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Photonic Topological Insulators

Photonic Topological Insulators. Y. Plotnik 1 , J.M. Zeuner 2 , M.C. Rechtsman 1 , Y. Lumer 1 , S. Nolte 2 , M. Segev 1 , A. Szameit 2. 1 Department of Physics, Technion – Israel Institute of Technology, Haifa, Israel

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Photonic Topological Insulators

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  1. Photonic Topological Insulators Y. Plotnik1, J.M. Zeuner2, M.C. Rechtsman1, Y. Lumer1, S. Nolte2, M. Segev1, A. Szameit2 1Department of Physics, Technion – Israel Institute of Technology, Haifa, Israel 2Institute of Applied Physics, Friedrich-Schiller-Universität, Jena, Germany

  2. Outline • What are Topological Insulators? • Topological protection of photons? • How can we get unidirectional edge states in photonics? Floquet! • Description of our experimental system: photonic lattices • First observation of topological insulators • -This is also the first observation of optical unidirectional • edge states in optics! • -Future directions

  3. What are Topological insulators? Magnetic field: Quantum Hall Effect Spin Orbit Interaction: Topological Insulator Regular insulator Conduction band Ef Unidirectional edge state Scattering protected Edge states • Main characteristics: • Edge conductance only • Immune to scattering/defects: • No back-scattering • No scattering into the bulk • Only for Topological insulators: • No need for external fields Valance band Kane and Mele, PRL (2005) Von Klitzing et al. PRL (1980)

  4. Motivation: No back scattering No back scattering → Robust Photon transport!

  5. Topological? Ef Ef

  6. Background: photonic topological protection by magnetic field For optical frequencies, magnetic response is weak Raghu, Haldane PRL (2008) Unidirectional edge state: Wang et. al. Nature (2009) Wang et. al., PRL (2008)

  7. We need a solution without a magnetic field Quantum hall No magnetic field Topological Insulator Kane and Mele, PRL (2005) von Klitzing et. al., PRL (1980) We need a type of Kane-Mele transition, but how, without Kramers’ degeneracy ? (1) Hafezi, Demler, Lukin, Taylor, Nature Phys. (2011): aperiodic coupled resonator system (2) Umucalilar and Carusotto, PRA (2011): using polarization as spin in PCs (3) Fang, Yu, Fan, Nature Photon. (2012): electrical modulation of refractive index in PCs (4) Khanikev et. al. Nature Mat. (2012): birefringent metamaterials

  8. Enter Floquet Topological Insulators We can explicitly break TR by modulating! Gu, Fertig, Arovas, Auerbach, PRL (2011). New Floquet eigenvalue equation: + Kitagawa, Berg, Rudner, Demler, PRB (2010). Lindner, Refael, Galitski, Nature Phys. (2011).

  9. Experimental system: photonic lattices Array of coupled waveguides Peleg et. al., PRL (2007) Paraxial approximation + + Maxwell Field envelope = Paraxial Schrödinger equation:

  10. Helical rotation induces a gauge field Coordinate Transformation Tight Binding Model (Peierls substitution) Paraxial Schrödinger equation +

  11. Graphene opens a Floquet gap for helical waveguides Band gap ky kx Edge states Top edge Bottom edge kxa kxa

  12. Experimental results: rectangular arrays Microscope image • No scattering from the corner • Armchair edge confinement

  13. “Time”-domain simulations

  14. Experimental results: group velocity vs. helix radius, R (e) R = 0µm (d) R = 6µm (a) (c) (b) R = 4µm R = 2µm R = 0µm (g) (j) (f) (h) (i) R =10µm R = 12µm R = 14µm R = 16µm R = 8µm b c d e f g h i j R =0 R =10µm R,

  15. Experimental results: triangular arrays with defects missing waveguide R = 8 µm z = 10cm

  16. Interactions: focusing nonlinearity gives solitons Band gap ky kx Y. Lumer et. al., (in preparation)

  17. Conclusion and Future work • First Optical Topological Insulator • First robust one way optical edge states (without any magnetic field!) • Future Work: - Non-scattering in optoelectronics - Topological cloak? - Disorder: Topological Anderson insulator? - What effect do interactions have on edge states? - many modes on-site.

  18. Acknowledgments Discussions: Daniel Podolsky

  19. Challenge of scaling down: Faraday effect is weak Largest Verdet constant (e.g. in TGG) is ~100 Faraday effect Optical wavelengths are the key to all nanophotonics applications The effect is too weak. We need another way!

  20. Theoretical proposals (1) Two copies of the QHE (2) Modulation to break TR Hafezi, Demler, Lukin, Taylor, Nature Phys. (2005). Fang, Yu, Fan, Nature Photon. (2012). Other theoretical papers in different systems: (3) Koch, Houck, Le Hur, Girvin, PRA (2010): cavity QED system (4) Umucalilar and Carusotto, PRA (2011): using spin as polarization in PCs (5) Khanikev et. al. Nature Mat. (2012): birefringent metamaterials

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