Abstract

We investigate the scattering of polychromatic plane light wave incident upon a system formed with two anisotropic particles in different distance. The analytical expression for the spectrum of the scattered field is derived. Numerical examples show the phenomena of spectral shifts and spectral switches of the scattered field. The influences of the scattering direction and the difference of the particles on the spectral switch are illustrated.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Wolf, “Invariance of the spectrum of light on propagation,” Phys. Rev. Lett.56(13), 1370–1372 (1986).
    [CrossRef] [PubMed]
  2. E. Wolf, “Red shifts and blue shifts of spectral lines emitted by two correlated sources,” Phys. Rev. Lett.58(25), 2646–2648 (1987).
    [CrossRef] [PubMed]
  3. E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of spectral lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A6(8), 1142–1149 (1989).
    [CrossRef]
  4. G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett.88(1), 013901 (2001).
    [CrossRef] [PubMed]
  5. J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun.162(1-3), 57–63 (1999).
    [CrossRef]
  6. L. Pan, C. Ding, and X. Yuan, “Spectral shifts and spectral switches of twisted Gaussian Schell-model beams passing through an aperture,” Opt. Commun.274(1), 100–104 (2007).
    [CrossRef]
  7. X. Ji, E. Zhang, and B. Lü, “Changes in the spectrum of Gaussian Schell-model beams propagating through turbulent atmosphere,” Opt. Commun.259(1), 1–6 (2006).
    [CrossRef]
  8. Z. Tong and O. Korotkova, “Spectral shifts and switches in random fields upon interaction with negative-phase materials,” Phys. Rev. A82(1), 013829 (2010).
    [CrossRef]
  9. D. G. Fischer and E. Wolf, “Inverse problems with quasi-homogeneous random media,” J. Opt. Soc. Am. A11(3), 1128–1135 (1994).
    [CrossRef]
  10. A. Dogariu and E. Wolf, “Spectral changes produced by static scattering on a system of particles,” Opt. Lett.23(17), 1340–1342 (1998).
    [CrossRef] [PubMed]
  11. M. Lahiri and E. Wolf, “Spectral changes of stochastic beams scattered on a deterministic medium,” Opt. Lett.37(13), 2517–2519 (2012).
    [CrossRef] [PubMed]
  12. T. Wang and D. Zhao, “Effects of source correlation on the spectral shift of light waves on scattering,” Opt. Lett.38(9), 1545–1547 (2013).
    [CrossRef] [PubMed]
  13. X. Du and D. Zhao, “Spectral shifts produced by scattering from rotational quasi-homogeneous anisotropic media,” Opt. Lett.36(24), 4749–4751 (2011).
    [CrossRef] [PubMed]
  14. X. Du and D. Zhao, “Frequency shifts of spectral lines induced by scattering from a rotational anisotropic particle,” Opt. Commun.285(6), 934–936 (2012).
    [CrossRef]
  15. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

2013 (1)

2012 (2)

M. Lahiri and E. Wolf, “Spectral changes of stochastic beams scattered on a deterministic medium,” Opt. Lett.37(13), 2517–2519 (2012).
[CrossRef] [PubMed]

X. Du and D. Zhao, “Frequency shifts of spectral lines induced by scattering from a rotational anisotropic particle,” Opt. Commun.285(6), 934–936 (2012).
[CrossRef]

2011 (1)

2010 (1)

Z. Tong and O. Korotkova, “Spectral shifts and switches in random fields upon interaction with negative-phase materials,” Phys. Rev. A82(1), 013829 (2010).
[CrossRef]

2007 (1)

L. Pan, C. Ding, and X. Yuan, “Spectral shifts and spectral switches of twisted Gaussian Schell-model beams passing through an aperture,” Opt. Commun.274(1), 100–104 (2007).
[CrossRef]

2006 (1)

X. Ji, E. Zhang, and B. Lü, “Changes in the spectrum of Gaussian Schell-model beams propagating through turbulent atmosphere,” Opt. Commun.259(1), 1–6 (2006).
[CrossRef]

2001 (1)

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett.88(1), 013901 (2001).
[CrossRef] [PubMed]

1999 (1)

J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun.162(1-3), 57–63 (1999).
[CrossRef]

1998 (1)

1994 (1)

1989 (1)

1987 (1)

E. Wolf, “Red shifts and blue shifts of spectral lines emitted by two correlated sources,” Phys. Rev. Lett.58(25), 2646–2648 (1987).
[CrossRef] [PubMed]

1986 (1)

E. Wolf, “Invariance of the spectrum of light on propagation,” Phys. Rev. Lett.56(13), 1370–1372 (1986).
[CrossRef] [PubMed]

Ding, C.

L. Pan, C. Ding, and X. Yuan, “Spectral shifts and spectral switches of twisted Gaussian Schell-model beams passing through an aperture,” Opt. Commun.274(1), 100–104 (2007).
[CrossRef]

Dogariu, A.

Du, X.

X. Du and D. Zhao, “Frequency shifts of spectral lines induced by scattering from a rotational anisotropic particle,” Opt. Commun.285(6), 934–936 (2012).
[CrossRef]

X. Du and D. Zhao, “Spectral shifts produced by scattering from rotational quasi-homogeneous anisotropic media,” Opt. Lett.36(24), 4749–4751 (2011).
[CrossRef] [PubMed]

Fischer, D. G.

Foley, J. T.

Gbur, G.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett.88(1), 013901 (2001).
[CrossRef] [PubMed]

Gori, F.

Ji, X.

X. Ji, E. Zhang, and B. Lü, “Changes in the spectrum of Gaussian Schell-model beams propagating through turbulent atmosphere,” Opt. Commun.259(1), 1–6 (2006).
[CrossRef]

Korotkova, O.

Z. Tong and O. Korotkova, “Spectral shifts and switches in random fields upon interaction with negative-phase materials,” Phys. Rev. A82(1), 013829 (2010).
[CrossRef]

Lahiri, M.

Lü, B.

X. Ji, E. Zhang, and B. Lü, “Changes in the spectrum of Gaussian Schell-model beams propagating through turbulent atmosphere,” Opt. Commun.259(1), 1–6 (2006).
[CrossRef]

Nemoto, S.

J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun.162(1-3), 57–63 (1999).
[CrossRef]

Pan, L.

L. Pan, C. Ding, and X. Yuan, “Spectral shifts and spectral switches of twisted Gaussian Schell-model beams passing through an aperture,” Opt. Commun.274(1), 100–104 (2007).
[CrossRef]

Pu, J.

J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun.162(1-3), 57–63 (1999).
[CrossRef]

Tong, Z.

Z. Tong and O. Korotkova, “Spectral shifts and switches in random fields upon interaction with negative-phase materials,” Phys. Rev. A82(1), 013829 (2010).
[CrossRef]

Visser, T. D.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett.88(1), 013901 (2001).
[CrossRef] [PubMed]

Wang, T.

Wolf, E.

Yuan, X.

L. Pan, C. Ding, and X. Yuan, “Spectral shifts and spectral switches of twisted Gaussian Schell-model beams passing through an aperture,” Opt. Commun.274(1), 100–104 (2007).
[CrossRef]

Zhang, E.

X. Ji, E. Zhang, and B. Lü, “Changes in the spectrum of Gaussian Schell-model beams propagating through turbulent atmosphere,” Opt. Commun.259(1), 1–6 (2006).
[CrossRef]

Zhang, H.

J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun.162(1-3), 57–63 (1999).
[CrossRef]

Zhao, D.

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

Opt. Commun. (4)

X. Du and D. Zhao, “Frequency shifts of spectral lines induced by scattering from a rotational anisotropic particle,” Opt. Commun.285(6), 934–936 (2012).
[CrossRef]

J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun.162(1-3), 57–63 (1999).
[CrossRef]

L. Pan, C. Ding, and X. Yuan, “Spectral shifts and spectral switches of twisted Gaussian Schell-model beams passing through an aperture,” Opt. Commun.274(1), 100–104 (2007).
[CrossRef]

X. Ji, E. Zhang, and B. Lü, “Changes in the spectrum of Gaussian Schell-model beams propagating through turbulent atmosphere,” Opt. Commun.259(1), 1–6 (2006).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

Z. Tong and O. Korotkova, “Spectral shifts and switches in random fields upon interaction with negative-phase materials,” Phys. Rev. A82(1), 013829 (2010).
[CrossRef]

Phys. Rev. Lett. (3)

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett.88(1), 013901 (2001).
[CrossRef] [PubMed]

E. Wolf, “Invariance of the spectrum of light on propagation,” Phys. Rev. Lett.56(13), 1370–1372 (1986).
[CrossRef] [PubMed]

E. Wolf, “Red shifts and blue shifts of spectral lines emitted by two correlated sources,” Phys. Rev. Lett.58(25), 2646–2648 (1987).
[CrossRef] [PubMed]

Other (1)

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Illustrating the notation relating to the scattering of a plane light wave by a system formed with two anisotropic particles.

Fig. 2
Fig. 2

The solid lines show the spectral shifts and spectral switches produced by the scattering system of two same anisotropic particles having σ x = σ ox = λ 0 , σ y = σ oy =2 λ 0 , and σ z = σ oz =3 λ 0 . We observe in the direction of scattering s= ( 0,1/2 , 3 /2 ) T . The off-center anisotropic particle is located with different distance: (a) d=5.01 λ 0 , (b) d=5.04 λ 0 , (c) d=5.046 λ 0 , (d) d=5.05 λ 0 . The dotted lines show the spectrum of the incident field.

Fig. 3
Fig. 3

Spectral shifts produced by the scattering system of two same anisotropic particles having σ x = σ ox = λ 0 , σ y = σ oy =2 λ 0 , and σ z = σ oz =3 λ 0 with distance d. We observe in the direction of scattering: (a) s= ( 0,1/2 , 3 /2 ) T , (b) s= ( 0, 3 /2 ,1/2 ) T .

Fig. 4
Fig. 4

Spectral shifts produced by the scattering system of two different anisotropic particles with distance d. The anisotropic particle centered at the origin is fixed with the effective radius σ x = λ 0 , σ y =2 λ 0 , and σ z =3 λ 0 . The solid line is calculated by choosing the effective radius of the off-center anisotropic particle as follows: σ ox = λ 0 , σ oy =2 λ 0 , and σ oz =3.1 λ 0 . The dotted line is calculated by choosing σ ox = λ 0 , σ oy =2 λ 0 , and σ oz =3.5 λ 0 . We observe in the direction of scattering s= ( 0,1/2 , 3 /2 ) T .

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

{ U ( i ) ( r ,ω ) }={ a( ω ) }exp( ik s 0 r ),
W ( i ) ( r 1 , r 2 ,ω )= U ( i ) ( r 1 ,ω ) U ( i ) ( r 2 ,ω ) ,
W ( i ) ( r 1 , r 2 ,ω )= S ( i ) ( ω )exp[ ik s 0 ( r 2 r 1 ) ],
S ( i ) ( ω )= a ( ω )a( ω )
S ( i ) ( ω )=Aexp[ ( ω ω 0 ) 2 2 Γ 0 2 ],
μ ( i ) ( r 1 , r 2 ,ω )=exp[ ik s 0 ( r 2 r 1 ) ],
W ( s ) ( r 1 , r 2 ,ω )= U ( s ) ( r 1 ,ω ) U ( s ) ( r 2 ,ω ) ,
U ( s ) ( r,ω )= U ( s ) ( rs,ω )= S ( i ) ( ω ) exp( ikr ) r D F( r ,ω )exp[ ik( s s 0 ) r ] d 3 r ,
F( r ,ω )=Bexp[ x 2 2 σ x 2 y 2 2 σ y 2 z 2 2 σ z 2 ],
F o ( r ,ω )=Bexp[ ( x x o ) 2 2 σ ox 2 ( y y o ) 2 2 σ oy 2 ( z z o ) 2 2 σ oz 2 ],
F( r ,ω )=Bexp( r T M r ),
M= 1 2 [ σ x 2 0 0 0 σ y 2 0 0 0 σ z 2 ].
F o ( r ,ω )=Bexp[ ( r r o ) T M o ( r r o ) ],
M o = 1 2 [ σ ox 2 0 0 0 σ oy 2 0 0 0 σ oz 2 ].
U ( s ) ( rs,ω )= S ( i ) ( ω ) exp( ikr ) r D F( r ,ω )exp( i r T K ) d 3 r ,
U ( s ) ( rs,ω )= π 3/2 B S ( i ) ( ω ) exp( ikr ) r [ det( M ) ] 1/2 exp( 1 4 K T M 1 K ),
U o ( s ) ( rs,ω )= π 3/2 B S ( i ) ( ω ) exp( ikr ) r [ det( M o ) ] 1/2 exp( 1 4 K T M o 1 K )exp( i r o T K ).
W ( s ) ( r s 1 ,r s 2 ,ω )= [ U ( s ) ( r s 1 ,ω )+ U o ( s ) ( r s 1 ,ω ) ] [ U ( s ) ( r s 2 ,ω )+ U o ( s ) ( r s 2 ,ω ) ] ,
S ( s ) ( rs,ω ) W ( s ) ( rs,rs,ω ).
S ( s ) ( rs,ω )= π 3 A B 2 r 2 exp[ ( ω ω 0 ) 2 2 Γ 0 2 ] | H( s,ω ) | 2 ,
H( s,ω )= [ det( M ) ] 1/2 exp( 1 4 K T M 1 K ) + [ det( M o ) ] 1/2 exp( 1 4 K T M o 1 K )exp( i r o T K ).
H( s,ω )= [ det( M ) ] 1/2 exp( 1 4 K T M 1 K )[ 1+exp( i r o T K ) ].

Metrics