Coherent Backscattering from Multiple Scattering Systems - KOPS ...
Coherent Backscattering from Multiple Scattering Systems - KOPS ... Coherent Backscattering from Multiple Scattering Systems - KOPS ...
4 Samples 0.09 0.08 0.07 relative particle number 0.06 0.05 0.04 0.03 0.02 0.01 0 80 100 120 140 160 180 200 particle diameter [µm] Figure 4.6: Particle size distribution in the fluidized bed. The size distribution was measured at the University of Magdeburg on a Retsch Technology Camsizer. 42
5 Experiments 5.1 Conservation of energy in coherent backscattering Conservation of energy is one of the most fundamental principles in physics. However, the intensity enhancement of the coherent backscattering cone is one instance where it seems to be violated at first glance: The origin of the backscattering enhancement lies in the interference of waves propagating along reciprocal paths. a This interference can only spatially re-distribute the light energy that emerges from the sample surface; it can not destroy photons or create new ones. The total amount of energy per unit time emerging from the sample must therefore be the same with and without interference: ∫ half-space ∫ α d (θ) dΩ = half-space α d (θ) + α c (θ) dΩ where diffuson α d (θ) and cooperon α c (θ) are the coherent and the incoherent addition of the photon flux as defined in sec. 2.7. It follows for the coherent backscattering enhancement that ∫ half-space α c (θ) dΩ = 0 (5.1) Thus the intensity enhancement of the coherent backscattering cone at small angles should be balanced by a corresponding intensity cutback to ensure conservation of energy. Unfortunately, such an intensity cutback had never been observed experimentally, and the theory of coherent backscattering as developed in sec. 2.7 does not predict an intensity cutback either. As the principle of conservation of energy holds in any case, the only possible conclusion is that both the experimental procedure and the theoretical description of the backscattering cone are too inaccurate to render the cone correctly. The question if the backscattering cone is depicted correctly by experiment and theory is not just of purely academic interest. The accurate measurement and description of the cone is important as the scaling of its width with the inverse product of the wave vector k of the scattered light and the transport mean free path l ∗ is commonly used to characterize multiple scattering materials. In particular in the study of Anderson localization of light [13] a reliable [a] The interference nature of coherent backscattering can be proved for example by the influence of Faraday rotation on the backscattering cone [35, 36, 37].
- Page 1 and 2: Dissertation Coherent Backscatterin
- Page 3 and 4: Ein kurzer Überblick Streuung ist
- Page 5 and 6: Ein kurzer Überblick portweglänge
- Page 7 and 8: Contents Ein kurzer Überblick i Da
- Page 9 and 10: 1 Introduction There have been many
- Page 11 and 12: 2 Theory In scattering theory, the
- Page 13 and 14: 2.2 Single scattering - Mie theory
- Page 15 and 16: 2.2 Single scattering - Mie theory
- Page 17 and 18: 2.3 Random walk and diffusion scatt
- Page 19 and 20: 2.3 Random walk and diffusion of pr
- Page 21 and 22: 2.4 The influence of boundaries Fig
- Page 23 and 24: 2.5 Photon flux from a surface The
- Page 25 and 26: 2.6 On polarization and interferenc
- Page 27 and 28: 2.6 On polarization and interferenc
- Page 29 and 30: 2.7 The theory of coherent backscat
- Page 31 and 32: 2.7 The theory of coherent backscat
- Page 33 and 34: 3 Setups 3.1 Laser System The key p
- Page 35 and 36: 3.2 Wide Angle Setup 1 .0 0 .8 h e
- Page 37 and 38: 3.3 Small Angle Setup 1 0.998 0.996
- Page 39 and 40: 3.3 Small Angle Setup Figure 3.6: T
- Page 41 and 42: 3.4 Time Of Flight Setup Figure 3.8
- Page 43 and 44: 4 Samples 4.1 Sample characterizati
- Page 45 and 46: 4.1 Sample characterization techniq
- Page 47 and 48: 4.2 The samples sample particle siz
- Page 49: 4.2 The samples Figure 4.5: Fluidiz
- Page 53 and 54: 5.1 Conservation of energy in coher
- Page 55 and 56: 5.1 Conservation of energy in coher
- Page 57 and 58: 5.1 Conservation of energy in coher
- Page 59 and 60: 5.1 Conservation of energy in coher
- Page 61 and 62: 5.1 Conservation of energy in coher
- Page 63 and 64: 5.1 Conservation of energy in coher
- Page 65 and 66: 5.2 The coherent backscattering con
- Page 67 and 68: 5.2 The coherent backscattering con
- Page 69 and 70: 5.2 The coherent backscattering con
- Page 71 and 72: 5.2 The coherent backscattering con
- Page 73 and 74: 5.2 The coherent backscattering con
- Page 75 and 76: 5.2 The coherent backscattering con
- Page 77 and 78: 6 Summary The focus of the work pre
- Page 79 and 80: Bibliography [1] http://www.schneid
- Page 81 and 82: Bibliography [34] E. Larose, L. Mar
- Page 83 and 84: Figures and Tables Figures Backscat
- Page 85 and 86: Figures and Tables Tables 4.1 Collo
- Page 87 and 88: MATLAB codes Angular intensity dist
- Page 89 and 90: Evaluation of the wide angle data E
- Page 91 and 92: Evaluation of the wide angle data %
- Page 93 and 94: Evaluation of the wide angle data f
- Page 95 and 96: Evaluation of the small angle data
- Page 97 and 98: Evaluation of the small angle data
- Page 99: Evaluation of the small angle data
5 Experiments<br />
5.1 Conservation of energy in coherent backscattering<br />
Conservation of energy is one of the most fundamental principles in physics. However, the<br />
intensity enhancement of the coherent backscattering cone is one instance where it seems to<br />
be violated at first glance:<br />
The origin of the backscattering enhancement lies in the interference of waves propagating<br />
along reciprocal paths. a This interference can only spatially re-distribute the light energy that<br />
emerges <strong>from</strong> the sample surface; it can not destroy photons or create new ones. The total<br />
amount of energy per unit time emerging <strong>from</strong> the sample must therefore be the same with<br />
and without interference:<br />
∫<br />
half-space<br />
∫<br />
α d (θ) dΩ =<br />
half-space<br />
α d (θ) + α c (θ) dΩ<br />
where diffuson α d (θ) and cooperon α c (θ) are the coherent and the incoherent addition of the<br />
photon flux as defined in sec. 2.7. It follows for the coherent backscattering enhancement that<br />
∫<br />
half-space<br />
α c (θ) dΩ = 0 (5.1)<br />
Thus the intensity enhancement of the coherent backscattering cone at small angles should be<br />
balanced by a corresponding intensity cutback to ensure conservation of energy.<br />
Unfortunately, such an intensity cutback had never been observed experimentally, and the<br />
theory of coherent backscattering as developed in sec. 2.7 does not predict an intensity cutback<br />
either. As the principle of conservation of energy holds in any case, the only possible<br />
conclusion is that both the experimental procedure and the theoretical description of the<br />
backscattering cone are too inaccurate to render the cone correctly.<br />
The question if the backscattering cone is depicted correctly by experiment and theory is not<br />
just of purely academic interest. The accurate measurement and description of the cone is<br />
important as the scaling of its width with the inverse product of the wave vector k of the<br />
scattered light and the transport mean free path l ∗ is commonly used to characterize multiple<br />
scattering materials. In particular in the study of Anderson localization of light [13] a reliable<br />
[a] The interference nature of coherent backscattering can be proved for example by the influence of Faraday<br />
rotation on the backscattering cone [35, 36, 37].
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