Coherent Backscattering from Multiple Scattering Systems - KOPS ...

2.7 The theory of coherent backscattering
cooperon [a.u.]
0.3
0.25
0.2
0.15
0.1
l abs
= 10 −5 m
l abs
= 3 ⋅ 10 −5 m
l abs
= 10 −4 m
no absorption
0.05
0
−90 −60 −30 0 30 60 90
scattering angle [deg]
Figure 2.14: Coherent backscattering with absorption – unnormalized cooperon. The
graph shows the unnormalized cooperon for different absorption lengths l abs = 3Dτ/l ∗
with λ = 590 nm, kl ∗ = 5, and non-reflective sample surface. Deviations from the
non-absorptive case at the cone flanks can be observed only for very short absorption
lengths, which are irrelevant for our experimental situations.
Both absorption and localization not only cause a rounding of the conetip, they also widen
the cooperon. However, in many experimental situations the normalization of the diffuson
and the cooperon by ∫ j(⃗r ⊥ , θ = 0) d⃗r ⊥ is unnecessary, as the experimental data are also not
normalized. Applying the above transformations only to the numerator of the cooperon in
eqn. 2.13 results in a lowered cone enhancement instead of a widened cooperon (fig. 2.14), so
that the cone flanks are unaffected by absorption or localization. In the measurement of kl ∗ ,
an imprecise rendition of the very tip of the backscattering cone – which is rather common for
narrow cones – is therefore no major source of errors, as the theory can be fitted to the flanks
of the cone.
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