Abstract

We report experimental and theoretical studies of the random lasing threshold and its fluctuation in an ensemble of highly packed spherical dielectric scatterers. The ratio of the sphere diameter to the lasing wavelength was varied in a wide range, which covered the transition from the weak Rayleigh scattering regime to the strong Mie scattering regime. Experimentally, when the diameters of monodispersed ZnO spherical particles changed from less than 100 to more than 600 nm we observed a drastic decrease of the lasing threshold at small-particle size followed by a plateau at large particle size. We attribute this effect to the particle-size dependence of transport mean free path lt, which was deduced from coherent backscattering measurements. Theoretical calculation of lt reproduced experimental behavior. Using the finite-difference time domain method, we obtained the lasing threshold and its standard deviation as functions of particle size in two-dimensional systems. The results of our numerical simulations are in qualitative agreement with the experimental data.

© 2004 Optical Society of America

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References

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  1. V. S. Letokhov, “Quantum statistics of multi-mode radiation from an ensemble of atoms,” Sov. Phys. JETP 26, 835–840 (1968).
  2. H. Cao, “Lasing in disordered media,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 2003), Vol. 45, and references therein.
  3. A. A. Chabanov and A. Z. Genack, “Photon localization in resonant media,” Phys. Rev. Lett. 87, 153901 (2001).
    [CrossRef] [PubMed]
  4. V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89, 016802 (2002).
    [CrossRef] [PubMed]
  5. A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
    [CrossRef]
  6. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, New York, 1995).
  7. M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
    [CrossRef] [PubMed]
  8. 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]
  9. Y.-L. Xu, “Electromagnetic scattering by an aggregate of spheres: far field,” Appl. Opt. 36, 9496–9508 (1997); computer codes are available at http://www.astro.ufl.edu/˜xu/.
    [CrossRef]
  10. M. Patra, “Theory for photon statistics of random lasers,” Phys. Rev. A 65, 043809 (2002).
    [CrossRef]
  11. A. Taflove, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, Boston, Mass., 1995).
  12. X. Y. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
    [CrossRef] [PubMed]
  13. C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).
    [CrossRef]
  14. E. W. Seelig, R. P. H. Chang, A. Yamilov, and H. Cao, “Self-assembled 3D photonic crystals from ZnO colloidal spheres,” Mater. Chem. Phys. 80, 257–263 (2003).
    [CrossRef]
  15. Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, X. Liu, and R. P. H. Chang, “Investigation of random lasers with resonant feedback,” Phys. Rev. A 64, 063808 (2001).
    [CrossRef]
  16. H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, “Probing localized states with spectrally resolved speckle techniques,” Phys. Rev. E 66, 025601 (2002).
    [CrossRef]
  17. J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
    [CrossRef] [PubMed]
  18. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  19. S. Kawato, T. Hattori, T. Takemori, and H. Nakatsuka, “Short-range interference effect in the diffusion of light in random media,” Phys. Rev. B 58, 6180–6193 (1998).
    [CrossRef]
  20. C. M. Soukoulis, M. Datta, and E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
    [CrossRef]
  21. X. Jing, P. Sheng, and M. Zhou, “Acoustic and electromagnetic quasimodes in dispersed random media,” Phys. Rev. B 46, 6513–6534 (1992).
    [CrossRef]
  22. D. Livdan and A. A. Lisyansky, “Diffusion of classical waves in random media with microstructure resonances,” J. Opt. Soc. Am. A 13, 844–850 (1996).
    [CrossRef]
  23. K. Busch, C. M. Soukoulis, and E. N. Economou, “Transport and scattering mean free paths of classical waves,” Phys. Rev. B 50, 93–98 (1994).
    [CrossRef]
  24. K. Busch and C. M. Soukoulis, “Transport properties of random media: an energy-density CPA approach,” Phys. Rev. B 54, 893–899 (1996).
    [CrossRef]
  25. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  26. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  27. P. Sheng, ed., Scattering and Localization of Classical Waves in Random Media, Vol. 8 of World Scientific Series on Directions in Condensed Matter Physics (World Scientific, Singapore, 1990).
  28. A. Yamilov and H. Cao, “A study of random laser modes in disordered photonic crystals,” http://arxiv.org/PS_cache/cond-mat/pdf/0209/0209680.pdf.

2003 (1)

E. W. Seelig, R. P. H. Chang, A. Yamilov, and H. Cao, “Self-assembled 3D photonic crystals from ZnO colloidal spheres,” Mater. Chem. Phys. 80, 257–263 (2003).
[CrossRef]

2002 (3)

M. Patra, “Theory for photon statistics of random lasers,” Phys. Rev. A 65, 043809 (2002).
[CrossRef]

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, “Probing localized states with spectrally resolved speckle techniques,” Phys. Rev. E 66, 025601 (2002).
[CrossRef]

V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89, 016802 (2002).
[CrossRef] [PubMed]

2001 (3)

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).
[CrossRef]

A. A. Chabanov and A. Z. Genack, “Photon localization in resonant media,” Phys. Rev. Lett. 87, 153901 (2001).
[CrossRef] [PubMed]

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, X. Liu, and R. P. H. Chang, “Investigation of random lasers with resonant feedback,” Phys. Rev. A 64, 063808 (2001).
[CrossRef]

2000 (1)

X. Y. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
[CrossRef] [PubMed]

1998 (1)

S. Kawato, T. Hattori, T. Takemori, and H. Nakatsuka, “Short-range interference effect in the diffusion of light in random media,” Phys. Rev. B 58, 6180–6193 (1998).
[CrossRef]

1997 (1)

1996 (3)

K. Busch and C. M. Soukoulis, “Transport properties of random media: an energy-density CPA approach,” Phys. Rev. B 54, 893–899 (1996).
[CrossRef]

D. Livdan and A. A. Lisyansky, “Diffusion of classical waves in random media with microstructure resonances,” J. Opt. Soc. Am. A 13, 844–850 (1996).
[CrossRef]

A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

1994 (2)

C. M. Soukoulis, M. Datta, and E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[CrossRef]

K. Busch, C. M. Soukoulis, and E. N. Economou, “Transport and scattering mean free paths of classical waves,” Phys. Rev. B 50, 93–98 (1994).
[CrossRef]

1992 (1)

X. Jing, P. Sheng, and M. Zhou, “Acoustic and electromagnetic quasimodes in dispersed random media,” Phys. Rev. B 46, 6513–6534 (1992).
[CrossRef]

1991 (1)

J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

1985 (2)

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a 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]

1968 (1)

V. S. Letokhov, “Quantum statistics of multi-mode radiation from an ensemble of atoms,” Sov. Phys. JETP 26, 835–840 (1968).

Apalkov, V. M.

V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89, 016802 (2002).
[CrossRef] [PubMed]

Burin, A. L.

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, “Probing localized states with spectrally resolved speckle techniques,” Phys. Rev. E 66, 025601 (2002).
[CrossRef]

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, X. Liu, and R. P. H. Chang, “Investigation of random lasers with resonant feedback,” Phys. Rev. A 64, 063808 (2001).
[CrossRef]

Busch, K.

K. Busch and C. M. Soukoulis, “Transport properties of random media: an energy-density CPA approach,” Phys. Rev. B 54, 893–899 (1996).
[CrossRef]

K. Busch, C. M. Soukoulis, and E. N. Economou, “Transport and scattering mean free paths of classical waves,” Phys. Rev. B 50, 93–98 (1994).
[CrossRef]

Cao, H.

E. W. Seelig, R. P. H. Chang, A. Yamilov, and H. Cao, “Self-assembled 3D photonic crystals from ZnO colloidal spheres,” Mater. Chem. Phys. 80, 257–263 (2003).
[CrossRef]

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, “Probing localized states with spectrally resolved speckle techniques,” Phys. Rev. E 66, 025601 (2002).
[CrossRef]

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, X. Liu, and R. P. H. Chang, “Investigation of random lasers with resonant feedback,” Phys. Rev. A 64, 063808 (2001).
[CrossRef]

Chabanov, A. A.

A. A. Chabanov and A. Z. Genack, “Photon localization in resonant media,” Phys. Rev. Lett. 87, 153901 (2001).
[CrossRef] [PubMed]

Chang, R. P. H.

E. W. Seelig, R. P. H. Chang, A. Yamilov, and H. Cao, “Self-assembled 3D photonic crystals from ZnO colloidal spheres,” Mater. Chem. Phys. 80, 257–263 (2003).
[CrossRef]

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, X. Liu, and R. P. H. Chang, “Investigation of random lasers with resonant feedback,” Phys. Rev. A 64, 063808 (2001).
[CrossRef]

Datta, M.

C. M. Soukoulis, M. Datta, and E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[CrossRef]

Economou, E. N.

C. M. Soukoulis, M. Datta, and E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[CrossRef]

K. Busch, C. M. Soukoulis, and E. N. Economou, “Transport and scattering mean free paths of classical waves,” Phys. Rev. B 50, 93–98 (1994).
[CrossRef]

Genack, A. Z.

A. A. Chabanov and A. Z. Genack, “Photon localization in resonant media,” Phys. Rev. Lett. 87, 153901 (2001).
[CrossRef] [PubMed]

Hattori, T.

S. Kawato, T. Hattori, T. Takemori, and H. Nakatsuka, “Short-range interference effect in the diffusion of light in random media,” Phys. Rev. B 58, 6180–6193 (1998).
[CrossRef]

Jiang, X. Y.

X. Y. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
[CrossRef] [PubMed]

Jing, X.

X. Jing, P. Sheng, and M. Zhou, “Acoustic and electromagnetic quasimodes in dispersed random media,” Phys. Rev. B 46, 6513–6534 (1992).
[CrossRef]

Kawato, S.

S. Kawato, T. Hattori, T. Takemori, and H. Nakatsuka, “Short-range interference effect in the diffusion of light in random media,” Phys. Rev. B 58, 6180–6193 (1998).
[CrossRef]

Lagendijk, A.

A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

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

Letokhov, V. S.

V. S. Letokhov, “Quantum statistics of multi-mode radiation from an ensemble of atoms,” Sov. Phys. JETP 26, 835–840 (1968).

Ling, Y.

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, “Probing localized states with spectrally resolved speckle techniques,” Phys. Rev. E 66, 025601 (2002).
[CrossRef]

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, X. Liu, and R. P. H. Chang, “Investigation of random lasers with resonant feedback,” Phys. Rev. A 64, 063808 (2001).
[CrossRef]

Lisyansky, A. A.

Liu, X.

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, X. Liu, and R. P. H. Chang, “Investigation of random lasers with resonant feedback,” Phys. Rev. A 64, 063808 (2001).
[CrossRef]

Livdan, D.

Maret, G.

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]

Nakatsuka, H.

S. Kawato, T. Hattori, T. Takemori, and H. Nakatsuka, “Short-range interference effect in the diffusion of light in random media,” Phys. Rev. B 58, 6180–6193 (1998).
[CrossRef]

Patra, M.

M. Patra, “Theory for photon statistics of random lasers,” Phys. Rev. A 65, 043809 (2002).
[CrossRef]

Pine, D. J.

J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

Raikh, M. E.

V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89, 016802 (2002).
[CrossRef] [PubMed]

Ratner, M. A.

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, X. Liu, and R. P. H. Chang, “Investigation of random lasers with resonant feedback,” Phys. Rev. A 64, 063808 (2001).
[CrossRef]

Sebbah, P.

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).
[CrossRef]

Seelig, E. W.

E. W. Seelig, R. P. H. Chang, A. Yamilov, and H. Cao, “Self-assembled 3D photonic crystals from ZnO colloidal spheres,” Mater. Chem. Phys. 80, 257–263 (2003).
[CrossRef]

Shapiro, B.

V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89, 016802 (2002).
[CrossRef] [PubMed]

Sheng, P.

X. Jing, P. Sheng, and M. Zhou, “Acoustic and electromagnetic quasimodes in dispersed random media,” Phys. Rev. B 46, 6513–6534 (1992).
[CrossRef]

Soukoulis, C. M.

X. Y. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
[CrossRef] [PubMed]

K. Busch and C. M. Soukoulis, “Transport properties of random media: an energy-density CPA approach,” Phys. Rev. B 54, 893–899 (1996).
[CrossRef]

C. M. Soukoulis, M. Datta, and E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[CrossRef]

K. Busch, C. M. Soukoulis, and E. N. Economou, “Transport and scattering mean free paths of classical waves,” Phys. Rev. B 50, 93–98 (1994).
[CrossRef]

Takemori, T.

S. Kawato, T. Hattori, T. Takemori, and H. Nakatsuka, “Short-range interference effect in the diffusion of light in random media,” Phys. Rev. B 58, 6180–6193 (1998).
[CrossRef]

van Albada, M. P.

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

van Tiggelen, B. A.

A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

Vanneste, C.

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).
[CrossRef]

Weitz, D. A.

J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

Wolf, P. E.

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]

Xu, J. Y.

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, “Probing localized states with spectrally resolved speckle techniques,” Phys. Rev. E 66, 025601 (2002).
[CrossRef]

Xu, Y.-L.

Yamilov, A.

E. W. Seelig, R. P. H. Chang, A. Yamilov, and H. Cao, “Self-assembled 3D photonic crystals from ZnO colloidal spheres,” Mater. Chem. Phys. 80, 257–263 (2003).
[CrossRef]

Zhou, M.

X. Jing, P. Sheng, and M. Zhou, “Acoustic and electromagnetic quasimodes in dispersed random media,” Phys. Rev. B 46, 6513–6534 (1992).
[CrossRef]

Zhu, J. X.

J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

Appl. Opt. (1)

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

Mater. Chem. Phys. (1)

E. W. Seelig, R. P. H. Chang, A. Yamilov, and H. Cao, “Self-assembled 3D photonic crystals from ZnO colloidal spheres,” Mater. Chem. Phys. 80, 257–263 (2003).
[CrossRef]

Phys. Rep. (1)

A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[CrossRef]

Phys. Rev. A (3)

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, X. Liu, and R. P. H. Chang, “Investigation of random lasers with resonant feedback,” Phys. Rev. A 64, 063808 (2001).
[CrossRef]

J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

M. Patra, “Theory for photon statistics of random lasers,” Phys. Rev. A 65, 043809 (2002).
[CrossRef]

Phys. Rev. B (5)

S. Kawato, T. Hattori, T. Takemori, and H. Nakatsuka, “Short-range interference effect in the diffusion of light in random media,” Phys. Rev. B 58, 6180–6193 (1998).
[CrossRef]

C. M. Soukoulis, M. Datta, and E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994).
[CrossRef]

X. Jing, P. Sheng, and M. Zhou, “Acoustic and electromagnetic quasimodes in dispersed random media,” Phys. Rev. B 46, 6513–6534 (1992).
[CrossRef]

K. Busch, C. M. Soukoulis, and E. N. Economou, “Transport and scattering mean free paths of classical waves,” Phys. Rev. B 50, 93–98 (1994).
[CrossRef]

K. Busch and C. M. Soukoulis, “Transport properties of random media: an energy-density CPA approach,” Phys. Rev. B 54, 893–899 (1996).
[CrossRef]

Phys. Rev. E (1)

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, “Probing localized states with spectrally resolved speckle techniques,” Phys. Rev. E 66, 025601 (2002).
[CrossRef]

Phys. Rev. Lett. (6)

X. Y. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
[CrossRef] [PubMed]

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).
[CrossRef]

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a 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]

A. A. Chabanov and A. Z. Genack, “Photon localization in resonant media,” Phys. Rev. Lett. 87, 153901 (2001).
[CrossRef] [PubMed]

V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89, 016802 (2002).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

V. S. Letokhov, “Quantum statistics of multi-mode radiation from an ensemble of atoms,” Sov. Phys. JETP 26, 835–840 (1968).

Other (8)

H. Cao, “Lasing in disordered media,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 2003), Vol. 45, and references therein.

P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, New York, 1995).

A. Taflove, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, Boston, Mass., 1995).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

P. Sheng, ed., Scattering and Localization of Classical Waves in Random Media, Vol. 8 of World Scientific Series on Directions in Condensed Matter Physics (World Scientific, Singapore, 1990).

A. Yamilov and H. Cao, “A study of random laser modes in disordered photonic crystals,” http://arxiv.org/PS_cache/cond-mat/pdf/0209/0209680.pdf.

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Figures (9)

Fig. 1
Fig. 1

SEM images (top view) of two pellets made from ZnO spheres with mean diameters (a) d=85 nm and (b) d=617 nm.

Fig. 2
Fig. 2

Measured spectra of emission from a ZnO pellet. The mean diameter of the ZnO spheres is 617 nm. The pump beam spot on the sample surface is 8 µm in diameter. The incident pumping intensities are (a) 6 MW/mm2 and (b) 11 MW/mm2. The integration times are (a) 15 and (b) 3 s.

Fig. 3
Fig. 3

Measured incident pump intensity at lasing threshold Ith versus ZnO sphere diameter d. Circles and squares correspond to pump spot diameters of 8 and 16 µm, respectively. Inset, calculated normalized scattering cross section σsc/σg of a single ZnO sphere as a function of its diameter d.

Fig. 4
Fig. 4

Measured CBS cones of the same ZnO pellet at three wavelengths λ. The mean diameter of the ZnO spheres is 233 nm.

Fig. 5
Fig. 5

Measured transport mean free path lt versus ZnO sphere diameter d at wavelengths λ=400, 633, 792 nm. Inset, measured lt/d versus nd/λ.

Fig. 6
Fig. 6

Calculated scattering length lsc normalized by sphere diameter d calculated for clusters of 5 (dashed curve) and 10 (solid thinner curve) spheres as a function of normalized particle size nd/λ. The solid thicker curve represents lsc calculated within an independent scattering approximation. The dashed–dotted curve gives the energy-density CPA result24 for f=0.5, n=1.7. Inset, calculated scattering efficiencies σsc/σg of a stand-alone single sphere (darker solid curve) and of spheres in clusters of 5 (dashed curve) and 10 (lighter solid curve) particles.

Fig. 7
Fig. 7

Calculated transport mean free path lt normalized by sphere diameter d calculated for clusters of 5 (dashed curve) and 10 (thinner solid curve) spheres as a function of normalized particle size nd/λ. The thicker solid curve represents lt calculated within an independent scattering approximation. Inset, calculated value of 〈cos(θ)〉 of a stand-alone single sphere (thicker solid curve), and spheres in clusters of 5 (dashed curve) and 10 (thinner solid curve) particles.

Fig. 8
Fig. 8

Calculated average lasing threshold γ=1/Q as a function of dimensionless particle size. Squares and circles represent TM and TE polarization, respectively. Error bars are too small to be shown. Inset, calculated scattering efficiency of a dielectric cylinder with n=2.2 for TE (thinner curve) and TM (thicker curve) polarization versus the dimensionless diameter.

Fig. 9
Fig. 9

Calculated standard deviation of lasing threshold δγ as a function of dimensionless particle size. Squares and circles, TM and TE polarization, respectively.

Tables (1)

Tables Icon

Table 1 Fluctuation of Lasing Threshold in Five Samples with 5-µm Pump Area

Equations (7)

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

lsc(ω)=1ρσsc(ω),
lt(ω)=lsc(ω)1-cos θ(ω),
σsc=83x4n2-1n2+22σg,
lscltλ4fπ4 λd3n2+2n2-12.
σpr=σext-σsccos(θ)=σabs+σsc[1-cos(θ)],
QTM=π28x3(n2-1)2,
QTE=π24x3n2-1n2+12,QTMQTE=(n2+1)22.

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