Abstract

Comparing the absorption spectrum of a single-crystalline material and the reflection spectrum of its powder, we have derived a simple empirical formula for the reflection coefficient of absorbing powder. The proposed equation, which slightly resembles the Lambert-Beer law for transmission, does not correspond to the equation derived in the approximation of a simple one-dimensional diffusion model.

© 2004 Optical Society of America

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  1. V. S. Letokhov, “Stimulated emission of an ensemble of scattering particles with negative absorption,” JETP Lett. 5, 212–215 (1967).
  2. V. S. Letokhov, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 26, 835–840 (1968).
  3. V. M. Markushev, V. F. Zolin, Ch. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
    [CrossRef]
  4. V. M. Markushev, N. È. Ter-Gabriélyan, Ch. M. Briskina, V. R. Belan, V. F. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Sov. J. Quantum Electron. 20, 772–777 (1990).
    [CrossRef]
  5. C. Gouedard, D. Husson, C. Sauteret, F. Auzel, A. Migus, “Generation of spatially incoherent short pulses in laser-pumped neodymium stoichiometric crystals and powders,” J. Opt. Soc. Am. B 10, 2358–2363 (1993).
    [CrossRef]
  6. M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, T. Thompson, M. Mahdi, 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]
  7. B. Li, G. Williams, S. C. Rand, T. Hinklin, R. M. Laine, “Continuous-wave ultraviolet laser action in strongly scattering Nd-doped alumina,” Opt. Lett. 27, 394–396 (2002).
    [CrossRef]
  8. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, E. Sauvain, “Laser action in strongly scattering medium,” Nature 368, 436–438 (1994).
    [CrossRef]
  9. H. Cao, “Random lasers with coherent feedback,” in Optical Properties of Nanostructured Random Media, V. M. Shalaev, ed., Vol. 82 of Topics in Applied Physics (Springer-Verlag, Berlin, 2002), p. 303.
    [CrossRef]
  10. S. V. Frolov, Z. V. Vardeny, K. Yoshino, “Cooperative and stimulated emission in poly(p-phenylene-vinylene) thin films and solutions,” Phys. Rev. B 57, 9141–9147 (1998).
    [CrossRef]
  11. R. C. Polson, J. D. Huang, Z. V. Vardeny, “Theories and simulations of random lasers,” in Photonic Crystals and Light Localization in the 21st Century, C. M. Soukoulis, ed., Vol. 563 of NATO Science Series, Series C: Mathematical and Physical Sciences, (Kluwer Academic, The Netherlands, 2001), p. 405.
    [CrossRef]
  12. H. Cao, J. Y. Xu, S.-H. Chang, S. T. Ho, “Transition from amplified spontaneous emission to laser action in strongly scattering media,” Phys. Rev. E 61, 1985–1989 (2000).
    [CrossRef]
  13. G. Williams, B. Bayram, S. C. Rand, T. Hinklin, R. M. Laine, “Laser action in strongly scattering rare-earth-doped dielectric nanophosphors,” Phys. Rev. A 65, 013807-1–013807-6 (2001).
    [CrossRef]
  14. A. A. Lichmanov, Ch. M. Briskina, N. P. Soshchin, V. F. Zolin, “Lasing in powders and its use for data processing,” Bull. Russ. Acad. Sci. Physics 63, 922–926 (1999).
  15. R. M. Balachandran, A. Pacheco, N. M. Lawandy, “Photonic textile fibers,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 114–115.
  16. S. Larochelle, P. Mathieu, V. Larochelle, J. Dubois, “Long range interrogation of laser paints for identification applications,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 143.
  17. M.A. Illarramendi, I. Aramburu, J. Fernádez, R. Balda, M.A. Noginov, “Characterization of light propagation in a closely packed lasercrystal powder,” Waves Random Media, submitted for publication.
  18. H.-D. Hattendorf, “Chrom-sensibilisierter neodym-aluminium-borat-laser,” Ph.D. dissertation (University of Hamburg, Hamburg, Germany, 1979).
  19. A. A. Kaminskii, Crystalline Lasers: Physical Processes and Operation Schemes (CRC, Boca Raton, Fla., 1996).
  20. M. A. Noginov, N. E. Noginova, S. U. Egarievwe, H. J. Caulfield, P. Venkateswarlu, A. Williams, S. B. Mirov, “Color-center powder laser: the effect of pulverization on color-center characteristics,” J. Opt. Soc. Am. B 14, 2153–2160 (1997).
    [CrossRef]
  21. N. T. Melamed, “Optical properties of powders. Part I. Optical absorption coefficients and the absolute value of the diffuse reflectance. Part II. Properties of luminescent powders,” J. Appl. Phys. 34, 560–570 (1963).
    [CrossRef]
  22. 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, V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
    [CrossRef]
  23. D. S. Wiersma, A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
    [CrossRef]
  24. M. Bahoura, M. A. Noginov, “Determination of the transport mean free path in a solid-state random laser,” J. Opt. Soc. Am. B 20, 2389–2394 (2003).
    [CrossRef]
  25. Z. Q. Zhang, S. K. Cheung, X. Zhang, A. A. Chabanov, A. Z. Genack, “Absence of diffusion in wave dynamics,” presented at Frontiers in Optics, the 87th OSA Annual Meeting (Oct. 5–9, 2003, Tucson, Ariz.).

2003 (1)

2002 (1)

2001 (2)

G. Williams, B. Bayram, S. C. Rand, T. Hinklin, R. M. Laine, “Laser action in strongly scattering rare-earth-doped dielectric nanophosphors,” Phys. Rev. A 65, 013807-1–013807-6 (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, V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

2000 (1)

H. Cao, J. Y. Xu, S.-H. Chang, S. T. Ho, “Transition from amplified spontaneous emission to laser action in strongly scattering media,” Phys. Rev. E 61, 1985–1989 (2000).
[CrossRef]

1999 (1)

A. A. Lichmanov, Ch. M. Briskina, N. P. Soshchin, V. F. Zolin, “Lasing in powders and its use for data processing,” Bull. Russ. Acad. Sci. Physics 63, 922–926 (1999).

1998 (1)

S. V. Frolov, Z. V. Vardeny, K. Yoshino, “Cooperative and stimulated emission in poly(p-phenylene-vinylene) thin films and solutions,” Phys. Rev. B 57, 9141–9147 (1998).
[CrossRef]

1997 (1)

1996 (2)

1994 (1)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, E. Sauvain, “Laser action in strongly scattering medium,” Nature 368, 436–438 (1994).
[CrossRef]

1993 (1)

1990 (1)

V. M. Markushev, N. È. Ter-Gabriélyan, Ch. M. Briskina, V. R. Belan, V. F. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Sov. J. Quantum Electron. 20, 772–777 (1990).
[CrossRef]

1986 (1)

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

1968 (1)

V. S. Letokhov, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 26, 835–840 (1968).

1967 (1)

V. S. Letokhov, “Stimulated emission of an ensemble of scattering particles with negative absorption,” JETP Lett. 5, 212–215 (1967).

1963 (1)

N. T. Melamed, “Optical properties of powders. Part I. Optical absorption coefficients and the absolute value of the diffuse reflectance. Part II. Properties of luminescent powders,” J. Appl. Phys. 34, 560–570 (1963).
[CrossRef]

Aramburu, I.

M.A. Illarramendi, I. Aramburu, J. Fernádez, R. Balda, M.A. Noginov, “Characterization of light propagation in a closely packed lasercrystal powder,” Waves Random Media, submitted for publication.

Auzel, F.

Bahoura, M.

Balachandran, R. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, E. Sauvain, “Laser action in strongly scattering medium,” Nature 368, 436–438 (1994).
[CrossRef]

R. M. Balachandran, A. Pacheco, N. M. Lawandy, “Photonic textile fibers,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 114–115.

Balda, R.

M.A. Illarramendi, I. Aramburu, J. Fernádez, R. Balda, M.A. Noginov, “Characterization of light propagation in a closely packed lasercrystal powder,” Waves Random Media, submitted for publication.

Bayram, B.

G. Williams, B. Bayram, S. C. Rand, T. Hinklin, R. M. Laine, “Laser action in strongly scattering rare-earth-doped dielectric nanophosphors,” Phys. Rev. A 65, 013807-1–013807-6 (2001).
[CrossRef]

Belan, V. R.

V. M. Markushev, N. È. Ter-Gabriélyan, Ch. M. Briskina, V. R. Belan, V. F. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Sov. J. Quantum Electron. 20, 772–777 (1990).
[CrossRef]

Briskina, Ch. M.

A. A. Lichmanov, Ch. M. Briskina, N. P. Soshchin, V. F. Zolin, “Lasing in powders and its use for data processing,” Bull. Russ. Acad. Sci. Physics 63, 922–926 (1999).

V. M. Markushev, N. È. Ter-Gabriélyan, Ch. M. Briskina, V. R. Belan, V. F. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Sov. J. Quantum Electron. 20, 772–777 (1990).
[CrossRef]

V. M. Markushev, V. F. Zolin, 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, S.-H. Chang, S. T. Ho, “Transition from amplified spontaneous emission to laser action in strongly scattering media,” Phys. Rev. E 61, 1985–1989 (2000).
[CrossRef]

H. Cao, “Random lasers with coherent feedback,” in Optical Properties of Nanostructured Random Media, V. M. Shalaev, ed., Vol. 82 of Topics in Applied Physics (Springer-Verlag, Berlin, 2002), p. 303.
[CrossRef]

Caulfield, H. J.

Chabanov, A. A.

Z. Q. Zhang, S. K. Cheung, X. Zhang, A. A. Chabanov, A. Z. Genack, “Absence of diffusion in wave dynamics,” presented at Frontiers in Optics, the 87th OSA Annual Meeting (Oct. 5–9, 2003, Tucson, Ariz.).

Chang, S.-H.

H. Cao, J. Y. Xu, S.-H. Chang, S. T. Ho, “Transition from amplified spontaneous emission to laser action in strongly scattering media,” Phys. Rev. E 61, 1985–1989 (2000).
[CrossRef]

Cheung, S. K.

Z. Q. Zhang, S. K. Cheung, X. Zhang, A. A. Chabanov, A. Z. Genack, “Absence of diffusion in wave dynamics,” presented at Frontiers in Optics, the 87th OSA Annual Meeting (Oct. 5–9, 2003, Tucson, Ariz.).

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, V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Dubois, J.

S. Larochelle, P. Mathieu, V. Larochelle, J. Dubois, “Long range interrogation of laser paints for identification applications,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 143.

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, V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Egarievwe, S. U.

Fernádez, J.

M.A. Illarramendi, I. Aramburu, J. Fernádez, R. Balda, M.A. Noginov, “Characterization of light propagation in a closely packed lasercrystal powder,” Waves Random Media, submitted for publication.

Frolov, S. V.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, “Cooperative and stimulated emission in poly(p-phenylene-vinylene) thin films and solutions,” Phys. Rev. B 57, 9141–9147 (1998).
[CrossRef]

Genack, A. Z.

Z. Q. Zhang, S. K. Cheung, X. Zhang, A. A. Chabanov, A. Z. Genack, “Absence of diffusion in wave dynamics,” presented at Frontiers in Optics, the 87th OSA Annual Meeting (Oct. 5–9, 2003, Tucson, Ariz.).

Gomes, A. S. L.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, E. Sauvain, “Laser action in strongly scattering medium,” Nature 368, 436–438 (1994).
[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, V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Hattendorf, H.-D.

H.-D. Hattendorf, “Chrom-sensibilisierter neodym-aluminium-borat-laser,” Ph.D. dissertation (University of Hamburg, Hamburg, Germany, 1979).

Hinklin, T.

B. Li, G. Williams, S. C. Rand, T. Hinklin, R. M. Laine, “Continuous-wave ultraviolet laser action in strongly scattering Nd-doped alumina,” Opt. Lett. 27, 394–396 (2002).
[CrossRef]

G. Williams, B. Bayram, S. C. Rand, T. Hinklin, R. M. Laine, “Laser action in strongly scattering rare-earth-doped dielectric nanophosphors,” Phys. Rev. A 65, 013807-1–013807-6 (2001).
[CrossRef]

Ho, S. T.

H. Cao, J. Y. Xu, S.-H. Chang, S. T. Ho, “Transition from amplified spontaneous emission to laser action in strongly scattering media,” Phys. Rev. E 61, 1985–1989 (2000).
[CrossRef]

Huang, J. D.

R. C. Polson, J. D. Huang, Z. V. Vardeny, “Theories and simulations of random lasers,” in Photonic Crystals and Light Localization in the 21st Century, C. M. Soukoulis, ed., Vol. 563 of NATO Science Series, Series C: Mathematical and Physical Sciences, (Kluwer Academic, The Netherlands, 2001), p. 405.
[CrossRef]

Husson, D.

Illarramendi, M.A.

M.A. Illarramendi, I. Aramburu, J. Fernádez, R. Balda, M.A. Noginov, “Characterization of light propagation in a closely packed lasercrystal powder,” Waves Random Media, submitted for publication.

Kaminskii, A. A.

A. A. Kaminskii, Crystalline Lasers: Physical Processes and Operation Schemes (CRC, Boca Raton, Fla., 1996).

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, 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, 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, V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Lagendijk, A.

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

Laine, R. M.

B. Li, G. Williams, S. C. Rand, T. Hinklin, R. M. Laine, “Continuous-wave ultraviolet laser action in strongly scattering Nd-doped alumina,” Opt. Lett. 27, 394–396 (2002).
[CrossRef]

G. Williams, B. Bayram, S. C. Rand, T. Hinklin, R. M. Laine, “Laser action in strongly scattering rare-earth-doped dielectric nanophosphors,” Phys. Rev. A 65, 013807-1–013807-6 (2001).
[CrossRef]

Larochelle, S.

S. Larochelle, P. Mathieu, V. Larochelle, J. Dubois, “Long range interrogation of laser paints for identification applications,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 143.

Larochelle, V.

S. Larochelle, P. Mathieu, V. Larochelle, J. Dubois, “Long range interrogation of laser paints for identification applications,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 143.

Lawandy, N. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, E. Sauvain, “Laser action in strongly scattering medium,” Nature 368, 436–438 (1994).
[CrossRef]

R. M. Balachandran, A. Pacheco, N. M. Lawandy, “Photonic textile fibers,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 114–115.

Letokhov, V. S.

V. S. Letokhov, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 26, 835–840 (1968).

V. S. Letokhov, “Stimulated emission of an ensemble of scattering particles with negative absorption,” JETP Lett. 5, 212–215 (1967).

Li, B.

Lichmanov, A. A.

A. A. Lichmanov, Ch. M. Briskina, N. P. Soshchin, V. F. Zolin, “Lasing in powders and its use for data processing,” Bull. Russ. Acad. Sci. Physics 63, 922–926 (1999).

Mahdi, M.

Markushev, V. M.

V. M. Markushev, N. È. Ter-Gabriélyan, Ch. M. Briskina, V. R. Belan, V. F. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Sov. J. Quantum Electron. 20, 772–777 (1990).
[CrossRef]

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

Mathieu, P.

S. Larochelle, P. Mathieu, V. Larochelle, J. Dubois, “Long range interrogation of laser paints for identification applications,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 143.

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, V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Melamed, N. T.

N. T. Melamed, “Optical properties of powders. Part I. Optical absorption coefficients and the absolute value of the diffuse reflectance. Part II. Properties of luminescent powders,” J. Appl. Phys. 34, 560–570 (1963).
[CrossRef]

Migus, A.

Mirov, S. B.

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, V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Noginov, M. A.

Noginov, M.A.

M.A. Illarramendi, I. Aramburu, J. Fernádez, R. Balda, M.A. Noginov, “Characterization of light propagation in a closely packed lasercrystal powder,” Waves Random Media, submitted for publication.

Noginova, N. E.

Ostroumov, V.

Pacheco, A.

R. M. Balachandran, A. Pacheco, N. M. Lawandy, “Photonic textile fibers,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 114–115.

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, 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, Z. V. Vardeny, “Theories and simulations of random lasers,” in Photonic Crystals and Light Localization in the 21st Century, C. M. Soukoulis, ed., Vol. 563 of NATO Science Series, Series C: Mathematical and Physical Sciences, (Kluwer Academic, The Netherlands, 2001), p. 405.
[CrossRef]

Rand, S. C.

B. Li, G. Williams, S. C. Rand, T. Hinklin, R. M. Laine, “Continuous-wave ultraviolet laser action in strongly scattering Nd-doped alumina,” Opt. Lett. 27, 394–396 (2002).
[CrossRef]

G. Williams, B. Bayram, S. C. Rand, T. Hinklin, R. M. Laine, “Laser action in strongly scattering rare-earth-doped dielectric nanophosphors,” Phys. Rev. A 65, 013807-1–013807-6 (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, V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Sauteret, C.

Sauvain, E.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, E. Sauvain, “Laser action in strongly scattering medium,” Nature 368, 436–438 (1994).
[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, V. I. Chizhikov, “Binary rare-earth scandium borates for diode-pumped lasers,” Opt. Mater. 18, 243–284 (2001).
[CrossRef]

Soshchin, N. P.

A. A. Lichmanov, Ch. M. Briskina, N. P. Soshchin, V. F. Zolin, “Lasing in powders and its use for data processing,” Bull. Russ. Acad. Sci. Physics 63, 922–926 (1999).

Ter-Gabriélyan, N. È.

V. M. Markushev, N. È. Ter-Gabriélyan, Ch. M. Briskina, V. R. Belan, V. F. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Sov. J. Quantum Electron. 20, 772–777 (1990).
[CrossRef]

Thompson, T.

Vardeny, Z. V.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, “Cooperative and stimulated emission in poly(p-phenylene-vinylene) thin films and solutions,” Phys. Rev. B 57, 9141–9147 (1998).
[CrossRef]

R. C. Polson, J. D. Huang, Z. V. Vardeny, “Theories and simulations of random lasers,” in Photonic Crystals and Light Localization in the 21st Century, C. M. Soukoulis, ed., Vol. 563 of NATO Science Series, Series C: Mathematical and Physical Sciences, (Kluwer Academic, The Netherlands, 2001), p. 405.
[CrossRef]

Venkateswarlu, P.

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[CrossRef]

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[CrossRef]

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[CrossRef]

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H. Cao, J. Y. Xu, S.-H. Chang, S. T. Ho, “Transition from amplified spontaneous emission to laser action in strongly scattering media,” Phys. Rev. E 61, 1985–1989 (2000).
[CrossRef]

Yoshino, K.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, “Cooperative and stimulated emission in poly(p-phenylene-vinylene) thin films and solutions,” Phys. Rev. B 57, 9141–9147 (1998).
[CrossRef]

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Z. Q. Zhang, S. K. Cheung, X. Zhang, A. A. Chabanov, A. Z. Genack, “Absence of diffusion in wave dynamics,” presented at Frontiers in Optics, the 87th OSA Annual Meeting (Oct. 5–9, 2003, Tucson, Ariz.).

Zhang, Z. Q.

Z. Q. Zhang, S. K. Cheung, X. Zhang, A. A. Chabanov, A. Z. Genack, “Absence of diffusion in wave dynamics,” presented at Frontiers in Optics, the 87th OSA Annual Meeting (Oct. 5–9, 2003, Tucson, Ariz.).

Zolin, V. F.

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[CrossRef]

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[CrossRef]

Bull. Russ. Acad. Sci. Physics (1)

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G. Williams, B. Bayram, S. C. Rand, T. Hinklin, R. M. Laine, “Laser action in strongly scattering rare-earth-doped dielectric nanophosphors,” Phys. Rev. A 65, 013807-1–013807-6 (2001).
[CrossRef]

Phys. Rev. B (1)

S. V. Frolov, Z. V. Vardeny, K. Yoshino, “Cooperative and stimulated emission in poly(p-phenylene-vinylene) thin films and solutions,” Phys. Rev. B 57, 9141–9147 (1998).
[CrossRef]

Phys. Rev. E (2)

H. Cao, J. Y. Xu, S.-H. Chang, S. T. Ho, “Transition from amplified spontaneous emission to laser action in strongly scattering media,” Phys. Rev. E 61, 1985–1989 (2000).
[CrossRef]

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

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

V. M. Markushev, N. È. Ter-Gabriélyan, Ch. M. Briskina, V. R. Belan, V. F. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Sov. J. Quantum Electron. 20, 772–777 (1990).
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Z. Q. Zhang, S. K. Cheung, X. Zhang, A. A. Chabanov, A. Z. Genack, “Absence of diffusion in wave dynamics,” presented at Frontiers in Optics, the 87th OSA Annual Meeting (Oct. 5–9, 2003, Tucson, Ariz.).

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Figures (6)

Fig. 1
Fig. 1

Absorption spectrum of NdAl3(BO3)4 single crystal; 1, Ec; 2, Ec; 3, averaged spectrum (digitized and recalculated from the transmission spectra published in Ref. 18).

Fig. 2
Fig. 2

Reflection spectra collection: (a) integrating sphere setup; (b) narrow-angle setup. θ ≈ 20°.

Fig. 3
Fig. 3

Reflection spectrum of NdAl3(BO3)4 powder recorded with an integrated sphere setup. Dashed curve, reflection off a close-to-ideal white scattering sample (filter paper qualitative grade 4, from Whatman); solid curve, experiment; squares, calculation [according to Eq. (1) with k abs 0 = 0.3 cm-1 and l = 0.08 cm].

Fig. 4
Fig. 4

Reflection spectrum of NdAl3(BO3)4 powder recorded with a narrow-angle setup.

Fig. 5
Fig. 5

Dependence of d (calculated by use of the reflection spectrum recorded in an integrated sphere setup) versus kabs*(λ) in NdAl3(BO3)4 powder. Circles, k abs 0 = 0; squares, k abs 0 = 0.3 cm-1.

Fig. 6
Fig. 6

Plots of ln[-ln(R)] versus ln(kabs*) obtained with (a) an integrated sphere setup and (b) a narrow-angle setup. Squares, experiment; circles, calculation according to Eq. (15) derived in the diffusion approximation. Solid lines, slopes η = 1/2 (photon diffusion) and η = 1/3 (experimental dependence).

Equations (17)

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Rexpλ=exp-lkabsλ1/3,
Tλ=IoutλIinλ=exp-kabsλd,
dkabsλ=-lnRλkabsλ.
kabs*λ=kabsλ+kabs 0.
d=lkabs*λ21/3
L  lt>λ,
lp=lalt/31/2.
ut=D 2ux2-cn kabs*u,
ux=u0exp-x/δ,
ui=F/c.
u0=ζuin,
K=0 kabs*ζFe-x/δdx=ζFδkabs*=ζFnc kabs*D1/2.
Rdiffcalc=1-KF=1-ζnDc kabs*1/2.
D=clt/3n.
Rdiffcalc=1-ζ3ltkabs*1/2.
Rexp=1-lkabs*1/3=1-ξltkabs*1/3.
D=s3-μ¯s,

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