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