Abstract

It is demonstrated that the occurence of backscattered polarization patterns relates to the conservation of angular momentum of light. Using the geometrical phase formalism in the spin space, we develop a model where the helicity-maintaining and the helicity-flipping multiple-scattering processes can be accounted for. The model explains practically all the symmetries present in the spatially resolved Mueller matrices.

© 2008 Optical Society of America

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References

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2006

2005

2004

2002

V. Rossetto and A. C. Maggsa, "Writhing geometry of stiff polymers and scattered light," Eur. Phys. J. B 29, 323-326 (2002).
[CrossRef]

2000

1999

1998

1997

1996

M. Dogariu and T. Asakura, "Photon pathlength distribution from polarized backscattering in random media," Opt. Eng. 35, 2234-2239 (1996).
[CrossRef]

1993

M. Dogariu and T. Asakura, "Polarization dependent backscattering patterns from weakly scattering media," J. Opt. (Paris) 24, 271-278 (1993).
[CrossRef]

1985

1980

Appl. Opt.

Eur. Phys. J. B

V. Rossetto and A. C. Maggsa, "Writhing geometry of stiff polymers and scattered light," Eur. Phys. J. B 29, 323-326 (2002).
[CrossRef]

J. Opt. (Paris)

M. Dogariu and T. Asakura, "Polarization dependent backscattering patterns from weakly scattering media," J. Opt. (Paris) 24, 271-278 (1993).
[CrossRef]

Opt. Eng.

M. Dogariu and T. Asakura, "Photon pathlength distribution from polarized backscattering in random media," Opt. Eng. 35, 2234-2239 (1996).
[CrossRef]

Opt. Express

Opt. Lett.

Other

J. W. Goodman, Statistical Optics (Wiley, 1985).

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Figures (6)

Fig. 1
Fig. 1

Mueller matrix elements of exact backscattered light that preserved its helicity.

Fig. 2
Fig. 2

Mueller matrix elements of exact backscattered light for which the helicity is mixed ( a = 0.5 ) .

Fig. 3
Fig. 3

Mueller matrix elements of exact backscattered light for an intermediate case of helicity mixing ( a = 0.75 ) .

Fig. 4
Fig. 4

Qualitative illustration of the geometrical phase perturbation introduced by off-axis light. (a) Description of light injection (on axis) and collection (over some finite angular acceptance). The collected light has a biased angular distribution. (b) Manifestation of the biased angular distribution of collected light on the helicity sphere (looking straight at the backward pole.)

Fig. 5
Fig. 5

Mueller matrix elements for a case of backscattered light that preserved its helicity and collection optics with a finite FOV [ a = exp ( i 0.1 ) ] .

Fig. 6
Fig. 6

Mueller matrix elements of backscattered light for an intermediate case of helicity mixing and collection optics with a finite FOV [ a = 0.85 exp ( i 0.1 ) ] .

Equations (15)

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E i = E L L ̂ + E R exp ( i δ ) R ̂ ,
E s = E L A L ( r , ϕ ) exp [ i ψ L ( r , ϕ ) ] exp ( i 2 ϕ ) L ̂
+ E R exp ( i δ ) A R ( r , ϕ ) exp [ i ψ R ( r , ϕ ) ] exp ( i 2 ϕ ) R ̂ ,
I = [ E L A L ( r , ϕ ) ] 2 + [ E R A R ( r , ϕ ) ] 2 ,
Q = 2 Re [ E L E R A L ( r , ϕ ) A R ( r , ϕ ) exp [ i ψ L ( r , ϕ ) i ψ R ( r , ϕ ) i δ ] exp ( i 4 ϕ ) ] ,
U = 2 Im [ E L E R A L ( r , ϕ ) A R ( r , ϕ ) exp [ i ψ L ( r , ϕ ) i ψ R ( r , ϕ ) i δ ] exp ( i 4 ϕ ) ] ,
V = [ E L A L ( r , ϕ ) ] 2 [ E R A R ( r , ϕ ) ] 2 .
I = ( E L 2 + E R 2 ) A 2 ( r ) ,
Q = 2 Re [ E L E R A 2 ( r ) exp ( i 4 ϕ ) ] = 2 E L E R A 2 ( r ) cos ( 4 ϕ + δ ) ,
U = 2 Im [ E L E R A 2 ( r ) exp ( i 4 ϕ ) ] = 2 E L E R A 2 ( r ) sin ( 4 ϕ + δ ) ,
V = ( E L 2 E R 2 ) A 2 ( r ) .
( E L ( s ) ( r , ϕ ) E R ( s ) ( r , ϕ ) ) = A 2 ( r ) [ a ( r ) exp ( i 2 ϕ ) ( 1 a ( r ) ) ( 1 a ( r ) ) a ( r ) exp ( i 2 ϕ ) ] ( E L ( i ) E R ( i ) , )
a = 1 b b b 2 2 b 1 .
p ( Ω ) = exp ( k 2 2 ) 2 π + k cos ( Ω ) 2 π exp [ k 2 sin 2 ( Ω ) 2 ] Φ [ k cos ( Ω ) ] ,
Φ ( z ) = 1 2 π z exp ( y 2 2 ) d y .

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