Abstract

The behavior of vector singularities in partially coherent inhomogeneously polarized optical beams, such as U contours with zero degree of polarization, is investigated by computer simulation for the most important cases of incoherent mixing of orthogonally polarized components (speckle fields and plane waves). Vector singularities in partially coherent combined beams are considered within the notion of the complex degree of polarization, with representation in the Stokes space. The dependences of U singularities on the intensity ratio obtained by simulation are compared with obtained early qualitative experimental results.

© 2014 Optical Society of America

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  1. V. K. Polyanskii and L. V. Kovalskii, “On fine structure of the field of scattered radiation,” Opt. Spectrosc. 35, 345–350 (1973).
  2. J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (Institute of Physics, 1999).
  3. M. V. Berry, “The electric and magnetic polarization singularities of paraxial waves,” J. Opt. Pure Appl. Opt. 6, 475–481 (2004).
  4. I. I. Mokhun, “Introduction to linear singular optics,” in Optical Correlation Techniques and Applications, O. V. Angelsky, ed. (SPIE, 2007), Chap. 1, pp. 1–133.
  5. N. B. Baranova, A. V. Mamaev, H. F. Pilipetskii, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73, 525–528 (1983).
    [CrossRef]
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  7. M. V. Berry and M. R. Dennis, “Quantum cores of optical phase singularities,” J. Opt. Pure Appl. Opt. 6, S178–S180 (2004).
  8. C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Reincarnation of optical singularities,” Proc. SPIE 7008, 70080A (2008).
  9. C. V. Felde, A. A. Chernyshov, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Polarization singularities in partially coherent combined beams,” JETP Lett. 88, 418–422 (2008).
    [CrossRef]
  10. A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, and P. V. Polyanskii, “Vector singularities at superposition of mutually incoherent orthogonally polarized beams,” Opt. Spectrosc. 107, 645–650 (2009).
    [CrossRef]
  11. A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Vector singularities of the combined beams assembled from mutually incoherent orthogonally polarized components,” J. Opt. Pure Appl. Opt. 11, 094010 (2009).
  12. P. V. Polyanskii, C. V. Felde, and A. A. Chernyshov, “Polarization degree singularities,” Proc. SPIE 7388, 73880A (2009).
    [CrossRef]
  13. M. S. Soskin and P. V. Polyanskii, “New polarization singularities of partially coherent light beams,” Proc. SPIE 7613, 76130G (2010).
    [CrossRef]
  14. O. V. Angelsky, P. V. Polyanskii, I. I. Mokhun, C. Y. Zenkova, H. V. Bogatyryova, C. V. Felde, V. T. Bachinskiy, T. M. Boichuk, and A. G. Ushenko, “Optical measurements: polarization and coherence of light fields,” in Modern Metrology Concerns, L. Cocco, ed. (InTech, 2012), Chap. 10, pp. 263–317.
  15. O. V. Angelsky, P. V. Polyanskii, P. P. Maksimyak, and I. I. Mokhun, “Some current views on metrology of coherence and polarization in sight of singular optics,” in Handbook of Coherent-Domain Optical Methods: Biomedical Diagnostics, Environmental Monitoring, and Materials Science, V. V. Tuchin, ed. (Springer Verlag, 2012), Chap. 2, pp. 1–41.
  16. V. K. Polyanskii, O. V. Angelsky, and P. V. Polyanskii, “Scattering-induced spectral changes as the singular optical effect,” Opt. Appl. 32, 843–848 (2002).
  17. M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, “Computer-synthesized hologram-based rainbow optical vortices,” New J. Phys. 6, 196, 1–8 (2004).
    [CrossRef]
  18. C. Wilson and M. J. Padgett, “A polyphonic acoustic vortex and its complementary chords,” New J. Phys. 12, 023018 (2010).
    [CrossRef]
  19. P. V. Polyanskii, “Some current views on singular optics,” Proc. SPIE 5477, 31–40 (2004).
  20. G. Gbur and T. D. Visser, “The structure of partially coherent fields,” Prog. Opt. 55, 285–341 (2010).
    [CrossRef]
  21. F. S. Crawford, Waves (McGraw-Hill, 1969), Vol. 3 (see Problem 8.18, c1).
  22. W. A. Shurcliff, Polarized Light: Production and Use (Harvard University, 1962).
  23. A. R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  24. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1997).
  25. J. W. Goodman, Statistical Optics (Wiley Interscience, 1985).
  26. E. Wolf and L. Mandel, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
    [CrossRef]
  27. J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, Inc., 1968).
  28. H. V. Bogatyryova, C. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28, 878–880 (2003).
    [CrossRef]
  29. S. A. Ponomarenko, “A class of partially coherent beams carrying optical vortices,” J. Opt. Soc. Am. A 18, 150–156 (2001).
    [CrossRef]
  30. G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222, 117–125 (2003).
    [CrossRef]
  31. L. Wang, S. A. Ponomarenko, and Z. Chen, “Spectral coherence anomalies,” Opt. Lett. 38, 2557–2559 (2013).
    [CrossRef]
  32. T. Iwai and T. Asakura, “Dynamic properties of speckled speckles with relation to velocity measurements of a diffuse object,” Opt. Laser Technol. 21, 31–36 (1989).
    [CrossRef]
  33. I. Freund and D. A. Kessler, “Singularities in speckled speckle: statistics,” Opt. Commun. 281, 5954–5967 (2008).
    [CrossRef]
  34. S. G. Hanson, F. Q. Iversen, and R. S. Hansen, “Dynamic properties of speckled speckles,” Opt. Commun. 281, 5954–5967 (2008).
    [CrossRef]

2013

2012

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “Emerging the field of correlation optics,” Optics Photonics News 23(4), 25–29 (2012).

2010

M. S. Soskin and P. V. Polyanskii, “New polarization singularities of partially coherent light beams,” Proc. SPIE 7613, 76130G (2010).
[CrossRef]

C. Wilson and M. J. Padgett, “A polyphonic acoustic vortex and its complementary chords,” New J. Phys. 12, 023018 (2010).
[CrossRef]

G. Gbur and T. D. Visser, “The structure of partially coherent fields,” Prog. Opt. 55, 285–341 (2010).
[CrossRef]

2009

A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, and P. V. Polyanskii, “Vector singularities at superposition of mutually incoherent orthogonally polarized beams,” Opt. Spectrosc. 107, 645–650 (2009).
[CrossRef]

A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Vector singularities of the combined beams assembled from mutually incoherent orthogonally polarized components,” J. Opt. Pure Appl. Opt. 11, 094010 (2009).

P. V. Polyanskii, C. V. Felde, and A. A. Chernyshov, “Polarization degree singularities,” Proc. SPIE 7388, 73880A (2009).
[CrossRef]

2008

C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Reincarnation of optical singularities,” Proc. SPIE 7008, 70080A (2008).

C. V. Felde, A. A. Chernyshov, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Polarization singularities in partially coherent combined beams,” JETP Lett. 88, 418–422 (2008).
[CrossRef]

I. Freund and D. A. Kessler, “Singularities in speckled speckle: statistics,” Opt. Commun. 281, 5954–5967 (2008).
[CrossRef]

S. G. Hanson, F. Q. Iversen, and R. S. Hansen, “Dynamic properties of speckled speckles,” Opt. Commun. 281, 5954–5967 (2008).
[CrossRef]

2004

M. V. Berry and M. R. Dennis, “Quantum cores of optical phase singularities,” J. Opt. Pure Appl. Opt. 6, S178–S180 (2004).

P. V. Polyanskii, “Some current views on singular optics,” Proc. SPIE 5477, 31–40 (2004).

M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, “Computer-synthesized hologram-based rainbow optical vortices,” New J. Phys. 6, 196, 1–8 (2004).
[CrossRef]

M. V. Berry, “The electric and magnetic polarization singularities of paraxial waves,” J. Opt. Pure Appl. Opt. 6, 475–481 (2004).

2003

2002

V. K. Polyanskii, O. V. Angelsky, and P. V. Polyanskii, “Scattering-induced spectral changes as the singular optical effect,” Opt. Appl. 32, 843–848 (2002).

2001

1989

T. Iwai and T. Asakura, “Dynamic properties of speckled speckles with relation to velocity measurements of a diffuse object,” Opt. Laser Technol. 21, 31–36 (1989).
[CrossRef]

1983

1973

V. K. Polyanskii and L. V. Kovalskii, “On fine structure of the field of scattered radiation,” Opt. Spectrosc. 35, 345–350 (1973).

1965

E. Wolf and L. Mandel, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

Angelsky, O. V.

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “Emerging the field of correlation optics,” Optics Photonics News 23(4), 25–29 (2012).

V. K. Polyanskii, O. V. Angelsky, and P. V. Polyanskii, “Scattering-induced spectral changes as the singular optical effect,” Opt. Appl. 32, 843–848 (2002).

O. V. Angelsky, P. V. Polyanskii, I. I. Mokhun, C. Y. Zenkova, H. V. Bogatyryova, C. V. Felde, V. T. Bachinskiy, T. M. Boichuk, and A. G. Ushenko, “Optical measurements: polarization and coherence of light fields,” in Modern Metrology Concerns, L. Cocco, ed. (InTech, 2012), Chap. 10, pp. 263–317.

O. V. Angelsky, P. V. Polyanskii, P. P. Maksimyak, and I. I. Mokhun, “Some current views on metrology of coherence and polarization in sight of singular optics,” in Handbook of Coherent-Domain Optical Methods: Biomedical Diagnostics, Environmental Monitoring, and Materials Science, V. V. Tuchin, ed. (Springer Verlag, 2012), Chap. 2, pp. 1–41.

Arkhelyuk, O. O.

M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, “Computer-synthesized hologram-based rainbow optical vortices,” New J. Phys. 6, 196, 1–8 (2004).
[CrossRef]

Asakura, T.

T. Iwai and T. Asakura, “Dynamic properties of speckled speckles with relation to velocity measurements of a diffuse object,” Opt. Laser Technol. 21, 31–36 (1989).
[CrossRef]

Azzam, A. R. M.

A. R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bachinskiy, V. T.

O. V. Angelsky, P. V. Polyanskii, I. I. Mokhun, C. Y. Zenkova, H. V. Bogatyryova, C. V. Felde, V. T. Bachinskiy, T. M. Boichuk, and A. G. Ushenko, “Optical measurements: polarization and coherence of light fields,” in Modern Metrology Concerns, L. Cocco, ed. (InTech, 2012), Chap. 10, pp. 263–317.

Baranova, N. B.

Bashara, N. M.

A. R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Berry, M. V.

M. V. Berry and M. R. Dennis, “Quantum cores of optical phase singularities,” J. Opt. Pure Appl. Opt. 6, S178–S180 (2004).

M. V. Berry, “The electric and magnetic polarization singularities of paraxial waves,” J. Opt. Pure Appl. Opt. 6, 475–481 (2004).

Bogatyryova, H. V.

A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Vector singularities of the combined beams assembled from mutually incoherent orthogonally polarized components,” J. Opt. Pure Appl. Opt. 11, 094010 (2009).

A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, and P. V. Polyanskii, “Vector singularities at superposition of mutually incoherent orthogonally polarized beams,” Opt. Spectrosc. 107, 645–650 (2009).
[CrossRef]

C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Reincarnation of optical singularities,” Proc. SPIE 7008, 70080A (2008).

C. V. Felde, A. A. Chernyshov, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Polarization singularities in partially coherent combined beams,” JETP Lett. 88, 418–422 (2008).
[CrossRef]

H. V. Bogatyryova, C. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28, 878–880 (2003).
[CrossRef]

O. V. Angelsky, P. V. Polyanskii, I. I. Mokhun, C. Y. Zenkova, H. V. Bogatyryova, C. V. Felde, V. T. Bachinskiy, T. M. Boichuk, and A. G. Ushenko, “Optical measurements: polarization and coherence of light fields,” in Modern Metrology Concerns, L. Cocco, ed. (InTech, 2012), Chap. 10, pp. 263–317.

Boichuk, T. M.

O. V. Angelsky, P. V. Polyanskii, I. I. Mokhun, C. Y. Zenkova, H. V. Bogatyryova, C. V. Felde, V. T. Bachinskiy, T. M. Boichuk, and A. G. Ushenko, “Optical measurements: polarization and coherence of light fields,” in Modern Metrology Concerns, L. Cocco, ed. (InTech, 2012), Chap. 10, pp. 263–317.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1997).

Chen, Z.

Chernyshov, A. A.

A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, and P. V. Polyanskii, “Vector singularities at superposition of mutually incoherent orthogonally polarized beams,” Opt. Spectrosc. 107, 645–650 (2009).
[CrossRef]

P. V. Polyanskii, C. V. Felde, and A. A. Chernyshov, “Polarization degree singularities,” Proc. SPIE 7388, 73880A (2009).
[CrossRef]

A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Vector singularities of the combined beams assembled from mutually incoherent orthogonally polarized components,” J. Opt. Pure Appl. Opt. 11, 094010 (2009).

C. V. Felde, A. A. Chernyshov, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Polarization singularities in partially coherent combined beams,” JETP Lett. 88, 418–422 (2008).
[CrossRef]

Crawford, F. S.

F. S. Crawford, Waves (McGraw-Hill, 1969), Vol. 3 (see Problem 8.18, c1).

Dennis, M. R.

M. V. Berry and M. R. Dennis, “Quantum cores of optical phase singularities,” J. Opt. Pure Appl. Opt. 6, S178–S180 (2004).

Felde, C. V.

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “Emerging the field of correlation optics,” Optics Photonics News 23(4), 25–29 (2012).

P. V. Polyanskii, C. V. Felde, and A. A. Chernyshov, “Polarization degree singularities,” Proc. SPIE 7388, 73880A (2009).
[CrossRef]

A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, and P. V. Polyanskii, “Vector singularities at superposition of mutually incoherent orthogonally polarized beams,” Opt. Spectrosc. 107, 645–650 (2009).
[CrossRef]

A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Vector singularities of the combined beams assembled from mutually incoherent orthogonally polarized components,” J. Opt. Pure Appl. Opt. 11, 094010 (2009).

C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Reincarnation of optical singularities,” Proc. SPIE 7008, 70080A (2008).

C. V. Felde, A. A. Chernyshov, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Polarization singularities in partially coherent combined beams,” JETP Lett. 88, 418–422 (2008).
[CrossRef]

H. V. Bogatyryova, C. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28, 878–880 (2003).
[CrossRef]

O. V. Angelsky, P. V. Polyanskii, I. I. Mokhun, C. Y. Zenkova, H. V. Bogatyryova, C. V. Felde, V. T. Bachinskiy, T. M. Boichuk, and A. G. Ushenko, “Optical measurements: polarization and coherence of light fields,” in Modern Metrology Concerns, L. Cocco, ed. (InTech, 2012), Chap. 10, pp. 263–317.

Freund, I.

I. Freund and D. A. Kessler, “Singularities in speckled speckle: statistics,” Opt. Commun. 281, 5954–5967 (2008).
[CrossRef]

Gbur, G.

G. Gbur and T. D. Visser, “The structure of partially coherent fields,” Prog. Opt. 55, 285–341 (2010).
[CrossRef]

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222, 117–125 (2003).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley Interscience, 1985).

Hansen, R. S.

S. G. Hanson, F. Q. Iversen, and R. S. Hansen, “Dynamic properties of speckled speckles,” Opt. Commun. 281, 5954–5967 (2008).
[CrossRef]

Hanson, S. G.

S. G. Hanson, F. Q. Iversen, and R. S. Hansen, “Dynamic properties of speckled speckles,” Opt. Commun. 281, 5954–5967 (2008).
[CrossRef]

Iversen, F. Q.

S. G. Hanson, F. Q. Iversen, and R. S. Hansen, “Dynamic properties of speckled speckles,” Opt. Commun. 281, 5954–5967 (2008).
[CrossRef]

Iwai, T.

T. Iwai and T. Asakura, “Dynamic properties of speckled speckles with relation to velocity measurements of a diffuse object,” Opt. Laser Technol. 21, 31–36 (1989).
[CrossRef]

Kessler, D. A.

I. Freund and D. A. Kessler, “Singularities in speckled speckle: statistics,” Opt. Commun. 281, 5954–5967 (2008).
[CrossRef]

Klauder, J. R.

J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, Inc., 1968).

Kovalskii, L. V.

V. K. Polyanskii and L. V. Kovalskii, “On fine structure of the field of scattered radiation,” Opt. Spectrosc. 35, 345–350 (1973).

Maksimyak, P. P.

O. V. Angelsky, P. V. Polyanskii, P. P. Maksimyak, and I. I. Mokhun, “Some current views on metrology of coherence and polarization in sight of singular optics,” in Handbook of Coherent-Domain Optical Methods: Biomedical Diagnostics, Environmental Monitoring, and Materials Science, V. V. Tuchin, ed. (Springer Verlag, 2012), Chap. 2, pp. 1–41.

Mamaev, A. V.

Mandel, L.

E. Wolf and L. Mandel, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

Mokhun, I. I.

O. V. Angelsky, P. V. Polyanskii, P. P. Maksimyak, and I. I. Mokhun, “Some current views on metrology of coherence and polarization in sight of singular optics,” in Handbook of Coherent-Domain Optical Methods: Biomedical Diagnostics, Environmental Monitoring, and Materials Science, V. V. Tuchin, ed. (Springer Verlag, 2012), Chap. 2, pp. 1–41.

O. V. Angelsky, P. V. Polyanskii, I. I. Mokhun, C. Y. Zenkova, H. V. Bogatyryova, C. V. Felde, V. T. Bachinskiy, T. M. Boichuk, and A. G. Ushenko, “Optical measurements: polarization and coherence of light fields,” in Modern Metrology Concerns, L. Cocco, ed. (InTech, 2012), Chap. 10, pp. 263–317.

I. I. Mokhun, “Introduction to linear singular optics,” in Optical Correlation Techniques and Applications, O. V. Angelsky, ed. (SPIE, 2007), Chap. 1, pp. 1–133.

Nye, J. F.

J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (Institute of Physics, 1999).

Padgett, M. J.

C. Wilson and M. J. Padgett, “A polyphonic acoustic vortex and its complementary chords,” New J. Phys. 12, 023018 (2010).
[CrossRef]

Pilipetskii, H. F.

Polyanskii, P. V.

O. V. Angelsky, P. V. Polyanskii, and C. V. Felde, “Emerging the field of correlation optics,” Optics Photonics News 23(4), 25–29 (2012).

M. S. Soskin and P. V. Polyanskii, “New polarization singularities of partially coherent light beams,” Proc. SPIE 7613, 76130G (2010).
[CrossRef]

A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, and P. V. Polyanskii, “Vector singularities at superposition of mutually incoherent orthogonally polarized beams,” Opt. Spectrosc. 107, 645–650 (2009).
[CrossRef]

P. V. Polyanskii, C. V. Felde, and A. A. Chernyshov, “Polarization degree singularities,” Proc. SPIE 7388, 73880A (2009).
[CrossRef]

A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Vector singularities of the combined beams assembled from mutually incoherent orthogonally polarized components,” J. Opt. Pure Appl. Opt. 11, 094010 (2009).

C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Reincarnation of optical singularities,” Proc. SPIE 7008, 70080A (2008).

C. V. Felde, A. A. Chernyshov, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Polarization singularities in partially coherent combined beams,” JETP Lett. 88, 418–422 (2008).
[CrossRef]

M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, “Computer-synthesized hologram-based rainbow optical vortices,” New J. Phys. 6, 196, 1–8 (2004).
[CrossRef]

P. V. Polyanskii, “Some current views on singular optics,” Proc. SPIE 5477, 31–40 (2004).

H. V. Bogatyryova, C. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28, 878–880 (2003).
[CrossRef]

V. K. Polyanskii, O. V. Angelsky, and P. V. Polyanskii, “Scattering-induced spectral changes as the singular optical effect,” Opt. Appl. 32, 843–848 (2002).

O. V. Angelsky, P. V. Polyanskii, I. I. Mokhun, C. Y. Zenkova, H. V. Bogatyryova, C. V. Felde, V. T. Bachinskiy, T. M. Boichuk, and A. G. Ushenko, “Optical measurements: polarization and coherence of light fields,” in Modern Metrology Concerns, L. Cocco, ed. (InTech, 2012), Chap. 10, pp. 263–317.

O. V. Angelsky, P. V. Polyanskii, P. P. Maksimyak, and I. I. Mokhun, “Some current views on metrology of coherence and polarization in sight of singular optics,” in Handbook of Coherent-Domain Optical Methods: Biomedical Diagnostics, Environmental Monitoring, and Materials Science, V. V. Tuchin, ed. (Springer Verlag, 2012), Chap. 2, pp. 1–41.

Polyanskii, V. K.

V. K. Polyanskii, O. V. Angelsky, and P. V. Polyanskii, “Scattering-induced spectral changes as the singular optical effect,” Opt. Appl. 32, 843–848 (2002).

V. K. Polyanskii and L. V. Kovalskii, “On fine structure of the field of scattered radiation,” Opt. Spectrosc. 35, 345–350 (1973).

Ponomarenko, S. A.

Shkunov, V. V.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light: Production and Use (Harvard University, 1962).

Soskin, M. S.

M. S. Soskin and P. V. Polyanskii, “New polarization singularities of partially coherent light beams,” Proc. SPIE 7613, 76130G (2010).
[CrossRef]

A. A. Chernyshov, C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Vector singularities of the combined beams assembled from mutually incoherent orthogonally polarized components,” J. Opt. Pure Appl. Opt. 11, 094010 (2009).

C. V. Felde, A. A. Chernyshov, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Polarization singularities in partially coherent combined beams,” JETP Lett. 88, 418–422 (2008).
[CrossRef]

C. V. Felde, H. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, “Reincarnation of optical singularities,” Proc. SPIE 7008, 70080A (2008).

M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, “Computer-synthesized hologram-based rainbow optical vortices,” New J. Phys. 6, 196, 1–8 (2004).
[CrossRef]

H. V. Bogatyryova, C. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28, 878–880 (2003).
[CrossRef]

Sudarshan, E. C. G.

J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, Inc., 1968).

Ushenko, A. G.

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Figures (8)

Fig. 1.
Fig. 1.

Complex circular polarization plane. The center of coordinates corresponds to left-circular polarization (analog of C point). The circle of unit radius separating gray and white areas corresponds to linear polarizations with changeable azimuth of polarization (analog of L contours separated into inhomogeneously polarized optical beams, the areas with left handedness and right handedness). The right-circular polarization point lies at infinity. The sign principle of the vector singular optics [4] is satisfied in this model.

Fig. 2.
Fig. 2.

Stokes-space representation of the partially polarized beams. The Poincaré sphere represents completely polarized fields. The interior of this sphere corresponds to partially polarized fields; the coordinate origin corresponds to an unpolarized field (U singularity).

Fig. 3.
Fig. 3.

Speckle pattern and plane wave.

Fig. 4.
Fig. 4.

Parametric dynamics of U singularities for various ratios of the mean intensity of speckle field and intensity of the orthogonally polarized reference wave IS/IR. Upper row illustrates the modifications of the U contours’ form; lower row illustrates the change of the orthogonal states’ polarizations areas. The intensity ratios are indicated under the corresponding frames.

Fig. 5.
Fig. 5.

Speckle patterns with equal average speckle size.

Fig. 6.
Fig. 6.

Parametric dynamics of U singularities for various intensity ratios IS1/IS2 of the speckle field S1 and the orthogonally polarized speckle field S2. Upper row illustrates the modifications of the U contours’ form; lower row illustrates the change of the orthogonal states’ polarizations areas. The ratios of mean intensities are indicated under the corresponding frames.

Fig. 7.
Fig. 7.

Speckle patterns of considerably different average speckle size with average intensities IL and IS, respectively.

Fig. 8.
Fig. 8.

Simulation of U contours clusterization in the partially coherent speckle field. IL and IS are the average intensities of large-scale and small-scale speckle size fields, respectively. Upper row illustrates the modifications of the U contours’ form; lower row illustrates the change of the orthogonal states’ polarizations areas. The ratio of mean intensities is indicated under the corresponding frames.

Equations (4)

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

P=Ip/(Ip+Iu);0P1,
P=PNχr,l,
P=S12+S22+S32S0s12+s22+s32S0=I0+I90,S1=I0I90,S3=I+45I45,S4=IrIl.
P=s12+s22+s32×N×tan(β+π/4)exp[itan1(s3/s2)].

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