

    Google Scholar 

  6. 6

    Plum, E. et al. Metamaterials: optical activity without chirality. Phys. Rev. Lett. 102, 113902 (2009).

    ADS  Article  Google Scholar 

  7. 7

    Kane, C. L. & Mele, E. J. Size, shape, and low energy electronic structure of carbon nanotubes. Phys. Rev. Lett. 78, 1932–1935 (1997).

    ADS  Article  Google Scholar 

  8. 8

    Guinea, F., Katsnelson, M. I. & Geim, A. K. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nature Phys. 6, 30–33 (2010).

    ADS  Article  Google Scholar 

  9. 9

    Peleg, O. et al. Conical diffraction and gap solitons in honeycomb photonic lattices. Phys. Rev. Lett. 98, 103901 (2007).

    ADS  Article  Google Scholar 

  10. 10

    Bahat-Treidel, O., Peleg, O. & Segev, M. Symmetry breaking in honeycomb photonic lattices. Opt. Lett. 33, 2251–2253 (2008).

    ADS  Article  Google Scholar 

  11. 11

    Bahat-Treidel, O. & Segev, M. Nonlinear wave dynamics in honeycomb lattices. Phys. Rev. A 84, 021802(R) (2011).

    ADS  Article  Google Scholar 

  12. 12

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

  13. 13

    Ablowitz, M. J., Nixon, S. D. & Zhu, Y. Conical diffraction in honeycomb lattices. Phys. Rev. A 79, 053830 (2009).

    ADS  Article  Google Scholar 

  14. 14

    Soljačić, M. & Joannopoulos, J. D. Enhancement of nonlinear effects using photonic crystals. Nature Mater. 3, 211–219 (2004).

    ADS  Article  Google Scholar 

  15. 15

    Molina, M. I. & Kivshar, Y. S. Discrete and surface solitons in photonic graphene nanoribbons. Opt. Lett. 35, 2895–2897 (2010).

    ADS  Article  Google Scholar 

  16. 16

    Birks, T. A., Knight, J. C. & Russell, P. S. J. Endlessly single-mode photonic crystal fiber. Opt. Lett. 22, 961–963 (1997).

    ADS  Article  Google Scholar 

  17. 17

    Christodoulides, D. N. & Joseph, R. I. Discrete self-focusing in nonlinear arrays of coupled waveguides. Opt. Lett. 13, 794–796 (1988).

    ADS  Article  Google Scholar 

  18. 18

    Fleischer, J. W., Segev, M., Efremidis, N. K. & Christodoulides, D. N. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature 422, 147–150 (2003).

    ADS  Article  Google Scholar 

  19. 19

    Eisenberg, H. S., Silberberg, Y., Morandotti, R., Boyd, A. R. & Aitchison, J. S. Discrete spatial optical solitons in waveguide arrays. Phys. Rev. Lett. 81, 3383–3386 (1998).

    ADS  Article  Google Scholar 

  20. 20

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

    ADS  Article  Google Scholar 

  21. 21

    Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007).

    ADS  Article  Google Scholar 

  22. 22

    Makris, K. G., Suntsov, S., Christodoulides, D. N., Stegeman, G. I. & Hache, A. Discrete surface solitons. Opt. Lett. 30, 2466–2468 (2005).

    ADS  Article  Google Scholar 

  23. 23

    Malkova, N., Hromada, I., Wang, X., Bryant, G. & Chen, Z. Observation of optical Shockley-like surface states in photonic superlattices. Opt. Lett. 34, 1633–1635 (2009).

    ADS  Article  Google Scholar 

  24. 24

    Longhi, S. Quantum-optical analogies using photonic structures. Laser Photon. Rev. 3, 243–261 (2009).

    ADS  Article  Google Scholar 

  25. 25

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

    ADS  Article  Google Scholar 

  26. 26

    Bahat-Treidel, O. et al. Klein tunneling in deformed honeycomb lattices. Phys. Rev. Lett. 104, 063901 (2010).

    ADS  Article  Google Scholar 

  27. 27

    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).

    ADS  Article  Google Scholar 

  28. 28

    Bravo-Abad, J., Joannopoulos, J. D. & Soljačić, M. Enabling single-mode behavior over large areas with photonic Dirac cones. Proc. Natl Acad. Sci. USA 109, 9761–9765 (2012).

    ADS  Article  Google Scholar 

  29. 29

    Yu, Z. & Fan, S. Complete optical isolation created by indirect interband photonic transitions. Nature Photon. 3, 91–94 (2009).

    ADS  Article  Google Scholar 

  30. 30

    Stone, M. Quantum Hall Effect (World Scientific, 1992).

    Google Scholar 

  31. 31

    Kohmoto, M. & Hasegawa, Y. Zero modes and edge states of the honeycomb lattice. Phys. Rev. B 76, 205402 (2007).

    ADS  Article  Google Scholar 

  32. 32

    Lodahl, P. et al. Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals. Nature 430, 654–657 (2004).

    ADS  Article  Google Scholar 

  33. 33

    Johnson, S. G., Fan, S., Villeneuve, P. R., Joannopoulos, J. D. & Kolodziejski, L. A. Guided modes in photonic crystal slabs. Phys. Rev. B 60, 5751–5758 (1999).

    ADS  Article  Google Scholar 

  34. 34

    Purcell, E. Spontaneous emission probabilities at radio frequencies. Phys. Rev. 69, 681 (1946).

    Article  Google Scholar 

  35. 35

    Akhmerov, A. R. & Beenakker, C. W. J. Boundary conditions for Dirac fermions on a terminated honeycomb lattice. Phys. Rev. B 77, 085423 (2008).

    ADS  Article  Google Scholar 

  36. 36

    Ruter, C. E. et al. Observation of parity-time symmetry in optics. Nature Phys. 6, 192–195 (2010).

    ADS  Article  Google Scholar 

  37. 37

    Guo, A. et al. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009).

    ADS  Article  Google Scholar 

  38. 38

    Kottos, T. Optical physics: broken symmetry makes light work. Nature Phys. 6, 166–167 (2010).

    ADS  Article  Google Scholar 

  39. 39

    Makris, K. G., El-Ganainy, R., Christodoulides, D. N. & Musslimani, Z. H. Beam dynamics in PT symmetric optical lattices. Phys. Rev. Lett. 100, 103904 (2008).

    ADS  Article  Google Scholar 

  40. 40

    Klaiman, S., Günther, U. & Moiseyev, N. Visualization of branch points in PT-symmetric waveguides. Phys. Rev. Lett. 101, 080402 (2008).

    ADS  MathSciNet  Article  Google Scholar 

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M.C.R. acknowledges the Azrieli Foundation for the award of an Azrieli fellowship. A.S. acknowledges support from the German Ministry of Education and Research (Center for Innovation Competence programme, grant 03Z1HN31). M.S. acknowledges support from the Israel Science Foundation, the USA–Israel Binational Science Foundation, and the Advanced Grant by the European Research Council.

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M.C.R. and J.M.Z. contributed equally. All authors contributed significantly.

Corresponding author

Correspondence to Mikael C. Rechtsman.

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The authors declare no competing financial interests.

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Rechtsman, M., Zeuner, J., Tünnermann, A. et al. Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures. Nature Photon 7, 153–158 (2013).

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