Abstract

Far-zone scattered intensity of a quasi-homogeneous medium illuminated with a plane scalar field is re-derived under the first Born approximation. Markov-like approximation is introduced to obtain a concise expression for the scattered intensity. Our work is an extension of the one in [Opt. Lett. 40, 1709, (2015)] to a more general mathematical model. Our result provides a convenient way for one to steer the scattered intensity with the prescribed weak scattering media. Two examples of novel media are introduced to illustrate the result.

© 2016 Optical Society of America

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References

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  1. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  2. D. G. Fischer and E. Wolf, “Inverse problems with quasi-homogeneous media,” J. Opt. Soc. Am. A 11(3), 1128–1135 (1994).
    [Crossref]
  3. O. Korotkova, “Design of weak scattering media for controllable light scattering,” Opt. Lett. 40(2), 284–287 (2015).
    [Crossref] [PubMed]
  4. O. Korotkova, “Can a sphere scatter light producing rectangular intensity patterns?” Opt. Lett. 40(8), 1709–1712 (2015).
    [Crossref] [PubMed]
  5. F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32(24), 3531–3533 (2007).
    [Crossref] [PubMed]
  6. J. Li and O. Korotkova, “Scattering of light from a stationary nonuniformly correlated medium,” Opt. Lett. 41(11), 2616–2619 (2016).
    [Crossref] [PubMed]
  7. R. A. Silverman and F. Ursell, “Scattering of plane waves by locally homogeneous dielectric noise,” Proc. Camb. Philos. Soc. 54(4), 530–537 (1958).
    [Crossref]
  8. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  9. O. Korotkova, S. Sahin, and E. Shchepakina, “Light scattering by three-dimensional objects with semi-hard boundaries,” J. Opt. Soc. Am. A 31(8), 1782–1787 (2014).
    [Crossref] [PubMed]
  10. O. Korotkova and E. Shchepakina, “Random sources for optical frames,” Opt. Express 22(9), 10622–10633 (2014).
    [Crossref] [PubMed]
  11. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  12. F. Wang and O. Korotkova, “Random sources for beams with azimuthal intensity variation,” Opt. Lett. 41(3), 516–519 (2016).
    [Crossref] [PubMed]
  13. Z. Mei, D. Zhao, O. Korotkova, and Y. Mao, “Gaussian Schell-model arrays,” Opt. Lett. 40(23), 5662–5665 (2015).
    [Crossref] [PubMed]
  14. S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
    [Crossref] [PubMed]
  15. C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of Cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
    [Crossref] [PubMed]

2016 (2)

2015 (3)

2014 (3)

2012 (1)

2007 (1)

1994 (1)

1958 (1)

R. A. Silverman and F. Ursell, “Scattering of plane waves by locally homogeneous dielectric noise,” Proc. Camb. Philos. Soc. 54(4), 530–537 (1958).
[Crossref]

Cai, Y.

Fischer, D. G.

Gori, F.

Korotkova, O.

Li, J.

Liang, C.

Liu, X.

Mao, Y.

Mei, Z.

Sahin, S.

Santarsiero, M.

Shchepakina, E.

Silverman, R. A.

R. A. Silverman and F. Ursell, “Scattering of plane waves by locally homogeneous dielectric noise,” Proc. Camb. Philos. Soc. 54(4), 530–537 (1958).
[Crossref]

Ursell, F.

R. A. Silverman and F. Ursell, “Scattering of plane waves by locally homogeneous dielectric noise,” Proc. Camb. Philos. Soc. 54(4), 530–537 (1958).
[Crossref]

Wang, F.

Wolf, E.

Zhao, D.

J. Opt. Soc. Am. A (2)

Opt. Express (1)

Opt. Lett. (8)

Proc. Camb. Philos. Soc. (1)

R. A. Silverman and F. Ursell, “Scattering of plane waves by locally homogeneous dielectric noise,” Proc. Camb. Philos. Soc. 54(4), 530–537 (1958).
[Crossref]

Other (3)

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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

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Figures (4)

Fig. 1
Fig. 1 Illustration of the far-field scattered spectral density distribution for selected values of the parameters M , namely, (a) M = 1 , (b) M = 40 . The other parameters are k δ o x = k δ o y = 20 , k δ i x = k δ i y = 40
Fig. 2
Fig. 2 Illustration of the far-field scattered spectral density distribution for selected values of the parameters M , namely, (a) M = 1 , (b) M = 40 . The other parameters are k δ o x = 10 , k δ o y = 20 , k δ i x = 15 , k δ i y = 30.
Fig. 3
Fig. 3 Illustration of the far-field scattered spectral density distribution for selected values of the parameters n , namely, (a) n = 3 , (b) n = 4 . In addition, k δ = 40 .
Fig. 4
Fig. 4 Illustration of the far-field scattered spectral density distribution for the parameters n = 0 . The other parameters are the same as in Fig. 3.

Equations (33)

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U ( i ) ( r , ω ) = a ( ω ) exp ( i k s 0 r ) .
S ( s ) ( r s )= 1 r 2 S ( i ) C F ~ [ k ( s s 0 ) , k ( s s 0 ) ] .
C F ~ ( K , K ) = D D C F ( r 1 ' , r 2 ' ) exp [ i K ( r 2 ' r 1 ' ) ] d 3 r 1 ' d 3 r 2 ' ,
C F ( r 1 ' , r 2 ' ) = F ( r 1 ' ) F ( r 2 ' ) m ,
F ( r ' ) = 1 4 π k 2 [ n 2 ( r ' ) 1 ] .
C F ( r 1 ' , r 2 ' ) = I F ( r 1 ' ) I F ( r 2 ' ) μ F ( r 2 ' r 1 ' ) ,
C F ( r 1 ' , r 2 ' ) = p ( v ) H 0 * ( r 1 ' , v ) H 0 ( r 2 ' , v ) d 3 v .
H 0 ( r ' , v ) = τ ( r ' ) exp ( i r ' v ) ,
C F ( r 1 ' , r 2 ' ) = τ * ( r 1 ' ) τ ( r 2 ' ) μ F ( r 2 ' r 1 ' ) ,
μ F ( r 2 ' r 1 ' ) = p ( v ) exp [ i v ( r 2 ' r 1 ' ) ] d 3 v .
C F ( r 1 ' , r 2 ' ) = τ 2 ( r 2 ' + r 1 ' 2 ) μ F ( r 2 ' r 1 ' ) .
r s ' = ( r 2 ' + r 1 ' ) / 2 , r d ' = r 2 ' r 1 ' ,
S ( s ) ( r s )= 1 r 2 S ( i ) I F D μ F ~ [ k ( s s 0 ) ] ,
I F D = D τ 2 ( r s ' ) d 3 r s '
μ F ~ ( K ) = D μ F ( r d ' ) exp ( i K r d ' ) d 3 r d '
μ F ( r d ' ) = δ ( z d ' ) μ F ( ρ d ' ) ,
μ F ( r d ' ) = p ( v ) e x p ( i v ρ d ' ) d 2 v exp ( i v z z d ' ) d v z = 2 π δ ( z d ' ) p ( v ) e x p ( i v ρ d ' ) d 2 v .
μ F ( ρ d ' ) = 2 π p ( v ) e x p ( i v ρ d ' ) d 2 v .
μ F ~ ( K ) = D μ F ( ρ d ' ) exp ( i K ρ ρ d ' ) d 2 ρ d ' δ ( z d ' ) exp ( i K z z d ' ) d z d ' = 2 π p ( v ) e x p ( i v ρ d ' ) exp ( i K ρ ρ d ' ) d 2 ρ d ' d 2 v = ( 2 π ) 3 p ( K ρ ) ,
S ( s ) ( r s )= (2 π ) 3 r 2 S ( i ) I F D p ( K ρ ) .
τ ( r ' ) = e x p ( r ' 2 2 σ 2 ) ,
I F D = π 3/2 σ 3 .
p ( v ) = p o ( v ) p i ( v ) ,
p o ( v ) = A C L 2 m = 1 M ( 1 ) m 1 ( M m ) exp ( m δ o x 2 v x 2 2 ) m = 1 M ( 1 ) m 1 ( M m ) exp ( m δ o y 2 v y 2 2 ) ,
p i ( v ) = A C L 2 m = 1 M ( 1 ) m 1 ( M m ) exp ( m δ i x 2 v x 2 2 ) m = 1 M ( 1 ) m 1 ( M m ) exp ( m δ i y 2 v y 2 2 ) ,
C L = m = 1 M ( 1 ) m 1 m ( M m ) ,
μ F ( ρ d ' ) = A C L 2 δ o x δ o y m = 1 M ( 1 ) m 1 m ( M m ) exp ( x d ' 2 2 m δ o x 2 ) m = 1 M ( 1 ) m 1 m ( M m ) exp ( y d ' 2 2 m δ o y 2 ) A C L 2 δ i x δ i y m = 1 M ( 1 ) m 1 m ( M m ) exp ( x d ' 2 2 m δ i x 2 ) m = 1 M ( 1 ) m 1 m ( M m ) exp ( y d ' 2 2 m δ i y 2 ) ,
A = ( 1 δ o x δ o y 1 δ i x δ i y ) 1 .
S ( s ) ( r s ) = 8 π 9 / 2 σ 3 S ( i ) r 2 C L 2 ( 1 δ o x δ o y 1 δ i x δ i y ) 1 × { m = 1 M ( 1 ) m 1 ( M m ) exp [ m δ o x 2 k 2 ( s x s 0 x ) 2 2 ] m = 1 M ( 1 ) m 1 ( M m ) exp ( m δ o y 2 k 2 ( s y s 0 y ) 2 2 ) m = 1 M ( 1 ) m 1 ( M m ) exp ( m δ i x 2 k 2 ( s x s 0 x ) 2 2 ) m = 1 M ( 1 ) m 1 ( M m ) exp ( m δ i y 2 k 2 ( s y s 0 y ) 2 2 ) } .
p ( v ) = B exp ( δ 2 v 2 ) cos 2 ( n φ 2 ) ,
μ F ( ρ d ' ) = π 2 B δ 2 exp ( ρ d ' 2 4 δ 2 ) + ( i ) n cos ( n φ d ' ) π 5 / 2 ρ d ' B 4 δ 3 exp ( ρ d ' 2 8 δ 2 ) × [ I ( n 1 ) / 2 ( ρ d ' 2 8 δ 2 ) I ( n + 1 ) / 2 ( ρ d ' 2 8 δ 2 ) ] ,
B = δ 2 π 2 .
S ( s ) ( r s )= 4 π 5 / 2 σ 3 S ( i ) δ 2 r 2 e x p ( K ρ 2 δ 2 ) cos 2 [ n ( φ K + π ) / 2 ] ,

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