Coherent Backscattering from Multiple Scattering Systems - KOPS ...

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
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