optical scattering resonances of metal nano particles and
TRANSCRIPT
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Thomas Søndergaard
Department of Physics and Nanotechnology
Aalborg University, Denmark
Optical scattering resonances of metal
nano particles and related structures
(PhD course: Optical at the nanoscale)
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Outline:
Gold coated spherical polystyrene particles
Alloys and other geometries
Metal nano strip resonators
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z
Reproduced from Averitt et al.,
JOSA B 16(10), 1824-32 (1999).
Quasistatic approximation
r1
r2
=Au2S
=Au
=liquid with e=1.78
The incident field is
oriented along the z-axis.
)cos(ˆ 00 rEEzinc E
cos1
cos,2r
BrA iiiii E
EE e ,0
Boundary conditions
01 ,0 EAB N
)(ˆ)(ˆ1 iiii rr
)(ˆ)(ˆ11 iiiiii rrrr ee
eNe1 e2....
rN-1
r1
r2
rdCN
NN rinc
E
k
ext3)(
)(Im2
0
0 rEEe
eee
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Exact calculation that includes retardation
1
)1(
1
)1(
1)1(12
00 )(ˆn
nenonnnnikz
inc iiEeEx nmE
1
)3(
1
)3(
,
)1(
1
)1(
,
)3(
1
)3(
,
)1(
1
)1(
,)1(12
0 )(n
nejnnejnnojnnojnnnnn
j ibibaaiE nnmmE
1
)3(
1
)3(
,
)1(
1
)1(
,
)3(
1
)3(
,
)1(
1
)1(
,)1(12
/)(0
n
nojnnojnnejnnejnnnnn
c
E
j iaiabbij
nnmmBe
fff
ˆ)(ˆ)(cos)( sin
cos)(cos)3,1(cos
sin1)3,1(
sin1)3,1(
1
1
d
dPnnnn
noe
kRzPkRz m
ff
ff
ˆ)(cos)(
ˆ)(ˆ)(cos)(
cossin
1')3,1(
sin1
sincos
)(cos')3,1(1sincos
1)3,1()1()3,1(
1
1
nnkR
d
dPnkRnnkR
nn
n
PkRkRz
kRkRzrPkRz noe
n
(x)1nP is a legendre function
(kR)zn)1( is a spherical Bessel function
(kR)zn)3( is a spherical Hankel function
References:
Aden and Kerker, J. Appl. Phys.
22 (10), 1242-46 (1951).
J.A. Stratton, Electromagnetic
theory, McGraw-Hill, 1941
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Gold coated polystyrene spheres
z
r1
r2
=PS
=Au
=liquid with e=1.78
The finite thickness of the gold layer will result in additional loss due to
surface scattering of electrons. This is sometimes taken into account to
some extent in models by modifying the gold dielectric constant in the
following way
g
ee
ii
p
bulk
p
bulk 2
2
2
2
)()(
)(
v
12 rrbulkFA
g
p=1.37*1016rad/s, vF=1.4*106m/s, g=3.33*1013s-1
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Reproduction of Fig. 11 of Shi et al., Langmuir 2005, 21, 1610-17
r1=148nm
r2 –r1 =15nm
A=3
r1=148nm
r2 –r1 =23nm
r1=148nm
r2 –r1 =36nm r1=148nm
r2 –r1 =23nm
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PS diameter = 50nm
Extinction cross section resonance found for gold layer of 3.5nm at
the wavelength 800nm
r1=25nm, r2=28.5nm, l=800nm
Gold coated polystyrene spheres
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r1=250nm, r2=265nm, l=800nm
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Spherical particles made of
an alloy of gold and silver
Other geometries of particles
made of pure gold or silver
[1] Luis M. Liz-Marzán, "Nanometal: formation and color",
materials today, 26-31, (Feb. 2004).
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Introduction to surface plasmon polaritons
Metal nano-strip
resonator
t
w
Gap-plasmon resonators
t
w
td
td
w
(Propagation along the x-direction)
Gap-PP
EyEy
SPP
Ey
LR-SPP
Ey
SR-SPP
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Metal nano-strip resonators
• The x-component of the electric field dominates inside the metal film
• The x- and y-components of the field are out of phase
• The mode becomes less strongly bound as the film thickness increases
xiey )()( ErEl
20 k
Ref.: T. Søndergaard, and S.I. Bozhevolnyi, Phys. Stat. Sol. (b) 245, 9-19 (2008).
Slow plasmon polaritons in a silver film
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Electric field magnitude enhancement (values >10 are set to 10)
fl
mnw slow
2=45
Ref.: T. Søndergaard, and S.I. Bozhevolnyi, Phys. Stat. Sol. (b) 245, 9-19 (2008).
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Cross section of resonant fields through
the center of the metal strips
Ref.: T. Søndergaard, and S.I. Bozhevolnyi, Phys. Rev. B 75, 073402 (2007).
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The resonance is robust towards a 20% increase in d (d=5→6nm) and towards shifting the position of the 5nm gap by 20nm
Ref.: T. Søndergaard, and S.I. Bozhevolnyi, Phys. Rev. B 75, 073402 (2007).
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Ref.: T. Søndergaard, J. Beermann, A. Boltasseva, and S.I. Bozhevolnyi, Phys. Rev. B 77, 115420 (2008).
Fabrication: A. Boltasseva
Measurements: J. Beermann
Gold nano-strip optical resonators: theory and experiment
fl
mnw slow
2
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wnm
slow
f
l
2
Ref.: T. Søndergaard et al, photonics north 2008.
w=100nm, l=708nm,
Bottom-illuminated
(Field magnitudes > 10
have been set to 10).
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Design of single-nano-strip optical resonators
Ref.: G. Della Valle, T. Søndergaard, and S.I. Bozhevolnyi, Optics Express 16, 6867 (2008).
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Q-factor and field enhancement
Ref.: G. Della Valle, T. Søndergaard, and S.I. Bozhevolnyi, Optics Express 16, 6867 (2008).
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Gap plasmon polaritons between two metal films
• The x-component of the electric field dominates inside the metal films
• The mode index is larger compared to the single film and increases withdecreasing gap and decreasing film thickness
xiey )()( ErE
Ref.: T. Søndergaard, and S.I. Bozhevolnyi, Phys. Stat. Sol. (b) 245, 9-19 (2008).
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Gap plasmon polariton resonator
fl
mnw slow
2
Ref.: T. Søndergaard, and S.I. Bozhevolnyi, Phys. Stat. Sol. (b) 245, 9-19 (2008).
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Ref.: T. Søndergaard, and S.I. Bozhevolnyi, Phys. Stat. Sol. (b) 245, 9-19 (2008).
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Ref.: T. Søndergaard, and S.I. Bozhevolnyi, Phys. Stat. Sol. (b) 245, 9-19 (2008).
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The gold gap plasmon metal nano-strip resonator
T. Søndergaard, J. Jung, S.I. Bozhevolnyi, G. D. Valle, New Journal of Physics, accepted.
- Contrary to using silver the scattering peaks are hardly observable for
the 3rd and 4th order resonances.
- Standing-wave fields are still clearly seen
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The gold gap plasmon metal nano-strip resonator
T. Søndergaard, J. Jung, S.I. Bozhevolnyi, G. D. Valle, New Journal of Physics, accepted.
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The gold gap plasmon metal nano-strip resonator
T. Søndergaard, J. Jung, S.I. Bozhevolnyi, G. D. Valle, New Journal of Physics, accepted.
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Single strip close to a thick metal block
J. Jung and T. Søndergaard, Proc. SPIE Vol. 6988, 69881N (Apr. 23, 2008)).
Electric field magnitude
Electric field magnitude
l=588nm l=685nm
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Ref. J. Jung and T. Søndergaard, Phys. Rev. B 77, 245310 (2008)
In this case we also use the Green’s function surface integral
equation method. However, we avoid the surface integral over
the infinite surface by using a specially constructed Green’s
function.
Gold-air gap plasmon resonators
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Ref. J. Jung and T. Søndergaard, Phys. Rev. B 77, 245310 (2008)
0',,
)()'(cos2
'4
1',
0
)'()(1
0
)2(
0
220
220
yy
derxxi
kHi
g
x
x
x
xx
yyki
x
p
xk
e
e
e rrrr
Special construction of Green’s function
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Conclusion on metal nanostrip resonators
- Optical scattering resonances for metal nano-strip resonators is due to excitation of
counter-propagating slow surface plasmon polaritons
-We can exploit the electromagnetics boundary conditions to obtain large field
magnitudes.
- Robust enhancement of the magnitude of the electric field by a factor ~20-30.
- Excellent match of calculated and measured scattering spectra
- Near-linear relation between resonance wavelength and strip width for both strip and
gap plasmon resonators
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Acknowledgements - projects:
The Danish Research Council for Technology and Production
The NABIIT project financed by the Danish Research Agency (contract 2106-05-033)
Acknowledgements - people:
Sergey I. BozhevolnyiJonas BeermannAlexandra BoltassevaJesper Jung