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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.

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

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  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. z Ez x Ex H 2 y 1 Stationary solution at boundary: • Flat boundary at z=0 • Wave propagating in one direction only (no reflection) • Ey = 0

  4. Plane wave at boundary (at z=0)(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 e1=e2 Plasmon solution for e2 =1, e1<-1, imaginary kz

  6. What? e < 0?! Lorentz model – electron on spring: Polarizability and dielectric constant: Drude model – cut the spring:

  7. e<0 , imaginary k, what about c? • Wavenumber: • Imaginary e -> absorption • Real e, imaginary N-> 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 _ _ _ _ _ _ +++ +++

  9. Some Plasmon Geometries • Multiple interfaces give new possibilities • More stable modes(up to 1 cm propagation)

  10. Coupling to light • Plasmon: • Light: • Momentum mismatch – requires help- Grating (discreet, periodic)- Roughness (periodic Fourier components)- Periodic due to curved surface - spheres

  11. The Cathedral Bit... Red color due to embedded gold particles spreading light

  12. An early application: • 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 Illustrations stolen from: David G. Stroud, Ohio State University Columbus OH

  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... Bohren&Huffman, Absorption &Scattering of Light by Small Particles (Wiley 1983)

  14. 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, e = -2

  15. Ag Bound electrons(Lorentz model) Free Electrons(Drude model) Frequency Dependence of Resonance Extinction (absorption+scattering) 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-Verlag:Berlin, 1995

  16. The Scattered Field q-components of the scattered field Destructive interference with incoming wave r=0.01l r=0.2l r=l Constructive interference with incoming wave Smallest particles – dipole field Larger particles – multipole contributions

  17. 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...

  18. Applications in biophysics • Gold Nanoparticles as markers • Shift in resonance gives dielectric constant of medium Forschungszentrum Jülich

  19. 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)

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