Coherent Backscattering from Multiple Scattering Systems - KOPS ...

4 Samples
3 0
2 5
n u m b e r o f p a rtic le s
2 0
1 5
1 0
5
0
1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0
p a rtic le d ia m e te r [n m ]
Figure 4.1: Particle size and polydispersity. From the electron microscope image
(left) the distribution of the particle sizes of R700 (right) was obtained by measuring the
diameters of approximately 150 particles [47].
and can quite easily be calculated by measuring the weight m and the spatial dimensions r
and h of the sample, while the mass density ρ of the scattering material can be obtained from
numerous literature sources.
For strong scattering and low mean free paths, the sample should be as dense as possible. If
however the filling fraction is larger than a certain value (which depends on the mismatch of
the refractive indices of scatterers and surrounding medium) [20], scattering takes place at the
holes rather than the particles, so that there is no use increasing the volume fraction beyond
this value.
4.1.3 Effective refractive index
The refractive index mismatch between the particles and the surrounding medium determines
the effectiveness of the scattering. In contrast, the effective refractive index, which is an average
over the indices of the scatterers, n scat , and the medium in between, n surr , describes
the sample as a whole and is for example needed to calculate the reflectivity of the sample
surface.
Linear approach
The most simple and straightforward approach to calculate the effective refractive index n eff
of a sample is to establish an average medium with an averaged refractive index
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n eff = f · n scat + (1− f ) · n surr