Nanoscale optical energy focusing using plasmonic structures is crucial for many applications, such as imaging and lithography. Thermal management for these nanostructures is of great importance to maintain their reliabilities but has not been investigated extensively yet, especially when the strong nonlocalities present in the nanostructures. Here, we report a multiphysics model to study the coupled optical and thermal responses of plasmonic nanofocusing structures. We applied the hydrodynamic Drude model to describe the nonlocality in the optical response and derived ballistic–diffusive equations for both electrons and phonons to model the nonlocal thermal transport. Strong nonlocal optothermal responses were observed.

References

References
1.
Schuller
,
J. A.
,
Barnard
,
E. S.
,
Cai
,
W. S.
,
Jun
,
Y. C.
,
White
,
J. S.
, and
Brongersma
,
M. L.
,
2010
, “
Plasmonics for Extreme Light Concentration and Manipulation
,”
Nat. Mater.
,
9
(
3
), pp.
193
204
.10.1038/nmat2630
2.
Giugni
,
A.
,
Torre
,
B.
,
Toma
,
A.
,
Francardi
,
M.
,
Malerba
,
M.
,
Alabastri
,
A.
,
Zaccaria
,
R. P.
,
Stockman
,
M. I.
, and
Di Fabrizio
,
E.
,
2013
, “
Hot-Electron Nanoscopy Using Adiabatic Compression of Surface Plasmons
,”
Nat. Nanotechnol.
,
8
(
11
), pp.
845
852
.10.1038/nnano.2013.207
3.
Kawata
,
S.
,
Inouye
,
Y.
, and
Verma
,
P.
,
2009
, “
Plasmonics for Near-Field Nano-Imaging and Superlensing
,”
Nat. Photonics
,
3
(
7
), pp.
388
394
.10.1038/nphoton.2009.111
4.
Luchowski
,
R.
,
Calander
,
N.
,
Shtoyko
,
T.
,
Apicella
,
E.
,
Borejdo
,
J.
,
Gryczynski
,
Z.
, and
Gryczynski
,
I.
,
2010
, “
Plasmonic Platforms of Self-Assembled Silver Nanostructures in Application to Fluorescence
,”
J. Nanophotonics
,
4
(
1
), p.
043516
.10.1117/1.3500463
5.
Bai
,
W. L.
,
Gan
,
Q. Q.
,
Song
,
G. F.
,
Chen
,
L. H.
,
Kafafi
,
Z.
, and
Bartoli
,
F.
,
2011
, “
Double Plasmonic Structure Design for Broadband Absorption Enhancement in Molecular Organic Solar Cells
,”
J. Photonics Energy
,
1
(
1
), p.
011121
.10.1117/1.3585876
6.
Fort
,
E.
, and
Grésillon
,
S.
,
2008
, “
Surface Enhanced Fluorescence
,”
J. Phys. D: Appl. Phys.
,
41
(
1
), p.
013001
.10.1088/0022-3727/41/1/013001
7.
Kumar
,
G. V. P.
,
2012
, “
Plasmonic Nano-Architectures for Surface Enhanced Raman Scattering: A Review
,”
J. Nanophotonics
,
6
(
1
), p.
064503
.10.1117/1.JNP.6.064503
8.
Zhou
,
N.
,
Kinzel
,
E. C.
, and
Xu
,
X. F.
,
2011
, “
Nanoscale Ridge Aperture as Near-Field Transducer for Heat-Assisted Magnetic Recording
,”
Appl. Opt.
,
50
(
31
), pp.
G42
G46
.10.1364/AO.50.000G42
9.
Pan
,
L.
, and
Bogy
,
D. B.
,
2009
, “
Heat-Assisted Magnetic Recording
,”
Nat. Photonics
,
3
(
4
), pp.
189
190
.10.1038/nphoton.2009.40
10.
Chao
,
I.
,
Pan
,
L.
,
Sun
,
C.
,
Zhang
,
X.
, and
Lavine
,
A.
,
2013
, “
A Coupled Electromagnetic and Thermal Model for Picosecond and Nanometer Scale Plasmonic Lithography Process
,”
ASME J. Micro Nano Manuf.
,
2
(
3
), p.
031003
.10.1115/1.4027589
11.
Pan
,
L.
,
Park
,
Y.
,
Xiong
,
Y.
,
Ulin-Avila
,
E.
,
Wang
,
Y.
,
Zeng
,
L.
,
Xiong
,
S. M.
,
Rho
,
J.
,
Sun
,
C.
,
Bogy
,
D. B.
, and
Zhang
,
X.
,
2011
, “
Maskless Plasmonic Lithography at 22 nm Resolution
,”
Sci. Rep.
,
1
, pp.
175
180
.10.1038/srep00175
12.
Ozbay
,
E.
,
2006
, “
Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions
,”
Science
,
311
(
5758
), pp.
189
193
.10.1126/science.1114849
13.
Verhagen
,
E.
,
Kuipers
,
L. K.
, and
Polman
,
A.
,
2010
, “
Plasmonic Nanofocusing in a Dielectric Wedge
,”
Nano Lett.
,
10
(
9
), pp.
3665
3669
.10.1021/nl102120p
14.
Choi
,
H.
,
Pile
,
D. F.
,
Nam
,
S.
,
Bartal
,
G.
, and
Zhang
,
X.
,
2009
, “
Compressing Surface Plasmons for Nano-Scale Optical Focusing
,”
Opt. Express
,
17
(
9
), pp.
7519
7524
.10.1364/OE.17.007519
15.
Baffou
,
G.
, and
Quidant
,
R.
,
2013
, “
Thermo-Plasmonics: Using Metallic Nanostructures as Nano-Sources of Heat
,”
Laser Photonics Rev.
,
7
(
2
), pp.
171
187
.10.1002/lpor.201200003
16.
Farahi
,
R. H.
,
Passian
,
A.
,
Ferrell
,
T. L.
, and
Thundat
,
T.
,
2005
, “
Marangoni Forces Created by Surface Plasmon Decay
,”
Opt. Lett.
,
30
(
6
), pp.
616
618
.10.1364/OL.30.000616
17.
Qiu
,
T. Q.
, and
Tien
,
C. L.
,
1993
, “
Heat Transfer Mechanisms During Short-Pulse Laser Heating of Metals
,”
ASME J. Heat Transfer
,
115
(
4
), pp.
835
841
.10.1115/1.2911377
18.
Qiu
,
T. Q.
, and
Tien
,
C. L.
,
1994
, “
Femtosecond Laser Heating of Multi-Layer Metals—I. Analysis
,”
Int. J. Heat Mass Transfer
,
37
(
17
), pp.
2789
2797
.10.1016/0017-9310(94)90396-4
19.
Chen
,
J. K.
, and
Beraun
,
J. E.
,
2001
, “
Numerical Study of Ultrashort Laser Pulse Interactions With Metal Films
,”
Numer. Heat Transfer, Part A
,
40
(
1
), pp.
1
20
.
20.
Chen
,
J. K.
,
Beraun
,
J. E.
, and
Tham
,
C. L.
,
2003
, “
Investigation of Thermal Response Caused by Pulse Laser Heating
,”
Numer. Heat Transfer, Part A
,
44
(
7
), pp.
705
722
.10.1080/716100520
21.
Baffou
,
G.
,
Quidant
,
R.
, and
Girard
,
C.
,
2009
, “
Heat Generation in Plasmonic Nanostructures: Influence of Morphology
,”
Appl. Phys. Lett.
,
94
(
15
), p.
153109
.10.1063/1.3116645
22.
Coppens
,
Z. J.
,
Li
,
W.
,
Walker
,
D. G.
, and
Valentine
,
J. G.
,
2013
, “
Probing and Controlling Photothermal Heat Generation in Plasmonic Nanostructures
,”
Nano Lett.
,
13
(
3
), pp.
1023
1028
.10.1021/nl304208s
23.
Ciraci
,
C.
,
Hill
,
R. T.
,
Mock
,
J. J.
,
Urzhumov
,
Y.
,
Fernandez-Dominguez
,
A. I.
,
Maier
,
S. A.
,
Pendry
,
J. B.
,
Chilkoti
,
A.
, and
Smith
,
D. R.
,
2012
, “
Probing the Ultimate Limits of Plasmonic Enhancement
,”
Science
,
337
(
6098
), pp.
1072
1074
.10.1126/science.1224823
24.
Wiener
,
A.
,
Fernandez-Dominguez
,
A. I.
,
Horsfield
,
A. P.
,
Pendry
,
J. B.
, and
Maier
,
S. A.
,
2012
, “
Nonlocal Effects in the Nanofocusing Performance of Plasmonic Tips
,”
Nano Lett.
,
12
(
6
), pp.
3308
3314
.10.1021/nl301478n
25.
Chen
,
G.
,
2001
, “
Ballistic–Diffusive Heat-Conduction Equations
,”
Phys. Rev. Lett.
,
86
(
11
), pp.
2297
2300
.10.1103/PhysRevLett.86.2297
26.
Yang
,
R. G.
,
Chen
,
G.
,
Laroche
,
M.
, and
Taur
,
Y.
,
2005
, “
Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic–Diffusive Equations and Phonon Boltzmann Equation
,”
ASME J. Heat Transfer
,
127
(
3
), pp.
298
306
.10.1115/1.1857941
27.
Hopkins
,
P. E.
, and
Stewart
,
D. A.
,
2009
, “
Contribution of D-Band Electrons to Ballistic Transport and Scattering During Electron–Phonon Nonequilibrium in Nanoscale Au Films Using an Ab Initio Density of States
,”
J. Appl. Phys.
,
106
(
5
), p.
053512
.10.1063/1.3211310
28.
Kanter
,
H.
,
1970
, “
Slow-Electron Mean Free Paths in Aluminum, Silver, and Gold
,”
Phys. Rev. B
,
1
(
2
), pp.
522
536
.10.1103/PhysRevB.1.522
29.
Kekatpure
,
R. D.
, and
Davids
,
P. S.
,
2011
, “
Channeling Light Into Quantum-Scale Gaps
,”
Phys. Rev. B
,
83
(
7
), p.
075408
.10.1103/PhysRevB.83.075408
30.
Esteban
,
R.
,
Borisov
,
A. G.
,
Nordlander
,
P.
, and
Aizpurua
,
J.
,
2012
, “
Bridging Quantum and Classical Plasmonics With a Quantum-Corrected Model
,”
Nat. Commun.
,
3
, pp.
825
833
.10.1038/ncomms1806
31.
Mayer
,
A.
,
Chung
,
M. S.
,
Lerner
,
P. B.
,
Weiss
,
B. L.
,
Miskovsky
,
N. M.
, and
Cutler
,
P. H.
,
2011
, “
Classical and Quantum Responsivities of Geometrically Asymmetric Metal–Vacuum–Metal Junctions Used for the Rectification of Infrared and Optical Radiations
,”
J. Vac. Sci. Technol.
,
29
(
4
), p.
041802
.10.1116/1.3599756
32.
Scholl
,
J. A.
,
Koh
,
A. L.
, and
Dionne
,
J. A.
,
2012
, “
Quantum Plasmon Resonances of Individual Metallic Nanoparticles
,”
Nature
,
483
(
7390
), pp.
421
427
.10.1038/nature10904
33.
Boardman
,
A. D.
,
1982
,
Electromagnetic Surface Modes
,
Wiley
,
New York
.
34.
Gramotnev
,
D. K.
, and
Vernon
,
K. C.
,
2007
, “
Adiabatic Nano-Focusing of Plasmons by Sharp Metallic Wedges
,”
Appl. Phys. B
,
86
(
1
), pp.
7
17
.10.1007/s00340-006-2387-7
35.
Choo
,
H.
,
Kim
,
M. K.
,
Staffaroni
,
M.
,
Seok
,
T. J.
,
Bokor
,
J.
,
Cabrini
,
S.
,
Schuck
,
P. J.
,
Wu
,
M. C.
, and
Yablonovitch
,
E.
,
2012
, “
Nanofocusing in A Metal–Insulator–Metal Gap Plasmon Waveguide With a Three-Dimensional Linear Taper
,”
Nat. Photonics
,
6
(
12
), pp.
837
843
.10.1038/nphoton.2012.277
36.
Stockman
,
M. I.
,
2004
, “
Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides
,”
Phys. Rev. Lett.
,
93
(
13
), p.
137404
.10.1103/PhysRevLett.93.137404
37.
Chen
,
G.
,
2002
, “
Ballistic–Diffusive Equations for Transient Heat Conduction From Nano to Macroscales
,”
ASME J. Heat Transfer
,
124
(
2
), pp.
320
328
.10.1115/1.1447938
38.
Toscano
,
G.
,
Raza
,
S.
,
Jauho
,
A. P.
,
Mortensen
,
N. A.
, and
Wubs
,
M.
,
2012
, “
Modified Field Enhancement and Extinction by Plasmonic Nanowire Dimers due to Nonlocal Response
,”
Opt. Express
,
20
(
4
), pp.
4176
4188
.10.1364/OE.20.004176
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