1. 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

2. Electromagnetic wave in homogeneous medium Maxwell equations, wave solution: Wave with frequency  and wavenumber k

3. Stationary solution at boundary: Flat boundary at z=0 Wave propagating in one direction only (no reflection) E y = 0 y z x H ExEx EzEz 2 1

4. Plane wave at boundary (at z=0) (no reflection) Fields Boundary conditions: y z x H ExEx EzEz 2 1 H

5. Solution at boundary Maxwell equations give (Raether 1988) And unless  1 =  2 Plasmon solution for  2 =1,  1 <-1, imaginary k z

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

7.  <0, imaginary k, what about c? Wavenumber: Imaginary  -> absorption Real , 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 +++ _ _ _ +++ _ _ _ x z 11 22

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 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)

14. Jumping to the Coefficients... m=N 1 /N air Resonance (in the limit of small x) at Lowest mode for metal particle in air (N air =1): N 1 2 = m 2 = -2,  = -2

15. Frequency Dependence of Resonance Ag Free Electrons (Drude model) Bound electrons (Lorentz model)  as function of frequency for silver Extinction (absorption+scattering) for gold particles in fluid Kreibig and Vollmer, Optical Properties of Metal Clusters, Springer-Verlag:Berlin, 1995 Elghanian et al, Science 277, 1078 (1997) Storhoff et al, JACS 120, 1959 (1998) Park and Stroud, PRB 68, 224201 (2003)]

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

17. 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...

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)