Optical scattering resonances of metal nano particles and ...

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)

Outline:

Gold coated spherical polystyrene particles

Alloys and other geometries

Metal nano strip resonators

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

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

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

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

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

r1=250nm, r2=265nm, l=800nm

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).

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

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

Electric field magnitude enhancement (values >10 are set to 10)

fl

mnw slow

2=45


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).

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).

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

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).

Design of single-nano-strip optical resonators

Ref.: G. Della Valle, T. Søndergaard, and S.I. Bozhevolnyi, Optics Express 16, 6867 (2008).

Q-factor and field enhancement

Ref.: G. Della Valle, T. Søndergaard, and S.I. Bozhevolnyi, Optics Express 16, 6867 (2008).

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


Gap plasmon polariton resonator

fl

mnw slow

2


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

The gold gap plasmon metal nano-strip resonator

T. Søndergaard, J. Jung, S.I. Bozhevolnyi, G. D. Valle, New Journal of Physics, accepted.

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

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

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

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

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

Optical scattering resonances of metal nano particles and ...

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