Coherent Backscattering from Multiple Scattering Systems - KOPS ...

5 Experiments
5.1 Conservation of energy in coherent backscattering
Conservation of energy is one of the most fundamental principles in physics. However, the
intensity enhancement of the coherent backscattering cone is one instance where it seems to
be violated at first glance:
The origin of the backscattering enhancement lies in the interference of waves propagating
along reciprocal paths. a This interference can only spatially re-distribute the light energy that
emerges from the sample surface; it can not destroy photons or create new ones. The total
amount of energy per unit time emerging from the sample must therefore be the same with
and without interference:
∫
half-space
∫
α d (θ) dΩ =
half-space
α d (θ) + α c (θ) dΩ
where diffuson α d (θ) and cooperon α c (θ) are the coherent and the incoherent addition of the
photon flux as defined in sec. 2.7. It follows for the coherent backscattering enhancement that
∫
half-space
α c (θ) dΩ = 0 (5.1)
Thus the intensity enhancement of the coherent backscattering cone at small angles should be
balanced by a corresponding intensity cutback to ensure conservation of energy.
Unfortunately, such an intensity cutback had never been observed experimentally, and the
theory of coherent backscattering as developed in sec. 2.7 does not predict an intensity cutback
either. As the principle of conservation of energy holds in any case, the only possible
conclusion is that both the experimental procedure and the theoretical description of the
backscattering cone are too inaccurate to render the cone correctly.
The question if the backscattering cone is depicted correctly by experiment and theory is not
just of purely academic interest. The accurate measurement and description of the cone is
important as the scaling of its width with the inverse product of the wave vector k of the
scattered light and the transport mean free path l ∗ is commonly used to characterize multiple
scattering materials. In particular in the study of Anderson localization of light [13] a reliable
[a] The interference nature of coherent backscattering can be proved for example by the influence of Faraday
rotation on the backscattering cone [35, 36, 37].