1. Plasmonic vector near-field for composite interference, SPP switch and optical simulator
Tao Li（李涛）
National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences Nanjing University
KITPC, Beijing,

2. Outline Introduction Plasmonic switch by composite interference
Plasmonic simulator for condensed matter physics
Conclusion

3. Introduction Surface Plasmon Polariton (SPP)
Vectorial configuration of SPP field
Sub-wavelength
Field enhancement

4. Polarization converter Polarized active display
Near-field interference
Chiral SPP in nanowire
Metasufaces and Berry phase

5. Part I Plasmonic switch by composite interference

6. Interference Far field to near field Classical to quantum
Michelson interference
Unidirectional excitation of SPP
Science 340, 328 (2013)
Quantum interference and quantum walk
PRL 108, (2012)
Far field to near field
Classical to quantum

7. Plasmonic logical gates
Plasmonic nanowire system
Prof. Xu HX group,
Nat. Comm. 2, 387 (2011)
Slot SPP waveguide
Prof. Gong QH group,
Nano Lett. 12, 5784 (2012)

8. For in-plane SPP Degiorgio relation, δL+δR=π unidirectional beam,
Appl. Phys. Lett. 81, 1762 (2002)
Degiorgio relation, δL+δR=π unidirectional beam,
In symmetric system，δL=δR=π/2
透反干涉 T-R interference
With a phase difference of π/2，
Beam will be selectively routed to either right or left  “switch”!

9. In-plane SPP switch
For external modulation

10. Interference result input output
25 micro
input
Port II
Port I
III
output IV
An ~80% interference depth is achieved

11. Interference within waveguides
6 micro
Switch between two outputs

12. Influence of waveguides width
Anti-synchronous
Shift! Why?

13. Possible explanation How to verify it? Remove the BS
to eliminate T-R part
T-R干涉
Field superposition
How to verify it?
Synchronous interference
No interference!?

14. Synchronous interference!
There must have some structures inside the cross region! Bragg grating  slit
Synchronous interference!
Reflection is
suppressed

15. Field superposition interference
In the case of non-reflection,
how does interference take place?
Dependence to the strip width
(simulation results)

16. Simulation results
constructive
distructive

17. Explanation – mode width
Constructive interference Ez
E//

18. Further confirmation
w=2 um

19. Field superposition interfer
Theoretical model
T-R proportion
T-R interfer
Field superposition interfer

20. Functionality

21. Summary – part I
Compact SPP switch is achieved based on the composite interference.
Two kinds of interferences are exploited in waveguide system.
Vector field in slit-waveguide plays an important role.
Laser & Photonics Reviews 8, L47 (2014) (DOI: /lpor )

22. Part II Plasmonic simulator for condensed matter physics

23. Background Plasmonic waveguides Waveguide array (lattice)
Guiding the light
Waveguide array (lattice)
Simulating quantum and condensed matter Physics
OE (2010)
Nature Common (2013)
Nature (2007)

24. (a) Simulation of massless Dirac Fermion
Coupled mode equation in binary waveguide array
Dispersion equation:
Hamiltonian:
Dirac Hamiltonian:
massless
m=0

25. Linear dispersion
Non-dispersive splitting of optical wave

26. positive/negative coupling
OE 35,11 (2010)
PRL 109,023602(2012)
APL 103,141101(2013) w h g
Vector field

27. Design and calculation
parameters：lambda=633nm
width=60nm
height=120nm
gap1=67nm
gap2=146nm
kappa=0.0177/

28. optimization
kappa=0.0177/
60 nm
100 nm
kappa= /

29. (b) Topologically protected interface state in PWAs
SSH model
polyethylene chain
Topological soliton: lower energy (< bulk mode) fractional charge robust against disorder
soliton

30. S0 S1 S2 Coupled waveguide system: bonds  coupling strength
defectless S0
strong coupled defect S1
kink
weak coupled defect S2
As we know the couple optical waveguides can be described by the coupled mode equation, which has the same mathematic form as the TBA of the PolyXXX chain. And the strong and weak coupling strength can be easily obtained in plasmonic waveguides by tuning the structure parameters to mimic double and single bonds respectively. So, it is reasonable to extent the SSH model to the Plasmonic waveguide system. Here, we define the binary periodic waveguide array as S0, two strong coupling defect as S1, and two weak coupling as S2.
anti-kink
strong Coupling
Weak Coupling

31. Plasmonic counterpart
Top view
Input
Simulation
Width=300nm
Output
Coupling coefficient
C1=0.188 , C2=

32. Experiment Results ? S0 S1 S2

33. Theory analysis S0 S1 S2 Notes: Excitation: Wave Packet
Number: 79 Structure: S0, S1, S2 S0 S1 S2

34. Band structure and zero mode
eigenvalue
eigenvector

35. As With the S1, S2 Also Processes the Topological Properties.
Gaussians1
Gaussians2
realistic excitation

36. Excitation Conditions
Eigen mode
Amplitude
Resultant
Mode Symmetry
Eigen State ↓
Amplitude Profile
Resultant Mode S1 S2

37. S1 S2
Here, the blue lines are the subtracted modes and red lines are the corresponding eigen modes. We will find the subtracted mode profile of S1 is rightly the half of the eigen mode, indicating a large information of the eigen mode is preserved. But for S2, the subtracted one greatly differs from the eigen mode, which predicts the loss of the interface state.

38. Robustness S1 S2 Introduce randomness in coupling strengths C1 and C2
Eigen mode
Amplitude
Amplitude with loss S1
Introduce randomness in coupling strengths C1 and C2
Now, we have realized the major point that why S2 structure does not demonstrate an interface mode in the realistic excitation of one waveguide input. Nevertheless, it topological property should be checked by analyzing its robustness against the disorders. Here, in our calculations, random disorders in structural parameters are introduced with respect different excitations, as results shown in the figures. We will find pure eigen mode for both samples are preserved in good localization, indicating the topological protection. As expected, for the amplitude excitation, only the S1 demonstrate the robustness. In experiments, the fabrication accuracy is about 10 nm, which means a randomly introduced disorders are evitable. The detected results of S1 is stable with localized outputs, but varies for S2 samples. So, It is well confirmed by our experiments. S2

39. Experimental evidences
topological property ↔ robust against disorder
Laser & Photonics Reviews 9, 392 (2015) (DOI /lpor )

40. Summary – Part II
Alternative coupling coefficients are modeled in the plasmonic ridge waveguide arrays, demonstrating the linear dispersion of massless Dirac Fermion.
SSH model is simulated in PWA system with an in-depth understanding of the topological interface state, and the influence of the excitation condition.

41. Conclusion
Vector field of SPP plays an important role in wave guiding

42. Thank you! Acknowledgement
Yulin Wang, Qingqing Cheng, Beibei Xu, S.N. Zhu
Grants: NSFC, 973 Project
Thank you!