Coherent Backscattering from Multiple Scattering Systems - KOPS ...

2.6 On polarization and interference
Figure 2.11: Theorem of reciprocity. Amplitudes and phases of direct and reversed
paths are equal if the incident and detected light is completely polarized, and if the
incident polarization P in,direct of the direct path is identical to the detected polarization
P out,reversed of the reversed path and vice versa [38]. With a single light source, direct and
reverted paths can not be distinguished, so that P in,direct = P in,reversed and P out,direct =
P out,reversed . For linear polarization we denote P in ‖ P out as the parallel polarization
channel and P in ⊥ P out as the crossed polarization channel. The respective channels for
circular polarization are called the helicity conserving and the helicity breaking channel.
2.6.2 Coherent backscattering
However, for multiply scattered photons that run on a certain path S 1 → S 2 → · · · → S n
and on its time-inverted path S n → S n−1 → · · · → S 1 the theorem of reciprocity (fig. 2.11)
predicts special correlations: Photons in the parallel polarized or helicity conserving channel
are always in phase when they leave the sample. This phase coherence is independent of the
pathlength or the exact positions of the scatterers, and therefore also insensitive to particle
motions, which are of course slow compared to the speed of light. The interference pattern of
the direct and time-inverted photons therefore survives any average over the random speckle
pattern.
Equal phases for photons on direct and time-inverted paths means also that in direct backscattering
direction all interferences are constructive, regardless of the end-to-end distances of the
photon paths that determine the angular intensity distributions of the interference patterns.
The intensity scattered in this direction is therefore twice the amount expected for an incoherent
superposition of the light waves. This all-constructive interference decays – for an
incoming spatially and temporally infinitely extended plane wave over an angular scale of
(kl ∗ ) −1 [11] – as constructive and destructive interferences superimpose for angles deviating
from backscattering direction. The resulting cone-shaped intensity enhancement is referred to
as the coherent backscattering cone.
2.6.3 Anderson localization
The concept of interference on time-inverted photon paths works also if the path forms a
closed loop inside the sample. Here, the place of the interference is the point where the light
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