Coherent Backscattering from Multiple Scattering Systems - KOPS ...
Coherent Backscattering from Multiple Scattering Systems - KOPS ...
Coherent Backscattering from Multiple Scattering Systems - KOPS ...
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5 Experiments<br />
is lower than 1 (fig. 5.5). At the wings of the backscattering cone an intensity cutback appears<br />
that balances the intensity enhancement of the cone.<br />
However, the effect of α (B+C)<br />
c is significant only for small kl ∗ . For kl ∗ 10 its influence is negligible,<br />
and the backscattering cone is well described by the cooperon α (A)<br />
c given in eqn. 2.15.<br />
In this regime the diffuson can be found <strong>from</strong> the large angle wings of the backscattering data<br />
[55]. For small kl ∗ the diffuson is hidden by the intensity cutback, and the proceeding devised<br />
above has to be used to extract the cooperon <strong>from</strong> the data.<br />
Small kl ∗ however means strongly scattering dense samples, where the scattering particles are<br />
in touching distance. In such systems, near-field effects become important for the scattering<br />
process. Strictly speaking, the random walk model developed for dilute systems and the<br />
deduction of the transport mean free path <strong>from</strong> the intensity distribution of Mie scattering<br />
and the anisotropy parameter 〈cos θ〉 are no longer valid. The kl ∗ obtained by fitting with the<br />
theory <strong>from</strong> Akkermans and Montambaux will therefore certainly have the correct order of<br />
magnitude, but might deviate slightly <strong>from</strong> the real value.<br />
5.1.4 The results of the test experiments<br />
To test the theoretical prediction made above, the coherent backscattering cones of various<br />
samples were measured with the wide angle setup. The diffusion coefficients lay in the range<br />
between 13 m2 /s and 250 m2 /s (see tab. 4.1), so that we expected to observe extremely wide<br />
backscattering cones with kl ∗ close to unity and a distinct intensity cutback as well as narrow<br />
cones with high kl ∗ where no cutback is visible.<br />
As the albedos of the titania samples are basically 1, the albedo mismatch of sample and<br />
reference is mainly given by the albedo of the teflon block. The latter was calculated with<br />
all three diffusion coefficients D = 27500 m2 /s, D = 16500 m2 /s, and D = 13300 m2 /s that can<br />
be derived <strong>from</strong> time of flight and small angle backscattering experiments, as discussed in<br />
sec. 4.2.2.<br />
The data quality of the wide angle backscattering experiments varies strongly, as the wide<br />
angle setup is extremely sensitive to parasitically scattered light. However, as stated above,<br />
the backscattering cone is evidentially caused by interference, so that the total amount of<br />
backscattered power must be the same both for the coherent and the incoherent addition of<br />
∫ π/2<br />
0<br />
a c (θ) sin θ dθ dφ of the cooperon is<br />
the backscattered intensity, and the integral E = ∫ 2π<br />
0<br />
necessarily zero. E can therefore be used as a criterion to judge the quality of the experimental<br />
data.<br />
Furthermore, it is also possible to substantiate the method to calculate the albedo that was<br />
developed earlier. In fig. 5.6 one observes that the data are approximately centered at E = 0<br />
if the albedo is calculated with D = 16500 m2 /s and D = 13300 m2 /s, but are shifted to E ≈<br />
−0.1 sterad for an albedo calculated with D = 27500 m2 /s. Therefore the data on average<br />
suggest conservation of energy for precisely those values of the diffusion coefficient which<br />
are obtained <strong>from</strong> the small angle measurements (see sec. 5.2.2). This strongly indicates that<br />
the values for the albedos are correct, although as proof further experiments on samples with<br />
other albedos than teflon or titania are necessary.<br />
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