Coherent Backscattering from Multiple Scattering Systems - KOPS ...

4 Samples
1
0.8
reflectivity
0.6
0.4
0.2
0
1 1.5 2 2.5 3
effective refractive index
Figure 4.3: Reflectivity. The graph shows the reflectivity of the sample-air interface as
a function of the effective refractive index of the sample. For the titania samples with
n eff of the order of 1.5 the reflectivity is roughly 0.5 to 0.6.
surrounding medium with refractive indices n eff and n surr can be estimated from Fresnel’s
equations as
R(η) = R ‖(η) + R ⊥ (η)
2
⎧
tan ⎪⎨
2 (θ − η)
= 2 tan 2 (θ + η) + sin2 (θ − η)
2 sin 2 (θ + η) for η ≤ arcsin n surr
n eff
⎪⎩
1 for η > arcsin n surr
n eff
were η and θ are the directions of the incident and the transmitted light beam.
reflectivity is then obtained from the boundary conditions at the surface [58]:
The total
R = 3C 2 + 2C 1
3C 2 − 2C 1 + 2
(4.2)
with
C 1 =
∫ π/2
0
R(η) sin η cos η dη , C 2 =
∫ 0
−π/2
R(η) sin η cos 2 η dη
4.2 The samples
For the experiments three kinds of multiple scattering samples were used: dense colloidal
samples of titanium dioxide, solid teflon as reference sample, and water-fluidized beds with
soda lime glass beads.
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