Abstract

Using the coherent backscattering technique, we have measured the transport mean-free-path lengths lt for photons in NdAl3(BO3)4 powder, a promising solid-state random laser material. The developed model allows one to calculate lt as a function of the mean particle size s in tightly packed powder or sintered ceramic. The experimentally determined value of lt is in good agreement with the model prediction.

© 2003 Optical Society of America

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  1. V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
    [CrossRef]
  2. C. Gouedard, D. Husson, C. Sauteret, F. Auzel, and A. Migus, “Generation of spatially incoherent short pulses in laser-pumped neodymium stoichiometic crystals and powders,” J. Opt. Soc. Am. B 10, 2358–2363 (1993).
    [CrossRef]
  3. M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, T. Thompson, M. Mahdi, and V. Ostroumov, “Short-pulsed stimulated emission in the powders of NdAl3(BO3)4, NdSc3(BO3)4, and Nd:Sr5(PO4)3F laser crystals,” J. Opt. Soc. Am. B 13, 2024–2033 (1996).
    [CrossRef]
  4. H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
    [CrossRef]
  5. R. M. Laine, T. Hinklin, G. Williams, and S. C. Rand, “Low-cost nanopowders for phosphor and laser applications by flame spray pyrolysis,” Mater. Sci. Forum 343, 500–510 (2000).
    [CrossRef]
  6. R. C. Polson, A. Chipouline, and Z. V. Vardeny, “Random lasing in p-conjugated films and infiltrated opals,” Adv. Mater. 13, 760–764 (2001).
    [CrossRef]
  7. M. A. Noginov, N. Noginova, S. U. Egarievwe, H. J. Caulfield, C. Cochrane, J. C. Wang, M. R. Kokta, and J. Paitz, “Study of the pumping regimes in Ti-sapphire and Nd0.5La0.5Al3(BO3)4 powders,” Opt. Mater. 10, 297–303 (1998).
    [CrossRef]
  8. D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
    [CrossRef]
  9. Y. Kuga and A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 1, 831–836 (1984).
    [CrossRef]
  10. M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
    [CrossRef] [PubMed]
  11. P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
    [CrossRef] [PubMed]
  12. P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
    [CrossRef]
  13. M. B. van der Mark, M. P. van Albada, and A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
    [CrossRef]
  14. H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
    [CrossRef] [PubMed]
  15. S. C. Rand, “Strong localization of light and photonic atoms,” Can. J. Phys. 78, 625–637 (2000).
    [CrossRef]
  16. R. C. Polson, J. D. Huang, and Z. V. Vardeny, “Random lasers in π-conjugated polymer films,” Synth. Met. 119, 7–12 (2001).
    [CrossRef]
  17. H.-D. Hattendorf, “Chrom-sensibilisierter Neodym-Aluminium-Borat-Laser,” Ph.D. dissertation (University of Hamburg, Hamburg, Germany, 1979).
  18. S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
    [CrossRef]
  19. E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
    [CrossRef] [PubMed]
  20. E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
    [CrossRef]
  21. S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
    [CrossRef]
  22. H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
    [CrossRef]
  23. H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
    [CrossRef] [PubMed]
  24. V. A. Rabinivich and Z. Ya. Khavin, Short Handbook on Chemistry [Kratkii Khimicheskii Spravochnik] (Khimia, Leningrad, 1977).
  25. D. R. Lide, Handbook of Chemistry and Physics, 82nd ed. (CRC Press, Boca Raton, Fla., 2001).
  26. M. Born and E. Wolf, Principles of Optics, 6th ed. (corrected) (Cambridge U. Press, Cambridge, UK, 1977).
  27. B. Michel, “MieCalc—freely configurable program for light scattering calculations (Mie theory),” http://www.lightscattering.de/MieCalc/eindex.html, Last modified, Jan. 6, 2002.
  28. J. G. Rivas, R. Sprik, A. Langendijk, L. D. Noordam, and C. W. Rella, “Static and dynamic transport of light close to the Anderson localization transition,” Phys. Rev. E 63, 046613 (2001).
    [CrossRef]

2001 (4)

R. C. Polson, A. Chipouline, and Z. V. Vardeny, “Random lasing in p-conjugated films and infiltrated opals,” Adv. Mater. 13, 760–764 (2001).
[CrossRef]

R. C. Polson, J. D. Huang, and Z. V. Vardeny, “Random lasers in π-conjugated polymer films,” Synth. Met. 119, 7–12 (2001).
[CrossRef]

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

J. G. Rivas, R. Sprik, A. Langendijk, L. D. Noordam, and C. W. Rella, “Static and dynamic transport of light close to the Anderson localization transition,” Phys. Rev. E 63, 046613 (2001).
[CrossRef]

2000 (4)

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

R. M. Laine, T. Hinklin, G. Williams, and S. C. Rand, “Low-cost nanopowders for phosphor and laser applications by flame spray pyrolysis,” Mater. Sci. Forum 343, 500–510 (2000).
[CrossRef]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

S. C. Rand, “Strong localization of light and photonic atoms,” Can. J. Phys. 78, 625–637 (2000).
[CrossRef]

1999 (1)

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[CrossRef]

1998 (2)

M. A. Noginov, N. Noginova, S. U. Egarievwe, H. J. Caulfield, C. Cochrane, J. C. Wang, M. R. Kokta, and J. Paitz, “Study of the pumping regimes in Ti-sapphire and Nd0.5La0.5Al3(BO3)4 powders,” Opt. Mater. 10, 297–303 (1998).
[CrossRef]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

1996 (2)

1993 (1)

1991 (1)

S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
[CrossRef]

1988 (3)

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[CrossRef]

M. B. van der Mark, M. P. van Albada, and A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

1986 (2)

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
[CrossRef]

1985 (2)

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

1984 (1)

Akkermans, E.

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

Auzel, F.

Briskina, Ch. M.

V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
[CrossRef]

Cao, H.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[CrossRef]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Caulfield, H. J.

M. A. Noginov, N. Noginova, S. U. Egarievwe, H. J. Caulfield, C. Cochrane, J. C. Wang, M. R. Kokta, and J. Paitz, “Study of the pumping regimes in Ti-sapphire and Nd0.5La0.5Al3(BO3)4 powders,” Opt. Mater. 10, 297–303 (1998).
[CrossRef]

M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, T. Thompson, M. Mahdi, and V. Ostroumov, “Short-pulsed stimulated emission in the powders of NdAl3(BO3)4, NdSc3(BO3)4, and Nd:Sr5(PO4)3F laser crystals,” J. Opt. Soc. Am. B 13, 2024–2033 (1996).
[CrossRef]

Chang, R. P. H.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[CrossRef]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Chang, S.-H.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Chipouline, A.

R. C. Polson, A. Chipouline, and Z. V. Vardeny, “Random lasing in p-conjugated films and infiltrated opals,” Adv. Mater. 13, 760–764 (2001).
[CrossRef]

Chizhikov, V. I.

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Cochrane, C.

M. A. Noginov, N. Noginova, S. U. Egarievwe, H. J. Caulfield, C. Cochrane, J. C. Wang, M. R. Kokta, and J. Paitz, “Study of the pumping regimes in Ti-sapphire and Nd0.5La0.5Al3(BO3)4 powders,” Opt. Mater. 10, 297–303 (1998).
[CrossRef]

Dai, J. Y.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Durmanov, S. T.

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Egarievwe, S. U.

M. A. Noginov, N. Noginova, S. U. Egarievwe, H. J. Caulfield, C. Cochrane, J. C. Wang, M. R. Kokta, and J. Paitz, “Study of the pumping regimes in Ti-sapphire and Nd0.5La0.5Al3(BO3)4 powders,” Opt. Mater. 10, 297–303 (1998).
[CrossRef]

Gouedard, C.

Hait, V. L.

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Hinklin, T.

R. M. Laine, T. Hinklin, G. Williams, and S. C. Rand, “Low-cost nanopowders for phosphor and laser applications by flame spray pyrolysis,” Mater. Sci. Forum 343, 500–510 (2000).
[CrossRef]

Ho, S. T.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[CrossRef]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Huang, J. D.

R. C. Polson, J. D. Huang, and Z. V. Vardeny, “Random lasers in π-conjugated polymer films,” Synth. Met. 119, 7–12 (2001).
[CrossRef]

Husson, D.

Ishimaru, A.

John, S.

S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
[CrossRef]

Kokta, M. R.

M. A. Noginov, N. Noginova, S. U. Egarievwe, H. J. Caulfield, C. Cochrane, J. C. Wang, M. R. Kokta, and J. Paitz, “Study of the pumping regimes in Ti-sapphire and Nd0.5La0.5Al3(BO3)4 powders,” Opt. Mater. 10, 297–303 (1998).
[CrossRef]

Kuga, Y.

Kutovoi, S. A.

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Kuzmicheva, G. M.

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Kuzmin, O. V.

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Lagendijk, A.

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[CrossRef]

M. B. van der Mark, M. P. van Albada, and A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
[CrossRef]

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

Laine, R. M.

R. M. Laine, T. Hinklin, G. Williams, and S. C. Rand, “Low-cost nanopowders for phosphor and laser applications by flame spray pyrolysis,” Mater. Sci. Forum 343, 500–510 (2000).
[CrossRef]

Langendijk, A.

J. G. Rivas, R. Sprik, A. Langendijk, L. D. Noordam, and C. W. Rella, “Static and dynamic transport of light close to the Anderson localization transition,” Phys. Rev. E 63, 046613 (2001).
[CrossRef]

Liu, X.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Mahdi, M.

Maret, G.

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

Markushev, V. M.

V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
[CrossRef]

Matrynov, A. A.

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Maynard, R.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

Migus, A.

Nesynov, E. K.

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Noginov, M. A.

M. A. Noginov, N. Noginova, S. U. Egarievwe, H. J. Caulfield, C. Cochrane, J. C. Wang, M. R. Kokta, and J. Paitz, “Study of the pumping regimes in Ti-sapphire and Nd0.5La0.5Al3(BO3)4 powders,” Opt. Mater. 10, 297–303 (1998).
[CrossRef]

M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, T. Thompson, M. Mahdi, and V. Ostroumov, “Short-pulsed stimulated emission in the powders of NdAl3(BO3)4, NdSc3(BO3)4, and Nd:Sr5(PO4)3F laser crystals,” J. Opt. Soc. Am. B 13, 2024–2033 (1996).
[CrossRef]

Noginova, N.

M. A. Noginov, N. Noginova, S. U. Egarievwe, H. J. Caulfield, C. Cochrane, J. C. Wang, M. R. Kokta, and J. Paitz, “Study of the pumping regimes in Ti-sapphire and Nd0.5La0.5Al3(BO3)4 powders,” Opt. Mater. 10, 297–303 (1998).
[CrossRef]

Noginova, N. E.

Noordam, L. D.

J. G. Rivas, R. Sprik, A. Langendijk, L. D. Noordam, and C. W. Rella, “Static and dynamic transport of light close to the Anderson localization transition,” Phys. Rev. E 63, 046613 (2001).
[CrossRef]

Ong, H. C.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Ostroumov, V.

Paitz, J.

M. A. Noginov, N. Noginova, S. U. Egarievwe, H. J. Caulfield, C. Cochrane, J. C. Wang, M. R. Kokta, and J. Paitz, “Study of the pumping regimes in Ti-sapphire and Nd0.5La0.5Al3(BO3)4 powders,” Opt. Mater. 10, 297–303 (1998).
[CrossRef]

Panyutin, V. L.

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Polson, R. C.

R. C. Polson, J. D. Huang, and Z. V. Vardeny, “Random lasers in π-conjugated polymer films,” Synth. Met. 119, 7–12 (2001).
[CrossRef]

R. C. Polson, A. Chipouline, and Z. V. Vardeny, “Random lasing in p-conjugated films and infiltrated opals,” Adv. Mater. 13, 760–764 (2001).
[CrossRef]

Rand, S. C.

R. M. Laine, T. Hinklin, G. Williams, and S. C. Rand, “Low-cost nanopowders for phosphor and laser applications by flame spray pyrolysis,” Mater. Sci. Forum 343, 500–510 (2000).
[CrossRef]

S. C. Rand, “Strong localization of light and photonic atoms,” Can. J. Phys. 78, 625–637 (2000).
[CrossRef]

Rella, C. W.

J. G. Rivas, R. Sprik, A. Langendijk, L. D. Noordam, and C. W. Rella, “Static and dynamic transport of light close to the Anderson localization transition,” Phys. Rev. E 63, 046613 (2001).
[CrossRef]

Rivas, J. G.

J. G. Rivas, R. Sprik, A. Langendijk, L. D. Noordam, and C. W. Rella, “Static and dynamic transport of light close to the Anderson localization transition,” Phys. Rev. E 63, 046613 (2001).
[CrossRef]

Rudnitsky, Yu. P.

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Sauteret, C.

Seelig, E. W.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[CrossRef]

Smirnov, G. V.

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Sprik, R.

J. G. Rivas, R. Sprik, A. Langendijk, L. D. Noordam, and C. W. Rella, “Static and dynamic transport of light close to the Anderson localization transition,” Phys. Rev. E 63, 046613 (2001).
[CrossRef]

Thompson, T.

van Albada, M. P.

M. B. van der Mark, M. P. van Albada, and A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
[CrossRef]

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

van der Mark, M. B.

M. B. van der Mark, M. P. van Albada, and A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
[CrossRef]

Vardeny, Z. V.

R. C. Polson, J. D. Huang, and Z. V. Vardeny, “Random lasers in π-conjugated polymer films,” Synth. Met. 119, 7–12 (2001).
[CrossRef]

R. C. Polson, A. Chipouline, and Z. V. Vardeny, “Random lasing in p-conjugated films and infiltrated opals,” Adv. Mater. 13, 760–764 (2001).
[CrossRef]

Venkateswarlu, P.

Wang, J. C.

M. A. Noginov, N. Noginova, S. U. Egarievwe, H. J. Caulfield, C. Cochrane, J. C. Wang, M. R. Kokta, and J. Paitz, “Study of the pumping regimes in Ti-sapphire and Nd0.5La0.5Al3(BO3)4 powders,” Opt. Mater. 10, 297–303 (1998).
[CrossRef]

Wang, Q. H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[CrossRef]

Wiersma, D. S.

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[CrossRef]

Williams, G.

R. M. Laine, T. Hinklin, G. Williams, and S. C. Rand, “Low-cost nanopowders for phosphor and laser applications by flame spray pyrolysis,” Mater. Sci. Forum 343, 500–510 (2000).
[CrossRef]

Wolf, P. E.

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

Wu, J. Y.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Xu, J. Y.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Zhang, D. Z.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Zhao, Y. G.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[CrossRef]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Zolin, V. F.

V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
[CrossRef]

Adv. Mater. (1)

R. C. Polson, A. Chipouline, and Z. V. Vardeny, “Random lasing in p-conjugated films and infiltrated opals,” Adv. Mater. 13, 760–764 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Can. J. Phys. (1)

S. C. Rand, “Strong localization of light and photonic atoms,” Can. J. Phys. 78, 625–637 (2000).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

J. Phys. (Paris) (2)

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media: an experimental study,” J. Phys. (Paris) 49, 63–75 (1988).
[CrossRef]

Mater. Sci. Forum (1)

R. M. Laine, T. Hinklin, G. Williams, and S. C. Rand, “Low-cost nanopowders for phosphor and laser applications by flame spray pyrolysis,” Mater. Sci. Forum 343, 500–510 (2000).
[CrossRef]

Opt. Mater. (2)

M. A. Noginov, N. Noginova, S. U. Egarievwe, H. J. Caulfield, C. Cochrane, J. C. Wang, M. R. Kokta, and J. Paitz, “Study of the pumping regimes in Ti-sapphire and Nd0.5La0.5Al3(BO3)4 powders,” Opt. Mater. 10, 297–303 (1998).
[CrossRef]

S. T. Durmanov, O. V. Kuzmin, G. M. Kuzmicheva, S. A. Kutovoi, A. A. Matrynov, E. K. Nesynov, V. L. Panyutin, Yu. P. Rudnitsky, G. V. Smirnov, V. L. Hait, and V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Phys. Rev. B (1)

M. B. van der Mark, M. P. van Albada, and A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988).
[CrossRef]

Phys. Rev. E (2)

J. G. Rivas, R. Sprik, A. Langendijk, L. D. Noordam, and C. W. Rella, “Static and dynamic transport of light close to the Anderson localization transition,” Phys. Rev. E 63, 046613 (2001).
[CrossRef]

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[CrossRef]

Phys. Rev. Lett. (6)

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[CrossRef]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef] [PubMed]

Phys. Today (1)

S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
[CrossRef]

Sov. J. Quantum Electron. (1)

V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
[CrossRef]

Synth. Met. (1)

R. C. Polson, J. D. Huang, and Z. V. Vardeny, “Random lasers in π-conjugated polymer films,” Synth. Met. 119, 7–12 (2001).
[CrossRef]

Other (5)

H.-D. Hattendorf, “Chrom-sensibilisierter Neodym-Aluminium-Borat-Laser,” Ph.D. dissertation (University of Hamburg, Hamburg, Germany, 1979).

V. A. Rabinivich and Z. Ya. Khavin, Short Handbook on Chemistry [Kratkii Khimicheskii Spravochnik] (Khimia, Leningrad, 1977).

D. R. Lide, Handbook of Chemistry and Physics, 82nd ed. (CRC Press, Boca Raton, Fla., 2001).

M. Born and E. Wolf, Principles of Optics, 6th ed. (corrected) (Cambridge U. Press, Cambridge, UK, 1977).

B. Michel, “MieCalc—freely configurable program for light scattering calculations (Mie theory),” http://www.lightscattering.de/MieCalc/eindex.html, Last modified, Jan. 6, 2002.

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Figures (9)

Fig. 1
Fig. 1

Distribution of NdAl3(BO3)4 powder particles by their sizes.

Fig. 2
Fig. 2

Absorption spectrum of a NdAl3(BO3)4 single crystal: 1, Ec; 2, Ec; 3, averaged spectrum (digitized and recalculated from the transmission spectra published in Ref. 17).

Fig. 3
Fig. 3

Setup for CBS measurements.

Fig. 4
Fig. 4

CBS cone in NdAl3(BO3)4 powder at 488 nm. Diamonds, experiment; solid curve, theoretical fitting following Refs. 13, 19, and 20. For the FWHM method, the width of the cone is W=8.1 mrad and for the cone fitting kabs=1.04 cm-1.

Fig. 5
Fig. 5

Experimentally determined values of the transport mean free path lt in NdAl3(BO3)4 powder obtained from the fitting of the CBS cones (diamonds) and from the FWHM measurements (squares). Solid line, calculated function ltλ4, corresponding to Rayleigh scattering.

Fig. 6
Fig. 6

(a) Schematic drawing of tightly packed powder, (b) propagation of a photon flux inside a particle, (c) steplike distribution of the photon flux intensity I(x) and approximated with an exponential function.

Fig. 7
Fig. 7

(a) Refraction of the light beam at the crystalline–air boundaries separating two particles of powder, (b) total internal reflection.

Fig. 8
Fig. 8

Calculated dependence 1/1-cos θ versus n1.

Fig. 9
Fig. 9

Normalized scattering cross section Qs of dielectric spheres with a refractive index of 2.02 as a function of the particle size s calculated for λ=0.41 μm with the help of the miecalc program.27

Tables (1)

Tables Icon

Table 1 Absorption and Transport Mean-Free-Path Length in the NdAl3(BO3)4 Powder a

Equations (11)

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

s=if(si)diif(si)=3.55μm.
lt0.7 λ2πW.
0I0exp(-x/ls)dx=0I(x)dx=0sI0dx,
lt=11-cos(θ) ls,
ρ=n1cos(φ)-n2cos(ψ)n1cos(φ)+n2cos(ψ)2,
ρ=n2cos(φ)-n1cos(ψ)n2cos(φ)+n1cos(ψ)2,
ρ=ρ2+ρ221/2.
ρeff=2ρ-ρ2,
τeff=1-2ρ+ρ2.
sin(φcrit)n1=sin(π/2)n2.
ltcorr(s)=ltQs(s)Qs,

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