nanoscale systems for opto-electronics 04 - kit - lti · - quantum dot lasers, quantum cascade...

1

1

Nanoscale Systems for Opto-Electronics

1.80 1.85 1.90 1.95 2.00 2.05

PL

inte

nsity

[arb

. uni

ts]

Energy [eV]

700 675 650 625 600 Wavelength [nm]

2

Readings

• Principles of Nano-Optics, L. Novotny and B. Hecht, Cambridge University Press, 2006• Absorption and Scattering of Light by Small Particles, C. F. Bohren and D. R. Huffman, John

Wiley& Sons, INC. 1998• Principles of Optics, Born and Wolf, Cambridge University Press• Surface plasmon, H. Raether, Springer Tracts in Modern Physics, Vol. 111, 1988 • Near-Filed Optics and Surface Plasmon Polaritons, S. Kawata, Springer Topics in Applied

Physics, 2001• Optical Properties of Metal Clusters, U. Kreibig, M. Vollmer, Springer, 1995

• Recent papers: Nature, Science Magazine, Phys. Rev. Lett. ...as indicated during leture series

3

Nanoscale Systems for Opto-ElectronicsLecture 4

Interaction of Light with Nanoscale Systems- general introdcution and motivation- nano-metals (Au, Ag, Cu, Al ...)

introduction to optical propertiesmie scatteringmie scattering in the near-fieldmie scattering with nano rods

- resonant optical antennas- artificial quantum structures (semiconductor quantum dots, metallic quantum dots, ...)- quantum dot lasers, quantum cascade lasers

Optical Interactions between Nanoscale Systems- Förster energy transfer (dipole-dipole interaction)- super-emitter concept- optical trapping- SERS (surface enhanced Raman spectroscopy: bio-sensors)- optical data storage

Beating the diffraction limit with Nanoscale Systems- light confinement- plasmonic chips- plasmonic nanolithography 4

Last Time: Mie Scattering

ckeeEzE x

ikzi

ω== , ˆ)( 0

2a

incident wave

sE scattered waveIε

IIε

2

5

Mie Scattering of Au Spheres

effic

ienc

y Q

s=

Cs/π

a2

dipolar resonance

quadrupolar resonance

6

Mie Scattering of Au Spheres

effic

ienc

y Q

s=

Cs/π

a2

effic

ienc

y Q

s=

Cs/π

a2

Note: size dependency is specific for a real material (dielectric function)-generally: no common sense or trend !-for 2a >> 300nm; continuum spectra

λππ 2 ;))12(2 2

1

222 =++== ∑

=

kbankI

WCn

nni

ssHere:

7

Mie Scattering of Al Spheres vs. DiameterLarge particles: electrostatic limit is no longer agood model-Finite phase delay between the front and the back side of the particle leads to excitation of multipolar modes (quadrupolar etc.)-General trend gives broadening and spectral red-shift of the resonance for increasing size parameter

Small partilces: electrostatic model OK-surface to volume increases which leads to increasing surface scattering-general broadening for decreasing sizes

8

Mie Scattering in the Near-field

Phys. Rev. B 24, pp.649, (1981)

ckeeEzE x

ikzi

ω== , ˆ)( 0

2a

incident wave

sE scattered waveIε

IIε

radiating dipole has e.m. near-field with radial field components

3

9


Phys. Rev. B 24, pp.649, (1981)

Qs = Cs/πa2 measures the ability of a sphere to extract power from an incident wave and redirect it as scattered power over all solid angles;

on resonance

Qs = Cs/πa2 >> 1nano metallic sphere acts as a local field intensifier

10


Phys. Rev. B 24, pp.649, (1981)

Qabs = Cabs/πa2 measures the ability of a sphere to absorb power from an incident wave and redistribute its energy as Ohmic losses in the particle or Joule heating;

sextabs

nnnext

nnns

QQQ

banka

Q

banka

Q

−=

++=

++=

∑

∑∞

=

∞

=

,}Re{)12()(

2

,))(12()(

2

12

1

222

11


source: Phys. Rev. B 70, pp.035418, (2004)

x=2πa/λ=0.3; ε =-2+0.2i

nano metallic sphere acts as a local field intensifier

12


Phys. Rev. B 70, pp.035418, (2004)

x=2πa/λ=0.3; ε =-2+0.2i

While the far field (R >> a)consists of electric fields (EΘ, EΦ), the near field (R = a) contains radial components (ER)

aRssNF ddEEaRQ =∫∫ ⋅= φθθ

π

ππ

sin)(

*

0

2

02

2 rr

kind second theof fct. Hankel

,))()(12(])()()1[({2

)2(1

2)2(22)2(1

2)2(1

2

n

nnnnnnNF

h

kahbnkahnkahnaQ ∑∞

=+− +++++=

4

13


Phys. Rev. B 70, pp.035418, (2004)

While the far field (R >> a)consists of electric fields (EΘ, EΦ), the near field (R = a) contains a radial component (ER)

aRssNF ddEEaRQ =∫∫ ⋅= φθθ

π

ππ

sin)(

*

0

2

02

2 rr

kind second theof fct. Hankel

,))()(12(])()()1[({2

)2(1

2)2(22)2(1

2)2(1

2

n

nnnnnnNF

h

kahbnkahnkahnaQ ∑∞

=+− +++++=

14


J Chem Phys. 116, pp 10895 (2002)

Au sphere, 2a = 210 nm

λexcitation = 830 nm

e.m. field enhancement around 20 at best !

2a

15

Mie Scattering with Non-spherical Particles (case: quasi-static approximation)

0)( EP ωα∝

factorshapeLwhereL

abc

s

IIIIs

III

,3)(3

4εεε

εεπα+−

−=

polarizability of elliptical particle:

2

22

2

2

1 );111ln

21(1

abe

ee

eeeLs −=−

−+−

=a

b

c

half axis (a=b=c): spherehalf axis (b=c): prolate spheroid e=1 (needle) to e=0 (sphere)half axis (a=b): oblate spheroid e=1 (disk) to e=0 (sphere)

16


1 1.5 2 2.5 3 3.5 4-12

-10

-8

-6

-4

-2

0

2

4

Energy / eV

dielectric function of Ag

note: infinite ‘flat‘ particle shows resonance at ε=0 (ωp plasma frequency)

prolate low freq. res.

prolate high freq. res.

5

17


note: infinite ‘flat‘ particle shows resonance at ε=0 (ωp plasma frequency)

source: C. Soennichsen, PhD Thesis, LMU Munich

18


case: Au ensemble

J Phys Chem B 103 pp 3073 1999

TEM pictureExtinction spectrum

19

Mie Scattering with Non-spherical Particles

Adv. Mater. 14, pp. 80, 2002 TEM pictures

Au rods Ag wires

Ag rods

spectral red shift

20

Mie Scattering with Non-spherical Particles

APL 77, pp. 3379 (2000)

Au nanowire

n indicates order of long. plasmon mode

6

21


case: Al (theory)

La=0.69, Lb=0.3, Lc=0.01a:b:c=1:2.3:23

pp

sphere ωω

ω ⋅≈= 577.03

0

20

εω

meN

p =

22

Mie Scattering with Non-spherical Particles (local e.m. intensifier aspect)

J Chem Phys. 116, pp 10895 (2002)


e.m. field enhancement localized at high curvature tail‘lightning rod effect‘ (concentration of e.m. fields at the tips by particle shape)

Au spheroid

23

Mie Scattering with Non-spherical Particles (local e.m. intensifier aspect)

HJ Eisler, unpublished data

e.m. field enhancement localized at high curvature tail‘lightning rod effect‘ (concentration of e.m. fields at the tips by particle shape)


Au spheroid

nanoscale systems for opto-electronics 04 - kit - lti · - quantum dot lasers, quantum cascade...

Documents