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Example Presentation at SlideShare

  1. 1. Title slide Light-matter interaction from: dielectric catastrophe to: localization
  2. 2. Content dielectric response there is a wavevector there is dispersion density of states
  3. 3. Dielectric response ... dielectric response there is a wavevector there is dispersion density of states
  4. 4. Restriction to dielectrics dielectric response no magnetic response no combined response
  5. 5. Restriction to linear response all amplitude-like observables scale with a single, overall amplitude factor all intensity-like observables scale with this factor squared
  6. 6. Light-matter interaction Light sees variation in speed of light Spatial variation in index of refraction
  7. 7. Describing wave propagation Why not solving the wave equation Problems: 1. often not possible 2. does not give necessarily insight 3. each case has to be done all over again
  8. 8. Non-stationary interaction varying with time: very complicated all our standard approaches fail unless: • fully adiabatic or • fully diabatic
  9. 9. Stationary interaction from now interaction is time-independent measurements might be time-dependent
  10. 10. Use symmetry time reversal
  11. 11. Translational symmetry If there is no translational symmetry there is no wavevector there is no dispersion relation you only have eigenfunctions, and you have many of them
  12. 12. When is there a wavevector? effective medium average over disorder lattice asymptotically free space
  13. 13. There is a wave vector From now on: there is a wavevector
  14. 14. There is a wave vector ... dielectric response there is a wavevector there is dispersion density of states
  15. 15. We have translational symmetry Translational symmetry full translational symmetry full translational symmetry after averaging lattice
  16. 16. Stationary Unless I state explicitly otherwise: stationary potential stationary measurement DC, no pulse, no frequency change, ...
  17. 17. Dielectric constant to first order Objects that can be polarized polarizability density Conclusion: is a measure for the interaction
  18. 18. Dielectric constant: local field effect Lorentz-Lorenz Clausius-Mossotti (zero frequency)
  19. 19. Interaction in photonic crystals volume fraction photonic strength
  20. 20. Localization
  21. 21. Why not use larger wave length?
  22. 22. Strength in terms of refractive index Assume no absorption: extinction = scattering Assumption there is no background with index
  23. 23. Is this localization? Where is the dispersion?
  24. 24. There is dispersion ... dielectric response there is a wavevector there is dispersion density of states
  25. 25. Driven harmonically bound charge (2) Force: Equation of motion:Long-time solution:
  26. 26. Everything known of HOs Driven harmonic oscillators frequency damping charge mass density We will lump them into 2 independent parameters
  27. 27. Minimize index of refraction
  28. 28. Overdamped system
  29. 29. Is this localization?
  30. 30. Delay plays no role The delay time, or slowness, plays no direct role
  31. 31. Background is dispersive real part of index of refraction determined by host imaginary part of index of refraction determined by impurities host scatterers
  32. 32. Photonic crystal waveguide
  33. 33. If there is a dispersion relation Wavevector in the localization criterion is no problem You give me a frequency and I will look the wavevector up in the graph waveguide, slab, sphere
  34. 34. Cross-section? single scatterer in waveguide, slab, sphere
  35. 35. Is this localization? Where is the density of states?
  36. 36. Density of states ... introducing group there is a wavevector there is dispersion density of states
  37. 37. Local density of states
  38. 38. LDOS is real part of refractive index You very often see: in localization criteria: Einstein relation Misleading as dynamical effects cancel
  39. 39. Criterion For single scatterer S with T-matrix: One should calculate
  40. 40. The end introducing group there is a wavevector there is dispersion density of states

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