Abstract

We investigated the statistics of random lasing modes in colloidal solutions with local pumping. The ensemble-averaged spectral correlation function of single-shot emission spectra exhibits regular oscillations. The statistical distribution of laser emission intensity follows a power-law decay, in comparison with an exponential decay of the statistical distribution of amplified spontaneous emission (ASE) intensity. The dramatic difference between the statistics of lasing peaks and that of the stochastic ASE spikes illustrates their distinct mechanisms.

© 2007 Optical Society of America

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  1. H. Cao, J. Phys. A 38, 10497 (2005), and references therein.
    [CrossRef]
  2. X. Wu, A. Yamilov, H. Noh, H. Cao, E. W. Seelig, and R. P. H. Chang, J. Opt. Soc. Am. B 21, 159 (2004).
    [CrossRef]
  3. K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 98, 143901 (2007).
    [CrossRef] [PubMed]
  4. S. Mujumdar, M. Ricci, R. Torre, and D. W. Wiersma, Phys. Rev. Lett. 93, 053903 (2004).
    [CrossRef] [PubMed]
  5. X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, Phys. Rev. A 74, 053812 (2006).
    [CrossRef]
  6. P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, Opt. Quantum Electron. 20, 395 (1988).
    [CrossRef]
  7. X. Wu, J. Andreasen, H. Cao, and A. Yamilov, J. Opt. Soc. Am. B 24, A26 (2007).
    [CrossRef]
  8. M. Patra, Phys. Rev. E 67, 016603 (2003).
    [CrossRef]
  9. V. M. Apalkov and M. E. Raikh, Phys. Rev. B 71, 054203 (2005).
    [CrossRef]
  10. O. Zaitsev, Phys. Rev. A 74, 063803 (2006).
    [CrossRef]

2007 (2)

K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 98, 143901 (2007).
[CrossRef] [PubMed]

X. Wu, J. Andreasen, H. Cao, and A. Yamilov, J. Opt. Soc. Am. B 24, A26 (2007).
[CrossRef]

2006 (2)

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, Phys. Rev. A 74, 053812 (2006).
[CrossRef]

O. Zaitsev, Phys. Rev. A 74, 063803 (2006).
[CrossRef]

2005 (2)

V. M. Apalkov and M. E. Raikh, Phys. Rev. B 71, 054203 (2005).
[CrossRef]

H. Cao, J. Phys. A 38, 10497 (2005), and references therein.
[CrossRef]

2004 (2)

X. Wu, A. Yamilov, H. Noh, H. Cao, E. W. Seelig, and R. P. H. Chang, J. Opt. Soc. Am. B 21, 159 (2004).
[CrossRef]

S. Mujumdar, M. Ricci, R. Torre, and D. W. Wiersma, Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

2003 (1)

M. Patra, Phys. Rev. E 67, 016603 (2003).
[CrossRef]

1988 (1)

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, Opt. Quantum Electron. 20, 395 (1988).
[CrossRef]

Andreasen, J.

Apalkov, V. M.

V. M. Apalkov and M. E. Raikh, Phys. Rev. B 71, 054203 (2005).
[CrossRef]

Asatryan, A. A.

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, Phys. Rev. A 74, 053812 (2006).
[CrossRef]

Botten, L. C.

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, Phys. Rev. A 74, 053812 (2006).
[CrossRef]

Cao, H.

X. Wu, J. Andreasen, H. Cao, and A. Yamilov, J. Opt. Soc. Am. B 24, A26 (2007).
[CrossRef]

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, Phys. Rev. A 74, 053812 (2006).
[CrossRef]

H. Cao, J. Phys. A 38, 10497 (2005), and references therein.
[CrossRef]

X. Wu, A. Yamilov, H. Noh, H. Cao, E. W. Seelig, and R. P. H. Chang, J. Opt. Soc. Am. B 21, 159 (2004).
[CrossRef]

Chabanov, A. A.

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, Phys. Rev. A 74, 053812 (2006).
[CrossRef]

Chang, R. P. H.

Fang, W.

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, Phys. Rev. A 74, 053812 (2006).
[CrossRef]

Lagendijk, A.

K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 98, 143901 (2007).
[CrossRef] [PubMed]

Meier, B.

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, Opt. Quantum Electron. 20, 395 (1988).
[CrossRef]

Mosk, A. P.

K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 98, 143901 (2007).
[CrossRef] [PubMed]

Mujumdar, S.

S. Mujumdar, M. Ricci, R. Torre, and D. W. Wiersma, Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

Noh, H.

Patra, M.

M. Patra, Phys. Rev. E 67, 016603 (2003).
[CrossRef]

Penzkofer, A.

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, Opt. Quantum Electron. 20, 395 (1988).
[CrossRef]

Raikh, M. E.

V. M. Apalkov and M. E. Raikh, Phys. Rev. B 71, 054203 (2005).
[CrossRef]

Ricci, M.

S. Mujumdar, M. Ricci, R. Torre, and D. W. Wiersma, Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

Seelig, E. W.

Spangler, W.

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, Opt. Quantum Electron. 20, 395 (1988).
[CrossRef]

Sperber, P.

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, Opt. Quantum Electron. 20, 395 (1988).
[CrossRef]

Tjerkstra, R. W.

K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 98, 143901 (2007).
[CrossRef] [PubMed]

Torre, R.

S. Mujumdar, M. Ricci, R. Torre, and D. W. Wiersma, Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

van der Molen, K. L.

K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 98, 143901 (2007).
[CrossRef] [PubMed]

Wiersma, D. W.

S. Mujumdar, M. Ricci, R. Torre, and D. W. Wiersma, Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

Wu, X.

Yamilov, A.

Zaitsev, O.

O. Zaitsev, Phys. Rev. A 74, 063803 (2006).
[CrossRef]

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

J. Phys. A (1)

H. Cao, J. Phys. A 38, 10497 (2005), and references therein.
[CrossRef]

Opt. Quantum Electron. (1)

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, Opt. Quantum Electron. 20, 395 (1988).
[CrossRef]

Phys. Rev. A (2)

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, Phys. Rev. A 74, 053812 (2006).
[CrossRef]

O. Zaitsev, Phys. Rev. A 74, 063803 (2006).
[CrossRef]

Phys. Rev. B (1)

V. M. Apalkov and M. E. Raikh, Phys. Rev. B 71, 054203 (2005).
[CrossRef]

Phys. Rev. E (1)

M. Patra, Phys. Rev. E 67, 016603 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 98, 143901 (2007).
[CrossRef] [PubMed]

S. Mujumdar, M. Ricci, R. Torre, and D. W. Wiersma, Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Single-shot spectra of emission from the 8.5 mM Stilbene 420 dye solutions (a)–(c) with and (d)–(f) without TiO 2 particles. The particle density ρ = 3 × 10 9 cm 3 in (a)–(c). The pump pulse energy E p = 0.05 μ J for (a) and (d), 0.09 μ J for (b) and (e), 0.13 μ J for (c) and (f).

Fig. 2
Fig. 2

(a) Ensemble-averaged spectral correlation function C ( Δ λ ) of single-shot emission spectra. M = 8.5 mM . ρ = 3 × 10 9 cm 3 in the main panel, and 0 in the inset. E p = 0.05 μ J (solid curves), 0.09 μ J (dashed curves) and 0.13 μ J (dotted curves). (b) Statistical distribution P ( δ λ ) of wavelength spacing δ λ between adjacent spikes or peaks selected by the three-point peak-finding method. ρ = 0 (circles), 3 × 10 9 cm 3 (squares). E p = 0.13 μ J . The solid curve is an exponential fit P ( δ λ ) = 22 exp ( δ λ 0.082 ) . Inset, P ( δ λ δ λ ) for ρ = 3 × 10 9 cm 3 and E p = 0.13 μ J , obtained with three methods: five-point peak-finding (squares), three-adjacent-point averaging followed by three-point peak-finding (crosses), or five-point peak-finding (triangles).

Fig. 3
Fig. 3

Statistical distributions of normalized emission intensities I ( λ ) I ( λ ) for 425 nm < λ < 431 nm . ρ = 3 × 10 9 cm 3 in (a), and 0 in (b). E p = 0.05 μ J (squares), 0.09 μ J (crosses), 0.13 μ J (circles). The solid lines represent curve fitting. In (a) P ( I I ) = 0.77 ( I I ) 3.3 (for crosses) and P ( I I ) = 0.38 ( I I ) 2.5 (for circles). In (b), P ( I I ) = 467 exp ( 5.1 I I ) .

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