Abstract

Within the accuracy of the Born approximation, it is shown that the light, which is generated by the scattering of an arbitrary coherent polychromatic wave from a quasi-homogeneous (QH) media can, display both spectral shifts and spectral switches. In our study, a pair of Young’s pinholes is utilized to modulate spatial coherence of the incident plane wave before it interacts with the scatterer. The spectral shifts are found to be highly dependent of the scattering angle, the correlation length of scatterer and the Young’s configuration parameter. Moreover, the spectral shifts can be converted from the red shift to blue one provided that the correlation length of scatterer is small enough. Derived results are confirmed by numerical simulations where influences of various factors on the spectrum are analyzed in detail.

© 2015 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  2. L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley Press, 2000).
  3. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, 2007).
  4. E. Wolf, “Invariance of the spectrum of light on propagation,” Phys. Rev. Lett. 56(13), 1370–1372 (1986).
    [Crossref] [PubMed]
  5. E. Wolf and D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59(6), 771–818 (1996).
    [Crossref]
  6. E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of spectral lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A 6(8), 1142–1149 (1989).
    [Crossref]
  7. J. T. Foley and E. Wolf, “Frequency shifts of spectral lines generated by scattering from space-time fluctuations,” Phys. Rev. A 40(2), 588–598 (1989).
    [Crossref] [PubMed]
  8. D. F. V. James, M. P. Savedoff, and E. Wolf, “Shifts of spectral lines caused by scattering from fluctuating random media,” Astrophys. J. 359, 67–71 (1990).
  9. T. Shirai and T. Asakura, “Spectral changes of light induced by scattering from spatially random media under the Rytov approximation,” J. Opt. Soc. Am. A 12(6), 1354–1363 (1995).
    [Crossref]
  10. T. Shirai and T. Asakura, “Multiple light scattering from spatially random media under the second-order Born approximation,” Opt. Commun. 123(1-3), 234–249 (1996).
    [Crossref]
  11. E. Wolf, “Far-zone spectral isotropy in weak scattering on spatially random media,” J. Opt. Soc. Am. A 14(10), 2820–2823 (1997).
    [Crossref]
  12. 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]
  13. J. Pu, O. Korotkova, and E. Wolf, “Invariance and noninvariance of the spectra of stochastic electromagnetic beams on propogation,” Opt. Lett. 31(14), 2097–2099 (2006).
    [Crossref] [PubMed]
  14. D. Zhao, O. Korotkova, and E. Wolf, “Application of correlation-induced spectral changes to inverse scattering,” Opt. Lett. 32(24), 3483–3485 (2007).
    [Crossref] [PubMed]
  15. T. Wang and D. Zhao, “Spectral switch of light induced by scattering from a system of particles,” PIER Lett. 14, 41–49 (2010).
    [Crossref]
  16. W. Gao, “Spectral changes of the light produced by scattering from tissue,” Opt. Lett. 35(6), 862–864 (2010).
    [Crossref] [PubMed]
  17. W. Gao, “Square law between spatial frequency of spatial correlation function of scattering potential of tissue and spectrum of scattered light,” J. Biomed. Opt. 15(3), 030502 (2010).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  20. 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]
  21. S. A. Ponomarenko and E. Wolf, “Spectral anomalies in a Fraunhofer diffraction pattern,” Opt. Lett. 27(14), 1211–1213 (2002).
    [Crossref] [PubMed]
  22. M. Born and E. Wolf, Principle of Optics (Cambridge University Press, 1995).
  23. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
    [Crossref]
  24. Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265(1), 63–72 (2006).
    [Crossref]
  25. T. D. Visser, D. G. Fischer, and E. Wolf, “Scattering of light from quasi-homogeneous sources by quasi-homogeneous media,” J. Opt. Soc. Am. A 23(7), 1631–1638 (2006).
    [Crossref] [PubMed]
  26. D. G. Fischer and E. Wolf, “Inverse problem with quasi-homogeneous random media,” J. Opt. Soc. Am. A 11(3), 1128–1135 (1994).
    [Crossref]
  27. D. G. Fischer and B. Cairns, “Inverse problems with quasi-homogeneous random media utilizing scattered pulses,” J. Mod. Opt. 42(3), 655–666 (1995).
    [Crossref]
  28. D. G. Fischer and E. Wolf, “Theory of diffraction tomography for quasi-homogeneous random objects,” Opt. Commun. 133(1-6), 17–21 (1997).
    [Crossref]
  29. Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, “Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media,” Opt. Commun. 278(2), 247–252 (2007).
    [Crossref]
  30. Y. Xin, Y. He, Y. Chen, and J. Li, “Correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media,” Opt. Lett. 35(23), 4000–4002 (2010).
    [Crossref] [PubMed]
  31. X. Du and D. Zhao, “Scattering of light by Gaussian-correlated quasi-homogeneous anisotropic media,” Opt. Lett. 35(3), 384–386 (2010).
    [Crossref] [PubMed]
  32. X. Du and D. Zhao, “Reciprocity relations for scattering from quasi-homogeneous anisotropic media,” Opt. Commun. 284(16-17), 3808–3810 (2011).
    [Crossref]
  33. P. S. Carney and E. Wolf, “An energy theorem for scattering of partially coherent beams,” Opt. Commun. 155(1-3), 1–6 (1998).
    [Crossref]
  34. S. A. Ponomarenko and E. Wolf, “Solution to the inverse scattering problem for strongly fluctuating media using partially coherent light,” Opt. Lett. 27(20), 1770–1772 (2002).
    [Crossref] [PubMed]
  35. C. Ding, Y. Cai, O. Korotkova, Y. Zhang, and L. Pan, “Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse,” Opt. Lett. 36(4), 517–519 (2011).
    [Crossref] [PubMed]
  36. Y. Zhang and D. Zhao, “Scattering of multi-Gaussian Schell-model beams on a random medium,” Opt. Express 21(21), 24781–24792 (2013).
    [Crossref] [PubMed]

2013 (1)

2011 (3)

2010 (6)

2007 (2)

D. Zhao, O. Korotkova, and E. Wolf, “Application of correlation-induced spectral changes to inverse scattering,” Opt. Lett. 32(24), 3483–3485 (2007).
[Crossref] [PubMed]

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, “Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media,” Opt. Commun. 278(2), 247–252 (2007).
[Crossref]

2006 (3)

2003 (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[Crossref]

2002 (2)

1999 (1)

S. A. Ponomarenko and E. Wolf, “Spectral changes of light produced by scattering from disordered anisotropic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(3), 3310–3313 (1999).
[Crossref] [PubMed]

1998 (2)

P. S. Carney and E. Wolf, “An energy theorem for scattering of partially coherent beams,” Opt. Commun. 155(1-3), 1–6 (1998).
[Crossref]

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]

1997 (2)

E. Wolf, “Far-zone spectral isotropy in weak scattering on spatially random media,” J. Opt. Soc. Am. A 14(10), 2820–2823 (1997).
[Crossref]

D. G. Fischer and E. Wolf, “Theory of diffraction tomography for quasi-homogeneous random objects,” Opt. Commun. 133(1-6), 17–21 (1997).
[Crossref]

1996 (2)

T. Shirai and T. Asakura, “Multiple light scattering from spatially random media under the second-order Born approximation,” Opt. Commun. 123(1-3), 234–249 (1996).
[Crossref]

E. Wolf and D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59(6), 771–818 (1996).
[Crossref]

1995 (2)

D. G. Fischer and B. Cairns, “Inverse problems with quasi-homogeneous random media utilizing scattered pulses,” J. Mod. Opt. 42(3), 655–666 (1995).
[Crossref]

T. Shirai and T. Asakura, “Spectral changes of light induced by scattering from spatially random media under the Rytov approximation,” J. Opt. Soc. Am. A 12(6), 1354–1363 (1995).
[Crossref]

1994 (1)

1990 (1)

D. F. V. James, M. P. Savedoff, and E. Wolf, “Shifts of spectral lines caused by scattering from fluctuating random media,” Astrophys. J. 359, 67–71 (1990).

1989 (2)

J. T. Foley and E. Wolf, “Frequency shifts of spectral lines generated by scattering from space-time fluctuations,” Phys. Rev. A 40(2), 588–598 (1989).
[Crossref] [PubMed]

E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of spectral lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A 6(8), 1142–1149 (1989).
[Crossref]

1986 (1)

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

Asakura, T.

T. Shirai and T. Asakura, “Multiple light scattering from spatially random media under the second-order Born approximation,” Opt. Commun. 123(1-3), 234–249 (1996).
[Crossref]

T. Shirai and T. Asakura, “Spectral changes of light induced by scattering from spatially random media under the Rytov approximation,” J. Opt. Soc. Am. A 12(6), 1354–1363 (1995).
[Crossref]

Cai, Y.

Cairns, B.

D. G. Fischer and B. Cairns, “Inverse problems with quasi-homogeneous random media utilizing scattered pulses,” J. Mod. Opt. 42(3), 655–666 (1995).
[Crossref]

Carney, P. S.

P. S. Carney and E. Wolf, “An energy theorem for scattering of partially coherent beams,” Opt. Commun. 155(1-3), 1–6 (1998).
[Crossref]

Chen, Y.

Y. Xin, Y. He, Y. Chen, and J. Li, “Correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media,” Opt. Lett. 35(23), 4000–4002 (2010).
[Crossref] [PubMed]

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, “Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media,” Opt. Commun. 278(2), 247–252 (2007).
[Crossref]

Ding, C.

Dogariu, A.

Du, X.

Fischer, D. G.

T. D. Visser, D. G. Fischer, and E. Wolf, “Scattering of light from quasi-homogeneous sources by quasi-homogeneous media,” J. Opt. Soc. Am. A 23(7), 1631–1638 (2006).
[Crossref] [PubMed]

D. G. Fischer and E. Wolf, “Theory of diffraction tomography for quasi-homogeneous random objects,” Opt. Commun. 133(1-6), 17–21 (1997).
[Crossref]

D. G. Fischer and B. Cairns, “Inverse problems with quasi-homogeneous random media utilizing scattered pulses,” J. Mod. Opt. 42(3), 655–666 (1995).
[Crossref]

D. G. Fischer and E. Wolf, “Inverse problem with quasi-homogeneous random media,” J. Opt. Soc. Am. A 11(3), 1128–1135 (1994).
[Crossref]

Foley, J. T.

E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of spectral lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A 6(8), 1142–1149 (1989).
[Crossref]

J. T. Foley and E. Wolf, “Frequency shifts of spectral lines generated by scattering from space-time fluctuations,” Phys. Rev. A 40(2), 588–598 (1989).
[Crossref] [PubMed]

Gao, W.

Gori, F.

He, Y.

James, D. F. V.

E. Wolf and D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59(6), 771–818 (1996).
[Crossref]

D. F. V. James, M. P. Savedoff, and E. Wolf, “Shifts of spectral lines caused by scattering from fluctuating random media,” Astrophys. J. 359, 67–71 (1990).

Korotkova, O.

Lee, H.

Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265(1), 63–72 (2006).
[Crossref]

Li, J.

Li, Y.

Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265(1), 63–72 (2006).
[Crossref]

Pan, L.

Ponomarenko, S. A.

Pu, J.

Savedoff, M. P.

D. F. V. James, M. P. Savedoff, and E. Wolf, “Shifts of spectral lines caused by scattering from fluctuating random media,” Astrophys. J. 359, 67–71 (1990).

Shirai, T.

T. Shirai and T. Asakura, “Multiple light scattering from spatially random media under the second-order Born approximation,” Opt. Commun. 123(1-3), 234–249 (1996).
[Crossref]

T. Shirai and T. Asakura, “Spectral changes of light induced by scattering from spatially random media under the Rytov approximation,” J. Opt. Soc. Am. A 12(6), 1354–1363 (1995).
[Crossref]

Visser, T. D.

Wang, T.

T. Wang and D. Zhao, “Spectral switch of light induced by scattering from a system of particles,” PIER Lett. 14, 41–49 (2010).
[Crossref]

Wolf, E.

D. Zhao, O. Korotkova, and E. Wolf, “Application of correlation-induced spectral changes to inverse scattering,” Opt. Lett. 32(24), 3483–3485 (2007).
[Crossref] [PubMed]

J. Pu, O. Korotkova, and E. Wolf, “Invariance and noninvariance of the spectra of stochastic electromagnetic beams on propogation,” Opt. Lett. 31(14), 2097–2099 (2006).
[Crossref] [PubMed]

T. D. Visser, D. G. Fischer, and E. Wolf, “Scattering of light from quasi-homogeneous sources by quasi-homogeneous media,” J. Opt. Soc. Am. A 23(7), 1631–1638 (2006).
[Crossref] [PubMed]

Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265(1), 63–72 (2006).
[Crossref]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[Crossref]

S. A. Ponomarenko and E. Wolf, “Solution to the inverse scattering problem for strongly fluctuating media using partially coherent light,” Opt. Lett. 27(20), 1770–1772 (2002).
[Crossref] [PubMed]

S. A. Ponomarenko and E. Wolf, “Spectral anomalies in a Fraunhofer diffraction pattern,” Opt. Lett. 27(14), 1211–1213 (2002).
[Crossref] [PubMed]

S. A. Ponomarenko and E. Wolf, “Spectral changes of light produced by scattering from disordered anisotropic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(3), 3310–3313 (1999).
[Crossref] [PubMed]

P. S. Carney and E. Wolf, “An energy theorem for scattering of partially coherent beams,” Opt. Commun. 155(1-3), 1–6 (1998).
[Crossref]

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]

E. Wolf, “Far-zone spectral isotropy in weak scattering on spatially random media,” J. Opt. Soc. Am. A 14(10), 2820–2823 (1997).
[Crossref]

D. G. Fischer and E. Wolf, “Theory of diffraction tomography for quasi-homogeneous random objects,” Opt. Commun. 133(1-6), 17–21 (1997).
[Crossref]

E. Wolf and D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59(6), 771–818 (1996).
[Crossref]

D. G. Fischer and E. Wolf, “Inverse problem with quasi-homogeneous random media,” J. Opt. Soc. Am. A 11(3), 1128–1135 (1994).
[Crossref]

D. F. V. James, M. P. Savedoff, and E. Wolf, “Shifts of spectral lines caused by scattering from fluctuating random media,” Astrophys. J. 359, 67–71 (1990).

J. T. Foley and E. Wolf, “Frequency shifts of spectral lines generated by scattering from space-time fluctuations,” Phys. Rev. A 40(2), 588–598 (1989).
[Crossref] [PubMed]

E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of spectral lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A 6(8), 1142–1149 (1989).
[Crossref]

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

Xin, Y.

Y. Xin, Y. He, Y. Chen, and J. Li, “Correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media,” Opt. Lett. 35(23), 4000–4002 (2010).
[Crossref] [PubMed]

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, “Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media,” Opt. Commun. 278(2), 247–252 (2007).
[Crossref]

Zhang, Y.

Zhao, D.

Zhao, Q.

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, “Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media,” Opt. Commun. 278(2), 247–252 (2007).
[Crossref]

Zhou, M.

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, “Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media,” Opt. Commun. 278(2), 247–252 (2007).
[Crossref]

Astrophys. J. (1)

D. F. V. James, M. P. Savedoff, and E. Wolf, “Shifts of spectral lines caused by scattering from fluctuating random media,” Astrophys. J. 359, 67–71 (1990).

J. Biomed. Opt. (1)

W. Gao, “Square law between spatial frequency of spatial correlation function of scattering potential of tissue and spectrum of scattered light,” J. Biomed. Opt. 15(3), 030502 (2010).
[Crossref] [PubMed]

J. Mod. Opt. (1)

D. G. Fischer and B. Cairns, “Inverse problems with quasi-homogeneous random media utilizing scattered pulses,” J. Mod. Opt. 42(3), 655–666 (1995).
[Crossref]

J. Opt. Soc. Am. A (6)

Opt. Commun. (6)

T. Shirai and T. Asakura, “Multiple light scattering from spatially random media under the second-order Born approximation,” Opt. Commun. 123(1-3), 234–249 (1996).
[Crossref]

D. G. Fischer and E. Wolf, “Theory of diffraction tomography for quasi-homogeneous random objects,” Opt. Commun. 133(1-6), 17–21 (1997).
[Crossref]

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, “Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media,” Opt. Commun. 278(2), 247–252 (2007).
[Crossref]

X. Du and D. Zhao, “Reciprocity relations for scattering from quasi-homogeneous anisotropic media,” Opt. Commun. 284(16-17), 3808–3810 (2011).
[Crossref]

P. S. Carney and E. Wolf, “An energy theorem for scattering of partially coherent beams,” Opt. Commun. 155(1-3), 1–6 (1998).
[Crossref]

Y. Li, H. Lee, and E. Wolf, “Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams,” Opt. Commun. 265(1), 63–72 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (10)

S. A. Ponomarenko and E. Wolf, “Solution to the inverse scattering problem for strongly fluctuating media using partially coherent light,” Opt. Lett. 27(20), 1770–1772 (2002).
[Crossref] [PubMed]

C. Ding, Y. Cai, O. Korotkova, Y. Zhang, and L. Pan, “Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse,” Opt. Lett. 36(4), 517–519 (2011).
[Crossref] [PubMed]

Y. Xin, Y. He, Y. Chen, and J. Li, “Correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media,” Opt. Lett. 35(23), 4000–4002 (2010).
[Crossref] [PubMed]

X. Du and D. Zhao, “Scattering of light by Gaussian-correlated quasi-homogeneous anisotropic media,” Opt. Lett. 35(3), 384–386 (2010).
[Crossref] [PubMed]

W. Gao, “Spectral changes of the light produced by scattering from tissue,” Opt. Lett. 35(6), 862–864 (2010).
[Crossref] [PubMed]

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]

J. Pu, O. Korotkova, and E. Wolf, “Invariance and noninvariance of the spectra of stochastic electromagnetic beams on propogation,” Opt. Lett. 31(14), 2097–2099 (2006).
[Crossref] [PubMed]

D. Zhao, O. Korotkova, and E. Wolf, “Application of correlation-induced spectral changes to inverse scattering,” Opt. Lett. 32(24), 3483–3485 (2007).
[Crossref] [PubMed]

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]

S. A. Ponomarenko and E. Wolf, “Spectral anomalies in a Fraunhofer diffraction pattern,” Opt. Lett. 27(14), 1211–1213 (2002).
[Crossref] [PubMed]

Phys. Lett. A (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003).
[Crossref]

Phys. Rev. A (1)

J. T. Foley and E. Wolf, “Frequency shifts of spectral lines generated by scattering from space-time fluctuations,” Phys. Rev. A 40(2), 588–598 (1989).
[Crossref] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

S. A. Ponomarenko and E. Wolf, “Spectral changes of light produced by scattering from disordered anisotropic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(3), 3310–3313 (1999).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

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

PIER Lett. (1)

T. Wang and D. Zhao, “Spectral switch of light induced by scattering from a system of particles,” PIER Lett. 14, 41–49 (2010).
[Crossref]

Rep. Prog. Phys. (1)

E. Wolf and D. F. V. James, “Correlation-induced spectral changes,” Rep. Prog. Phys. 59(6), 771–818 (1996).
[Crossref]

Other (4)

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

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley Press, 2000).

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

M. Born and E. Wolf, Principle of Optics (Cambridge University Press, 1995).

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Figures (8)

Fig. 1
Fig. 1 Schematic diagram of the scattering theory of light waves from a scatterer, while the Young’s pinholes are used to block the incident plane wave to modulate its spatial coherence.
Fig. 2
Fig. 2 Normalized spectrum of scattered field S N ( ) ( θ , ω ) varies versus the scattering angle θ , while different values of d / R are selected for comparisons. The correlation length δ η = λ 0 . (a) d / R = 0 , (b) d / R = 0.5 , (c) d / R = 1 , (d) d / R = 2.
Fig. 3
Fig. 3 Normalized spectrum of scattered field S N ( ) ( θ , ω ) varies versus d / R , while different correlation length δ η are selected for comparisons. The scattering angle θ = 0. (a) δ η = 2 λ 0 , (b) δ η = λ 0 , (c) δ η = 0.5 λ 0 , (d) δ η = 0.2 λ 0 .
Fig. 4
Fig. 4 Normalized spectrum of scattered field S N ( ) ( θ , ω ) varies versus the correlation length δ η , while different scattering angles are selected for comparisons. The Young’s configuration parameter d / R = 0.5. (a) θ = 0 , (b) θ = π / 6 , (c) θ = π / 3 , (d) θ = π / 2.
Fig. 5
Fig. 5 Normalized spectrum of scattered field S N ( ) ( θ , ω ) varies versus different scattering angles θ = 0 , π / 4 , π / 2 . The correlation length δ η = λ 0 . S ( i ) ( ω ) denotes the spectrum of the initial incident plane waves. (a) d / R = 2 , (b) d / R = 0.5.
Fig. 6
Fig. 6 Normalized spectrum of scattered field S N ( ) ( θ , ω ) varies with different d/R = 0, 1, 2. (a) θ = 0 , (b) θ = π / 2.
Fig. 7
Fig. 7 Normalized spectrum of scattered field S N ( ) ( θ , ω ) varies with the correlation length δ η = λ0, 0.5λ0 and 0.2λ0. d/R = 0.5, θ = 0, S ( i ) ( ω ) denotes the spectrum of incident plane waves.
Fig. 8
Fig. 8 Relative spectral shift of scattered field δ ω / ω 0 varies with δ η / λ 0 , while different scattering angles are selected for comparisons. (a) θ = 0, π/4, π/2, d/R = 1. (b) d/R = 0, 1, 2, θ = 0.

Equations (33)

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[ U ( f ) ( r ^ 1 ' , ω ) U ( f ) ( r ^ 2 ' , ω ) ] = [ i ω exp ( i ω c R 11 ) 2 π c R 11 d S i ω exp ( i ω c R 12 ) 2 π c R 12 d S i ω exp ( i ω c R 21 ) 2 π c R 21 d S i ω exp ( i ω c R 22 ) 2 π c R 22 d S ] [ U ( i ) ( ρ ^ 1 , ω ) U ( i ) ( ρ ^ 2 , ω ) ] = i ω 2 π c [ exp ( i ω c R 11 ) R 11 U ( i ) ( ρ ^ 1 , ω ) exp ( i ω c R 12 ) R 12 U ( i ) ( ρ ^ 2 , ω ) exp ( i ω c R 21 ) R 21 U ( i ) ( ρ ^ 1 , ω ) exp ( i ω c R 22 ) R 22 U ( i ) ( ρ ^ 2 , ω ) ] ,
U ( i ) ( ρ ^ j , ω ) = a ( ω ) exp ( i ω c s ^ 0 ρ ^ j ) , ( j = 1 , 2 ) ,
W ( f ) ( r ^ 1 ' , r ^ 2 ' , ω ) = U ( f ) ( r ^ 1 ' , ω ) U ( f ) ( r ^ 2 ' , ω ) ,
W ( f ) ( r ^ 1 ' , r ^ 2 ' , ω ) = ( ω d S 2 π c ) 2 S ( i ) ( ω ) { exp [ i ω c ( R 11 R 21 ) ] R 21 R 11 exp [ i ω c ( R 12 R 21 ) ] R 21 R 12 exp [ i ω c s ^ 0 ( ρ ^ 1 ρ ^ 2 ) ] exp [ i ω c ( R 11 R 22 ) ] R 22 R 11 exp [ i ω c s ^ 0 ( ρ ^ 2 ρ ^ 1 ) ] + exp [ i ω c ( R 12 R 22 ) ] R 12 R 22 } ,
R α β R , ( α = 1 , 2 ; β = 1 , 2 ) .
| ρ ^ 1 | cos φ 1 = | ρ ^ 2 | cos φ 2 = R ' .
R 21 R 11 ( r ' 2 r ' 1 ) d 2 R ,
R 22 R 12 ( r ' 2 r ' 1 ) d 2 R ,
R 12 R 11 r ' 1 d R ,
R 22 R 21 r ' 2 d R ,
r ' 1 = r ^ 1 ' e ^ 0 ,
r ' 2 = r ^ 2 ' e ^ 0 ,
e ^ 0 s ^ 0 = 0.
W ( f ) ( r ^ 1 ' , r ^ 2 ' , ω ) = ( ω d S 2 π c R ) 2 S ( i ) ( ω ) { 2 exp [ i ω ( r ^ 2 ' r ^ 1 ' ) e ^ 0 2 c R d ] + exp [ i ω ( r ^ 2 ' + r ^ 1 ' ) e ^ 0 2 c R d ] + exp [ i ω ( r ^ 2 ' + r ^ 1 ' ) e ^ 0 2 c R d ] } .
W ( ) ( r s ^ 1 , r s ^ 2 , ω ) = exp [ i ω c ( r 2 r 1 ) ] r 2 r 1 D D W ( f ) ( r ^ 1 ' , r ^ 2 ' , ω ) C F ( r ^ 1 ' , r ^ 2 ' , ω ) exp [ i ω c ( s ^ 2 r ^ 2 ' s ^ 1 r ^ 1 ' ) ] d 3 r ^ 1 ' d 3 r ^ 2 ' ,
C F ( r ^ 1 ' , r ^ 2 ' , ω ) = S F ( r ^ 1 ' + r ^ 2 ' 2 , ω ) η F ( r ^ 2 ' r ^ 1 ' , ω ) ,
r ^ 2 ' + r ^ 1 ' = R ^ + ,
r ^ 2 ' r ^ 1 ' = R ^ .
W ( ) ( r s ^ 1 , r s ^ 2 , ω ) = ( ω d S 2 π c R ) 2 exp [ i ω c ( r 2 r 1 ) ] r 2 r 1 S ( i ) ( ω ) D D S F ( R ^ + 2 ) η F ( R ^ ) × { 2 exp [ i ω 2 c ( s ^ 2 s ^ 1 + d R e ^ 0 ) R ^ + i ω 2 c ( s ^ 1 + s ^ 2 ) R ^ ] + exp [ i ω 2 c ( s ^ 2 s ^ 1 ) R ^ + i ω 2 c ( s ^ 1 + s ^ 2 d R e ^ 0 ) R ^ ] + exp [ i ω 2 c ( s ^ 2 s ^ 1 ) R ^ + i ω 2 c ( s ^ 1 + s ^ 2 + d R e ^ 0 ) R ^ ] } d 3 R ^ + d 3 R ^ .
W ( ) ( r s ^ 1 , r s ^ 2 , ω ) = ( ω d S 2 π c R ) 2 exp [ i ω c ( r 2 r 1 ) ] r 2 r 1 S ( i ) ( ω ) { 2 S ˜ F [ ω c ( s ^ 2 s ^ 1 + d R e ^ 0 ) ] η ˜ F [ ω 2 c ( s ^ 1 + s ^ 2 ) ] + S ˜ F [ ω c ( s ^ 2 s ^ 1 ) ] η ˜ F [ ω 2 c ( s ^ 1 + s ^ 2 d R e ^ 0 ) ] + S ˜ F [ ω c ( s ^ 2 s ^ 1 ) ] η ˜ F [ ω 2 c ( s ^ 1 + s ^ 2 + d R e ^ 0 ) ] } .
S ( ) ( r s ^ , ω ) = ( ω d S 2 π c R r ) 2 S ( i ) ( ω ) { 2 S ˜ F ( d R e ^ 0 ) η ˜ F ( ω c s ^ ) + S ˜ F ( 0 ) η ˜ F [ ω c ( s ^ d 2 R e ^ 0 ) ] + S ˜ F ( 0 ) η ˜ F [ ω c ( s ^ + d 2 R e ^ 0 ) ] } ,
{ S ˜ F ( d R e ^ 0 ) < < S ˜ F ( 0 ) , S ˜ F ( d R e ^ 0 ) = S ˜ F ( 0 ) , d R > 0 d R = 0 .
η ˜ F ( ω c s ^ ) η ˜ F [ ω c ( s ^ d 2 R e ^ 0 ) ] η ˜ F [ ω c ( s ^ + d 2 R e ^ 0 ) ] .
S ( ) ( r s ^ , ω ) = { ( ω d S π c R r ) 2 S ( i ) ( ω ) S ˜ F ( 0 ) η ˜ F ( ω c s ^ ) , ( ω d S 2 π c R r ) 2 S ( i ) ( ω ) S ˜ F ( 0 ) { η ˜ F [ ω c ( s ^ d 2 R e ^ 0 ) ] + η ˜ F [ ω c ( s ^ + d 2 R e ^ 0 ) ] } , d R = 0 d R > 0 .
S F ( R ^ + ) = A ( 2 π δ s 2 ) 3 / 2 exp [ ( R ^ + ) 2 2 δ s 2 ] ,
η F ( R ^ ) = B ( 2 π δ η 2 ) 3 / 2 exp [ ( R ^ ) 2 2 δ η 2 ] ,
S ( ) ( θ , ω ) = { ( ω d S 2 π c R r ) 2 S ( i ) ( ω ) A B { exp [ ω 2 2 c 2 δ η 2 ( 1 + d 2 4 R 2 d 4 R sin θ ) ] + exp [ ω 2 2 c 2 δ η 2 ( 1 + d 2 4 R 2 + d 4 R sin θ ) ] } , ( ω d S π c R r ) 2 S ( i ) ( ω ) A B exp ( ω 2 2 c 2 δ η 2 ) , d R > 0 d R = 0 .
S N ( ) ( r S ^ , ω ) = S ( ) ( r S , ω ) 0 S ( ) ( r S ^ , ω ) d ω .
S ( i ) ( ω ) = exp [ ( ω ω 0 ) 2 2 σ 0 2 ] ,
S N ( ) ( θ , ω ) = ω 2 exp [ 1 2 ( 1 σ 0 2 + δ η 2 c 2 ) ω 2 + ω 0 σ 0 2 ω ] M + ( θ , ω ) + M ( θ , ω ) , d R > 0 ,
S N ( ) ( θ , ω ) = ω 2 exp [ 1 2 ( 1 σ 0 2 + δ η 2 c 2 ) ω 2 + ω 0 σ 0 2 ω ] ω 0 ( 1 2 σ 0 + σ 0 2 c 2 δ η 2 ) 2 + π 1 2 ( ϖ 0 2 8 σ 0 4 + 1 8 σ 0 2 + δ η 2 8 c 2 ) ( 1 2 σ 0 2 + δ η 2 2 c 2 ) 5 2 exp ( ω 0 2 2 σ 0 2 + 2 δ η 2 c 2 σ 0 4 ) { 1 e r f [ ω 0 ( 2 σ 0 2 + 2 δ η 2 c 2 σ 0 4 ) 1 2 ] } , d R = 0 ,
M ± ( θ , ω ) = ω 0 [ 1 2 σ 0 + σ 0 2 c 2 δ η 2 ( 1 + d 2 4 R 2 ± d 4 R sin θ ) ] 2 + π 1 2 [ ω 0 2 8 σ 0 4 + 1 8 σ 0 2 + δ η 2 8 c 2 ( 1 + d 2 4 R 2 ± d 4 R sin θ ) ] [ 1 2 σ 0 2 + δ η 2 2 c 2 ( 1 + d 2 4 R 2 ± d 4 R sin θ ) ] 5 2 × exp [ ω 0 2 2 σ 0 2 + σ 0 4 c 2 δ η 2 ( 1 + d 2 4 R 2 ± d 4 R sin θ ) ] { 1 e r f [ ω 0 2 σ 0 2 + σ 0 4 c 2 δ η 2 ( 1 + d 2 4 R 2 ± d 4 R sin θ ) ] } ,
δ ω ω 0 = ω max ω 0 ω 0 ,

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