Gothic Cathedrals and Solar Cells and maybe a Grail

1
Gothic Cathedrals and Solar Cells (and maybe a
Grail?)

• A short introduction to the phenomenon of
  Surface Plasmonsand their role in the
  scattering of light

Martin Kirkengen, Fysisik Institutt,
Universitetet i Oslo
2
Electromagnetic wave in homogeneous medium

• Maxwell equations, wave solution
• Wave with frequency w and wavenumber k

3
Stationary solution at boundary

• Flat boundary at z0
• Wave propagating in one direction only (no
  reflection)
• Ey 0

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Plane wave at boundary (at z0)(no reflection)

• Fields
• Boundary conditions

z
Ez
H
x
Ex
H
2
y
1
5
Solution at boundary

• Maxwell equations give (Raether 1988)
• And unless e1e2
• Plasmon solution for e2 1, e1lt-1, imaginary kz

6
What? e lt 0?!

• Lorentz model electron on spring

Polarizability and dielectric constant
Drude model cut the spring
7
elt0 , imaginary k, what about c?

• Wavenumber

• Imaginary e -gt absorption
• Real e, imaginary N-gt no penetration, no
  absorption

8
Back to the Surface Plasmons...

• Visible light, metal/air interface
• Real wave number along x
• Imaginary wave number along y
• Longitudinal charge fluctuations at surface
• Evanescent waves no propagated power

z
?1
?2
x
_ _ _
_ _ _


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Some Plasmon Geometries

• Multiple interfaces give new possibilities
• More stable modes(up to 1 cm propagation)

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Coupling to light

• Plasmon

• Light

• Momentum mismatch requires help- Grating
  (discreet, periodic)- Roughness (periodic
  Fourier components)- Periodic due to curved
  surface - spheres

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The Cathedral Bit...
Red color due to embedded gold particles
spreading light
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An early application
Illustrations stolen from David G. Stroud, Ohio
State University Columbus OH

• The Lycurgus Cup (British museum 400 A.D.)
• When illuminated from within, it glows red.
  Again due to gold particles embedded in the
  glass, with an absorption peak at around 520 nm

13
Light scattering from spheresMie Theory

• Solve Wave equations in spherical coordinates
• Expand a plane wave in spherical harmonics
• Determine coefficients for the scattered wave and
  for the internal field of the sphere
• Try to extract some physical meaning...

BohrenHuffman, Absorption Scattering of Light
by Small Particles (Wiley 1983)
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Jumping to the Coefficients...

• mN1/Nair
• Resonance (in the limit of small x) at

• Lowest mode for metal particle in air (Nair1)
• N12 m2 -2, e -2

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Frequency Dependence of Resonance
Extinction (absorptionscattering) for gold
particles in fluid
e as function of frequency for silver
Elghanian et al, Science 277, 1078
(1997) Storhoff et al, JACS 120, 1959 (1998)Park
and Stroud, PRB 68, 224201 (2003)
Kreibig and Vollmer , Optical Properties of Metal
Clusters , Springer-VerlagBerlin, 1995
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The Scattered Field
q-components of the scattered field
Destructive interference with incoming wave
r0.01l
r0.2l
rl
Constructive interference with incoming wave
Smallest particles dipole field Larger
particles multipole contributions
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Changing the resonance

• SizeLarger particles, higher modes contribute,
  each mode red-shifted
• ShapeElliptic shape, flatter particles have
  red-shifted resonance
• Coating/substrateResonance is given as a
  relative refraction index, changing surroundings
  changes resonance
• Arrays/clustersLoads of opportunities...

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Applications in biophysics

• Gold Nanoparticles as markers
• Shift in resonance gives dielectric constant of
  medium

Forschungszentrum Jülich
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Applications in Solar Cells

• Placing small particles of a reflective medium at
  surface reduces reflection...
• Strong coupling between plasmons and waveguides
  increased fields in the active part of the solar
  cell.
• The reverse process (LED) has been shown to gain
  a factor 8 from plasmon coupling
• No Solar Cell demonstrated yet...

Catchpole Pillai School of Photovoltaic and
Renewable Energy Engeneering UNSW, Australia JoAP
100, 044504 (2006)