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?
Spin Orbit Interaction:
Topological Insulator
Scattering protected
Edge states
Kane and Mele, PRL (2005)
Magnetic field:
Quantum Hall Effect
Unidirectional
edge state
Von Klitzing et al. PRL (1980)
Valance band
Conduction band Ef
Regular insulator
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

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

5. Topological? Ef
Robust to small changes

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

7. Challenge of scaling down:
weak magnetic response

8. 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

9. 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).

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

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

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

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

14. “Time”-domain simulations

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

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

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

18. 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.

19. Acknowledgments
Discussions: Daniel Podolsky

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

21. (2) Modulation to break TR
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