Journal of Experimental and Theoretical Physics

, Volume 126, Issue 2, pp 159–173 | Cite as

Method for Describing the Angular Distribution of Optical Radiation Scattered by a Monolayer of Ordered Spherical Particles (Normal Illumination)

Atoms, Molecules, Optics
  • 14 Downloads

Abstract

We have developed a method for describing the angular distribution of intensity of radiation scattered by a monolayer of homogeneous spatially ordered monodisperse spherical particles normally illuminated by a plane circularly polarized electromagnetic wave. The method is based on the quasicrystalline approximation (QCA) of the theory of multiple scattering of waves (TMSW) using the multipole expansion of fields and the tensor Green function in vectorial spherical wavefunctions. The method is applied for analyzing the characteristics of radiation scattered by a partially ordered monolayer and a monolayer with a nonideal lattice. The results of calculations are compared with the available experimental data on the position of the first-order diffraction peak on the angular and spectral dependences of the intensity of radiation scattered by a closely packed monolayer with a nonideal triangular lattice of SiO2 particles. Good conformity of the results has been established.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. Alfrey, E. B. Bradford, J. W. Vanderhof, et al., J. Opt. Soc. Am. 44, 603 (1954).ADSCrossRefGoogle Scholar
  2. 2.
    I. M. Krieger and F. M. O’Neill, J. Am. Chem. Soc. 90, 3114 (1968).CrossRefGoogle Scholar
  3. 3.
    P. A. Hiltner and I. M. Krieger, J. Phys. Chem. 73, 2386 (1969).CrossRefGoogle Scholar
  4. 4.
    V. N. Bogomolov, S. V. Gaponenko, I. N. Germanenko, et al., Phys. Rev. E 55, 7619 (1997).ADSCrossRefGoogle Scholar
  5. 5.
    T. Yamasaki and T. Tsutsui, Jpn. J. Appl. Phys. 38, 5916 (1999).ADSCrossRefGoogle Scholar
  6. 6.
    W. Sun, G. Videen, and B. Lin, Appl. Opt. 46, 1150 (2007).ADSCrossRefGoogle Scholar
  7. 7.
    B. Wang, Yi Jin, and S. He, J. Appl. Phys. 106, 014508 (2009).ADSCrossRefGoogle Scholar
  8. 8.
    B. K. Nayak, K. Sun, Ch. Rothenbach, et al., Appl. Opt. 50, 2349 (2011).ADSCrossRefGoogle Scholar
  9. 9.
    G. Fujii, T. Matsumoto, and T. Takahashi, Opt. Express 20, 7300 (2012).ADSCrossRefGoogle Scholar
  10. 10.
    X. H. Wu, A. Yamilov, H. Noh, et al., J. Opt. Soc. B 21, 159 (2004).ADSCrossRefGoogle Scholar
  11. 11.
    Y. Rho, M. Wanit, J. Yeo, et al., J. Phys. D: Appl. Phys. 46, 024006 (2013).ADSCrossRefGoogle Scholar
  12. 12.
    D. S. Wiersma, Nat. Photon. 7, 188 (2013).ADSCrossRefGoogle Scholar
  13. 13.
    I. Kim, D. S. Jeong, W. S. Lee, et al., Opt. Express 22, A1431 (2014).CrossRefGoogle Scholar
  14. 14.
    V. A. Loiko and A. A. Miskevich, Opt. Spectrosc. 115, 274 (2013).ADSCrossRefGoogle Scholar
  15. 15.
    A. A. Miskevich and V. A. Loiko, J. Quant. Spectrosc. Radiat. Transfer 136, 58 (2014).ADSCrossRefGoogle Scholar
  16. 16.
    A. A. Miskevich and V. A. Loiko, J. Quant. Spectrosc. Radiat. Transfer 146, 355 (2014).ADSCrossRefGoogle Scholar
  17. 17.
    A. A. Miskevich and V. A. Loiko, J. Quant. Spectrosc. Radiat. Transfer 167, 23 (2015).ADSCrossRefGoogle Scholar
  18. 18.
    V. A. Loiko and A. A. Miskevich, Opt. Spectrosc. 122, 799 (2017).ADSCrossRefGoogle Scholar
  19. 19.
    K. Ohtaka, J. Phys. C: Solid State Phys. 13, 667 (1980).ADSCrossRefGoogle Scholar
  20. 20.
    K. Ohtaka, Y. Suda, and S. Nagano, Phys. Rev. B 61, 5267 (2000).ADSCrossRefGoogle Scholar
  21. 21.
    A. Modinos, Phys. A 141, 575 (1987).CrossRefGoogle Scholar
  22. 22.
    N. Stefanou and A. Modinos, J. Phys: Condens. Matter 3, 8135 (1991).ADSGoogle Scholar
  23. 23.
    N. Stefanou and A. Modinos, J. Phys: Condens. Matter 5, 8859 (1993).ADSGoogle Scholar
  24. 24.
    L. L. Foldy, Phys. Rev. 67, 107 (1945).ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    M. Lax, Rev. Mod. Phys. 23, 287 (1951).ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    M. Lax, Phys. Rev. 85, 621 (1952).ADSCrossRefGoogle Scholar
  27. 27.
    V. Twersky, J. Appl. Phys. 23, 407 (1952).ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    V. Twersky, J. Math. Phys. 16, 633 (1975).ADSCrossRefGoogle Scholar
  29. 29.
    J. G. Fikioris and P. C. Waterman, J. Math. Phys. 5, 1413 (1964); J. Quant. Spectrosc. Radiat. Transfer 123, 8 (2013).ADSCrossRefGoogle Scholar
  30. 30.
    N. C. Mathur and K. C. Yeh, J. Math. Phys. 5, 1619 (1964).ADSCrossRefGoogle Scholar
  31. 31.
    V. V. Varadan and V. K. Varadan, Phys. Rev. D 21, 388 (1980).ADSCrossRefGoogle Scholar
  32. 32.
    L. Tsang and J. A. Kong, Radio Sci. 18, 1260 (1983).ADSCrossRefGoogle Scholar
  33. 33.
    L. Tsang, C.-T. Chen, A. T. C. Chang, et al., Radio Sci. 35, 731 (2000).ADSCrossRefGoogle Scholar
  34. 34.
    K. M. Hong, J. Opt. Soc. Am. 70, 821 (1980).ADSCrossRefGoogle Scholar
  35. 35.
    D. Mackowski, Proc. R. Soc. London A 433, 599 (1991); J. Opt. Soc. Am. A 11, 2851 (1994).ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    Y. Xu, Appl. Opt. 34, 4573 (1995); Phys. Lett. A 249, 30 (1998).ADSCrossRefGoogle Scholar
  37. 37.
    V. G. Vereshchagin, A. N. Ponyavina, and N. I. Sil’vanovich, Dokl. Akad. Nauk BSSR 34, 123 (1990).Google Scholar
  38. 38.
    A. N. Ponyavina, J. Appl. Spectrosc. 65, 752 (1998).ADSCrossRefGoogle Scholar
  39. 39.
    A. N. Ponyavina, S. M. Kachan, and N. I. Sil’vanovich, J. Opt. Soc. Am. B 21, 1866 (2004).ADSCrossRefGoogle Scholar
  40. 40.
    V. Loiko and V. Molochko, Part. Part. Syst. Charact. 13, 227 (1996).CrossRefGoogle Scholar
  41. 41.
    V. A. Loiko, V. P. Dick, and A. P. Ivanov, J. Opt. Soc. Am. A 17, 2040 (2000).ADSCrossRefGoogle Scholar
  42. 42.
    V. A. Loiko and A. A. Miskevich, Appl. Opt. 44, 3759 (2005).ADSCrossRefGoogle Scholar
  43. 43.
    V. A. Loiko and A. A. Miskevich, Opt. Spectrosc. 98, 61 (2005).ADSCrossRefGoogle Scholar
  44. 44.
    M. I. Mishchenko, L. Liu, D. W. Mackowski, et al., Opt. Express 15, 2822 (2007).ADSCrossRefGoogle Scholar
  45. 45.
    Y. Okada and A. A. Kokhanovsky, J. Quant. Spectrosc Radiat. Transfer 110, 902 (2009).ADSCrossRefGoogle Scholar
  46. 46.
    A. García-Valenzuela, E. Gutiérrez-Reyes, and R. Barrera, J. Opt. Soc. Am. A 29, 1161 (2012).ADSCrossRefGoogle Scholar
  47. 47.
    J. Ziman, Models of Disorder (Cambridge Univ. Press, Cambridge, 1979), p. 525.Google Scholar
  48. 48.
    V. I. Iveronova and G. P. Revkevich, The Theory of X-Ray Dispersion (Mosk. Gos. Univ., Moscow, 1978), p. 278 [in Russian].Google Scholar
  49. 49.
    J. K. Percus and G. J. Yevick, Phys. Rev. 110, 1 (1958).ADSMathSciNetCrossRefGoogle Scholar
  50. 50.
    A. A. Miskevich and V. A. Loiko, J. Quant. Spectrosc. Radiat. Transfer 112, 1082 (2011).ADSCrossRefGoogle Scholar
  51. 51.
    A. A. Miskevich and V. A. Loiko, J. Exp. Theor. Phys. 113, 1 (2011).ADSCrossRefGoogle Scholar
  52. 52.
    A. A. Miskevich and V. A. Loiko, Nanosyst.: Phys. Chem. Math. 4, 778 (2013).Google Scholar
  53. 53.
    A. A. Miskevich and V. A. Loiko, J. Exp. Theor. Phys. 119, 211 (2014).CrossRefGoogle Scholar
  54. 54.
    A. A. Miskevich and V. A. Loiko, J. Quant. Spectrosc. Radiat. Transfer 151, 260 (2015).ADSCrossRefGoogle Scholar
  55. 55.
    A. P. Ivanov, V. A. Loiko, and V. P. Dik, Light Propagation in Densely Packed Disperse Media (Nauka Tekhnika, Minsk, 1988), p. 191 [in Russian].Google Scholar
  56. 56.
    P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).MATHGoogle Scholar
  57. 57.
    V. A. Babenko, L. G. Astafyeva, and V. N. Kuzmin, Electromagnetic Scattering in Disperse Media: Inhomogeneous and Anisotropic Particles (Springer, Berlin, 2003), p. 434.Google Scholar
  58. 58.
    L. S. Ornstein and F. Zernike, Proc. Acad. Sci. 17, 793 (1914).Google Scholar
  59. 59.
    U. Fano, Phys. Rev. 124, 1866 (1961).ADSCrossRefGoogle Scholar
  60. 60.
    A. B. Evlyukhin, C. Reinhardt, A. Seidel, et al., Phys. Rev. B 82, 045404 (2010).ADSCrossRefGoogle Scholar
  61. 61.
    A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).ADSCrossRefGoogle Scholar
  62. 62.
    M. V. Rybin, I. S. Sinev, K. B. Samusev, and M. F. Limonov, Phys. Solid State 56, 580 (2014).ADSCrossRefGoogle Scholar
  63. 63.
    V. Berdnik and V. Loiko, Quantum electronics 36, 1016 (2006).ADSCrossRefGoogle Scholar
  64. 64.
    Handbook of Optical Constants of Solids, Ed. by E. D. Palik (Academic, San Diego, 1985), Vol. 1.Google Scholar
  65. 65.
    Y. Kurokawa, H. Miyazaki, and Y. Jimba, Phys. Rev. B 69, 155117 (2004).ADSCrossRefGoogle Scholar
  66. 66.
    D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (Nauka, Leningrad, 1975; World Sci., Singapore, 1988).CrossRefGoogle Scholar
  67. 67.
    G. V. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists, 7th. ed. (Academic Press, Oxford, 2012).MATHGoogle Scholar
  68. 68.
    C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, NY, 1983).Google Scholar
  69. 69.
    M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Univ. Press, Cambridge, 2002).Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Stepanov Institute of PhysicsNational Academy of Sciences of BelarusMinskBelarus

Personalised recommendations