Optical antennas: Intro and basics

2328-12

Preparatory School to the Winter College on Optics and the Winter College on Optics: Advances in Nano-Optics and Plasmonics

J. Aizpurua

30 January - 17 February, 2012

Center for Materials Physics, CSIC-UPV/EHU and Donostia International Physics Center - DIPC

Spain

Optical antennas: Intro and basics

Optical antennas: Intro and basics

Javier Aizpurua

Center for Materials Physics, CSIC-UPV/EHU

and Donostia International Physics Center - DIPC

Donostia-San Sebastián, the Basque Country, Spain

http://cfm.ehu.es/nanophotonics

Winter College on Optics: Advances in Nano-Optics and Plasmonics

February 6-17, 2012 The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

Outline

Optical antennas: Basics

Playing with modes

Optical antennas for Enhanced

Spectroscopy: SERS and SEIRA More applications of Optical antennas

Lecture given by J. Aizpurua at the Winter College on Optics, Trieste, Feb. 2012

Different types of radio antennas

Omni-directional antenna often used at master station sites

Directional Yagi antenna Commonly used at remote field sites

/4 antenna

/2 Dipole

Yagi

Parabolic

Horizontal radiation pattern


Vertical radiation pattern

Biconical antenna

Combilog antenna

Horn antenna Yagi-Uda antenna

Monopole antenna

Half wave dipole antennas

Parabolic antenna Active loop antenna

Radio Frequency Antennas


Scaling down in size Scaling down in wavelength

Visible light Optical antenna Nanoantenna

/2 nanoantenna


Optical nanoantennas

Design of plasmonic nanoparticles: size, shape, interactions, ...

Analogy with radio-wave antennas Mühlschlegel et al. Science 308, 1607 (2005)


Applications: biosensing, nonlinear optics / SERS, fluorescence, quantum optics,...

Van Hulst, ICFO - Single molecule, scanning probe

Quidant, ICFO Antenna-gap sensing

Halas, Nordlander Plasmonic photodetector

Alivisatos, Giessen Pd-antenna sensor

Capasso Antenna QCL

Optical nanoantennas


+ +

+

- - -

hE

Absorption

Scattering

Extinction

The simplest optical antenna: a metallic particle

Enhancement of absorption and emission: Bringing effectively the far-field into the near-field


Metal particle plasmons

Standard textbooks: - Kreibig, Vollmer, Optical properties of metal clusters, Springer1995 - Bohren, Huffmann, Absorption and scattering of light by small particles, Wiley 1983


Metallic nanorod as a /2 optical antenna

L= /2

In analogy to a /2 radiowave antenna,

we call a nanosized rod-like metallic

structure a /2 optical antenna .

YES BUT, it is just similar, and not equal because of plasmons


Bulk plasmons

24 ep

e

n em

A plasmon is a collective oscillation of the conduction electrons

Bulk plasmon: The rigid displacement of the electrons induces a dipolar moment and an electric field opposing the displacement

(t):

All the electrons are involved in the oscillation. The energy of those oscillations in typical metals might be triggered out by external probes.

+ +

+ +

+ +

- -

- -

- -

E(t) (t)

Harmonic oscillator

22 2

2 ( ) ( ) 4 ( )ednm t enE t n e tdt

=>

Electron density


Surface plasmons

2p

Electromagnetic surface waves which exist at the interface between 2 media whose have opposite sign.

+ + + + + - - + + - - - - + + Ex

Ez Metal ( 1= 1´+i 1´´)

=ckx

kx

x Hy Dielectric ( 2= 2´+i 2´´)

2

21 p

2p

s

(1)( )(1) (1) xi k x t zoE E e 1 2

¨1 2

x x xk k ikc

Drude model

Surface plasmons

Dispersion relation


e -

2


Surface plasmons

2p

Electromagnetic surface waves which exist at the interface between 2 media whose have opposite sign.

+ + + + + - - + + - - - - + + Ex

Ez Metal ( 1= 1´+i 1´´)

=ckx

kx

x Hy Dielectric ( 2= 2´+i 2´´)

2

21 p

2p

s

(1)( )(1) (1) xi k x t zoE E e 1 2

¨1 2

x x xk k ikc

Drude model

Surface plasmons

Dispersion relation


Methods of SPP excitation

nprism > nL !!


Confined fields:

- Nanooptics Enhanced field:

- Lighting rod effect Tunability:

- Geometry Coupling: Wavelength range:

- Visible Infrared

Nano-optics with localised plasmons

Characteristics Resonances dependence with size

with material

with shape

with coupling

Confined plasmon

+ + +

k

k

p

ck

s

+ + + + Plasmon polariton


Light-particle interaction

General case: <= a

Phase shifts in the particles: retardation, multipole excitations

k

E t t0

x 2a

+ E i +

+

- - -

2a k

E

x

E t t0

Quasi-static case: >> a

Homogeneous polarization: All points of an object respond simultaneously to the incoming (exciting) field. Helmholtz eq. reduces to Laplace equation: el. field:

k 2a

02


Small sphere

The electric fields inside (E1) and outside (E2) the sphere can be obtained from the scalar potentials

11E

22E 022

with

with

,,r

Solve Lapace equation in spherical coordinates:

Boundary conditions: )(11 ar

)(22

11 ar

rr

012

continuity of the tangential electric fields

continuity of the normal component of the electric displacement

02 sca tter


Small sphere

cos000 rExEHomogeneous electric field along x-direction:

The following potentials satisfy the Laplace equation and boundary conditions:

The field is independent of the azimuth angle which is a result of the symetry implied by the direction of the applied electric field.

EFrom we obtain


Small sphere

23

21

21002

cos2

cosr

aErESmall sphere:

Dipole: 2

2

cos4 r

pdipole

The field outside the sphere is the superposition of the applied field and the field of an ideal dipole at the sphere origin The dipole moment is given by

021

21320 2

4 Ep a

Polarizability of the sphere: 21

213

24 a

020 EpGenerally the dipole moment is defined by


Small sphere

Radiation zone: kr >> 1 (r>>

Near-field zone: kr << 1 (r <<

tier 3

0

34

1)( ppnnrE

electrostatic dipole field

harmonic time dependency

tkriekr 0

2

4)( npn

rE

3

3

raE

r

E

0 0

2a a

propagating wave

tiikr

eikrr

kr

eppnnnpnrE 311

41)( 2

0

nrr

with

We can describe the light scattering of a small sphere by plane wave scattering at an ideal point dipole with dipole moment derived on the previous slides. The dipole field is given by:


90°

0° 180°

270°

Far-field scattering (transverse fields)

Far- and near-field calculations for a sphere a <<

E ink

+ +

+

- - -

2a

Pointing vector always radial!

Near-field scattering

- 2 - 1 0 1 2- 2

- 1

0

1

2

- 2 - 1 0 1 2- 2

- 1

0

1

2

2

particleinI EE

r/a r/a

r/a r/a

Pointing vector is not always radial


Absorption cross section:

Csca83k4a6 m

2 m

2k4

62 Im

2Im4 3 kkaC

m

mabs

Scattering cross section:

- stronger scattering at shorter wavelength (Rayleigh scattering, blue sky) - for large particle extinction is dominated by scattering whereas for small particles it is associated with absorption - scattering of single particles <10nm is difficult to measure (low signal/noise and low signal/background)

Optical cross sections of small spheres

4

6aC sca

3aCabs

Integrating the Poynting vector Ssca (Sabs) over a close spherical surface we obtain the totally scattered (absorbed) power Psca (Pabs) from which we can calculate the scattering (absorption) cross section Csca = Psca/Ii (Cabs = Pabs/Ii):


Dielectric function of metals

Collective free electron oscillations (plasmons)

plasma frequency (longitudinal oscillation)

= -2


0.5 1 1.5 2

0.51

1.52

2.53

Drude model

ip

2.01 2

2

0.5 1 1.5 2

0.51

1.52

2.53

p

p

Optical cross sections of small spheres

21

21Arg

0.5 1 1.5 2

2

4

6

8

0.5 1 1.5 2

0.5

1

1.5

2

2.5

0.5 1 1.5 2

-5

-2.5

2.5

5

7.5

p

scaC2

21

absC21Imoptical phase of

scattered light

opt. field amplitude

p

p

Excitation of a plasmon by a pulse

Rice University, Houston Lecture given by J. Aizpurua at the Winter College on Optics, Trieste, Feb. 2012

Localised Surface Plasmon: a swimming pool of e-


+ +

+

- - -

hE

Absorption

Scattering

Extinction

The simplest optical antenna: a metallic particle

Enhancement of absorption and emission: Bringing effectively the far-field into the near-field


frequency (cm-1) 1000 10000

wavelength ( m) 10 1 30

10

20

0

Plasmon polariton resonance

Au

SiC

Ag

Phonon polariton resonance

0.5

polarizability: m

ma2

4 3

2 mresonance at

+ E in +

+

- - -

2a k

Small particle resonances

E0 /Ein

E0 enhanced field at

in0 22 EE

m

m

m 1


Lycurgus Cup

(British Museum; 4th century AD)

Illumination: from outside from inside

(strong absorption at and below 520 nm)

Nanotechnology with plasmonics: before the nanorevolution


Extinction vs. scattering


Near-field versus far-field

Near-field distribution Far-field distribution

Spectral information

50 nm gold nanoparticle


Near-field versus far-field


Higher multipole resonances in quasistatic limit

111

L p

mediuml

l

In the quasistatic limit the Mie theory yields the resonance positions of the higher multipoles at

However, higher multipoles in the quasistatic limit are negligible compared to the dipole contribution (l=1)

p1

1

2

L

1L medium

ll

Drude

medium= 1


Aizpurua et al. Physical Review B 71, 235420 (2005)

Antenna modes: D=80nm,L=200nm; ratio=2.5

Higher order modes: l

Dipole response: L /2

-Q Q - - - - - +

+ + + +

~ L


An alternative to excite high order modes in a sphere

Probability of losing energy h for a 50-keV electron moving at grazing incidence on an aluminum sphere of radius a=10nm

e

Ferrell and Echenique, PRL 55, 1526 (1985)

l=1

l=2 l

222

2 20 0

4( , , ) Im ( )ll

lm m ll m

q a bP a b v A Kv a v v

3´

( ) 1( )( ) ( 1) /l a

l l

EELS in nanoparticles

a b

- v


Mie-theory

Mie-theory is an electrodynamic theory for optical properties of spherical particles. The solution is divided into two parts: the elctromagnetic one which is treated from first principles (Maxwell equations) and the material problem with is solved by using phenomenological dielectric functions taken from experiments or model calculations

See also Bohren/Huffman

Kreibig/Vollmer


Mie theory - results

Kreibig/Vollmer

Fig. 2.6 shows farfield distribution at the surface of a large sphere centered at the small cluster


90°

0° 180°

270° Pointing vector always radial!

Scattering characteristics (far-field)

Small particle Large particle (Mie calculation)

Strong forward scattering


Spherical plasmons:

2 1l pl

l

a

l=1 mode

2

21 p

Drude-like metal


Effect of finite size on the resonant frequency

Jin et. al., Science 294, 1901 (2001)

same shape, different size redshift due to higher multipoles


mxyzm

mxyz L

abc34

Shape: Polarizability of small ellipsoids

geometrical factors

31

zyx LLLsphere:

zyx LLLgenerally:

3 resonances at

quasistatic approximation:

xyzm L

11

inEp

z

y

x

000000

For a geometry like above:

zyx


0

20

40

60

80

100

120

300 400 500 600 800 12000

4

8

E0 || long axis 10 nm / 3 nm 100 nm / 30 nm

|E| /

|E0|

E0 || short axis

[nm]

Ei

ki

E2

l = 528nm

b

a

E2 b a

l = 340 nm

Ei

ki

Silver ellipsoid illuminated by a plane wave

size shifts dipole resonance for

E0 || long axis

Calculation by J. Renger, TU Dresden Lecture given by J. Aizpurua at the Winter College on Optics, Trieste, Feb. 2012

Plasmon resonances:dependence on the geometry


Control over the plasmon frequencies by playing with particle shapes and coupling

Nanorods, nanoshells, nanorings, dimers,.....

Coupled systems

Apertureless NSOM

Nanometrology, sensing, spectroscopy

More complex geometries


Donostia International Physics Center (DIPC)

boundary element method JGA and Howie

finite difference in the time domain Joannopoulos photonic crystals

transfer matrix approach Pendry

finite geometries

periodic systems

convergence for high

dielectric contrast (e.g., in metals)

effective dimensionality of the problem

discrete-dipole approximation Purcell+Pennypacker: optical modes of grains Martin: Green-function formulation

multiple scatter ing Ohtaka: LEED-like methods to photons Wang, Stefanou, Sheng: photonic crystals JGA: finite systems

plane wave expansions Leung

Numerical solutions to the 3D electromagnetic problem


medium j

jS

rc

i

jje

rG

1r

Boundary Element Method

ic

E r A r r

ext j

j jS

d GA r A r s r s h s

ext j

j jS

d Gr r s r s s

(1 and 2 refer to the interface sides). The surface integrals are now discretized using N representative points si. This leads to a system of 8N linear equations with h1(si), h2(si), 1(si), and 2(si) as unknowns.

The boundary conditions lead to a set of surface integral equations with the interface currents hj and charges j as variables. For example, the continuity of leads to

ext ext1 1 2 2 2 1 ,

jS

d ' G ' ' G ' 's s s s s s s s s

García de Abajo and Howie, PRB 65, 115418 (2002) García de Abajo and Aizpurua, PRB 56, 15873 (1997)


An example of Optical Antenna: Optical properties of metallic nanorings

d/a smaller -> red shift

Aizpurua et al. Phys. Rev. Lett. 90, 057401 (2003)

Disk Nanoring d

a


Optical properties of metallic nanoshells


Modes in a nanoring. The twisted slab

1/ 2(1 )kds e

d

2 dkd n d nL a

d a

+ +

+ + -

-

-

-

+ +

+ + -

-

-

-


Field-enhancement in a nanoring


Biconical antenna

Combilog antenna

Horn antenna Yagi-Uda antenna

Monopole antenna

Half wave dipole antennas

Parabolic antenna Active loop antenna

Radio Frequency Antennas





/4 antenna

/2 Dipole

Yagi

Parabolic





Taminiau et al., Nature Photonics 2, 234 (2008)

/4 optical antenna

Neubrech et al., App. Phys. Lett. 89, 253104 (2006)

/2 nanoantenna

2000 3000 4000 5000 6000

0.94

0.96

0.98

1.00

5.00 3.33 2.50 2.00 1.67

L 1.5 m, D = 100nm,

parallel polarsiation,

substrate: CaF2

wavelength [ m]

rela

tive

trans

mitt

ance

wavenumber [cm-1]





Vertical

Dipole

Yagi

Parabolic





Taminiau et al., Optics Express 14, 10858 (2008)

Yagi-Uda antenna





Vertical

Dipole

Yagi

Parabolic





N. Mirin and N. Halas, Nano Letters 9, 1255 (2009)

Parabolic-like optical nanoantennas



20

40

60

80

100

120

140

Ar

Ar -

50 nm

E

Nature 453, 731 (2008)

Bowtie antennas

Taminiau et al., Nature Photonics 2, 234 (2008)

/4 optical antenna


Plasmonic antennas


Thank you for your attention!

http://cfm.ehu.es/nanophotonics

Documents

Optical antennas: Intro and basics