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