Abstract

A three-dimensional multi-Gaussian function, being a finite sum of Gaussian functions, is adopted for modeling of a spherically symmetric scatterer with a semisoft boundary, i.e. such that has continuous and adjustable drop in the index of refraction. A Gaussian sphere and a hard sphere are the two limiting cases when the number of terms in multi-Gaussian distribution is one and infinity, respectively. The effect of the boundary’s softness on the intensity distribution of the scattered wave is revealed. The generalization of the model to random scatterers with semisoft boundaries is also outlined.

© 2011 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge U. Press, 1999).
  2. E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  3. T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
    [CrossRef] [PubMed]
  4. F. Gori, Opt. Commun. 107, 335 (1994).
    [CrossRef]
  5. Y. Li, H. Lee, and E. Wolf, Opt. Eng. 42, 2707 (2003).
    [CrossRef]
  6. S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
    [CrossRef]
  7. J. Yin, W. Gao, and Y. Zhu, in Progress in Optics 44, E.Wolf, ed. (North-Holland, 2003), pp. 119–204.
    [CrossRef]
  8. F. Gori and O. Korotkova, Opt. Commun. 282, 3859(2009).
    [CrossRef]
  9. O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609(2007).
    [CrossRef]
  10. S. Sahin and O. Korotkova, Opt. Lett. 34, 1762 (2009).
    [CrossRef] [PubMed]
  11. T. D. Visser and E. Wolf, Phys. Rev. E 59, 2355(1999).
    [CrossRef]

2010 (1)

T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef] [PubMed]

2009 (2)

2007 (1)

O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609(2007).
[CrossRef]

2003 (1)

Y. Li, H. Lee, and E. Wolf, Opt. Eng. 42, 2707 (2003).
[CrossRef]

1999 (1)

T. D. Visser and E. Wolf, Phys. Rev. E 59, 2355(1999).
[CrossRef]

1994 (1)

F. Gori, Opt. Commun. 107, 335 (1994).
[CrossRef]

1988 (1)

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[CrossRef]

Born, M.

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

De Silvestri, S.

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[CrossRef]

Fischer, D. G.

T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef] [PubMed]

Gao, W.

J. Yin, W. Gao, and Y. Zhu, in Progress in Optics 44, E.Wolf, ed. (North-Holland, 2003), pp. 119–204.
[CrossRef]

Gori, F.

F. Gori and O. Korotkova, Opt. Commun. 282, 3859(2009).
[CrossRef]

F. Gori, Opt. Commun. 107, 335 (1994).
[CrossRef]

Korotkova, O.

F. Gori and O. Korotkova, Opt. Commun. 282, 3859(2009).
[CrossRef]

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

O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609(2007).
[CrossRef]

Laporta, P.

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[CrossRef]

Lee, H.

Y. Li, H. Lee, and E. Wolf, Opt. Eng. 42, 2707 (2003).
[CrossRef]

Li, Y.

Y. Li, H. Lee, and E. Wolf, Opt. Eng. 42, 2707 (2003).
[CrossRef]

Magni, V.

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[CrossRef]

Sahin, S.

Svelto, O.

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[CrossRef]

van Dijk, T.

T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef] [PubMed]

Visser, T. D.

T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef] [PubMed]

T. D. Visser and E. Wolf, Phys. Rev. E 59, 2355(1999).
[CrossRef]

Wolf, E.

T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef] [PubMed]

O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609(2007).
[CrossRef]

Y. Li, H. Lee, and E. Wolf, Opt. Eng. 42, 2707 (2003).
[CrossRef]

T. D. Visser and E. Wolf, Phys. Rev. E 59, 2355(1999).
[CrossRef]

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

E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge U. Press, 2007).

Yin, J.

J. Yin, W. Gao, and Y. Zhu, in Progress in Optics 44, E.Wolf, ed. (North-Holland, 2003), pp. 119–204.
[CrossRef]

Zhu, Y.

J. Yin, W. Gao, and Y. Zhu, in Progress in Optics 44, E.Wolf, ed. (North-Holland, 2003), pp. 119–204.
[CrossRef]

IEEE J. Quantum Electron. (1)

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, IEEE J. Quantum Electron. 24, 1172 (1988).
[CrossRef]

Opt. Commun. (2)

F. Gori and O. Korotkova, Opt. Commun. 282, 3859(2009).
[CrossRef]

F. Gori, Opt. Commun. 107, 335 (1994).
[CrossRef]

Opt. Eng. (1)

Y. Li, H. Lee, and E. Wolf, Opt. Eng. 42, 2707 (2003).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (2)

O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609(2007).
[CrossRef]

T. D. Visser and E. Wolf, Phys. Rev. E 59, 2355(1999).
[CrossRef]

Phys. Rev. Lett. (1)

T. van Dijk, D. G. Fischer, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 104, 173902 (2010).
[CrossRef] [PubMed]

Other (3)

J. Yin, W. Gao, and Y. Zhu, in Progress in Optics 44, E.Wolf, ed. (North-Holland, 2003), pp. 119–204.
[CrossRef]

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

E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge U. Press, 2007).

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Figures (4)

Fig. 1
Fig. 1

Scattering potential for solid particles calculated from Eq. (7) for several values of M: M = 1 , dashed–dotted curve; M = 4 , dashed curve; M = 10 , dotted curve; and M = 40 , solid thick curve.

Fig. 2
Fig. 2

Same as in Fig. 1 but calculated from Eq. (9).

Fig. 3
Fig. 3

Contour plot of the spectral density of the far field calculated from Eq. (8) for M = 1 (top) and M = 40 (bottom).

Fig. 4
Fig. 4

Same as Fig. 3, but calculated from Eq. (10).

Equations (14)

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U ( i ) ( r , ω ) = S ( i ) ( ω ) e i k s 0 · r ,
S ( s ) ( r s , ω ) = 1 r 2 S ( i ) ( ω ) C ˜ F [ k ( s s 0 ) , k ( s s 0 ) , ω ] .
C ˜ F ( K 1 , K 2 , ω ) = D D C F ( r 1 , r 2 , ω ) × exp [ i ( K 1 · r 1 + K 2 · r 2 ) ] d 3 r 1 d 3 r 2 ,
C F ( r 1 , r 2 , ω ) = F * ( r 1 , ω ) F ( r 2 , ω ) m .
F ( r , ω ) = { k 2 4 π [ n 2 ( r , ω ) 1 ] , r D 0 , otherwise .
C F ( r 1 , r 2 , ω ) = F * ( r 1 , ω ) F ( r 2 , ω ) .
F ( r ; ω ) = B C 0 m = 1 M ( 1 ) m 1 M ( M m ) e m x 2 + y 2 + ( z d ) 2 2 σ 2 ,
C 0 = m = 1 M ( 1 ) m 1 M ( M m )
S ( s ) ( r s ; ω ) = B 2 ( 2 π ) 5 σ 6 s z 2 k 2 r 2 C 0 2 ( m = 1 M ( 1 ) m 1 M ( M m ) ( 1 / m ) 3 exp [ k 2 σ 2 ( s s 0 ) 2 / m ] ) 2 .
F ( r ; ω ) = B C 0 m = 1 M ( 1 ) m 1 M × ( e m x 2 + y 2 + ( z d ) 2 2 σ o 2 e m x 2 + y 2 + ( z d ) 2 2 σ p 2 ) ,
S ( s ) ( r s ; ω ) = B 2 ( 2 π ) 5 σ 6 s z 2 k 2 r 2 C 0 2 × ( m = 1 M ( 1 ) m 1 M m 3 ( e k 2 σ o 2 ( s s 0 ) 2 m e k 2 σ p 2 ( s s 0 ) 2 m ) ) 2 .
C F ( r 1 , r 2 , ω ) = I F ( r 1 , ω ) I F ( r 2 , ω ) μ F ( r 2 r 1 , ω ) ,
C F ( r 1 , r 2 , ω ) = I F ( r 1 + r 2 2 , ω ) μ F ( r 2 r 1 , ω ) ,
μ F ( G ) ( r 2 r 1 , ω ) = exp ( | r 1 r 2 | 2 2 δ 2 )

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