Coherent Backscattering from Multiple Scattering Systems - KOPS ...

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Contents 5 Experiments 43 5.1 Conservation of energy in coherent backscattering . . . . . . . . . . . . . . . . . 43 5.2 The coherent backscattering cone in high resolution . . . . . . . . . . . . . . . . 56 6 Summary 69 Bibliography 74 Figures and Tables 75 MATLAB codes 79 Angular intensity distribution of single scattering . . . . . . . . . . . . . . . . . . . . . . 79 Evaluation of the wide angle data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Evaluation of the small angle data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 vi
1 Introduction There have been many spectacular findings in the field of multiple scattering of light in random media, from the theoretical work of P. W. Anderson in the 1950s [13] and its application to electromagnetic waves [14, 28] to the discovery of the coherent backscattering cone some 30 years ago [31, 52, 57] and the resent find of the onset of Anderson localization [5, 6, 48]. This work however focusses on the equally important improvements of the experimental techniques for the investigation of multiple scattering phenomenons. Of particular interest were experiments on the coherent backscattering cone, an interference effect that causes a twofold intensity enhancement in the direction opposite to the incoming wave. Although it can be observed not only on visible light in the laboratory, but also in space [24], on microwaves [18], seismic waves [34], sound waves [15], or the de Broglie waves of electrons in metals [29], the laboratory experiments with visible light have two major advantages over other systems: There are no rivaling effects like interaction between the scattered particles or binding in deep minima of the random potential, except for absorption, and the necessary technical effort is comparatively low. Multiple scattering with electromagnetic waves in the visible range is therefore used as model system to experimentally investigate multiple scattering of waves [14, 28]. From the shape of the coherent backscattering cone one can read all kinds of information about the scattering process in the medium. The cone width for example is a measure for the transport mean free path l ∗ and therefore for the turbidity of the medium. The shape of the conetip gives evidence of absorption and in some cases even the transition to a localizing state. The experiments however require highly sensitive setups and refined theoretical descriptions to precisely depict the angular distribution of the backscattered light and to correctly fit the scattering parameters. This thesis reports the work on two experimental setups, one to record the backscattered radiation over a wide angular range, the other for detailed measurement of the intensity distribution close to backscattering direction. The theoretical basis is laid in sec. 2, where the mathematical description of coherent backscattering is developed starting from the wave equation. Along the way, some insight is also given in phenomena like single scattering at Mie particles and Anderson localization. Sec. 3 gives technical information about the setups used for the scattering experiments. These are not only the two backscattering setups this work focusses on, but also a time of flight setup which is used to record the time-dependent scattering in transmission. The next section presents the samples used in the experiments alongside with some additional characterizing methods. Finally, sec. 5 reports the revision process of the two setups. For the wide angle setup the evaluation procedure was refined, and an improved theory of coherent backscattering was developed, while the small angle setup was tested in experiments on strongly scattering titanium dioxide samples, on teflon as an example of a weakly scattering material, and on water-fluidized beds of glass beads. The MATLAB [2] codes used for the evaluations can be found in the appendix.
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: Contents Ein kurzer Überblick i Da
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
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5.1 Conservation of energy in coher
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5.2 The coherent backscattering con
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6 Summary The focus of the work pre
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Bibliography [1] http://www.schneid
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Bibliography [34] E. Larose, L. Mar
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Figures and Tables Figures Backscat
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Figures and Tables Tables 4.1 Collo
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MATLAB codes Angular intensity dist
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Evaluation of the wide angle data E
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Evaluation of the wide angle data %
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Evaluation of the wide angle data f
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Evaluation of the small angle data
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