Title Light in Strongly Scattering and Amplifying Random Media English 1.6 MB 144
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Page 72

72 Experimental evidence for recurrent multiple scattering

the third term describes double scattering. The higher order terms of the
prefactor generate all recurrent diagrams in Eq. (4.12).

The vector Green’s function G(ra − r b), which depends only on the
relative positions of both scatterers r = ra − r b, can be decomposed into
a longitudinal part Q(r) and a transverse part P (r):

G(r) = P (kr)∆∆r +Q(kr)r̂r̂, (4.14)

with P and Q given by :

P (y) =
k

(
−1 +

1

iy
+

1

y2

)
eiy

y
(4.15)

and

Q(y) = −2
k

(
1

iy
+

1

y2

)
eiy

y
, (4.16)

where y = k r, and the matrices ∆∆r and r̂r̂ are projections respectively to
and along the direction of r.

To calculate the two particle bistatic coefficient, we need the total two
particle vertex ΓΓ

(2)
, which is the square of the two particle t-matrix:

ΓΓ
(2)
ab (r1, r2, r3, r4) = T

(2)
ab (r1, r2) T

(2)∗
ab (r3, r4). (4.17)

With Eq. (4.13), we have a closed expression for ΓΓ
(2)
. Some terms con-

tributing to ΓΓ
(2)

are:

ΓΓ
(2)

=

×

×

+

× ×

× ×

+

× ×

× ×

+

×
'& %\$

× ×

×

+

×
'& %\$

× ×

× × ×