Abstract

We study the variation of the coherent modes in the emission of a coherent random laser based on nonresonant feedback at critical excitation. A baseline-finding algorithm is applied to separate the coherent and incoherent components from the complete spectrum. By applying intensity thresholds to the isolated coherent spectrum, the modal density is measured as a function of mode intensity, which shows an exponential decay, corresponding to the probability of amplified extended modes. We measure the magnitude of the coherent intensity in the maximally coherent modes, whose distribution shows the presence of equal magnitude of coherent and incoherent fraction in any mode. Upon higher-than-critical excitation, instead of increasing the coherent fraction in the modes, the system tends to increase the number of modes that leads to self-averaging of the spectrum, thereby compromising the coherence.

© 2011 Optical Society of America

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2011 (1)

2010 (3)

2009 (2)

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photon. 3, 279–282 (2009).
[CrossRef]

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Relaxation oscillations in long-pulsed random lasers,” Phys. Rev. A 80, 055803 (2009).
[CrossRef]

2008 (3)

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646(2008).
[CrossRef] [PubMed]

D. S. Wiersma, “The physics and applications of random lasers,” Nature Phys. 4, 359–367 (2008).
[CrossRef]

X. Wu and H. Cao, “Statistical studies of random-lasing modes and amplified spontaneous-emission spikes in weakly scattering systems,” Phys. Rev. A 77, 013832 (2008).
[CrossRef]

2007 (4)

S. Lepri, S. Cavalieri, G.-L. Oppo, and D. S. Wiersma, “Statistical regimes of random laser fluctuations,” Phys. Rev. A 75, 063820 (2007).
[CrossRef]

R. Pierrat and R. Carminati, “Threshold of random lasers in the incoherent transport regime,” Phys. Rev. A 76, 023821(2007).
[CrossRef]

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98, 143902 (2007).
[CrossRef] [PubMed]

S. Mujumdar, V. Tuerck, R. Torre, and D. S. Wiersma, “Chaotic behavior of random lasers with static disorder,” Phys. Rev. A 76, 033807 (2007).
[CrossRef]

2006 (4)

F. A. Pinheiro and L. C. Sampaio, “Lasing threshold of diffusive random lasers in three dimensions,” Phys. Rev. A 73, 013826 (2006).
[CrossRef]

D. Sharma, H. Ramachandran, and N. Kumar, “Lévy statistical fluctuations from a random amplifying medium,” Fluc. Noise Lett. 6, L95–L101 (2006).
[CrossRef]

O. Zaitsev, “Mode statistics in random lasers,” Phys. Rev. A 74, 063803 (2006).
[CrossRef]

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Intrinsic intensity fluctuations in random lasers,” Phys. Rev. A 74, 053808 (2006).
[CrossRef]

2005 (1)

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[CrossRef]

2004 (2)

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

2003 (1)

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101 (2003).
[CrossRef]

2002 (2)

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65, 041103 (2002).
[CrossRef]

M. Bahoura, K. J. Morris, and M. A. Noginov, “Threshold and slope efficiency of Nd0.5La0.5Al3(BO3)4 ceramic random laser: effect of the pumped spot size,” Opt. Commun. 201, 405–411(2002).
[CrossRef]

2001 (3)

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

H. Cao, Y. Ling, J. Y. Xu, C. Q. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86, 4524–4527 (2001).
[CrossRef] [PubMed]

D. S. Wiersma and S. A. Cavalieri, “A temperature-tunable random laser,” Nature 414, 708–709 (2001).
[CrossRef] [PubMed]

2000 (2)

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, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997(2000).
[CrossRef]

1999 (2)

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughmann, “Stimulated emission in high-gain organic media,” Phys. Rev. B 59, R5284–R5287 (1999).
[CrossRef]

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 (1)

C. W. J. Beenakker, “Thermal radiation and amplified spontaneous emission from a random medium,” Phys. Rev. Lett. 81, 1829–1832 (1998).
[CrossRef]

1994 (1)

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

1968 (1)

V. S. Letokhov, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 16, 835–840 (1968).

Ania-Castañón, J. D.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photon. 4, 231–235 (2010).
[CrossRef]

Babin, S. A.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photon. 4, 231–235 (2010).
[CrossRef]

Bahoura, M.

M. Bahoura, K. J. Morris, and M. A. Noginov, “Threshold and slope efficiency of Nd0.5La0.5Al3(BO3)4 ceramic random laser: effect of the pumped spot size,” Opt. Commun. 201, 405–411(2002).
[CrossRef]

Balachandran, R. M.

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

Baughmann, R. H.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughmann, “Stimulated emission in high-gain organic media,” Phys. Rev. B 59, R5284–R5287 (1999).
[CrossRef]

Beenakker, C. W. J.

C. W. J. Beenakker, “Thermal radiation and amplified spontaneous emission from a random medium,” Phys. Rev. Lett. 81, 1829–1832 (1998).
[CrossRef]

Cao, C. Q.

H. Cao, Y. Ling, J. Y. Xu, C. Q. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86, 4524–4527 (2001).
[CrossRef] [PubMed]

Cao, H.

X. Wu and H. Cao, “Statistical studies of random-lasing modes and amplified spontaneous-emission spikes in weakly scattering systems,” Phys. Rev. A 77, 013832 (2008).
[CrossRef]

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98, 143902 (2007).
[CrossRef] [PubMed]

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[CrossRef]

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101 (2003).
[CrossRef]

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65, 041103 (2002).
[CrossRef]

H. Cao, Y. Ling, J. Y. Xu, C. Q. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86, 4524–4527 (2001).
[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, J. Y. Xu, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997(2000).
[CrossRef]

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]

Carminati, R.

R. Pierrat and R. Carminati, “Threshold of random lasers in the incoherent transport regime,” Phys. Rev. A 76, 023821(2007).
[CrossRef]

Cavalieri, S.

S. Lepri, S. Cavalieri, G.-L. Oppo, and D. S. Wiersma, “Statistical regimes of random laser fluctuations,” Phys. Rev. A 75, 063820 (2007).
[CrossRef]

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

Cavalieri, S. A.

D. S. Wiersma and S. A. Cavalieri, “A temperature-tunable random laser,” Nature 414, 708–709 (2001).
[CrossRef] [PubMed]

Chang, R. P. H.

H. Cao, J. Y. Xu, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997(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]

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]

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]

Churkin, D. V.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photon. 4, 231–235 (2010).
[CrossRef]

De Lin, J.

Dietz, R. J. B.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photon. 3, 279–282 (2009).
[CrossRef]

El-Taher, A. E.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photon. 4, 231–235 (2010).
[CrossRef]

Fallert, J.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photon. 3, 279–282 (2009).
[CrossRef]

Frolov, S. V.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughmann, “Stimulated emission in high-gain organic media,” Phys. Rev. B 59, R5284–R5287 (1999).
[CrossRef]

Ge, L.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646(2008).
[CrossRef] [PubMed]

Gomes, A. S. L.

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

Gottardo, S.

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

Harper, P.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photon. 4, 231–235 (2010).
[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, 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]

Huang, B.-Y.

Huang, S.-Y.

Jiang, X.

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101 (2003).
[CrossRef]

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65, 041103 (2002).
[CrossRef]

Kablukov, S. I.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photon. 4, 231–235 (2010).
[CrossRef]

Kalt, H.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photon. 3, 279–282 (2009).
[CrossRef]

Karalekas, V.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photon. 4, 231–235 (2010).
[CrossRef]

Klingshirn, C.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photon. 3, 279–282 (2009).
[CrossRef]

Kumar, N.

D. Sharma, H. Ramachandran, and N. Kumar, “Lévy statistical fluctuations from a random amplifying medium,” Fluc. Noise Lett. 6, L95–L101 (2006).
[CrossRef]

Kumar, P.

H. Cao, Y. Ling, J. Y. Xu, C. Q. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86, 4524–4527 (2001).
[CrossRef] [PubMed]

Kuo, C.-T.

Lagendijk, A.

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Relaxation oscillations in long-pulsed random lasers,” Phys. Rev. A 80, 055803 (2009).
[CrossRef]

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Intrinsic intensity fluctuations in random lasers,” Phys. Rev. A 74, 053808 (2006).
[CrossRef]

Lawandy, N. M.

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

Lee, C.-R.

Lepri, S.

S. Lepri, S. Cavalieri, G.-L. Oppo, and D. S. Wiersma, “Statistical regimes of random laser fluctuations,” Phys. Rev. A 75, 063820 (2007).
[CrossRef]

Letokhov, V. S.

V. S. Letokhov, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 16, 835–840 (1968).

Lin, S.-H.

Ling, Y.

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101 (2003).
[CrossRef]

H. Cao, Y. Ling, J. Y. Xu, C. Q. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86, 4524–4527 (2001).
[CrossRef] [PubMed]

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]

Mo, T.-S.

Morris, K. J.

M. Bahoura, K. J. Morris, and M. A. Noginov, “Threshold and slope efficiency of Nd0.5La0.5Al3(BO3)4 ceramic random laser: effect of the pumped spot size,” Opt. Commun. 201, 405–411(2002).
[CrossRef]

Mosk, A. P.

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Relaxation oscillations in long-pulsed random lasers,” Phys. Rev. A 80, 055803 (2009).
[CrossRef]

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Intrinsic intensity fluctuations in random lasers,” Phys. Rev. A 74, 053808 (2006).
[CrossRef]

Mujumdar, S.

R. Uppu and S. Mujumdar, “Statistical fluctuations of coherent and incoherent intensity in random lasers with nonresonant feedback,” Opt. Lett. 35, 2831–2833 (2010).
[CrossRef] [PubMed]

S. Mujumdar, V. Tuerck, R. Torre, and D. S. Wiersma, “Chaotic behavior of random lasers with static disorder,” Phys. Rev. A 76, 033807 (2007).
[CrossRef]

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

Noginov, M.

M. Noginov, Solid State Random Lasers, Vol.  105 of Series in Optical Sciences (Springer, 2005).

Noginov, M. A.

M. Bahoura, K. J. Morris, and M. A. Noginov, “Threshold and slope efficiency of Nd0.5La0.5Al3(BO3)4 ceramic random laser: effect of the pumped spot size,” Opt. Commun. 201, 405–411(2002).
[CrossRef]

Oppo, G.-L.

S. Lepri, S. Cavalieri, G.-L. Oppo, and D. S. Wiersma, “Statistical regimes of random laser fluctuations,” Phys. Rev. A 75, 063820 (2007).
[CrossRef]

Pierrat, R.

R. Pierrat and R. Carminati, “Threshold of random lasers in the incoherent transport regime,” Phys. Rev. A 76, 023821(2007).
[CrossRef]

Pinheiro, F. A.

F. A. Pinheiro and L. C. Sampaio, “Lasing threshold of diffusive random lasers in three dimensions,” Phys. Rev. A 73, 013826 (2006).
[CrossRef]

Podivilov, E. V.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photon. 4, 231–235 (2010).
[CrossRef]

Ramachandran, H.

D. Sharma, H. Ramachandran, and N. Kumar, “Lévy statistical fluctuations from a random amplifying medium,” Fluc. Noise Lett. 6, L95–L101 (2006).
[CrossRef]

Ricci, M.

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

Rotter, S.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646(2008).
[CrossRef] [PubMed]

Sampaio, L. C.

F. A. Pinheiro and L. C. Sampaio, “Lasing threshold of diffusive random lasers in three dimensions,” Phys. Rev. A 73, 013826 (2006).
[CrossRef]

Sartor, J.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photon. 3, 279–282 (2009).
[CrossRef]

Sauvain, E.

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

Schneider, D.

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photon. 3, 279–282 (2009).
[CrossRef]

Sebbah, P.

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98, 143902 (2007).
[CrossRef] [PubMed]

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

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, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997(2000).
[CrossRef]

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]

Sharma, D.

D. Sharma, H. Ramachandran, and N. Kumar, “Lévy statistical fluctuations from a random amplifying medium,” Fluc. Noise Lett. 6, L95–L101 (2006).
[CrossRef]

Soukoulis, C. M.

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101 (2003).
[CrossRef]

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65, 041103 (2002).
[CrossRef]

Stone, A. D.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646(2008).
[CrossRef] [PubMed]

Torre, R.

S. Mujumdar, V. Tuerck, R. Torre, and D. S. Wiersma, “Chaotic behavior of random lasers with static disorder,” Phys. Rev. A 76, 033807 (2007).
[CrossRef]

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

Tuerck, V.

S. Mujumdar, V. Tuerck, R. Torre, and D. S. Wiersma, “Chaotic behavior of random lasers with static disorder,” Phys. Rev. A 76, 033807 (2007).
[CrossRef]

Türeci, H. E.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646(2008).
[CrossRef] [PubMed]

Turitsyn, S. K.

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photon. 4, 231–235 (2010).
[CrossRef]

Uppu, R.

van der Molen, K. L.

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Relaxation oscillations in long-pulsed random lasers,” Phys. Rev. A 80, 055803 (2009).
[CrossRef]

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Intrinsic intensity fluctuations in random lasers,” Phys. Rev. A 74, 053808 (2006).
[CrossRef]

Vanneste, C.

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98, 143902 (2007).
[CrossRef] [PubMed]

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

Vardeny, Z. V.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughmann, “Stimulated emission in high-gain organic media,” Phys. Rev. B 59, R5284–R5287 (1999).
[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, “The physics and applications of random lasers,” Nature Phys. 4, 359–367 (2008).
[CrossRef]

S. Lepri, S. Cavalieri, G.-L. Oppo, and D. S. Wiersma, “Statistical regimes of random laser fluctuations,” Phys. Rev. A 75, 063820 (2007).
[CrossRef]

S. Mujumdar, V. Tuerck, R. Torre, and D. S. Wiersma, “Chaotic behavior of random lasers with static disorder,” Phys. Rev. A 76, 033807 (2007).
[CrossRef]

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

D. S. Wiersma and S. A. Cavalieri, “A temperature-tunable random laser,” Nature 414, 708–709 (2001).
[CrossRef] [PubMed]

Wu, X.

X. Wu and H. Cao, “Statistical studies of random-lasing modes and amplified spontaneous-emission spikes in weakly scattering systems,” Phys. Rev. A 77, 013832 (2008).
[CrossRef]

Xu, J. Y.

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101 (2003).
[CrossRef]

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65, 041103 (2002).
[CrossRef]

H. Cao, Y. Ling, J. Y. Xu, C. Q. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86, 4524–4527 (2001).
[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, J. Y. Xu, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997(2000).
[CrossRef]

Yaroshchuk, O.

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

Yeh, H.-C.

Yoshino, K.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughmann, “Stimulated emission in high-gain organic media,” Phys. Rev. B 59, R5284–R5287 (1999).
[CrossRef]

Zaitsev, O.

O. Zaitsev, “Mode statistics in random lasers,” Phys. Rev. A 74, 063803 (2006).
[CrossRef]

Zakhidov, A.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughmann, “Stimulated emission in high-gain organic media,” Phys. Rev. B 59, R5284–R5287 (1999).
[CrossRef]

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]

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]

Appl. Phys. Lett. (1)

H. Cao, J. Y. Xu, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997(2000).
[CrossRef]

Fluc. Noise Lett. (1)

D. Sharma, H. Ramachandran, and N. Kumar, “Lévy statistical fluctuations from a random amplifying medium,” Fluc. Noise Lett. 6, L95–L101 (2006).
[CrossRef]

J. Phys. A (1)

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[CrossRef]

Nat. Photon. (2)

J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photon. 3, 279–282 (2009).
[CrossRef]

S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photon. 4, 231–235 (2010).
[CrossRef]

Nature (2)

D. S. Wiersma and S. A. Cavalieri, “A temperature-tunable random laser,” Nature 414, 708–709 (2001).
[CrossRef] [PubMed]

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

Nature Phys. (1)

D. S. Wiersma, “The physics and applications of random lasers,” Nature Phys. 4, 359–367 (2008).
[CrossRef]

Opt. Commun. (1)

M. Bahoura, K. J. Morris, and M. A. Noginov, “Threshold and slope efficiency of Nd0.5La0.5Al3(BO3)4 ceramic random laser: effect of the pumped spot size,” Opt. Commun. 201, 405–411(2002).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (8)

S. Mujumdar, V. Tuerck, R. Torre, and D. S. Wiersma, “Chaotic behavior of random lasers with static disorder,” Phys. Rev. A 76, 033807 (2007).
[CrossRef]

F. A. Pinheiro and L. C. Sampaio, “Lasing threshold of diffusive random lasers in three dimensions,” Phys. Rev. A 73, 013826 (2006).
[CrossRef]

R. Pierrat and R. Carminati, “Threshold of random lasers in the incoherent transport regime,” Phys. Rev. A 76, 023821(2007).
[CrossRef]

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Relaxation oscillations in long-pulsed random lasers,” Phys. Rev. A 80, 055803 (2009).
[CrossRef]

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Intrinsic intensity fluctuations in random lasers,” Phys. Rev. A 74, 053808 (2006).
[CrossRef]

X. Wu and H. Cao, “Statistical studies of random-lasing modes and amplified spontaneous-emission spikes in weakly scattering systems,” Phys. Rev. A 77, 013832 (2008).
[CrossRef]

O. Zaitsev, “Mode statistics in random lasers,” Phys. Rev. A 74, 063803 (2006).
[CrossRef]

S. Lepri, S. Cavalieri, G.-L. Oppo, and D. S. Wiersma, “Statistical regimes of random laser fluctuations,” Phys. Rev. A 75, 063820 (2007).
[CrossRef]

Phys. Rev. B (3)

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65, 041103 (2002).
[CrossRef]

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101 (2003).
[CrossRef]

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughmann, “Stimulated emission in high-gain organic media,” Phys. Rev. B 59, R5284–R5287 (1999).
[CrossRef]

Phys. Rev. Lett. (8)

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

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

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98, 143902 (2007).
[CrossRef] [PubMed]

C. W. J. Beenakker, “Thermal radiation and amplified spontaneous emission from a random medium,” Phys. Rev. Lett. 81, 1829–1832 (1998).
[CrossRef]

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]

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93, 053903 (2004).
[CrossRef] [PubMed]

H. Cao, Y. Ling, J. Y. Xu, C. Q. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86, 4524–4527 (2001).
[CrossRef] [PubMed]

Science (1)

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646(2008).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

V. S. Letokhov, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 16, 835–840 (1968).

Other (1)

M. Noginov, Solid State Random Lasers, Vol.  105 of Series in Optical Sciences (Springer, 2005).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup. Lens L1 focuses the pump beam onto the cuvette holding the sample. Lens L2 focuses the collected emission into the spectrometer. (a) Schematic of the scatterers with an illustrative extended mode that supports the avalanche gain of a photon generated in the system. (b) Resulting ultrasharp spectral line.

Fig. 2
Fig. 2

(a) Representative spectrum with coherent modes, along with the ensemble-averaged spectrum (dotted curve). Two baselines, calculated with 8-point baseline finder (blue) and 16-point baseline finder (red) are shown. The 16-point algorithm is adopted for analysis due to stronger correlation with the ensemble-averaged curve. (b) Bandwidth narrowing of the ensemble-averaged spectrum, indicating a critical energy at 0.8 μJ , where every spectrum emits ultranarrowband modes. (c) Characteristic Levy statistics (blue curve) of intensity emitted at the critical excitation, compared to Gaussian statistics at low energy.

Fig. 3
Fig. 3

Exponentially decaying modal density [ exp ( 9.8 × ) ] of coherent modes as a function of mode intensity threshold. The inset shows the pedestal-subtracted spectrum yielding only coherent modes, to which three representative thresholds are applied. The number of modes with intensity above these thresholds is taken as the modal intensity.

Fig. 4
Fig. 4

Ratio of coherent to incoherent intensities of the stron gest coherent mode in a spectrum. The distribution peaks at i coh / i inc = 1 , while the tail indicates the generation of modes with up to 80% energy in the coherent fraction.

Fig. 5
Fig. 5

Scatterplot of the ratio of the second maximum to the first maximum, plotted against the first maximum. Points closer to 1 indicate comparable intensity in the coherent modes. Points to the right of i f _ max = 0.5 deviate away from 1, which indicates the suppression of a large number of strongly coherent modes arising due to gain competition.

Fig. 6
Fig. 6

Emission line shape from the random laser at critical excitation ( 0.8 μJ ) shows prominent coherent modes, while at a stronger pump energy above threshold ( 1.5 μJ ), it shows a smoother line profile, devoid of coherent modes. This can be attributed to the self-averaging resulting from excessive generation of coherent modes within the lasing band.

Fig. 7
Fig. 7

Shift in the centroid of scatterplots of maximum coherent intensity versus total emitted intensity, under large excitation intensity. The centroids are marked as yellow squares. (a) Distribution at low excitation energies is skewed with a large dispersion in the first quadrant. (b) The centroid shifts to the right due to self-averaging, which results in compactness of the scatterplot.

Equations (1)

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η = m ( S m inc S ¯ inc ) ( S inc m S ¯ inc ) ( m ( S m inc S ¯ inc ) 2 ) ( n ( S inc n S ¯ inc ) 2 ) ,

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