Nanophotonics Class 2 - Surface Plasmon Polaritons
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Transcript of Nanophotonics Class 2 - Surface Plasmon Polaritons
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Nanophotonics
Class 2
Surface plasmon polaritons
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Surface plasmon polariton: EM wave at metal-dielectric interface
EM wave is coupled to the plasma oscillations of the surface charges
tzkxkidd
zxeEtzxE 0,,,
tzkxkimm
zxeEtzxE 0,),,(
For propagating bound waves:- kx is real- kz is imaginary
x
z
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Derivation of surface plasmon dispersion relation: k()
Wave equation:
Substituting SP wave + boundary conditions leads to the
Dispersion relation: 2/1
"'
dm
dmxxx c
ikkk
2,
2
,0,0,2
t
EE md
mdmdmd
x-direction:
ckNote: in regular dielectric:
2
k
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Dispersion relation:
2/1
"'
dm
dmxxx c
ikkk
x-direction:
Bound SP mode: kz imaginary: m + d < 0, kx real: m < 0
so: m < -d
2/12
,,, "'
dm
mmzmzmz c
ikkk
z-direction:
ck
2
k
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iim
Ne
E
Nex
E
P p
2
2
20
2
00
1111
0
2
m
Nep
Dielectric constant of metals
Drude model: conduction electrons with damping: equation of motion
with collision frequency and plasma frequency
If << p, then:
3
2
2
2
",1' pp
tieEdt
dxm
dt
xdm e02
2
no restoring force
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Measured data and model for Ag:
3
2
2
2
",1' pp
3
2
2
2
",' pp
Drude model:
Modified Drude model:
Contribution of bound electrons
Ag: 45.5
200 400 600 800 1000 1200 1400 1600 1800-150
-100
-50
0
50
Measured data: ' "
Drude model: ' "
Modified Drude model: '
"
Wavelength (nm)
'
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Bound SP modes: m < -d
200 400 600 800 1000 1200 1400 1600 1800-150
-100
-50
0
50
Measured data: ' "
Drude model: ' "
Modified Drude model: '
"
Wavelength (nm)
'
bound SP mode: m < -d
-d
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p
d
p
1
Re kx
real kx
real kz
imaginary kx
real kz
real kx
imaginary kz
d
xck
Bound modes
Radiative modes
Quasi-bound modes
Surface plasmon dispersion relation:
Dielectric: d
Metal: m = m' +
m"
x
z
'm > 0)
d < 'm < 0)
('m < d)
2/1
dm
dmx c
k
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Re kx
d
xck
Surface plasmons dispersion:
large k
small wavelength
Ar laser: vac = 488 nmdiel = 387 nmSP = 100 nmAg/SiO2
3.4 eV(360 nm)
X-ray wavelengthsat optical frequencies
2/1
dm
dmx c
k
2
k
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Surface plasmon dispersion for thin filmsDrude model
ε1(ω)=1-(ωp/ω) 2 Two modes appear
L-
L-(symm)
Thinner film:Shorter SP wavelength
Example:HeNe = 633 nm
SP = 60 nm
L+(asymm)
Propagationlengths: cm !!!(infrared)
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Cylindrical metal waveguides
k
E
z
rFundamentalSPP modeon cylinder:
E
• Can this adiabatic coupling scheme be realized in practice?
taper theory first demonstrated byStockman, PRL 93, 137404 (2004)
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Delivering light to the nanoscale
0.0 0.2 0.4 0.6 0.8 1.01.7
1.8
1.9
2.0
2.1
2.2
2.3
neff =
kSPP/k
0
Waveguide width (µm)
1 µm
1 µm
|E|Field symmetry at tip similar to SPP mode in conical waveguide
E
++++++
+
Ewold Verhagen, Kobus Kuipers
k
E
xz
nanoscaleconfinement
Optics Express 16, 45 (2008)
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Concentration of light in a plasmon taper: experiment
Ewold Verhagen, Kobus Kuipers
Au
Er
Al2O3
λ = 1.5 μm
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exc = 1490 nm
PL
Inte
nsi
ty (
counts
/s)
10 µm
Ewold Verhagen, Kobus Kuipers (1
49
0 n
m)
Er3+
ene
rgy
leve
ls
transmission
1 µm
60 nm apex diam.
Nano Lett. 7, 334 (2007)
Concentration of light in a plasmon taper: experiment
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550 nm
660 nm
• Detecting upconversion luminescence from the air side of the film (excitation of SPPs at substrate side)
Ewold Verhagen, Kobus Kuipers
Plasmonic hot-spot
Optics Express 16, 45 (2008)
k
E
xz
Theory: Stockman, PRL 93, 137404 (2004)
Concentration of light in a plasmon taper: experiment
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FDTD Simulation: nanofocussing to < 100 nm
z = -35 nm
• Nanofocusing predicted: 100 x |E|2 at 10 nm from tip
• 3D subwavelength confinement: 1.5 µm light focused to 92 nm (/16)
• limited by taper apex (r=30 nm)
n1 = 1
n2 = 1.74
1 µm
1 µm
|E|2
starttip
+ ++++++
E
Ewold Verhagen, Kobus Kuipers
Optics Express 16, 45 (2008)
sym asym
Et, H
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Coaxial MIM plasmon waveguides
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FIB milling of coaxial waveguides
100 nm 100 nm
• Silica substrates with 250-500 nm thick Ag
• Ring width: 50-100 nm
• Two-step milling process
• ~7° taper angle
<w>=100 nm, L=485 nm <w>=50 nm, L=485 nm
René de Waele, Stanley BurgosNano Lett. 9, in press (2009)
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Narrow channels show negative index
• Excitation above resonance, >sp
• 25 nm-wide channel in Ag filled with GaP
• Simulation shows negative phase velocity with respect to power flow
• Negative refractive index of -2
René de Waele, Stanley Burgos
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Positive and negative index modes
René de Waele, Stanley Burgos
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Plasmonic toolbox: , (), d - Engineer ()
0 200 400 600 800 1000
-1.0
-0.5
0.0
0.5
1.0
Y A
xis
Titl
e
Distance (nm)
thin section
Plasmonic concentrator Plasmonic lens
Plasmonic multiplexer
And much more …..
Plasmonic integrated circuits
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Conclusions: surface plasmon polariton
Surface plasmon: bound EM wave at metal-dielectric interface
Dispersion: (k) diverges near the plasma resonance: large k, small
Control dispersion: control (k), losses, concentration
Manipulate light at length scalesbelow the diffraction limit