CLEO-PR graphene

1. 1idc.sutd.edu.sg
Giant All-optical Nonlinear Switching in Graphene
Plasmonic Waveguides
Kelvin J. A. Ooi
Postdoctoral Research Fellow
SUTD-MIT International Design Centre
Singapore University of Technology and Design
for CLEO-PR 2017
2 August 2017

2. 22
1. Optical Properties of Graphene
2. All-optical nonlinear graphene
plasmonics
1. Electronic Scattering in nonlinear
graphene plasmonics
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Contents

3. 33
• Graphene possesses a 2-D optical conductivity which
is described by the Kubo formula [L. A. Falkovsky, J.
Phys.: Conf. Ser. 129 (2008)]
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Linear optical properties
( ) ( )
[ ]
[ ] ( ) 















+−+
++
−







 −+
++
















+








−+
+
=
−
22
2
2
221
2
1
2
2
1
22)(
2)(
ln
22
2)(
tan5.0
4
1exp2ln
2)(
2
)(
TkEi
Eii
Tk
Eiie
Tk
E
Tk
E
i
Tkie
BF
F
B
F
B
F
B
FB
νω
νω
π
νω
νωπ
ωσ





4. 44
• In graphene, due to high β and low
ω, nplasmon can range from 40 – 70
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Basics: Wave-vector, extreme confinement
4

5. 55
• Note: 3.8ps pulse
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High nonlinearity in graphene

6. 66idc.sutd.edu.sg
0.25eV

7. 7idc.sutd.edu.sg
All optical switching on graphene plasmonic
waveguides

8. 88idc.sutd.edu.sg
All optical switching in graphene plasmonic
waveguides
Plasmon signal
Cross-phase modulation:
Top illumination
Cross-phase modulation:
Co-propagating pump
Self-phase modulation

9. 99idc.sutd.edu.sg
Nonlinearity of graphene
• Nonlinear index data in the mid-IR
(from J. L. Cheng and J. E. Sipe)

10. 1010
• Nonlinear plasmon index scales
inversely proportional to Fermi-
level.
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Nonlinear Plasmon index, real and
imaginary

11. 1111
• Nonlinear enhancement scales as a factor
of 4n4
, where n is the plasmon index.
• Since plasmon index is in range of 2 orders
(typically 40 – 70), the enhancement is in
the order of 106
– 107
.
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Surface-induced Nonlinear Enhancement

12. 1212
• Extremely high phase and loss
modulation is achieved with intensities
only in the range of MW/cm2
• Loss modulation performance is better
by 1 order
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Phase Change and Loss Change
10 15 20 25 30
1.00
1.25
1.50
1.75
2.00
2.25
2.50
10 15 20 25 30
1.00
1.25
1.50
1.75
2.00
2.25
2.50
00.025000.050000.075000.10000.12500.15000.17500.20000.22500.25000.27500.30000.32500.35000.37500.40000.42500.45000.47500.50000.52500.55000.57500.60000.62500.65000.67500.70000.72500.75000.77500.80000.82500.85000.87500.90000.92500.95000.97501.0001.0251.0501.0751.1001.1251.1501.1751.2001.2251.2501.2751.3001.3251.3501.3751.4001.4251.4501.4751.5001.5251.5501.5751.6001.6251.6501.6751.7001.7251.7501.7751.8001.8251.8501.8751.9001.9251.9501.9752.0002.0252.0502.0752.1002.1252.1502.1752.2002.2252.2502.2752.3002.3252.3502.3752.4002.4252.4502.4752.500
0
2.00
1.50
2.00π
1.75π
1.50π
1.25π
1.00π
0.75π
∆φ (π)
1.00
Intensity(MW/cm
2
)
Wavelength (µm)
0.50
>2.50
EF
=0.1eV
10 15 20 25 30
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
10 15 20 25 30
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
-90%
-80%
-70%
-60%
Intensity(MW/cm
2
)
Wavelength (µm)
-100.0-99.67-99.33-99.00-98.67-98.33-98.00-97.67-97.33-97.00-96.67-96.33-96.00-95.67-95.33-95.00-94.67-94.33-94.00-93.67-93.33-93.00-92.67-92.33-92.00-91.67-91.33-91.00-90.67-90.33-90.00-89.67-89.33-89.00-88.67-88.33-88.00-87.67-87.33-87.00-86.67-86.33-86.00-85.67-85.33-85.00-84.67-84.33-84.00-83.67-83.33-83.00-82.67-82.33-82.00-81.67-81.33-81.00-80.67-80.33-80.00-79.67-79.33-79.00-78.67-78.33-78.00-77.67-77.33-77.00-76.67-76.33-76.00-75.67-75.33-75.00-74.67-74.33-74.00-73.67-73.33-73.00-72.67-72.33-72.00-71.67-71.33-71.00-70.67-70.33-70.00-69.67-69.33-69.00-68.67-68.33-68.00-67.67-67.33-67.00-66.67-66.33-66.00-65.67-65.33-65.00-64.67-64.33-64.00-63.67-63.33-63.00-62.67-62.33-62.00-61.67-61.33-61.00-60.67-60.33-60.00-59.67-59.33-59.00-58.67-58.33-58.00-57.67-57.33-57.00-56.67-56.33-56.00-55.67-55.33-55.00-54.67-54.33-54.00-53.67-53.33-53.00-52.67-52.33-52.00-51.67-51.33-51.00-50.67-50.33-50.00
∆α/α (%)
-90
-80
-70
-60
-50
EF
=0.1eV
∆α/α (%)
-100
-50%

13. 13idc.sutd.edu.sg
Electronic scattering on nonlinear graphene plasmonic
waveguides

14. 1414
• A high-velocity electron travelling parallel/non-
touching trajectory and near to a metal surface
can excite surface plasmon polaritons.
• [J. Lecante, Y. Ballu, and D. M. Newns, Phys.
Rev. Lett. 38, 36–40 (1977)].
• The main excitation occurs at the intersection
of the electron velocity line and the SPP
dispersion line.
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Aloof-scattering of free electrons can
generate SPP

15. 1515
• The loss probability for aloof-
scattering excitation is given as [F. J.
Garcia de Abajo, Rev. Mod. Phys. 82,
209 (2010)]
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Loss probability and loss
function
( ) 





⋅





⋅=Γ
d
p
SP
r
v
z
K
v
Le
εε
ω
π
ω
0
02
2
Im
22

Electron velocity term,
measures how readily
the electron is able to
transfer energy per unit
trajectory
Impact parameter term, measures
distance- and momentum-dependent
interaction between electron and
sample
Loss-function term,
measures how readily
the material is able to
accept energy transfer

16. 1616idc.sutd.edu.sg
Performance of graphene vs.
metals

17. 1717
• 1 electron travelling at 0.01c
(25.6eV) 10nm above graphene
(0.2eV Fermi level)
Total induced E-fields
and nonlinear modulation
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0.0 1.0 2.0 3.0 4.0
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0 4.71x1014
3.17x1014
×1014
×108
Graphene, 0.2eV
Graphene, Modulated
v = 0.01c
AngularFrequency,ω(Hz)
Wave Vector, k (m-1
)
3.17x10
14
4.72x10
14
0.0 1.0 2.0 3.0 4.0 5.0 6.0
0
2
4
6
8
10
12
×10
14
LossProbability,ΓSP
Angular Frequency, ω (Hz)
×10
-23

18. 1818
Phase and Loss Modulation
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0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0
2
4
6
8
10
PhaseModulation(π)
Angular Frequency, ω (Hz)
2 3 4 5
0
100
200
300
400
500
×1014
PhaseModulation(π)
Angular Frequency, ω (Hz)
×1014
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0
1
2
3
4
5
6
7
8
×1014
Modulation depth
Loss, modulatedLoss(db/µm)
Angular Frequency, ω (Hz)
Loss, 0.2eV
-100
-80
-60
-40
-20
0
ModulationDepth(%)

19. 19
Thank You!
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Acknowledgments:
SUTD-MIT IDC Grants, SUTD-ZJU
Collaboration
MOE ACRF Tier 2