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Transcript
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 qcomponents 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...