Abstract

Wavelength dependence of the light scattering coefficient of nanostructured glasses (phase-separated glasses and glass-ceramics) is often described by the power law with a constant exponent (−p). Based on this experimental fact, we apply the approach of Debye and Bueche to the theoretical description of interference effects in such a light scattering and derive the expression for the angular distribution (phase function) of the scattered light. The phase function includes the value of p (p > 2) as parameter and is independent of wavelength. The asymmetry parameter for the scattered light is positive at p < 4 and negative at p > 4. The results are in satisfactory agreement with experimental data.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Asymmetry parameter for anomalous scattering of light in nanostructured glasses

Michael P. Shepilov
Opt. Lett. 42(21) 4513-4516 (2017)

Light scattering in glass-ceramics: revision of the concept

Michael P. Shepilov, Olga S. Dymshits, and Aleksander A. Zhilin
J. Opt. Soc. Am. B 35(7) 1717-1724 (2018)

Light scattering in Eu3+-doped glass-ceramics containing SrIINbIVO3 nanocrystals

M. P. Shepilov, G. Upender, O. S. Dymshits, and A. A. Zhilin
J. Opt. Soc. Am. B 35(12) 3116-3121 (2018)

References

  • View by:
  • |
  • |
  • |

  1. N. S. Andreev, “Scattering of visible light by glasses undergoing phase separation and homogenization,” J. Non-Cryst. Solids 30(2), 99–126 (1978).
    [Crossref]
  2. M. P. Shepilov, O. S. Dymshits, and A. A. Zhilin, “Light scattering in glass-ceramics: revision of the concept,” J. Opt. Soc. Am. B 35(7), 1717–1724 (2018).
    [Crossref]
  3. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2004).
  4. J. P. Kerwawycz and M. Tomozawa, “Structural origin of the light scattering from a phase‐separated glass,” J. Appl. Phys. 51(8), 4391–4398 (1980).
    [Crossref]
  5. M. P. Shepilov, “The problem of theoretically describing anomalous light scattering by liquating glasses, caused by interparticle interference,” J. Opt. Technol. 70(12), 882–887 (2003).
    [Crossref]
  6. M. P. Shepilov, “On the problem of theoretical description of anomalous light scattering by phase separated glasses,” Phys. Chem. Glasses 46(2), 173–177 (2005).
  7. M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, A. E. Kalmykov, and G. A. Sycheva, “Features of the anomalous scattering of light in two-phase sodium borosilicate glass,” J. Opt. Technol. 80(11), 706–713 (2013).
    [Crossref]
  8. A. A. Zhilin, G. T. Petrovskii, O. S. Dymshits, V. V. Golubkov, and M. P. Shepilov, “Effect of phase transformations in Na2O–Nb2O5–SiO2 glasses on their transparency and Kerr coefficient variation,” Phys. Chem. Glasses 46(2), 232–235 (2005).
  9. M. P. Shepilov, O. S. Dymshits, V. V. Golubkov, and A. A. Zhilin, “Anomalously low light scattering in the Na2O-Nb2O5-SiO2 glass-ceramics,” Adv. Mat. Res. 39–40, 270–273 (2008).
  10. M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
    [Crossref]
  11. S. Hendy, “Light scattering in transparent glass ceramics,” Appl. Phys. Lett. 81(7), 1171–1173 (2002).
    [Crossref]
  12. M. Goldstein, “Theory of scattering for diffusion‐controlled phase separations,” J. Appl. Phys. 34(7), 1928–1934 (1963).
    [Crossref]
  13. J. J. Hammel and S. M. Ohlberg, “Light scattering from diffusion-controlled phase separations in glass,” J. Appl. Phys. 36(4), 1442–1447 (1965).
    [Crossref]
  14. D. M. Shetterly and R. J. Stubler, “Electromagnetic scattering from metastable immiscible droplets in glass,” J. Am. Ceram. Soc. 82(1), 5–16 (1999).
  15. A. Edgar, “Core-shell particle model for optical transparency in glass ceramics,” Appl. Phys. Lett. 89(4), 041909 (2006).
    [Crossref]
  16. H. Li, Y. Zhang, D. Zhong, S. Xu, Q. Fei, and D. Wang, “Influence of blue-light polarization on light scattering in nanocrystal luminescent glass for white light-emitting-diodes,” Optoelectron. Lett. 6(3), 164–167 (2010).
    [Crossref]
  17. R. W. Hopper, “Stochastic theory of scattering from idealized spinodal structures: II. Scattering in general and for the basic late stage model,” J. Non-Cryst. Solids 70(1), 111–142 (1985).
    [Crossref]
  18. M. P. Shepilov, “On light scattering in fluorozirconate glass-ceramics containing BaCl2 nano-crystals,” Opt. Mater. 30(6), 839–846 (2008).
    [Crossref]
  19. M. P. Shepilov, “Asymmetry parameter for anomalous scattering of light in nanostructured glasses,” Opt. Lett. 42(21), 4513–4516 (2017).
    [Crossref] [PubMed]
  20. M. P. Shepilov, “Light scattering in optical material containing polydisperse spherical nano-particles,” Opt. Mater. 31(2), 385–390 (2008).
    [Crossref]
  21. P. Debye and A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20(6), 518–525 (1949).
    [Crossref]
  22. M. Kerker, The Scattering of Light (Academic, 1969) (see Section 8.4).
  23. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (NASA, Cambridge University Press, 2004).
  24. L. A. Dombrovsky and D. Baillis, Thermal Radiation in Disperse Systems: An Engineering Approach (Begell Haus, 2010), http://www.begellhouse.com/ebook_platform/6d17e856430c0b8d.html .
  25. M. Tomozawa and J. P. Kerwawycz, “Depolarized light scattering from a phase‐separated glass,” J. Appl. Phys. 50(5), 3644–3647 (1979).
    [Crossref]
  26. M. I. Mishchenko, “Asymmetry parameters of the phase function for densely packed scattering grains,” J. Quant. Spectrosc. Radiat. Transf. 52(1), 95–110 (1994).
    [Crossref]
  27. R. Gómez-Medina, L. S. Froufe-Pérez, M. Yépez, F. Scheffold, M. Nieto-Vesperinas, and J. J. Sáenz, “Negative scattering asymmetry parameter for dipolar particles: Unusual reduction of the transport mean free path and radiation pressure,” Phys. Rev. A 85(3), 035802 (2012).
    [Crossref]
  28. B. X. Wang and C. Y. Zhao, “Achieving a strongly negative scattering asymmetry factor in random media composed of dual-dipolar particles,” Phys. Rev. A (Coll. Park) 97(2), 023836 (2018).
    [Crossref]
  29. J. J. Hammel, J. Mickey, and H. R. Golob, “Diffusion coefficients from light scattering in glass,” J. Coll. Int. Sci. 27(3), 329–335 (1968).
    [Crossref]
  30. A. I. Kolyadin, “Anomalous light scattering in glass,” Dokl. Akad. Nauk SSSR 109, 64 (1956) (in Russian) [Soviet Phys.‐Doklady 1, 406 (1956)].
  31. A. I. Kolyadin, “Anomalous light scattering in glass,” Opt. Spektrosk. 1, 907 (1956) (in Russian).
  32. A. I. Kolyadin, “Anomalous light scattering in glass,” in The Structure of Glass, Proceedings of the Third All‐Union Conference on the Glassy State, Leningrad, 1959, (Consultants Bureau, New York, 1960), p. 202.
  33. A. I. Kolyadin, “Study of scattering and absorption of light in ultrapure glasses and optical ceramics,” Report of Vavilov State Optical Institute, NIR-XIY TT12–416–82/1F11–03–82 (Leningrad, 1984). (p. 36–39). (in Russian).

2018 (2)

B. X. Wang and C. Y. Zhao, “Achieving a strongly negative scattering asymmetry factor in random media composed of dual-dipolar particles,” Phys. Rev. A (Coll. Park) 97(2), 023836 (2018).
[Crossref]

M. P. Shepilov, O. S. Dymshits, and A. A. Zhilin, “Light scattering in glass-ceramics: revision of the concept,” J. Opt. Soc. Am. B 35(7), 1717–1724 (2018).
[Crossref]

2017 (2)

M. P. Shepilov, “Asymmetry parameter for anomalous scattering of light in nanostructured glasses,” Opt. Lett. 42(21), 4513–4516 (2017).
[Crossref] [PubMed]

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
[Crossref]

2013 (1)

2012 (1)

R. Gómez-Medina, L. S. Froufe-Pérez, M. Yépez, F. Scheffold, M. Nieto-Vesperinas, and J. J. Sáenz, “Negative scattering asymmetry parameter for dipolar particles: Unusual reduction of the transport mean free path and radiation pressure,” Phys. Rev. A 85(3), 035802 (2012).
[Crossref]

2010 (1)

H. Li, Y. Zhang, D. Zhong, S. Xu, Q. Fei, and D. Wang, “Influence of blue-light polarization on light scattering in nanocrystal luminescent glass for white light-emitting-diodes,” Optoelectron. Lett. 6(3), 164–167 (2010).
[Crossref]

2008 (3)

M. P. Shepilov, O. S. Dymshits, V. V. Golubkov, and A. A. Zhilin, “Anomalously low light scattering in the Na2O-Nb2O5-SiO2 glass-ceramics,” Adv. Mat. Res. 39–40, 270–273 (2008).

M. P. Shepilov, “On light scattering in fluorozirconate glass-ceramics containing BaCl2 nano-crystals,” Opt. Mater. 30(6), 839–846 (2008).
[Crossref]

M. P. Shepilov, “Light scattering in optical material containing polydisperse spherical nano-particles,” Opt. Mater. 31(2), 385–390 (2008).
[Crossref]

2006 (1)

A. Edgar, “Core-shell particle model for optical transparency in glass ceramics,” Appl. Phys. Lett. 89(4), 041909 (2006).
[Crossref]

2005 (2)

A. A. Zhilin, G. T. Petrovskii, O. S. Dymshits, V. V. Golubkov, and M. P. Shepilov, “Effect of phase transformations in Na2O–Nb2O5–SiO2 glasses on their transparency and Kerr coefficient variation,” Phys. Chem. Glasses 46(2), 232–235 (2005).

M. P. Shepilov, “On the problem of theoretical description of anomalous light scattering by phase separated glasses,” Phys. Chem. Glasses 46(2), 173–177 (2005).

2003 (1)

2002 (1)

S. Hendy, “Light scattering in transparent glass ceramics,” Appl. Phys. Lett. 81(7), 1171–1173 (2002).
[Crossref]

1999 (1)

D. M. Shetterly and R. J. Stubler, “Electromagnetic scattering from metastable immiscible droplets in glass,” J. Am. Ceram. Soc. 82(1), 5–16 (1999).

1994 (1)

M. I. Mishchenko, “Asymmetry parameters of the phase function for densely packed scattering grains,” J. Quant. Spectrosc. Radiat. Transf. 52(1), 95–110 (1994).
[Crossref]

1985 (1)

R. W. Hopper, “Stochastic theory of scattering from idealized spinodal structures: II. Scattering in general and for the basic late stage model,” J. Non-Cryst. Solids 70(1), 111–142 (1985).
[Crossref]

1980 (1)

J. P. Kerwawycz and M. Tomozawa, “Structural origin of the light scattering from a phase‐separated glass,” J. Appl. Phys. 51(8), 4391–4398 (1980).
[Crossref]

1979 (1)

M. Tomozawa and J. P. Kerwawycz, “Depolarized light scattering from a phase‐separated glass,” J. Appl. Phys. 50(5), 3644–3647 (1979).
[Crossref]

1978 (1)

N. S. Andreev, “Scattering of visible light by glasses undergoing phase separation and homogenization,” J. Non-Cryst. Solids 30(2), 99–126 (1978).
[Crossref]

1968 (1)

J. J. Hammel, J. Mickey, and H. R. Golob, “Diffusion coefficients from light scattering in glass,” J. Coll. Int. Sci. 27(3), 329–335 (1968).
[Crossref]

1965 (1)

J. J. Hammel and S. M. Ohlberg, “Light scattering from diffusion-controlled phase separations in glass,” J. Appl. Phys. 36(4), 1442–1447 (1965).
[Crossref]

1963 (1)

M. Goldstein, “Theory of scattering for diffusion‐controlled phase separations,” J. Appl. Phys. 34(7), 1928–1934 (1963).
[Crossref]

1956 (2)

A. I. Kolyadin, “Anomalous light scattering in glass,” Dokl. Akad. Nauk SSSR 109, 64 (1956) (in Russian) [Soviet Phys.‐Doklady 1, 406 (1956)].

A. I. Kolyadin, “Anomalous light scattering in glass,” Opt. Spektrosk. 1, 907 (1956) (in Russian).

1949 (1)

P. Debye and A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20(6), 518–525 (1949).
[Crossref]

Alekseeva, I. P.

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
[Crossref]

Andreev, N. S.

N. S. Andreev, “Scattering of visible light by glasses undergoing phase separation and homogenization,” J. Non-Cryst. Solids 30(2), 99–126 (1978).
[Crossref]

Bueche, A. M.

P. Debye and A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20(6), 518–525 (1949).
[Crossref]

Debye, P.

P. Debye and A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20(6), 518–525 (1949).
[Crossref]

Dymshits, O. S.

M. P. Shepilov, O. S. Dymshits, and A. A. Zhilin, “Light scattering in glass-ceramics: revision of the concept,” J. Opt. Soc. Am. B 35(7), 1717–1724 (2018).
[Crossref]

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
[Crossref]

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, A. E. Kalmykov, and G. A. Sycheva, “Features of the anomalous scattering of light in two-phase sodium borosilicate glass,” J. Opt. Technol. 80(11), 706–713 (2013).
[Crossref]

M. P. Shepilov, O. S. Dymshits, V. V. Golubkov, and A. A. Zhilin, “Anomalously low light scattering in the Na2O-Nb2O5-SiO2 glass-ceramics,” Adv. Mat. Res. 39–40, 270–273 (2008).

A. A. Zhilin, G. T. Petrovskii, O. S. Dymshits, V. V. Golubkov, and M. P. Shepilov, “Effect of phase transformations in Na2O–Nb2O5–SiO2 glasses on their transparency and Kerr coefficient variation,” Phys. Chem. Glasses 46(2), 232–235 (2005).

Edgar, A.

A. Edgar, “Core-shell particle model for optical transparency in glass ceramics,” Appl. Phys. Lett. 89(4), 041909 (2006).
[Crossref]

Fei, Q.

H. Li, Y. Zhang, D. Zhong, S. Xu, Q. Fei, and D. Wang, “Influence of blue-light polarization on light scattering in nanocrystal luminescent glass for white light-emitting-diodes,” Optoelectron. Lett. 6(3), 164–167 (2010).
[Crossref]

Froufe-Pérez, L. S.

R. Gómez-Medina, L. S. Froufe-Pérez, M. Yépez, F. Scheffold, M. Nieto-Vesperinas, and J. J. Sáenz, “Negative scattering asymmetry parameter for dipolar particles: Unusual reduction of the transport mean free path and radiation pressure,” Phys. Rev. A 85(3), 035802 (2012).
[Crossref]

Goldstein, M.

M. Goldstein, “Theory of scattering for diffusion‐controlled phase separations,” J. Appl. Phys. 34(7), 1928–1934 (1963).
[Crossref]

Golob, H. R.

J. J. Hammel, J. Mickey, and H. R. Golob, “Diffusion coefficients from light scattering in glass,” J. Coll. Int. Sci. 27(3), 329–335 (1968).
[Crossref]

Golubkov, V. V.

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
[Crossref]

M. P. Shepilov, O. S. Dymshits, V. V. Golubkov, and A. A. Zhilin, “Anomalously low light scattering in the Na2O-Nb2O5-SiO2 glass-ceramics,” Adv. Mat. Res. 39–40, 270–273 (2008).

A. A. Zhilin, G. T. Petrovskii, O. S. Dymshits, V. V. Golubkov, and M. P. Shepilov, “Effect of phase transformations in Na2O–Nb2O5–SiO2 glasses on their transparency and Kerr coefficient variation,” Phys. Chem. Glasses 46(2), 232–235 (2005).

Gómez-Medina, R.

R. Gómez-Medina, L. S. Froufe-Pérez, M. Yépez, F. Scheffold, M. Nieto-Vesperinas, and J. J. Sáenz, “Negative scattering asymmetry parameter for dipolar particles: Unusual reduction of the transport mean free path and radiation pressure,” Phys. Rev. A 85(3), 035802 (2012).
[Crossref]

Hammel, J. J.

J. J. Hammel, J. Mickey, and H. R. Golob, “Diffusion coefficients from light scattering in glass,” J. Coll. Int. Sci. 27(3), 329–335 (1968).
[Crossref]

J. J. Hammel and S. M. Ohlberg, “Light scattering from diffusion-controlled phase separations in glass,” J. Appl. Phys. 36(4), 1442–1447 (1965).
[Crossref]

Hendy, S.

S. Hendy, “Light scattering in transparent glass ceramics,” Appl. Phys. Lett. 81(7), 1171–1173 (2002).
[Crossref]

Hopper, R. W.

R. W. Hopper, “Stochastic theory of scattering from idealized spinodal structures: II. Scattering in general and for the basic late stage model,” J. Non-Cryst. Solids 70(1), 111–142 (1985).
[Crossref]

Hubetsov, A. A.

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
[Crossref]

Kalmykov, A. E.

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
[Crossref]

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, A. E. Kalmykov, and G. A. Sycheva, “Features of the anomalous scattering of light in two-phase sodium borosilicate glass,” J. Opt. Technol. 80(11), 706–713 (2013).
[Crossref]

Kerwawycz, J. P.

J. P. Kerwawycz and M. Tomozawa, “Structural origin of the light scattering from a phase‐separated glass,” J. Appl. Phys. 51(8), 4391–4398 (1980).
[Crossref]

M. Tomozawa and J. P. Kerwawycz, “Depolarized light scattering from a phase‐separated glass,” J. Appl. Phys. 50(5), 3644–3647 (1979).
[Crossref]

Kolyadin, A. I.

A. I. Kolyadin, “Anomalous light scattering in glass,” Dokl. Akad. Nauk SSSR 109, 64 (1956) (in Russian) [Soviet Phys.‐Doklady 1, 406 (1956)].

A. I. Kolyadin, “Anomalous light scattering in glass,” Opt. Spektrosk. 1, 907 (1956) (in Russian).

Li, H.

H. Li, Y. Zhang, D. Zhong, S. Xu, Q. Fei, and D. Wang, “Influence of blue-light polarization on light scattering in nanocrystal luminescent glass for white light-emitting-diodes,” Optoelectron. Lett. 6(3), 164–167 (2010).
[Crossref]

Mickey, J.

J. J. Hammel, J. Mickey, and H. R. Golob, “Diffusion coefficients from light scattering in glass,” J. Coll. Int. Sci. 27(3), 329–335 (1968).
[Crossref]

Mishchenko, M. I.

M. I. Mishchenko, “Asymmetry parameters of the phase function for densely packed scattering grains,” J. Quant. Spectrosc. Radiat. Transf. 52(1), 95–110 (1994).
[Crossref]

Myasoedov, A. V.

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
[Crossref]

Nieto-Vesperinas, M.

R. Gómez-Medina, L. S. Froufe-Pérez, M. Yépez, F. Scheffold, M. Nieto-Vesperinas, and J. J. Sáenz, “Negative scattering asymmetry parameter for dipolar particles: Unusual reduction of the transport mean free path and radiation pressure,” Phys. Rev. A 85(3), 035802 (2012).
[Crossref]

Ohlberg, S. M.

J. J. Hammel and S. M. Ohlberg, “Light scattering from diffusion-controlled phase separations in glass,” J. Appl. Phys. 36(4), 1442–1447 (1965).
[Crossref]

Petrovskii, G. T.

A. A. Zhilin, G. T. Petrovskii, O. S. Dymshits, V. V. Golubkov, and M. P. Shepilov, “Effect of phase transformations in Na2O–Nb2O5–SiO2 glasses on their transparency and Kerr coefficient variation,” Phys. Chem. Glasses 46(2), 232–235 (2005).

Sáenz, J. J.

R. Gómez-Medina, L. S. Froufe-Pérez, M. Yépez, F. Scheffold, M. Nieto-Vesperinas, and J. J. Sáenz, “Negative scattering asymmetry parameter for dipolar particles: Unusual reduction of the transport mean free path and radiation pressure,” Phys. Rev. A 85(3), 035802 (2012).
[Crossref]

Scheffold, F.

R. Gómez-Medina, L. S. Froufe-Pérez, M. Yépez, F. Scheffold, M. Nieto-Vesperinas, and J. J. Sáenz, “Negative scattering asymmetry parameter for dipolar particles: Unusual reduction of the transport mean free path and radiation pressure,” Phys. Rev. A 85(3), 035802 (2012).
[Crossref]

Shepilov, M. P.

M. P. Shepilov, O. S. Dymshits, and A. A. Zhilin, “Light scattering in glass-ceramics: revision of the concept,” J. Opt. Soc. Am. B 35(7), 1717–1724 (2018).
[Crossref]

M. P. Shepilov, “Asymmetry parameter for anomalous scattering of light in nanostructured glasses,” Opt. Lett. 42(21), 4513–4516 (2017).
[Crossref] [PubMed]

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
[Crossref]

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, A. E. Kalmykov, and G. A. Sycheva, “Features of the anomalous scattering of light in two-phase sodium borosilicate glass,” J. Opt. Technol. 80(11), 706–713 (2013).
[Crossref]

M. P. Shepilov, O. S. Dymshits, V. V. Golubkov, and A. A. Zhilin, “Anomalously low light scattering in the Na2O-Nb2O5-SiO2 glass-ceramics,” Adv. Mat. Res. 39–40, 270–273 (2008).

M. P. Shepilov, “On light scattering in fluorozirconate glass-ceramics containing BaCl2 nano-crystals,” Opt. Mater. 30(6), 839–846 (2008).
[Crossref]

M. P. Shepilov, “Light scattering in optical material containing polydisperse spherical nano-particles,” Opt. Mater. 31(2), 385–390 (2008).
[Crossref]

A. A. Zhilin, G. T. Petrovskii, O. S. Dymshits, V. V. Golubkov, and M. P. Shepilov, “Effect of phase transformations in Na2O–Nb2O5–SiO2 glasses on their transparency and Kerr coefficient variation,” Phys. Chem. Glasses 46(2), 232–235 (2005).

M. P. Shepilov, “On the problem of theoretical description of anomalous light scattering by phase separated glasses,” Phys. Chem. Glasses 46(2), 173–177 (2005).

M. P. Shepilov, “The problem of theoretically describing anomalous light scattering by liquating glasses, caused by interparticle interference,” J. Opt. Technol. 70(12), 882–887 (2003).
[Crossref]

Shetterly, D. M.

D. M. Shetterly and R. J. Stubler, “Electromagnetic scattering from metastable immiscible droplets in glass,” J. Am. Ceram. Soc. 82(1), 5–16 (1999).

Stubler, R. J.

D. M. Shetterly and R. J. Stubler, “Electromagnetic scattering from metastable immiscible droplets in glass,” J. Am. Ceram. Soc. 82(1), 5–16 (1999).

Sycheva, G. A.

Tomozawa, M.

J. P. Kerwawycz and M. Tomozawa, “Structural origin of the light scattering from a phase‐separated glass,” J. Appl. Phys. 51(8), 4391–4398 (1980).
[Crossref]

M. Tomozawa and J. P. Kerwawycz, “Depolarized light scattering from a phase‐separated glass,” J. Appl. Phys. 50(5), 3644–3647 (1979).
[Crossref]

Wang, B. X.

B. X. Wang and C. Y. Zhao, “Achieving a strongly negative scattering asymmetry factor in random media composed of dual-dipolar particles,” Phys. Rev. A (Coll. Park) 97(2), 023836 (2018).
[Crossref]

Wang, D.

H. Li, Y. Zhang, D. Zhong, S. Xu, Q. Fei, and D. Wang, “Influence of blue-light polarization on light scattering in nanocrystal luminescent glass for white light-emitting-diodes,” Optoelectron. Lett. 6(3), 164–167 (2010).
[Crossref]

Xu, S.

H. Li, Y. Zhang, D. Zhong, S. Xu, Q. Fei, and D. Wang, “Influence of blue-light polarization on light scattering in nanocrystal luminescent glass for white light-emitting-diodes,” Optoelectron. Lett. 6(3), 164–167 (2010).
[Crossref]

Yépez, M.

R. Gómez-Medina, L. S. Froufe-Pérez, M. Yépez, F. Scheffold, M. Nieto-Vesperinas, and J. J. Sáenz, “Negative scattering asymmetry parameter for dipolar particles: Unusual reduction of the transport mean free path and radiation pressure,” Phys. Rev. A 85(3), 035802 (2012).
[Crossref]

Zapalova, S. S.

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
[Crossref]

Zhang, Y.

H. Li, Y. Zhang, D. Zhong, S. Xu, Q. Fei, and D. Wang, “Influence of blue-light polarization on light scattering in nanocrystal luminescent glass for white light-emitting-diodes,” Optoelectron. Lett. 6(3), 164–167 (2010).
[Crossref]

Zhao, C. Y.

B. X. Wang and C. Y. Zhao, “Achieving a strongly negative scattering asymmetry factor in random media composed of dual-dipolar particles,” Phys. Rev. A (Coll. Park) 97(2), 023836 (2018).
[Crossref]

Zhilin, A. A.

M. P. Shepilov, O. S. Dymshits, and A. A. Zhilin, “Light scattering in glass-ceramics: revision of the concept,” J. Opt. Soc. Am. B 35(7), 1717–1724 (2018).
[Crossref]

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
[Crossref]

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, A. E. Kalmykov, and G. A. Sycheva, “Features of the anomalous scattering of light in two-phase sodium borosilicate glass,” J. Opt. Technol. 80(11), 706–713 (2013).
[Crossref]

M. P. Shepilov, O. S. Dymshits, V. V. Golubkov, and A. A. Zhilin, “Anomalously low light scattering in the Na2O-Nb2O5-SiO2 glass-ceramics,” Adv. Mat. Res. 39–40, 270–273 (2008).

A. A. Zhilin, G. T. Petrovskii, O. S. Dymshits, V. V. Golubkov, and M. P. Shepilov, “Effect of phase transformations in Na2O–Nb2O5–SiO2 glasses on their transparency and Kerr coefficient variation,” Phys. Chem. Glasses 46(2), 232–235 (2005).

Zhong, D.

H. Li, Y. Zhang, D. Zhong, S. Xu, Q. Fei, and D. Wang, “Influence of blue-light polarization on light scattering in nanocrystal luminescent glass for white light-emitting-diodes,” Optoelectron. Lett. 6(3), 164–167 (2010).
[Crossref]

Adv. Mat. Res. (1)

M. P. Shepilov, O. S. Dymshits, V. V. Golubkov, and A. A. Zhilin, “Anomalously low light scattering in the Na2O-Nb2O5-SiO2 glass-ceramics,” Adv. Mat. Res. 39–40, 270–273 (2008).

Appl. Phys. Lett. (2)

S. Hendy, “Light scattering in transparent glass ceramics,” Appl. Phys. Lett. 81(7), 1171–1173 (2002).
[Crossref]

A. Edgar, “Core-shell particle model for optical transparency in glass ceramics,” Appl. Phys. Lett. 89(4), 041909 (2006).
[Crossref]

Dokl. Akad. Nauk SSSR (1)

A. I. Kolyadin, “Anomalous light scattering in glass,” Dokl. Akad. Nauk SSSR 109, 64 (1956) (in Russian) [Soviet Phys.‐Doklady 1, 406 (1956)].

J. Am. Ceram. Soc. (1)

D. M. Shetterly and R. J. Stubler, “Electromagnetic scattering from metastable immiscible droplets in glass,” J. Am. Ceram. Soc. 82(1), 5–16 (1999).

J. Appl. Phys. (5)

P. Debye and A. M. Bueche, “Scattering by an inhomogeneous solid,” J. Appl. Phys. 20(6), 518–525 (1949).
[Crossref]

M. Tomozawa and J. P. Kerwawycz, “Depolarized light scattering from a phase‐separated glass,” J. Appl. Phys. 50(5), 3644–3647 (1979).
[Crossref]

M. Goldstein, “Theory of scattering for diffusion‐controlled phase separations,” J. Appl. Phys. 34(7), 1928–1934 (1963).
[Crossref]

J. J. Hammel and S. M. Ohlberg, “Light scattering from diffusion-controlled phase separations in glass,” J. Appl. Phys. 36(4), 1442–1447 (1965).
[Crossref]

J. P. Kerwawycz and M. Tomozawa, “Structural origin of the light scattering from a phase‐separated glass,” J. Appl. Phys. 51(8), 4391–4398 (1980).
[Crossref]

J. Coll. Int. Sci. (1)

J. J. Hammel, J. Mickey, and H. R. Golob, “Diffusion coefficients from light scattering in glass,” J. Coll. Int. Sci. 27(3), 329–335 (1968).
[Crossref]

J. Non-Cryst. Solids (3)

N. S. Andreev, “Scattering of visible light by glasses undergoing phase separation and homogenization,” J. Non-Cryst. Solids 30(2), 99–126 (1978).
[Crossref]

M. P. Shepilov, O. S. Dymshits, A. A. Zhilin, V. V. Golubkov, A. E. Kalmykov, I. P. Alekseeva, A. V. Myasoedov, A. A. Hubetsov, and S. S. Zapalova, “Effect of low NiO doping on anomalous light scattering in zinc aluminosilicate glass-ceramics,” J. Non-Cryst. Solids 473, 152–169 (2017).
[Crossref]

R. W. Hopper, “Stochastic theory of scattering from idealized spinodal structures: II. Scattering in general and for the basic late stage model,” J. Non-Cryst. Solids 70(1), 111–142 (1985).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Opt. Technol. (2)

J. Quant. Spectrosc. Radiat. Transf. (1)

M. I. Mishchenko, “Asymmetry parameters of the phase function for densely packed scattering grains,” J. Quant. Spectrosc. Radiat. Transf. 52(1), 95–110 (1994).
[Crossref]

Opt. Lett. (1)

Opt. Mater. (2)

M. P. Shepilov, “Light scattering in optical material containing polydisperse spherical nano-particles,” Opt. Mater. 31(2), 385–390 (2008).
[Crossref]

M. P. Shepilov, “On light scattering in fluorozirconate glass-ceramics containing BaCl2 nano-crystals,” Opt. Mater. 30(6), 839–846 (2008).
[Crossref]

Opt. Spektrosk. (1)

A. I. Kolyadin, “Anomalous light scattering in glass,” Opt. Spektrosk. 1, 907 (1956) (in Russian).

Optoelectron. Lett. (1)

H. Li, Y. Zhang, D. Zhong, S. Xu, Q. Fei, and D. Wang, “Influence of blue-light polarization on light scattering in nanocrystal luminescent glass for white light-emitting-diodes,” Optoelectron. Lett. 6(3), 164–167 (2010).
[Crossref]

Phys. Chem. Glasses (2)

A. A. Zhilin, G. T. Petrovskii, O. S. Dymshits, V. V. Golubkov, and M. P. Shepilov, “Effect of phase transformations in Na2O–Nb2O5–SiO2 glasses on their transparency and Kerr coefficient variation,” Phys. Chem. Glasses 46(2), 232–235 (2005).

M. P. Shepilov, “On the problem of theoretical description of anomalous light scattering by phase separated glasses,” Phys. Chem. Glasses 46(2), 173–177 (2005).

Phys. Rev. A (1)

R. Gómez-Medina, L. S. Froufe-Pérez, M. Yépez, F. Scheffold, M. Nieto-Vesperinas, and J. J. Sáenz, “Negative scattering asymmetry parameter for dipolar particles: Unusual reduction of the transport mean free path and radiation pressure,” Phys. Rev. A 85(3), 035802 (2012).
[Crossref]

Phys. Rev. A (Coll. Park) (1)

B. X. Wang and C. Y. Zhao, “Achieving a strongly negative scattering asymmetry factor in random media composed of dual-dipolar particles,” Phys. Rev. A (Coll. Park) 97(2), 023836 (2018).
[Crossref]

Other (6)

M. Kerker, The Scattering of Light (Academic, 1969) (see Section 8.4).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (NASA, Cambridge University Press, 2004).

L. A. Dombrovsky and D. Baillis, Thermal Radiation in Disperse Systems: An Engineering Approach (Begell Haus, 2010), http://www.begellhouse.com/ebook_platform/6d17e856430c0b8d.html .

A. I. Kolyadin, “Anomalous light scattering in glass,” in The Structure of Glass, Proceedings of the Third All‐Union Conference on the Glassy State, Leningrad, 1959, (Consultants Bureau, New York, 1960), p. 202.

A. I. Kolyadin, “Study of scattering and absorption of light in ultrapure glasses and optical ceramics,” Report of Vavilov State Optical Institute, NIR-XIY TT12–416–82/1F11–03–82 (Leningrad, 1984). (p. 36–39). (in Russian).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2004).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 Phase functions P u , p ( θ ) in Eq. (10) for scattering of unpolarized incident light in (a) Cartesian and (b) polar presentation. The results are presented for several values of the parameter p , which determines the wavelength dependence of SC (1).
Fig. 2
Fig. 2 Asymmetry parameter g p in Eq. (12) as a function of absolute value p ( p > 2 ) of exponent in wavelength dependence of SC (1).
Fig. 3
Fig. 3 Comparison of the experimental data on angular distribution of light scattered by sodium borosilicate glass obtained by Kolyadin [30,31] (crosses and circles) with the phase function calculated by Eq. (8) for p = 8 and two polarizations (5a) and (5b) (curves). The value p = 8 was observed in this glass experimentally [30,31].
Fig. 4
Fig. 4 Experimental phase functions at λ = 546 nm for glass KF-7 [33] in comparison with the phase functions calculated by Eq. (8) with the experimentally determined value of p = 4.8 [33]. Two polarizations (5a) and (5b) of incident light are used.
Fig. 5
Fig. 5 Experimental phase functions at λ = 546 nm for organic glass ST-1 [33] in comparison with the phase functions calculated by Eq. (8) with the experimentally determined value of p = 3 [33]. Two polarizations (5a) and (5b) of incident light are used.
Fig. 6
Fig. 6 Experimental data on angular distribution of light scattered by inhomogeneous sodium borosilicate glass [32] in comparison with the curves calculated by the Goldstein theory [12] and by Eq. (8).
Fig. 7
Fig. 7 Experimental data on angular distribution of light scattered by phase-separated borosilicate glass [25] in comparison with the curves calculated by the Goldstein theory [12] and by Eq. (8).
Fig. 8
Fig. 8 Experimental data on angular distribution of light scattered by phase-separated borosilicate glass heat-treated for different times t [4] in comparison with the curves calculated by Eq. (8) with p = 6 and 6.6 .

Equations (15)

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

α s ( λ ) a λ p , ( a , p = constant, λ min < λ < λ max ) ,
η ( r ' ) η ( r + r ) r ' = γ ( r ) ( η ( r ' ) ) 2 r ' : = γ ( r )   η 2 ¯
I ( θ ) I 0 =   η 2 ¯ є 2   π 2   V λ m 4 R 2   ω ( 4 π   sin ( θ / 2 ) / λ m ) i ( θ ) .
ω ( q ) =   γ ( r )   e i q r d 3 r = 4 π 0 sin q r q r   γ ( r ) r 2 d r
i ( θ ) = i = 1 ,   ( incident   light   polarized   perpendicular   to   the   scattering   plane ,   V V ) ;
i ( θ ) = i = cos 2 θ ,   ( incident   light   polarized   parallel to   the   scattering   plane ,   H H ) ;
i ( θ ) = i u = ( i + i ) / 2 = ( 1 + cos 2 θ ) / 2 ,     ( unpolarized   incident   light ) .
α s ( λ ) = π 3 η 2 ¯ λ 4 0 π sin θ   ( 1 + cos 2 θ )   ω ( 4 π n sin ( θ / 2 ) / λ ) d θ .
ω ( 4 π n sin ( θ / 2 ) / λ ) b ( 4 π n sin ( θ / 2 ) / λ ) p 4 ,       ( b = constant,   p > 2) .
I ( θ ) P p ( θ ) i ( θ )   ( sin ( θ / 2 ) ) p 4 ,       ( p > 2 ) ,
P u , p ( θ ) = ( 1 + cos 2 θ ) ( sin ( θ / 2) ) p 4 / 2 .
P u , p ( θ ) = ( 1 + cos 2 θ ) ( sin ( θ / 2) ) p 4 / { 8 [ ( p 2 ) 1 2 p 1 + 2 ( p + 2 ) 1 ] } .
0 π sin θ P u , p ( θ ) d θ = 1
g p = cos θ = 0 π cos θ sin θ P u , p ( θ ) d θ / 0 π sin θ P u , p ( θ ) d θ = [ ( p 2 ) 1 4 p 1 + 6 ( p + 2 ) 1 4 ( p + 4 ) 1 ] / [ ( p 2 ) 1 2 p 1 + 2 ( p + 2 ) 1 ] .
α s,G ( λ ) λ 8 , P G ( C , θ ) [ sin ( θ / 2 ) ] 4 , ( for i and C 0.5 ) .