1. Resonances and optical constants of dielectrics: basic light-matter interaction

2. Understanding the Rainbow

3. Dielectric materials: All charges are attached to specific atoms or molecules Response to an electric field E: Microscopic displacement of charges Relative dielectric permittivity  describes how a material is polarized in response to an electric field  depends on frequency:  (  )

4. If we know the relation between P and E we can solve Maxwell’s equations leading to the wave equation: In vacuum (P = J = 0):

5. Deriving the relation between P and E in a dielectric Equation of motion of the electron:  : damping coefficient for given material k: restoring-force constant resonance frequency: assume E is varying harmonically, and also

6. Inserting P(E) in wave equation gives: solution: with complex propagation constant k z =  + iα : So that…

7. So that we find the refractive index of the dielectric: For a dielectric with multiple resonances:

8. Rainbow: why red outside, blue inside ?

10. Blue (high frequency): larger n Red (small frequency): smaller n Rainbow: why red outside, blue inside ?

11. Light scattering from small resonant particles Metal nanoparticle plasmons

13. What is a plasmon? Plasmons in the bulk oscillate at determined by the free electron density and effective mass Plasmons confined to surfaces that can interact with light to form propagating “surface plasmon polaritons (SPP)” Confinement effects result in resonant SPP modes in nanoparticles +++ --- +-+ k “plasma-oscillation”: density fluctuation of free electrons

14. Sphere in a uniform static electric field Bohren and Huffman (1983), p.136  particle can be considered as a dipole: in a metal cluster placed in an electric field, the negative charges are displaced from the positive ones electric polarizability of a sphere α ε = ε 1 (ω)+i ε 2 (ω) = dielectric constant of the metal particle ε m = dielectric constant of the embedding medium usually real and taken independent of frequency  negative real dielectric constant ε 1 (ω) resonant enhancement of p if

15. y E inc x k y x k Derivation using quasi-static approximation

16. E0E0 mm  z r  a Jackson (1998), p.157 Bohren and Huffman (1983), p.136 Boundary conditions: Derivation using quasi-static approximation Equations:

17. E0E0 mm  z r  a Solution: with: Sphere in electro- magnetic field (a << ): Jackson (1998), p.157 Bohren and Huffman (1983), p.136 Derivation using quasi-static approximation

18. 550nm 20 Au n=1.5 I enh Metal nanoparticles: Extinction = scattering + absorption Large field enhancement near particle At resonance, both scattering and absorption are large albedo = scattering / extinction =  sca /(  abs +  sca )

19. Reosnance spectra Extinction spectra in water Groupings of 35nm Au NPs are obtained after surface ligand exchange (thio-PEG instead of BSPP)

20. Resonance tunable by dielectric environment Ag, D=100 nm Si 3 N 4 (n=2.00) Si (n=3.5) D Q D Q O H Optics Express (2008), in press

21. Resonance spectra for particles on surface σ scat normalized to particle area 30 nm 10 nm D Q Appl. Phys. Lett. 93, 191113 (2008) tot sub

22. Different materials/shapes: distinct colors Old:New: All particles are driven by the external field and by each other Focusing and guidance of light at nanometer length scales (but the same principle) Other applications of nanoparticles Au colloids in water (M. Faraday ~1856) (image: CALTECH)

23. LONGITUDINAL: restoring force reduced by coupling to neighbor  Resonance shifts to lower frequency TRANSVERSE: restoring force increased by coupling to neighbor  Resonance shifts to higher frequency An isolated sphere is symmetric, so the polarization direction does not matter. Interaction between particles Near field enhancement in gaps between particles: nanoscale antenna