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

Gothic Cathedrals and Solar Cells
(and maybe a Grail?)
A short introduction to the
phenomenon of
Surface Plasmons
and their role in the scattering of light
Martin Kirkengen, Fysisik Institutt, Universitetet i Oslo
Electromagnetic wave in
homogeneous medium
• Maxwell equations, wave solution:
• Wave with frequency w and wavenumber k
Stationary solution at boundary:
• Flat boundary at z=0
• Wave propagating in one direction only (no
reflection)
• Ey = 0
z
Ez
H
y
x
Ex
2
1
Plane wave at boundary (at z=0)
(no reflection)
• Fields
z
Ez
HH E
x
y
• Boundary conditions:
2
1
x
Solution at boundary
Maxwell equations give (Raether 1988)
And unless 1=2
Plasmon solution for 2 =1, 1<-1, imaginary kz
What?  < 0?!
Lorentz model – electron on spring:
Polarizability and dielectric constant:
Drude model – cut the spring:
<0 , imaginary k, what about c?
• Wavenumber:
• Imaginary  -> absorption
• Real , imaginary N
-> no penetration, no absorption
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
1
z
2
+++
___
+++
___
x
Some Plasmon
Geometries
• Multiple interfaces give
new possibilities
• More stable modes
(up to 1 cm propagation)
Coupling to light
• Plasmon:
• Light:
• Momentum mismatch – requires help
- Grating (discreet, periodic)
- Roughness (periodic Fourier components)
- Periodic due to curved surface - spheres
The Cathedral Bit...
Red color due
to embedded
gold particles
spreading light
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
Light scattering from spheres
Mie 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...
Bohren&Huffman, Absorption &Scattering of Light by Small Particles (Wiley 1983)
Jumping to the Coefficients...
• m=N1/Nair
• Resonance (in the limit of small x) at
• Lowest mode for metal particle in air (Nair=1):
N12 = m2 = -2,  = -2
Frequency Dependence of
Resonance
Ag
Bound
electrons
(Lorentz
model)
Free Electrons
(Drude model)
Extinction (absorption+scattering)
for gold particles in fluid
Elghanian et al, Science 277, 1078 (1997)
Storhoff et al, JACS 120, 1959 (1998)
Park and Stroud, PRB 68, 224201 (2003)]
 as function of frequency for silver
Kreibig and Vollmer , Optical Properties of Metal
Clusters , Springer-Verlag:Berlin, 1995
The Scattered Field
qcomponents of the scattered field
Destructive interference
with incoming wave
r=0.01l
r=0.2l
Smallest particles – dipole field
Larger particles – multipole contributions
r=l
Constructive interference
with incoming wave
Changing the resonance
• Size
Larger particles, higher modes contribute, each
mode red-shifted
• Shape
Elliptic shape, flatter particles have red-shifted
resonance
• Coating/substrate
Resonance is given as a relative refraction
index, changing surroundings changes
resonance
• Arrays/clusters
Loads of opportunities...
Applications in biophysics
• Gold Nanoparticles as markers
• Shift in resonance gives dielectric constant
of medium
Forschungszentrum
Jülich
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.
Catchpole & Pillai
School of Photovoltaic and
Renewable Energy
Engeneering UNSW, Australia
JoAP 100, 044504 (2006)
• The reverse process (LED) has been shown to gain a factor 8 from
plasmon coupling
• No Solar Cell demonstrated – yet...