Abstract

The cross-spectral density function of the scattered field that is produced by scattering of a coherent plane light wave incident on a collection of different types of anisotropic particles is derived. We show the phenomena of interference of the fields scattered by each of the particles in the system. Numerical results indicate that the information about the shape, the distance, and the relative orientation of the particles may be obtained from far-zone measurements of the scattered field.

© 2010 Optical Society of America

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  1. D. G. Fischer and E. Wolf, J. Opt. Soc. Am. A 11, 1128 (1994).
    [CrossRef]
  2. D. G. Fischer and E. Wolf, Opt. Commun. 133, 17 (1997).
    [CrossRef]
  3. D. Zhao, O. Korotkova, and E. Wolf, Opt. Lett. 32, 3483 (2007).
    [CrossRef] [PubMed]
  4. M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
    [CrossRef] [PubMed]
  5. E. Baleine and A. Dogariu, Opt. Lett. 29, 1233 (2004).
    [CrossRef] [PubMed]
  6. E. Baleine and A. Dogariu, Phys. Rev. Lett. 95, 193904 (2005).
    [CrossRef] [PubMed]
  7. A. Dogariu and E. Wolf, Opt. Lett. 23, 1340 (1998).
    [CrossRef]
  8. G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
    [CrossRef]
  9. S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
    [CrossRef]
  10. S. Sahin and O. Korotkova, Opt. Lett. 34, 1762 (2009).
    [CrossRef] [PubMed]
  11. T. Wang and D. Zhao, Opt. Lett. 35, 318 (2010).
    [CrossRef] [PubMed]
  12. X. Du and D. Zhao, Opt. Lett. 35, 384 (2010).
    [CrossRef] [PubMed]
  13. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).
  14. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999).

2010

2009

S. Sahin and O. Korotkova, Opt. Lett. 34, 1762 (2009).
[CrossRef] [PubMed]

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
[CrossRef] [PubMed]

2008

S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
[CrossRef]

2007

2005

E. Baleine and A. Dogariu, Phys. Rev. Lett. 95, 193904 (2005).
[CrossRef] [PubMed]

2004

1999

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[CrossRef]

1998

1997

D. G. Fischer and E. Wolf, Opt. Commun. 133, 17 (1997).
[CrossRef]

1994

Baleine, E.

E. Baleine and A. Dogariu, Phys. Rev. Lett. 95, 193904 (2005).
[CrossRef] [PubMed]

E. Baleine and A. Dogariu, Opt. Lett. 29, 1233 (2004).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999).

Dogariu, A.

Du, X.

Fischer, D. G.

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
[CrossRef] [PubMed]

D. G. Fischer and E. Wolf, Opt. Commun. 133, 17 (1997).
[CrossRef]

D. G. Fischer and E. Wolf, J. Opt. Soc. Am. A 11, 1128 (1994).
[CrossRef]

Gbur, G.

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[CrossRef]

Korotkova, O.

Lahiri, M.

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
[CrossRef] [PubMed]

Sahin, S.

S. Sahin and O. Korotkova, Opt. Lett. 34, 1762 (2009).
[CrossRef] [PubMed]

S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
[CrossRef]

Shirai, T.

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
[CrossRef] [PubMed]

Wang, T.

Wolf, E.

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
[CrossRef] [PubMed]

D. Zhao, O. Korotkova, and E. Wolf, Opt. Lett. 32, 3483 (2007).
[CrossRef] [PubMed]

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[CrossRef]

A. Dogariu and E. Wolf, Opt. Lett. 23, 1340 (1998).
[CrossRef]

D. G. Fischer and E. Wolf, Opt. Commun. 133, 17 (1997).
[CrossRef]

D. G. Fischer and E. Wolf, J. Opt. Soc. Am. A 11, 1128 (1994).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999).

Zhao, D.

J. Opt. Soc. Am. A

Opt. Commun.

D. G. Fischer and E. Wolf, Opt. Commun. 133, 17 (1997).
[CrossRef]

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[CrossRef]

Opt. Lett.

Phys. Rev. A

S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
[CrossRef]

Phys. Rev. Lett.

E. Baleine and A. Dogariu, Phys. Rev. Lett. 95, 193904 (2005).
[CrossRef] [PubMed]

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
[CrossRef] [PubMed]

Other

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999).

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Figures (3)

Fig. 1
Fig. 1

Illustrating the notation relating to the scattering of a plane wave by a system of anisotropic particles.

Fig. 2
Fig. 2

Normalized spectral density of the scattered field as a function of the direction of scattering s. The two particles are located at the positions ( 0 , 4 λ , 0 ) and ( 0 , 4 λ , 0 ) . The effective radii are chosen as follows: (a) σ 1 x = σ 1 y = σ 1 z = σ 2 x = σ 2 y = σ 2 z = λ ; (b) σ 1 x = σ 1 y = σ 1 z = 0.5 λ and σ 2 x = σ 2 y = σ 2 z = λ ; (c) σ 1 x = σ 2 x = 0.5 λ , σ 1 y = σ 2 y = λ , and σ 1 z = σ 2 z = 1.5 λ ; (d) σ 1 x = 0.5 λ , σ 1 y = λ , σ 1 z = 1.5 λ , σ 2 x = λ , σ 2 y = 1.5 λ , and σ 2 z = 2 λ .

Fig. 3
Fig. 3

Normalized spectral density of the scattered field. There are two anisotropic particles forming the system with the effective radii: σ 1 x = 0.5 λ , σ 1 y = λ , σ 1 z = 1.5 λ , σ 2 x = λ , σ 2 y = 1.5 λ , and σ 2 z = 2 λ . The positions are chosen as follows: (a) ( 0 , 8 λ , 0 ) and (0,0,0); (b) ( 0 , 8 λ , 0 ) and ( 0 , 8 λ , 0 ) ; (c) ( 8 λ , 0 , 0 ) and ( 0 , 8 λ , 0 ) ; (d) ( 0 , 0 , 32 λ ) and ( 0 , 0 , 32 λ ) .

Equations (16)

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W ( i ) ( r 1 , r 2 , ω ) = S ( i ) ( ω ) exp [ i k s 0 ( r 2 r 1 ) ] ,
F ( r , ω ) = l = 1 L m = 1 M ( l ) f l ( r r l m , ω ) ,
f ( r , ω ) = ( ω c ) 2 η ( r , ω ) = 1 4 π ( ω c ) 2 [ n 2 ( r , ω ) 1 ]
W ( s ) ( r 1 , r 2 , ω ) = D D W ( i ) ( r 1 , r 2 , ω ) F * ( r 1 , ω ) F ( r 2 , ω ) × G * ( | r 1 r 1 | , ω ) G ( | r 2 r 2 | , ω ) d 3 r 1 d 3 r 2 ,
F * ( r 1 , ω ) F ( r 2 , ω ) = l = 1 L j = 1 L m = 1 M ( l ) n = 1 N ( j ) f l * ( r 1 r l m , ω ) f j ( r 2 r j n , ω ) ,
W ( s ) ( r s 1 , r s 2 , ω ) = 1 r 2 S ( i ) ( ω ) D D F * ( r 1 , ω ) F ( r 2 , ω ) exp { i k [ r 1 ( s 1 s 0 ) + r 2 ( s 2 s 0 ) ] } d 3 r 1 d 3 r 2 .
f l ( r r l m , ω ) = B exp [ ( x x l m ) 2 2 σ l x 2 ( y y l m ) 2 2 σ l y 2 ( z z l m ) 2 2 σ l z 2 ] ,
F ¯ ( r 12 , ω ) = F * ( r 1 , ω ) F ( r 2 , ω ) = B 2 l = 1 L j = 1 L m = 1 M ( l ) n = 1 N ( j ) exp [ ( r 12 r l j m n ) T M ¯ l j ( r 12 r l j m n ) ] ,
M ¯ l j = [ M l 0 0 M j ] ,
M ( l , j ) = [ σ ( l , j ) x 2 2 0 σ ( l , j ) y 2 2 0 σ ( l , j ) z 2 2 ] .
W ( s ) ( r s 12 , ω ) = 1 r 2 S ( i ) ( ω ) D F ¯ ( r 12 , ω ) exp ( i r 12 T K 12 ) d 6 r 12 ,
K 12 = k I ¯ ( s 12 s 00 ) ,
W ( s ) ( r s 12 , ω ) = π 3 B 2 r 2 S ( i ) ( ω ) l = 1 L j = 1 L m = 1 M ( l ) n = 1 N ( j ) [ Det ( M ¯ l j ) ] 1 2 × exp ( 1 4 K 12 T M ¯ l j 1 K 12 ) exp ( i r l j m n T K 12 ) ,
W ( s ) ( r s 12 , ω ) = 8 π 3 B 2 r 2 S ( i ) ( ω ) l = 1 L m = 1 M ( l ) σ l x σ l y σ l z exp { 1 2 k 2 [ ( s 1 x s 0 x ) 2 σ l x 2 + ( s 1 y s 0 y ) 2 σ l y 2 + ( s 1 z s 0 z ) 2 σ l z 2 ] } exp { i k [ x l m ( s 1 x s 0 x ) + y l m ( s 1 y s 0 y ) + z l m ( s 1 z s 0 z ) ] } j = 1 L n = 1 N ( j ) σ j x σ j y σ j z exp { 1 2 k 2 [ ( s 2 x s 0 x ) 2 σ j x 2 + ( s 2 y s 0 y ) 2 σ j y 2 + ( s 2 z s 0 z ) 2 σ j z 2 ] } exp { i k [ x j n ( s 2 x s 0 x ) + y j n ( s 2 y s 0 y ) + z j n ( s 2 z s 0 z ) ] } .
S ( s ) ( r s , ω ) = 8 π 3 B 2 r 2 S ( i ) ( ω ) | H ( s ) | 2 ,
H ( s ) = l = 1 L m = 1 M ( l ) σ l x σ l y σ l z exp { 1 2 k 2 [ ( s x s 0 x ) 2 σ l x 2 + ( s y s 0 y ) 2 σ l y 2 + ( s z s 0 z ) 2 σ l z 2 ] } exp { i k [ x l m ( s x s 0 x ) + y l m ( s y s 0 y ) + z l m ( s z s 0 z ) ] } .

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