Abstract

We have studied numerically the optimal range of the transport mean free path lt and the absorption length (at the pumping wavelength) la, which minimize the threshold and maximize the slope efficiency of a random laser with non-resonant feedback. The results of the calculations are in a good agreement with the experimental results obtained in the GaAs/Al2O3 random laser.

© 2005 Optical Society of America

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References

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  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, and Ch. M. Briskina, �??Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,�?? Sov. J. Quant. Electron. 16, 281-283 (1986).
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  7. W. L. Sha, C.-H. Liu, and R. R. Alfano, �??Spectral and temporal measurements of laser action of rhodamine 640 dye in strongly scattering media,�?? Opt. Lett. 19, 1922-1924 (1994).
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  8. M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, �??Line narrowing in the dye solution with scattering centers,�?? Opt. Commun. 118, 430-437 (1995).
    [CrossRef]
  9. F. Hide, B. J. Schwartz, M. A. Día-García, and A. J. Heeger, �??Laser emission from solutions and films containing semiconducting polymer and titanium dioxide nanocrystals,�?? Chem. Phys. Lett. 256, 424-403 (1996).
    [CrossRef]
  10. Mikhail A. Noginov, Solid-State Random Lasers (Springer, New York, 2005).
  11. M. Bahoura, and M. A. Noginov, �??Determination of the transport mean free path in a solid-state random laser,�?? JOSA B 20, 2389-2394 (2003).
    [CrossRef]
  12. S. John, and G. Pang �??Theory of lasing in a multiple-scattering medium,�?? Phys. Rev. A 54, 3642-3652 (1996).
    [CrossRef] [PubMed]
  13. D. S. Wiersma, and A. Lagendijk, �??Light diffusion with gain and random lasers,�?? Phys. Rev. E 54, 4256-4265 (1996).
    [CrossRef]
  14. G. A. Berger, M. Kempe, and A. Z. Genack, �??Dynamics of stimulated emission from random media,�?? Phys. Rev. E 56, 6118-6122 (1997).
    [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) 8 pages.
    [CrossRef]
  16. A. L. Burin, H. Cao, and M. A. Ratner, �??Two-photon pumping of a random laser,�?? IEEE J. Selected Topics Quant. Electron. 9, 124-127 (2003).
    [CrossRef]
  17. M. A. Noginov, G. Zhu, A. A. Frantz, J. Novak, S. N. Williams, and I. Fowlkes, �??Dependence of NdSc3(BO3)4 random laser parameters on particle size,�?? JOSA B 21, 191-200 (2004).
    [CrossRef]
  18. K. Totsuka, G. van Soest, T. Ito, Ad Lagendijk, and M. Tomita, �??Amplification and diffusion of spontaneous emission in strongly scattering medium,�?? J. Appl. Phys. 87, 7623-7628 (2000).
    [CrossRef]
  19. M. A. Noginov, J. Novak, D. Grigsby, and L. Deych, �??Applicability of the diffusion model to random lasers with non-resonant feedback,�?? submitted for publication. M. A. Noginov, J. Novak, and L. Deych �??Photon motion in a random laser medium with gain: Is it diffusion?,�?? will be presented at the Frontiers in Optics conference, Tucson, Az, Oct 16-20, 2005, paper #FWQ2.
  20. M. A. Noginov, J. Novak, and S. Williams, �??Modeling of photon density dynamics in random lasers,�?? Phys. Rev. A 70, 063810 (2004) (5 pages).
    [CrossRef]
  21. M. A. Noginov, N. Noginova, S. Egarievwe, J. C. Wang, M. R. Kokta, J. Paitz, �??Study of light propagation in scattering powder laser materials,�?? Opt. Mat. 11, 1-7 (1998).
    [CrossRef]
  22. A. Ishimaru, Wave Propagation and Scattering in Random Media, (Academic New York, 1978), vol. 1, p. 250.
  23. 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 semiconducor polycrystalline films,�?? Appl. Phys. Lett. 73, 3656-3658 (1998).
    [CrossRef]
  24. 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]
  25. H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chan, 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]
  26. M. A. Noginov, G. Zhu, I. Fowlkes, and M. Bahoura, �??GaAs random laser,�?? Laser Phys. Lett. 1, 291-293 (2004).
    [CrossRef]
  27. Yu. A. Goldberg, and N. M. Schmidt, �??Gallium Indium Arsenide (AlxIn1-xAs),�?? in Handbook series on semiconductor parameters, M. Levinshtein, S. Rumyantsev, and M. Shur. Eds. (World Scientific, London, 1999), vol. 2, pp. 62-88.

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 semiconducor polycrystalline films,�?? Appl. Phys. Lett. 73, 3656-3658 (1998).
[CrossRef]

Chem. Phys. Lett. (1)

F. Hide, B. J. Schwartz, M. A. Día-García, and A. J. Heeger, �??Laser emission from solutions and films containing semiconducting polymer and titanium dioxide nanocrystals,�?? Chem. Phys. Lett. 256, 424-403 (1996).
[CrossRef]

IEEE J. Selected Topics Quant. Electron (1)

A. L. Burin, H. Cao, and M. A. Ratner, �??Two-photon pumping of a random laser,�?? IEEE J. Selected Topics Quant. Electron. 9, 124-127 (2003).
[CrossRef]

J. Appl. Phys. (1)

K. Totsuka, G. van Soest, T. Ito, Ad Lagendijk, and M. Tomita, �??Amplification and diffusion of spontaneous emission in strongly scattering medium,�?? J. Appl. Phys. 87, 7623-7628 (2000).
[CrossRef]

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

JOSA B (2)

M. A. Noginov, G. Zhu, A. A. Frantz, J. Novak, S. N. Williams, and I. Fowlkes, �??Dependence of NdSc3(BO3)4 random laser parameters on particle size,�?? JOSA B 21, 191-200 (2004).
[CrossRef]

M. Bahoura, and M. A. Noginov, �??Determination of the transport mean free path in a solid-state random laser,�?? JOSA B 20, 2389-2394 (2003).
[CrossRef]

Laser Phys. Lett. (1)

M. A. Noginov, G. Zhu, I. Fowlkes, and M. Bahoura, �??GaAs random laser,�?? Laser Phys. Lett. 1, 291-293 (2004).
[CrossRef]

Nature (1)

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

Opt. Commun. (1)

M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, and M. Mahdi, �??Line narrowing in the dye solution with scattering centers,�?? Opt. Commun. 118, 430-437 (1995).
[CrossRef]

Opt. Lett. (1)

Opt. Mat. (1)

M. A. Noginov, N. Noginova, S. Egarievwe, J. C. Wang, M. R. Kokta, J. Paitz, �??Study of light propagation in scattering powder laser materials,�?? Opt. Mat. 11, 1-7 (1998).
[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) 8 pages.
[CrossRef]

M. A. Noginov, J. Novak, and S. Williams, �??Modeling of photon density dynamics in random lasers,�?? Phys. Rev. A 70, 063810 (2004) (5 pages).
[CrossRef]

S. John, and G. Pang �??Theory of lasing in a multiple-scattering medium,�?? Phys. Rev. A 54, 3642-3652 (1996).
[CrossRef] [PubMed]

Phys. Rev. E (2)

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

G. A. Berger, M. Kempe, and A. Z. Genack, �??Dynamics of stimulated emission from random media,�?? Phys. Rev. E 56, 6118-6122 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

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. Chan, 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]

Sov. J. Quant. 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. Quant. Electron. 16, 281-283 (1986).
[CrossRef]

Sov. Phys.-JETP (2)

V. S. Letokhov, �??Stimulated emission of an ensemble of scattering particles with negative absorption,�?? Sov. Phys.-JETP 5, 212-215 (1967).

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

Other (4)

Mikhail A. Noginov, Solid-State Random Lasers (Springer, New York, 2005).

A. Ishimaru, Wave Propagation and Scattering in Random Media, (Academic New York, 1978), vol. 1, p. 250.

M. A. Noginov, J. Novak, D. Grigsby, and L. Deych, �??Applicability of the diffusion model to random lasers with non-resonant feedback,�?? submitted for publication. M. A. Noginov, J. Novak, and L. Deych �??Photon motion in a random laser medium with gain: Is it diffusion?,�?? will be presented at the Frontiers in Optics conference, Tucson, Az, Oct 16-20, 2005, paper #FWQ2.

Yu. A. Goldberg, and N. M. Schmidt, �??Gallium Indium Arsenide (AlxIn1-xAs),�?? in Handbook series on semiconductor parameters, M. Levinshtein, S. Rumyantsev, and M. Shur. Eds. (World Scientific, London, 1999), vol. 2, pp. 62-88.

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Figures (5)

Fig. 1.
Fig. 1.

(a) The profile of the absorbed pumping (trace 1) and time-integrated stimulated emission (trace 2) in a strip consisting of 100 cells at lt =5.5 μm and la =55 μm. (b) The dynamics of stimulated emission in a strip consisting of 100 lasing cells, calculated at lt =5.5 μm, la =55 μm, and pumping energy approximately two times exceeding its threshold value. The left column exhibits the temporal profile of the Gaussian pumping pulse with the maximum at 20 nm. The intensity color scale is shown in the right column. Trace 2 of Fig. (a) is obtained via integrating the emission intensity in Fig. (b) over time.

Fig. 2.
Fig. 2.

(a) The slope efficiency (equal to the fraction of absorbed pumping energy) calculated at different parameters la and lt in one-dimensional strip consisting of 100 1μm lasing cells. Line 1, given by the formula l p = l t l a = 55 μ m , outlines the upper right corner where the sample has relatively high transmission. Line 2 (same as in Fig. 4) separates the ranges of “diffusion” and “skin layer” regimes of operation. (b) The fraction of absorbed pumping energy predicted by a classical diffusion model ( A = l t l a ) in a semi-infinite random laser medium.

Fig. 3.
Fig. 3.

Kinetics of population inversion calculated at three different pumping energies, E3>E2>E1, in cell #30 (a) and cell #1 (b). The “locking” of the population inversion in Fig. (a) manifests an onset of the stimulated emission. lt =5.5 μm, la =55 μm.

Fig. 4.
Fig. 4.

The relative values of the stimulated emission threshold calculated in different (lt ,la ) points. The intensity color scale is shown in the right column.

Fig. 5.
Fig. 5.

The dependence of the threshold (a) and the slope efficiency (b) in mixed GaAs/Al2O3 random lasers on the content of GaAs in the mixture. 1 - experiment, 2 - calculation (in relative units, scaled to fit the experiment).

Tables (1)

Tables Icon

Table. 1. Transport mean free paths lt and absorption lengths la in mixed GaAs samples studied.

Equations (3)

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dn dt = P abs ( t ) h v p S l p n τ E h v e c σ e n ,
dE dt = E τ res + ζ n τ h v e + E c σ e n ,
A = l t l a .

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