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On some prerequisites of correlation singular optics as a branch of information optics

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Abstract

Singular optics is the important and dynamically developed area of modern photonics merging with nono-physics, metamaterials, biomedical optics and having promising applications in metrology, interferometry, manipulation of minute quantities of a matter, as well as in information optics, including optical computing and telecommunications. Since the beginning of the Third Millenium, singular optics trends toward expansing on partially coherent, heterogeneously polarized and polychromatic light fields. We consider here some early forerunners of this trend showing that important prereqisities of correlation singular optics lie in the fundamentals of classical optics, such as the notions of diffraction, partial coherence and partial polarization, that put in evidence logicality and prospects of this field of research.

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References

  1. Soskin, M.S. and Vasnetsov, M.V., Singular optics, in Progress in Optics, Wolf, E., Ed., 2001, vol. 42, pp. 219–276.

    Article  Google Scholar 

  2. Gbur, G.J., Singular Optics, NY: CRC Press, 2016.

    Book  MATH  Google Scholar 

  3. Nye, J.F. and Berry, M.V., Dislocations in wave trains, Proc. R. Soc. Lond. A, 1974, vol. 336, pp. 165–190.

    Article  MathSciNet  MATH  Google Scholar 

  4. Kittel, Ch., Introduction to Solid State Physics, 8th ed., NY: Wiley, 2004.

    MATH  Google Scholar 

  5. Dirac, P.A.M., Quantized singularities in the electromagnetic field, Proc. R. Soc. A, 1931, vol. 133, pp. 1–13.

    Article  Google Scholar 

  6. Baranova, N.B., Zel’dovich, B.Ya., Mamaev, A.V., Pilipetskii, N.F., and Shkunov, V.V., Dislocations of the wave-front of a speckle-inhomogeneous field (theory and experiment), JETP Lett., 1981, vol. 33, pp. 206–210.

    Google Scholar 

  7. Baranova, N.B., Mamaev, A.V., Pilipetsky, N.F., Shkunov, V.V., and Zel’dovich, B.Ya., Wave-front dislocations: topological limitations for adaptive systems with phase conjugation, J. Opt. Soc. Am., 1983, vol. 73, pp. 525–528.

    Article  Google Scholar 

  8. Zel’dovich, B.Ya., Pilipetsky, N.F., and Shkunov, V.V., Principles of Phase Conjugation, Berlin: Springer, 1985.

    Book  Google Scholar 

  9. Zel’dovich, B.Ya., Shkunov, V.V, and Yakovleva, T.V., Holograms of speckle fields, Sov. Phys. Usp., 1986, vol. 29, pp. 678–702.

    Article  Google Scholar 

  10. Bazhenov, V.Yu., Vasnetsov, M.V., and Soskin M.S., Laser beams with screw dislocations in their wave-fronts, JETP Lett., 1990, vol. 52, pp. 429–431.

    Google Scholar 

  11. Heckenberg, N.R., McDuff, R., Smith, C.P., and White, A.G., Generation of optical singularities by computergenerated holograms, Opt. Lett., 1992, vol. 17, pp. 221–223.

    Article  Google Scholar 

  12. Schurcliff, W.A., Polarized Light: Production and Use, Cambridge, Massachusetts: Harvard Univ. Press, 1962.

    Book  Google Scholar 

  13. Crawford, F.S., Waves, Berkeley Physics Course, vol. 3, McGraw-Hill, 1971.

    Google Scholar 

  14. Polyanskii, V.K. and Kovalskii, L.V., On fine structure of the scattered radiation field, Opt. Spectrosc., 1973, vol. 35, pp. 345–350.

    Google Scholar 

  15. Nye, J.F. and Hajnal, J.V., The wave structure of monochromatic electromagnetic radiation, Proc. R. Soc. London A, 1987, vol. 409, pp. 21–36.

    Article  MathSciNet  MATH  Google Scholar 

  16. Hajnal, J.V., Singularities in the transverse fields of electromagnetic waves, I: Theory, Proc. R. Soc. London A, 1987, vol. 414, pp. 433–446.

    Article  MathSciNet  Google Scholar 

  17. Hajnal, J.V., Singularities in the transverse fields of electromagnetic waves, II, Proc. R. Soc. London A, 1987, vol. 414, pp. 447–466.

    Article  Google Scholar 

  18. Nye, J.F., Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations, Bristol and Philadelphia: Institute of Physics Publishing, 1999.

    MATH  Google Scholar 

  19. Freund, I. and Shwartsman, N., Wave-field singularities: The sign principle, Phys. Rev., 1994, vol. 50, pp. 5164–5172.

    Article  MathSciNet  Google Scholar 

  20. Freund, I., Mokhun, A.I., Soskin, M.S., Angelsky, O.V., and Mokhun, I.I., Stokes singularity relations, Opt. Lett., 2002, vol. 27, pp. 545–547.

    Article  Google Scholar 

  21. Angelsky, O.V., Gorsky, M.P., Hanson, S.G., Lukin, V.P., Mokhun, I.I., Polyanskii, P.V., and Ryabiy, P.A., Optical correlation algorithm for reconstructing phase skeleton of complex optical fields for solving the phase problem, Opt. Expr., 2014, vol. 22, pp. 6186–6193.

    Article  Google Scholar 

  22. Angelsky, O.V., Polyanskii, P.V., and Felde, Ch.V., Emerging the field of correlation optics, Opt. Phot. News, 2012, vol. 4, pp. 25–29.

    Article  Google Scholar 

  23. Wolf, E., Optics in terms of observable quantities, Nuovo Cimento, 1954, vol. 12, pp. 884–888.

    Article  MATH  Google Scholar 

  24. Born, M. and Wolf, E., Principles of Optics, 7th ed., Cambridge: Cambridge Univ. Press, 1999.

    Book  Google Scholar 

  25. Goodman, J.W., Statistical Optics, New York: Wiley, 2015.

    Google Scholar 

  26. Polyanskii, P.V., Some current views on singular optics, Proc. SPIE, 2004, vol. 5477, pp. 31–40.

    Article  Google Scholar 

  27. Gbur, G. and Visser, T.D., The structure of partially coherent fields, in Progress in Optics, Wolf, E., 2010, vol. 55C, pp. 285–341.

    Article  Google Scholar 

  28. Felde, Ch.V., Chernyshov, A.A., Bogatyryova, G.V., Polyanskii, P.V., and Soskin, M.S., Polarization singularities in partially coherent combined beams, JETP Lett., 2008, vol. 88, pp. 418–422.

    Article  Google Scholar 

  29. Soskin, M.S. and Polyanskii, P.V., New polarization singularities of partially coherent light beams, Proc. SPIE, 2010, vol. 7613 0G, pp. 1–11.

    Google Scholar 

  30. Felde, Ch.V., Polyanskii, P.V., Zelinskii, Ye.V., and Oleksyuk, M.V., Young’s diagnostics of the space correlation and polarization phase singularities inherent in combined Hermite-Gaussian beams, Proc. SPIE, 2015, vol. 9809, 980903, pp. 1–10.

    Google Scholar 

  31. Mokhun, I.I., Introduction to Linear Singular Optics, in: Optical Correlation: Techniques and Applications, Angelsky, O., Bellingham: SPIE Press, 2007, pp. 1–131.

    Google Scholar 

  32. Gbur, G., Partially coherent beam propagation in atmospheric turbulence, J. Opt. Soc. Am. A, 2014, vol. 31, pp. 2038–2045.

    Article  Google Scholar 

  33. Sommerfeld, A., Optik–Vorlesungen über theoretische Physik Band 4, Dieterich’sche Verlagsbuchhandlung, 1950.

    MATH  Google Scholar 

  34. Berry, M.V., Geometry of phase and polarization singularities, illustrated by edge diffraction and the tides, Proc. SPIE, 2001, vol. 4403, pp. 1–12.

    Article  Google Scholar 

  35. Wolf, E. and Thompson, B., Two-beam interference with partially coherent light, J. Opt. Soc. Am., 1957, vol. 47, pp. 895–902.

    Article  MathSciNet  Google Scholar 

  36. Thompson, B., Illustration of the phase change in two-beam interference with partially coherent light, J. Opt. Soc. Am., 1958, vol. 48, pp. 95–97.

    Article  Google Scholar 

  37. Chernyshov, A.A., Felde, Ch.V., Bogatyryova, H.V., Polyanskii, P.V., and Soskin, M.S., Vector singularities of the combined beams assembled from mutually incoherent orthogonally polarized components, J. Opt. A: Pure Appl. Opt., 2009, vol. 11, pp. 1–8.

    Article  Google Scholar 

  38. Ponomarenko, S.A., A class of partially coherent vortex beams carrying optical vortices, J. Opt. Soc. Am. A, 2001, vol. 18, pp. 150–156.

    Article  Google Scholar 

  39. Bogatyryova, G.V., Felde, Ch.V., Polyanskii, P.V., Ponomarenko, S.A., Soskin, M.S., and Wolf, E., Partially coherent vortex beams with a separable phase, Opt. Lett., 2003, vol. 28, pp. 878–880.

    Article  Google Scholar 

  40. Polyanskii, V.K., Spectral characteristics of colorless glass with rough surface, J. Appl. Spectr., 1970, vol. 13, pp. 1039–1942.

    Article  Google Scholar 

  41. Polyanskii, P.V., Optical correlation diagnostics of phase singularities in polychromatic fields, in Optical Correlation: Techniques and Applications, Angelsky, O., Ed., Bellingham: SPIE Press, 2007, pp. 133–165.

    Chapter  Google Scholar 

  42. Reif, F., Statistical Physics, Berkeley Physics Course, vol. 5, McGraw-Hill, 1988.

    Google Scholar 

  43. Knop, K., Color pictures using the zew diffraction order of phase grating structures, Opt. Commun., 1976, vol. 18, pp. 3–10.

    Article  Google Scholar 

  44. Dashtdar, M. and Tavassoly, M.T., Determination of height distribution on a rough interface by measuring the coherently transmitted or reflected light intensity, J. Opt. Soc. Am. A, 2008, vol. 25, pp. 2509–2517.

    Article  Google Scholar 

  45. Evans, R.M., An Introduction to Color, New Yokr: Wiley, 1959.

    Google Scholar 

  46. Berry, M., Exploiting the colors of dark light, New J. Phys., 2002, vol. 4, pp. 74.1–74.14.

    Google Scholar 

  47. Goodman, J.W., Introduction to Fourier Optics, New York: McGraw-Hill, 1996.

    Google Scholar 

  48. Azzam, R.M.A. and Bashara, N.M., Ellipsometry and Polarized Light, North-Holland Publ. Comp., 1977.

    Google Scholar 

  49. Klauder J.R. and Sudarshan, E.C.G., Fundamentals of Quantum Optics, New York: Benjamin, 1968.

    Google Scholar 

  50. Zenkova, C.Yu., Gorskii, M.P., Soltys I.V., and Angelsky, P.O., The investigation of the peculiarities of the motion of testing nanoobjects in the inhomogeneously polarized optical field, Opt. Mem. Neural Networks, 2012, vol. 21, pp. 34–44.

    Article  Google Scholar 

  51. Kushnerick, L.Ya., Bodnar, L.B., Gorski, M.P. and Sydor, M., Statistical and correlation structure of Fourier spectra polarizationally filtered laser images of optically anisotropic biological networks, Opt. Mem. Neural Networks, 2013, vol. 22, pp. 118–125.

    Article  Google Scholar 

  52. Polyanskii, P.V., Felde, Ch.V., Konovchuk, A.V., and Oleksyuk, M.V., On the role of higher-order nonlinearities in implementing second-order hologram-based associative memories, Opt. Mem. Neural Networks, 2015, vol. 24, pp. 230–234.

    Article  Google Scholar 

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Authors and Affiliations

  1. Chernivtsi National University, Chernivtsi, Ukraine

    P. V. Polyanskii, Ch. V. Felde, Y. V. Zelinskii & A. V. Konovhuk

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  1. P. V. Polyanskii
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  2. Ch. V. Felde
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  3. Y. V. Zelinskii
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  4. A. V. Konovhuk
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Correspondence to P. V. Polyanskii.

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Polyanskii, P.V., Felde, C.V., Zelinskii, Y.V. et al. On some prerequisites of correlation singular optics as a branch of information optics. Opt. Mem. Neural Networks 26, 207–215 (2017). https://doi.org/10.3103/S1060992X17030067

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  • DOI: https://doi.org/10.3103/S1060992X17030067

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