Coherent Backscattering from Multiple Scattering Systems - KOPS ...

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5 Experiments As it seems to be the most well-founded value, all further evaluations were performed with the diffusion coefficient obtained from the small angle experiments, D = 13300 m2 /s. On good data sets with E ≈ 0 one can then observe the anticipated intensity cutback at the wings of the backscattering cone which balances the intensity enhancement of the cone (fig. 5.7). Especially for small kl ∗ the measured data therefore deviate considerably from α (A) c , which earlier was used to fit the backscattering data [22, 23, 47]. In contrast, the agreement with α (A) c + α (B+C) c is nearly perfect, except for a slight drop in the measured data at scattering angles close to 90 ◦ , which however suspiciously looks as if it was caused by some technical problem in the setup. These findings confirm that the improved theory developed by E. Akkermans and G. Montambaux can indeed be applied to describe coherent backscattering, and conversely allow to judge the experimental data not only by conservation of energy, but also by their agreement with the theoretical curve. A combination of both criteria should hereby yield the best results, as good agreement with the theory can also be found for E that deviate somewhat from zero, and on the other hand even a few measurements with E ≈ 0 deviate from the theory (fig. 5.8). 5.2 The coherent backscattering cone in high resolution The high resolution backscattering setup introduced in sec. 3.3 was developed as a possible means to investigate Anderson localization. The photons that are trapped on closed loops in the photon paths not only lead to a different path length distribution in time-resolved transmission experiments, but also change the shape of the coherent backscattering cone. This is because localization strongly reduces the number of photons emerging from long photon paths, which leads to a rounding of the tip of the backscattering cone similar to that caused by absorption (see sec. 2.7). At the same time the setup was built as a means to measure the transport mean free path of samples with high kl ∗ and consequently extremely narrow cones, which of course have other applications than the search for Anderson localization. 5.2.1 Tip rounding of the coherent backscattering cone In time of flight experiments the titania powder R700 has shown an onset of localization [5, 6, 48], so that it was our first choice to test if the small angle setup is applicable in the search for Anderson localization. If the setup is indeed able to resolve the effect of localization, the measured rounding of the cone tip will deviate from the theoretical prediction for pure absorption given in eqn. 2.18. If on the other hand the rounding due to localization can not be observed, this is a strong indication that the concept of the small angle setup is not suitable to detect localization effects. To evaluate the small angle backscattering data of R700, the procedure proposed in sec. 3.3 has to be altered a little: The backscattering cone of the titania powder is too wide to directly find the backscattering direction – the white region in the binary image is too frayed as that the center of mass could reliably identify the tip of the backscattering cone. Instead, the backscattering direction is derived from a teflon reference measurement, where the conetip can be found quite precisely (fig. 5.9). As the direction θ = 0 is determined only by the 56
5.2 The coherent backscattering cone in high resolution 2048 3.7 2048 x 10 4 4.4 3.6 4.2 1024 3.5 3.4 3.3 3.2 x 10 4 1 1024 2048 1024 4 3.8 3.6 3.1 3.4 1 1 1024 2048 3 1 3.2 Figure 5.9: CCD images of R700 and teflon. As the backscattering cone of R700 is very wide, it is not possible to find the backscattering direction θ = 0 from the CCD image (left). Instead, a teflon reference (right) has to be used, which gives the same position for the conetip if the optical path is not readjusted between the measurements. incoming laser beam and not by the sample, the backscattering directions of the titania sample and the teflon reference are identical. The resulting coherent backscattering cone of R700 is depicted in fig. 5.10. Although the measured data do not contradict the theory for coherent backscattering, it is obvious that it is impossible to derive more than the vague statement that the conetip is not triangular but somehow rounded. The data are much too noisy to draw any further conclusions. This disappointing result is however easy to explain. The small angle setup requires to have a lot of optical components between the sample and the camera. As none of these are ideal, they all scatter and give rise to the slightly inhomogenous and noisy background illumination that can be observed on the CCD images. This noise can not even be removed by the azimuthal average, as in the center the data are averaged over a comparatively low number of pixels. Therefore even low-intensity speckles or other disturbances are enough to hide the effect we are looking for. Altogether, it must be stated that the small angle setup in its present form can provide no information about Anderson localization. For investigations about this phenomenon other experiments like time of flight measurements have proven to be a lot more suitable [5, 6, 48]. 5.2.2 The transport mean free path of weakly scattering samples In terms of intensity resolution, measuring the transport mean free path of weakly scattering samples with large kl ∗ with the small angle setup is less challenging. The mean free path of teflon, our standard reference sample, can be estimated from eqn. 2.7 to be something like 220 µm, if the velocity of energy transport is given by the speed of light in a material 57
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 and 50: 4.2 The samples Figure 4.5: Fluidiz
Page 51 and 52: 5 Experiments 5.1 Conservation of e
Page 53 and 54: 5.1 Conservation of energy in coher
Page 63: 5.1 Conservation of energy in coher
Page 67 and 68: 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
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