Abstract

Stochastic noise is incorporated in the numerical simulation of weakly scattering random lasers, which qualitatively captures lasing phenomena that have been observed experimentally. We examine the behavior of the emission spectrum while pumping only part of the entire one-dimensional random system. A decrease in the density of lasing states is the dominant mechanism for observing discrete lasing peaks when absorption exists in the unpumped region. Without such absorption, the density of lasing states does not reduce as dramatically but the statistical distribution of (linear) lasing thresholds is broadened. This may facilitate incremental observation of lasing in smaller-threshold modes in the emission spectrum with fine adjustments of the pumping rate.

© 2011 Optical Society of America

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  22. M. Terraneo, and I. Guarneri, “Distribution of resonance widths in localized tight-binding models,” Eur. Phys. J. B 18, 303–309 (2000).
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  23. F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing anderson localization of light via decay rate statistics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 026605 (2004).
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    [CrossRef]
  30. E. V. Chelnokov, N. Bityurin, I. Ozerov, and W. Marine, “Two-photon pumped random laser in nanocrystalline ZnO,” Appl. Phys. Lett. 89, 171119 (2006).
    [CrossRef]
  31. 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).
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    [CrossRef] [PubMed]
  34. J. Andreasen, and H. Cao, “Finite-different time-domain formulation of stochastic noise in macroscopic atomic systems,” J. Lightwave Technol. 27, 4530–4535 (2009).
    [CrossRef]
  35. 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]
  36. X. Wu, A. Yamilov, H. Noh, H. Cao, E. W. Seelig, and R. P. H. Chang, “Random lasing in closely packed resonant scatterers,” J. Opt. Soc. Am. B 21, 159–167 (2004).
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    [CrossRef]
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    [CrossRef] [PubMed]
  41. P. D. Drummond, and M. G. Raymer, “Quantum theory of propagation of nonclassical radiation in a near-resonant medium,” Phys. Rev. A 44, 2072–2085 (1991).
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  44. J. Andreasen, and H. Cao, “Numerical study of amplified spontaneous emission and lasing in random media,” Phys. Rev. A 82, 063835 (2010).
    [CrossRef]
  45. P. J. Bardroff, and S. Stenholm, “Quantum theory of excess noise,” Phys. Rev. A 60, 2529–2533 (1999).
    [CrossRef]
  46. J. Andreasen, and H. Cao, “Creation of new lasing modes with spatially nonuniform gain,” Opt. Lett. 34, 3586–3588 (2009).
    [CrossRef] [PubMed]
  47. D. W. Scott, “On optimal and data-based histograms,” Biometrika 66, 605–610 (1979).
    [CrossRef]
  48. O. Frazão, C. Correia, J. L. Santos, and J. M. Baptista, “Raman fibre Bragg-grating laser sensor with cooperative Rayleigh scattering for strain-temperature measurement,” Meas. Sci. Technol. 20, 045203 (2009).
    [CrossRef]
  49. S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, and S. I. Kablukov, “J. D. Ania-Casta˜n’on, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4, 231–235 (2010).
    [CrossRef]

2011 (1)

2010 (3)

J. Andreasen, C. Vanneste, L. Ge, and H. Cao, “Effects of spatially nonuniform gain on lasing modes in weakly scattering random systems,” Phys. Rev. A 81, 043818 (2010).
[CrossRef]

J. Andreasen, and H. Cao, “Numerical study of amplified spontaneous emission and lasing in random media,” Phys. Rev. A 82, 063835 (2010).
[CrossRef]

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

2009 (3)

2008 (3)

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]

J. Andreasen, H. Cao, A. Taflove, P. Kumar, and C. Cao, “Finite-difference time-domain simulation of thermal noise in open cavities,” Phys. Rev. A 77, 023810 (2008).
[CrossRef]

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

2007 (2)

X. Wu, J. Andreasen, H. Cao, and A. Yamilov, “Effect of local pumping on random laser modes in one dimension,” J. Opt. Soc. Am. B 24, A26–A33 (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]

2006 (3)

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A 74, 053812 (2006).
[CrossRef]

E. V. Chelnokov, N. Bityurin, I. Ozerov, and W. Marine, “Two-photon pumped random laser in nanocrystalline ZnO,” Appl. Phys. Lett. 89, 171119 (2006).
[CrossRef]

G. J. de Valc’arcel, E. Rold’an, and F. Prati, “Semiclassical theory of amplification and lasing,” Rev. Mex. Fis. 52, 198–214 (2006).

2005 (4)

L. I. Deych, “Effects of spatial nonuniformity on laser dynamics,” Phys. Rev. Lett. 95, 043902 (2005).
[CrossRef] [PubMed]

M. Bahoura, K. J. Morris, G. Zhu, and M. A. Noginov, “Dependence of the neodymium random laser threshold on the diameter of the pumped spot,” IEEE J. Quantum Electron. 41, 677–685 (2005).
[CrossRef]

V. M. Apalkov, and M. E. Raikh, “Universal fluctuations of the random lasing threshold in a sample of a finite area,” Phys. Rev. B 71, 054203 (2005).
[CrossRef]

A. Yamilov, X. Wu, H. Cao, and A. L. Burin, “Absorption-induced confinement of lasing modes in diffusive random media,” Opt. Lett. 30, 2430–2432 (2005).
[CrossRef] [PubMed]

2004 (2)

F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing anderson localization of light via decay rate statistics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 026605 (2004).
[CrossRef]

X. Wu, A. Yamilov, H. Noh, H. Cao, E. W. Seelig, and R. P. H. Chang, “Random lasing in closely packed resonant scatterers,” J. Opt. Soc. Am. B 21, 159–167 (2004).
[CrossRef]

2003 (3)

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, “Breakdown of diffusion in dynamics of extended waves in mesoscopic media,” Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef] [PubMed]

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]

M. Patra, “Decay rate distributions of disordered slabs and application to random lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67, 016603 (2003).
[CrossRef]

2002 (2)

X. Jiang, and C. M. Soukoulis, “Localized random lasing modes and a path for observing localization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65, 025601 (2002).
[CrossRef]

P. Sebbah, and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66, 144202 (2002).
[CrossRef]

2001 (2)

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]

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

2000 (3)

M. Terraneo, and I. Guarneri, “Distribution of resonance widths in localized tight-binding models,” Eur. Phys. J. B 18, 303–309 (2000).
[CrossRef]

A. D. Mirlin, “Statistics of energy levels and eigenfunctions in disordered systems,” Phys. Rep. 326, 259–382 (2000).
[CrossRef]

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

1999 (4)

G. van Soest, M. Tomita, and A. Lagendijk, “Amplifying volume in scattering media,” Opt. Lett. 24, 306–308 (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]

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

P. J. Bardroff, and S. Stenholm, “Quantum theory of excess noise,” Phys. Rev. A 60, 2529–2533 (1999).
[CrossRef]

1998 (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 semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

1995 (3)

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

D. S. Wiersma, M. P. van Albada, and A. Lagendijk, “Random laser?” Nature 373, 203–204 (1995).
[CrossRef]

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52, 3082–3094 (1995).
[CrossRef] [PubMed]

1994 (2)

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]

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).
[CrossRef] [PubMed]

1993 (1)

1991 (1)

P. D. Drummond, and M. G. Raymer, “Quantum theory of propagation of nonclassical radiation in a near-resonant medium,” Phys. Rev. A 44, 2072–2085 (1991).
[CrossRef] [PubMed]

1986 (1)

V. M. Markushev, V. F. Zolin, and C. M. Briskina, “Powder laser,” Zh. Prikl. Spektrosk. 45, 847–849 (1986).

1979 (1)

D. W. Scott, “On optimal and data-based histograms,” Biometrika 66, 605–610 (1979).
[CrossRef]

1968 (1)

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

Alfano, R. R.

Andreasen, J.

Apalkov, V. M.

V. M. Apalkov, and M. E. Raikh, “Universal fluctuations of the random lasing threshold in a sample of a finite area,” Phys. Rev. B 71, 054203 (2005).
[CrossRef]

Arnold, J. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52, 3082–3094 (1995).
[CrossRef] [PubMed]

Asatryan, A.

Asatryan, A. A.

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A 74, 053812 (2006).
[CrossRef]

Babin, S. A.

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

Bahoura, M.

M. Bahoura, K. J. Morris, G. Zhu, and M. A. Noginov, “Dependence of the neodymium random laser threshold on the diameter of the pumped spot,” IEEE J. Quantum Electron. 41, 677–685 (2005).
[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]

Baptista, J. M.

O. Frazão, C. Correia, J. L. Santos, and J. M. Baptista, “Raman fibre Bragg-grating laser sensor with cooperative Rayleigh scattering for strain-temperature measurement,” Meas. Sci. Technol. 20, 045203 (2009).
[CrossRef]

Bardroff, P. J.

P. J. Bardroff, and S. Stenholm, “Quantum theory of excess noise,” Phys. Rev. A 60, 2529–2533 (1999).
[CrossRef]

Baughman, R. H.

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

Bityurin, N.

E. V. Chelnokov, N. Bityurin, I. Ozerov, and W. Marine, “Two-photon pumped random laser in nanocrystalline ZnO,” Appl. Phys. Lett. 89, 171119 (2006).
[CrossRef]

Botten, L.

Botten, L. C.

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A 74, 053812 (2006).
[CrossRef]

Briskina, C. M.

V. M. Markushev, V. F. Zolin, and C. M. Briskina, “Powder laser,” Zh. Prikl. Spektrosk. 45, 847–849 (1986).

Burin, A. L.

A. Yamilov, X. Wu, H. Cao, and A. L. Burin, “Absorption-induced confinement of lasing modes in diffusive random media,” Opt. Lett. 30, 2430–2432 (2005).
[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]

Byrne, M.

Cao, C.

J. Andreasen, H. Cao, A. Taflove, P. Kumar, and C. Cao, “Finite-difference time-domain simulation of thermal noise in open cavities,” Phys. Rev. A 77, 023810 (2008).
[CrossRef]

Cao, H.

J. Andreasen, A. Asatryan, L. Botten, M. Byrne, H. Cao, L. Ge, L. Labont’e, P. Sebbah, A. D. Stone, H. E. T¨ureci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photon. 3, 88–127 (2011).
[CrossRef]

J. Andreasen, C. Vanneste, L. Ge, and H. Cao, “Effects of spatially nonuniform gain on lasing modes in weakly scattering random systems,” Phys. Rev. A 81, 043818 (2010).
[CrossRef]

J. Andreasen, and H. Cao, “Numerical study of amplified spontaneous emission and lasing in random media,” Phys. Rev. A 82, 063835 (2010).
[CrossRef]

J. Andreasen, and H. Cao, “Finite-different time-domain formulation of stochastic noise in macroscopic atomic systems,” J. Lightwave Technol. 27, 4530–4535 (2009).
[CrossRef]

J. Andreasen, and H. Cao, “Creation of new lasing modes with spatially nonuniform gain,” Opt. Lett. 34, 3586–3588 (2009).
[CrossRef] [PubMed]

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]

J. Andreasen, H. Cao, A. Taflove, P. Kumar, and C. Cao, “Finite-difference time-domain simulation of thermal noise in open cavities,” Phys. Rev. A 77, 023810 (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]

X. Wu, J. Andreasen, H. Cao, and A. Yamilov, “Effect of local pumping on random laser modes in one dimension,” J. Opt. Soc. Am. B 24, A26–A33 (2007).
[CrossRef]

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A 74, 053812 (2006).
[CrossRef]

A. Yamilov, X. Wu, H. Cao, and A. L. Burin, “Absorption-induced confinement of lasing modes in diffusive random media,” Opt. Lett. 30, 2430–2432 (2005).
[CrossRef] [PubMed]

X. Wu, A. Yamilov, H. Noh, H. Cao, E. W. Seelig, and R. P. H. Chang, “Random lasing in closely packed resonant scatterers,” J. Opt. Soc. Am. B 21, 159–167 (2004).
[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]

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]

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, 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 semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Caulfield, H. J.

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

Chabanov, A. A.

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A 74, 053812 (2006).
[CrossRef]

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, “Breakdown of diffusion in dynamics of extended waves in mesoscopic media,” Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef] [PubMed]

Chang, R. P. H.

X. Wu, A. Yamilov, H. Noh, H. Cao, E. W. Seelig, and R. P. H. Chang, “Random lasing in closely packed resonant scatterers,” J. Opt. Soc. Am. B 21, 159–167 (2004).
[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]

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, 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 semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Chelnokov, E. V.

E. V. Chelnokov, N. Bityurin, I. Ozerov, and W. Marine, “Two-photon pumped random laser in nanocrystalline ZnO,” Appl. Phys. Lett. 89, 171119 (2006).
[CrossRef]

Churkin, D. V.

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

Correia, C.

O. Frazão, C. Correia, J. L. Santos, and J. M. Baptista, “Raman fibre Bragg-grating laser sensor with cooperative Rayleigh scattering for strain-temperature measurement,” Meas. Sci. Technol. 20, 045203 (2009).
[CrossRef]

Dai, J. Y.

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 semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

de Valc’arcel, G. J.

G. J. de Valc’arcel, E. Rold’an, and F. Prati, “Semiclassical theory of amplification and lasing,” Rev. Mex. Fis. 52, 198–214 (2006).

Deych, L. I.

L. I. Deych, “Effects of spatial nonuniformity on laser dynamics,” Phys. Rev. Lett. 95, 043902 (2005).
[CrossRef] [PubMed]

Drummond, P. D.

P. D. Drummond, and M. G. Raymer, “Quantum theory of propagation of nonclassical radiation in a near-resonant medium,” Phys. Rev. A 44, 2072–2085 (1991).
[CrossRef] [PubMed]

El-Taher, A. E.

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

Fang, W.

X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A 74, 053812 (2006).
[CrossRef]

Frazão, O.

O. Frazão, C. Correia, J. L. Santos, and J. M. Baptista, “Raman fibre Bragg-grating laser sensor with cooperative Rayleigh scattering for strain-temperature measurement,” Meas. Sci. Technol. 20, 045203 (2009).
[CrossRef]

Frolov, S. V.

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

Ge, L.

J. Andreasen, A. Asatryan, L. Botten, M. Byrne, H. Cao, L. Ge, L. Labont’e, P. Sebbah, A. D. Stone, H. E. T¨ureci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photon. 3, 88–127 (2011).
[CrossRef]

J. Andreasen, C. Vanneste, L. Ge, and H. Cao, “Effects of spatially nonuniform gain on lasing modes in weakly scattering random systems,” Phys. Rev. A 81, 043818 (2010).
[CrossRef]

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

Genack, A. Z.

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, “Breakdown of diffusion in dynamics of extended waves in mesoscopic media,” Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef] [PubMed]

Gogny, D. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52, 3082–3094 (1995).
[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]

Gouedard, C.

Guarneri, I.

M. Terraneo, and I. Guarneri, “Distribution of resonance widths in localized tight-binding models,” Eur. Phys. J. B 18, 303–309 (2000).
[CrossRef]

Harper, P.

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

Ho, S. T.

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, 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 semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Husson, D.

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]

X. Jiang, and C. M. Soukoulis, “Localized random lasing modes and a path for observing localization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65, 025601 (2002).
[CrossRef]

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

Kablukov, S. I.

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

Kumar, P.

J. Andreasen, H. Cao, A. Taflove, P. Kumar, and C. Cao, “Finite-difference time-domain simulation of thermal noise in open cavities,” Phys. Rev. A 77, 023810 (2008).
[CrossRef]

Labont’e, L.

Lagendijk, A.

G. van Soest, M. Tomita, and A. Lagendijk, “Amplifying volume in scattering media,” Opt. Lett. 24, 306–308 (1999).
[CrossRef]

D. S. Wiersma, M. P. van Albada, and A. Lagendijk, “Random laser?” Nature 373, 203–204 (1995).
[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]

Letokhov, V. S.

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

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]

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]

Liu, C.-H.

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]

Marine, W.

E. V. Chelnokov, N. Bityurin, I. Ozerov, and W. Marine, “Two-photon pumped random laser in nanocrystalline ZnO,” Appl. Phys. Lett. 89, 171119 (2006).
[CrossRef]

Markushev, V. M.

V. M. Markushev, V. F. Zolin, and C. M. Briskina, “Powder laser,” Zh. Prikl. Spektrosk. 45, 847–849 (1986).

Mirlin, A. D.

A. D. Mirlin, “Statistics of energy levels and eigenfunctions in disordered systems,” Phys. Rep. 326, 259–382 (2000).
[CrossRef]

Morris, K. J.

M. Bahoura, K. J. Morris, G. Zhu, and M. A. Noginov, “Dependence of the neodymium random laser threshold on the diameter of the pumped spot,” IEEE J. Quantum Electron. 41, 677–685 (2005).
[CrossRef]

Noginov, M. A.

M. Bahoura, K. J. Morris, G. Zhu, and M. A. Noginov, “Dependence of the neodymium random laser threshold on the diameter of the pumped spot,” IEEE J. Quantum Electron. 41, 677–685 (2005).
[CrossRef]

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

Noginova, N. E.

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

Noh, H.

Ong, H. C.

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 semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Orlowski, A.

F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing anderson localization of light via decay rate statistics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 026605 (2004).
[CrossRef]

Ozerov, I.

E. V. Chelnokov, N. Bityurin, I. Ozerov, and W. Marine, “Two-photon pumped random laser in nanocrystalline ZnO,” Appl. Phys. Lett. 89, 171119 (2006).
[CrossRef]

Patra, M.

M. Patra, “Decay rate distributions of disordered slabs and application to random lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67, 016603 (2003).
[CrossRef]

Pinheiro, F. A.

F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing anderson localization of light via decay rate statistics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 026605 (2004).
[CrossRef]

Prati, F.

G. J. de Valc’arcel, E. Rold’an, and F. Prati, “Semiclassical theory of amplification and lasing,” Rev. Mex. Fis. 52, 198–214 (2006).

Raikh, M. E.

V. M. Apalkov, and M. E. Raikh, “Universal fluctuations of the random lasing threshold in a sample of a finite area,” Phys. Rev. B 71, 054203 (2005).
[CrossRef]

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]

Raymer, M. G.

P. D. Drummond, and M. G. Raymer, “Quantum theory of propagation of nonclassical radiation in a near-resonant medium,” Phys. Rev. A 44, 2072–2085 (1991).
[CrossRef] [PubMed]

Rold’an, E.

G. J. de Valc’arcel, E. Rold’an, and F. Prati, “Semiclassical theory of amplification and lasing,” Rev. Mex. Fis. 52, 198–214 (2006).

Rotter, S.

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

Rusek, M.

F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing anderson localization of light via decay rate statistics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 026605 (2004).
[CrossRef]

Santos, J. L.

O. Frazão, C. Correia, J. L. Santos, and J. M. Baptista, “Raman fibre Bragg-grating laser sensor with cooperative Rayleigh scattering for strain-temperature measurement,” Meas. Sci. Technol. 20, 045203 (2009).
[CrossRef]

Sauteret, C.

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]

Scott, D. W.

D. W. Scott, “On optimal and data-based histograms,” Biometrika 66, 605–610 (1979).
[CrossRef]

Sebbah, P.

J. Andreasen, A. Asatryan, L. Botten, M. Byrne, H. Cao, L. Ge, L. Labont’e, P. Sebbah, A. D. Stone, H. E. T¨ureci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photon. 3, 88–127 (2011).
[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]

P. Sebbah, and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66, 144202 (2002).
[CrossRef]

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

Seelig, E. W.

X. Wu, A. Yamilov, H. Noh, H. Cao, E. W. Seelig, and R. P. H. Chang, “Random lasing in closely packed resonant scatterers,” J. Opt. Soc. Am. B 21, 159–167 (2004).
[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]

Sha, W. L.

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]

X. Jiang, and C. M. Soukoulis, “Localized random lasing modes and a path for observing localization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65, 025601 (2002).
[CrossRef]

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

Stenholm, S.

P. J. Bardroff, and S. Stenholm, “Quantum theory of excess noise,” Phys. Rev. A 60, 2529–2533 (1999).
[CrossRef]

Stone, A. D.

T¨ureci, H. E.

Taflove, A.

J. Andreasen, H. Cao, A. Taflove, P. Kumar, and C. Cao, “Finite-difference time-domain simulation of thermal noise in open cavities,” Phys. Rev. A 77, 023810 (2008).
[CrossRef]

Terraneo, M.

M. Terraneo, and I. Guarneri, “Distribution of resonance widths in localized tight-binding models,” Eur. Phys. J. B 18, 303–309 (2000).
[CrossRef]

Tomita, M.

Turitsyn, S. K.

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

van Albada, M. P.

D. S. Wiersma, M. P. van Albada, and A. Lagendijk, “Random laser?” Nature 373, 203–204 (1995).
[CrossRef]

van Soest, G.

van Tiggelen, B. A.

F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing anderson localization of light via decay rate statistics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 026605 (2004).
[CrossRef]

Vanneste, C.

J. Andreasen, A. Asatryan, L. Botten, M. Byrne, H. Cao, L. Ge, L. Labont’e, P. Sebbah, A. D. Stone, H. E. T¨ureci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photon. 3, 88–127 (2011).
[CrossRef]

J. Andreasen, C. Vanneste, L. Ge, and H. Cao, “Effects of spatially nonuniform gain on lasing modes in weakly scattering random systems,” Phys. Rev. A 81, 043818 (2010).
[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]

P. Sebbah, and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66, 144202 (2002).
[CrossRef]

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. Baughman, “Stimulated emission in high-gain organic media,” Phys. Rev. B 59, R5284–R5287 (1999).
[CrossRef]

Venkateswarlu, P.

M. A. Noginov, H. J. Caulfield, N. E. Noginova, and P. Venkateswarlu, “Line narrowing in the dye solution with scattering centers,” Opt. Commun. 118, 430–437 (1995).
[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, M. P. van Albada, and A. Lagendijk, “Random laser?” Nature 373, 203–204 (1995).
[CrossRef]

Wu, J. Y.

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 semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Wu, X.

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]

Yamilov, A.

Yoshino, K.

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

Zakhidov, A.

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

Zhang, Z. Q.

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, “Breakdown of diffusion in dynamics of extended waves in mesoscopic media,” Phys. Rev. Lett. 90, 203903 (2003).
[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]

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 semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Zhu, G.

M. Bahoura, K. J. Morris, G. Zhu, and M. A. Noginov, “Dependence of the neodymium random laser threshold on the diameter of the pumped spot,” IEEE J. Quantum Electron. 41, 677–685 (2005).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52, 3082–3094 (1995).
[CrossRef] [PubMed]

Zolin, V. F.

V. M. Markushev, V. F. Zolin, and C. M. Briskina, “Powder laser,” Zh. Prikl. Spektrosk. 45, 847–849 (1986).

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Figures (6)

Fig. 1
Fig. 1

Steady-state intensity spectra |E(k)|2 for uniform pumping (G/L = 1). (a) Pr = 1.00. A broad peak is centered around ka. (b) Pr = 1.10. The broad peak narrows around ka. (c) Pr = 1.22. Multiple peaks appear on top of the broad peak. (d) Pr = 1.56. Eight visible peaks are marked with arrows. From (f) Pr = 1.74 to (g) Pr = 2.00, the dominant peaks are revealed.

Fig. 2
Fig. 2

Steady-state intensity spectra |E(k)|2 for partial pumping (G/L = 1/3). (a) Pr = 1.00. A broad peak is centered around ka. (b) Pr = 1.10. The broad peak narrows around ka and multiple peaks already emerge on top of the broad peak. (c) Pr = 1.22. More peaks emerge. (d) Pr = 1.56. Seven visible peaks are marked with arrows. From (f) Pr = 1.74 to (g) Pr = 2.00, the dominant peaks are revealed. The number of modes is less than the case with uniform pumping and the lasing modes are more separated in frequency.

Fig. 3
Fig. 3

Steady-state intensity spectra |E(k)|2 for partial pumping (G/L = 1/3) and absorption in the unpumped region (a = 170 nm). (a) Pr = 1.00. A broad peak is centered around ka. (b) Pr = 1.10. The broad peak narrows around ka and multiple peaks already emerge on top of the broad peak. (c) Pr = 1.22. More peaks emerge. (d) Pr = 1.56. Five visible peaks are marked with arrows. From (f) Pr = 1.74 to (g) Pr = 2.00, the dominant peaks are revealed. The number of modes is less than the case of partial pumping without absorption and the lasing modes are more separated in frequency.

Fig. 4
Fig. 4

(Color online) The frequencies k and thresholds ni of lasing modes with linear gain. (a) TLM solutions for (diamonds) uniform pumping (G/L = 1), (circles) partial pumping (G/L = 1/3), and (squares) partial pumping with absorption in the unpumped region (a = 170 nm). The filled symbols represent the modes which are visible in the emission spectra of the SMB simulations. The enlarged filled diamonds are TLMs for uniform pumping that disappear for partial pumping without absorption. The vertical dashed gray line marks the center frequency of the gain spectrum ka in the SMB simulations. (b) Real (green) and Imaginary (red) zero lines of M22 in the (k,ni) plane for partial pumping over the frequency range of the filled circles in (a). TLM solutions are marked by white circles.

Fig. 5
Fig. 5

(Color online) (a) Probability distributions of lasing thresholds for uniform pumping (dashed black lines) and partial pumping (solid red lines). Partial pumping increases lasing thresholds. The inset shows the re-normalized probability distribution (solid dark-red lines) for partial pumping. The rising slope of the first main peak is 4.5 times greater with uniform pumping than with partial pumping. (b) Probability distributions of thresholds normalized to the most probable threshold. Partial pumping redistributes lasing thresholds by destroying small-threshold modes and creating large-threshold modes. The number of large-threshold modes (found by the area under the curve for ni > 0.175 or ni/nm > 1.55) is 25% of the total number of modes. The inset shows the shape of the main peak with partial pumping almost the same as that with uniform pumping but slightly narrower.

Fig. 6
Fig. 6

(Color online) (a) Probability distributions of lasing thresholds for partial pumping without absorption (solid dark-red lines) and with absorption (dotted blue lines). The distribution without absorption excludes large-threshold modes and has been re-normalized. Absorption increases lasing thresholds. The inset shows the rising slope is roughly 1.3 times greater with absorption than without absorption. (b) Probability distributions of thresholds normalized to the most probable threshold for uniform pumping (dashed black lines), partial pumping (solid red lines), and partial pumping with absorption (dotted blue lines). The inset shows partial pumping with absorption narrows the main peak.

Equations (1)

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n ˜ ( x ) = n 2 ( x ) + n y 2 ( x ) + i n y ( x ) ,

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