Abstract

We have developed a numerical method based on the transfer matrix to calculate the quasi modes and lasing modes in one-dimensional random systems. Depending on the relative magnitude of the localization length versus the system size, there are two regimes in which the quasi modes are distinct in spatial profile and frequency distribution. In the presence of uniform gain, the lasing modes have one-to-one correspondence to the quasi modes in both regimes. Local excitation may enhance the weight of a mode within the gain region due to local amplification, especially in a weakly scattering system.

© 2007 Optical Society of America

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  1. H. Cao, "Lasing in random media," Waves Random Media 13, R1-R39 (2003).
    [CrossRef]
  2. V. S. Letokhov, "Quantum statistics of multi-mode radiation from an ensemble of atoms," Sov. Phys. JETP 26, 1246-1251 (1968).
  3. 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]
  4. C. Vanneste and P. Sebbah, "Selective excitation of localized modes in active random media," Phys. Rev. Lett. 87, 183903 (2001).
    [CrossRef]
  5. X. Y. Jiang and C. M. Soukoulis, "Localized random lasing modes and a path for observing localization," Phys. Rev. E 65, 025601 (2002).
    [CrossRef]
  6. 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]
  7. H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, "Probing localized states with spectrally resolved speckle techniques," Phys. Rev. E 66, R025601 (2002).
    [CrossRef]
  8. L. I. Deych, "Effects of spatial nonuniformity on laser dynamics," Phys. Rev. Lett. 95, 043902 (2005).
    [CrossRef] [PubMed]
  9. H. E. Türeci, A. D. Stone, and B. Collier, "Self-consistent multimode lasing theory for complex or random lasing media," Phys. Rev. A 74, 043822 (2006).
    [CrossRef]
  10. H. E. Türeci, A. D. Stone, and L. Ge, "Theory of the spatial structure of non-linear lasing modes," http://arxiv.org/PSlowbarcache/cond-mat/pdf/0610/0610229v1.pdf.
  11. A. Yamilov, X. Wu, H. Cao, and A. Burin, "Absorption-induced confinement of lasing modes in diffusive random medium," Opt. Lett. 30, 2430-2432 (2005).
    [CrossRef] [PubMed]
  12. T. Sh. Misirpashaev and C. W. J. Beenakker, "Lasing threshold and mode competition in chaotic cavities," Phys. Rev. A 57, 2041-2045 (1998).
    [CrossRef]
  13. Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, C. Liu, and R. P. H. Chang, "Investigation of random lasers with resonant feedback," Phys. Rev. A 64, 063808 (2001).
    [CrossRef]
  14. M. Patra, "Decay rate distributions of disordered slabs and application to random lasers," Phys. Rev. E 67, 016603 (2003).
    [CrossRef]
  15. S. H. Chang, H. Cao, and S. T. Ho, "Cavity formation and light propagation in partially ordered and completely random one-dimensional systems," IEEE J. Quantum Electron. 39, 364-374 (2003).
    [CrossRef]
  16. 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]
  17. G. Hackenbroich, "Statistical theory of multimode random lasers," J. Phys. A 38, 10537-10543 (2005).
    [CrossRef]
  18. T. Kottos, "Statistics of resonances and delay times in random media: beyond random matrix theory," J. Phys. A 38, 10761-10786 (2005).
    [CrossRef]
  19. K. L. van der Molen, A. P. Mosk, and A. Lagendijk, "Intrinsic intensity fluctuations in random lasers," Phys. Rev. A 74, 053808 (2006).
    [CrossRef]
  20. H. Kogelnik and C. V. Shank, "Coupled-wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327-2335 (1972).
    [CrossRef]
  21. S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. A. Zakhidov, and R. H. Baughman, "Stimulated emission in high-gain organic media," Phys. Rev. B 59, R5284-R5287 (1999).
    [CrossRef]
  22. R. C. Polson and Z. V. Vardeny, "Organic random lasers in the weak-scattering regime," Phys. Rev. B 71, 045205 (2005).
    [CrossRef]
  23. X. Wu, 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]
  24. S. M. Dutra and G. Nienhuis, "Quantized mode of a leaky cavity," Phys. Rev. A 62, 063805 (2000).
    [CrossRef]
  25. X. Y. Jiang and C. M. Soukoulis, "Symmetry between absorption and amplification in disordered media," Phys. Rev. B 59, R9007-R9010 (1999).
    [CrossRef]
  26. C. Vanneste, P. Sebbah, and H. Cao, "Lasing with coherent feedback in the diffusive regime," Phys. Rev. Lett. 98, 143902 (2007).
    [CrossRef] [PubMed]

2007 (1)

C. Vanneste, P. Sebbah, and H. Cao, "Lasing with coherent feedback in the diffusive regime," Phys. Rev. Lett. 98, 143902 (2007).
[CrossRef] [PubMed]

2006 (3)

X. Wu, 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]

H. E. Türeci, A. D. Stone, and B. Collier, "Self-consistent multimode lasing theory for complex or random lasing media," Phys. Rev. A 74, 043822 (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 (6)

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]

G. Hackenbroich, "Statistical theory of multimode random lasers," J. Phys. A 38, 10537-10543 (2005).
[CrossRef]

T. Kottos, "Statistics of resonances and delay times in random media: beyond random matrix theory," J. Phys. A 38, 10761-10786 (2005).
[CrossRef]

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

R. C. Polson and Z. V. Vardeny, "Organic random lasers in the weak-scattering regime," Phys. Rev. B 71, 045205 (2005).
[CrossRef]

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

2003 (3)

M. Patra, "Decay rate distributions of disordered slabs and application to random lasers," Phys. Rev. E 67, 016603 (2003).
[CrossRef]

S. H. Chang, H. Cao, and S. T. Ho, "Cavity formation and light propagation in partially ordered and completely random one-dimensional systems," IEEE J. Quantum Electron. 39, 364-374 (2003).
[CrossRef]

H. Cao, "Lasing in random media," Waves Random Media 13, R1-R39 (2003).
[CrossRef]

2002 (3)

X. Y. Jiang and C. M. Soukoulis, "Localized random lasing modes and a path for observing localization," Phys. Rev. E 65, 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]

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, "Probing localized states with spectrally resolved speckle techniques," Phys. Rev. E 66, R025601 (2002).
[CrossRef]

2001 (2)

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

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

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]

S. M. Dutra and G. Nienhuis, "Quantized mode of a leaky cavity," Phys. Rev. A 62, 063805 (2000).
[CrossRef]

1999 (2)

X. Y. Jiang and C. M. Soukoulis, "Symmetry between absorption and amplification in disordered media," Phys. Rev. B 59, R9007-R9010 (1999).
[CrossRef]

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

1998 (1)

T. Sh. Misirpashaev and C. W. J. Beenakker, "Lasing threshold and mode competition in chaotic cavities," Phys. Rev. A 57, 2041-2045 (1998).
[CrossRef]

1972 (1)

H. Kogelnik and C. V. Shank, "Coupled-wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327-2335 (1972).
[CrossRef]

1968 (1)

V. S. Letokhov, "Quantum statistics of multi-mode radiation from an ensemble of atoms," Sov. Phys. JETP 26, 1246-1251 (1968).

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]

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]

Asatryan, A. A.

X. Wu, 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]

Baughman, R. H.

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

Beenakker, C. W. J.

T. Sh. Misirpashaev and C. W. J. Beenakker, "Lasing threshold and mode competition in chaotic cavities," Phys. Rev. A 57, 2041-2045 (1998).
[CrossRef]

Botten, L. C.

X. Wu, 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]

Burin, A.

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, R025601 (2002).
[CrossRef]

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

Cao, H.

C. Vanneste, P. Sebbah, and H. Cao, "Lasing with coherent feedback in the diffusive regime," Phys. Rev. Lett. 98, 143902 (2007).
[CrossRef] [PubMed]

X. Wu, 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. Burin, "Absorption-induced confinement of lasing modes in diffusive random medium," Opt. Lett. 30, 2430-2432 (2005).
[CrossRef] [PubMed]

S. H. Chang, H. Cao, and S. T. Ho, "Cavity formation and light propagation in partially ordered and completely random one-dimensional systems," IEEE J. Quantum Electron. 39, 364-374 (2003).
[CrossRef]

H. Cao, "Lasing in random media," Waves Random Media 13, R1-R39 (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, R025601 (2002).
[CrossRef]

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

Chabanov, A. A.

X. Wu, 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]

Chang, R. P. H.

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

Chang, S. H.

S. H. Chang, H. Cao, and S. T. Ho, "Cavity formation and light propagation in partially ordered and completely random one-dimensional systems," IEEE J. Quantum Electron. 39, 364-374 (2003).
[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]

Collier, B.

H. E. Türeci, A. D. Stone, and B. Collier, "Self-consistent multimode lasing theory for complex or random lasing media," Phys. Rev. A 74, 043822 (2006).
[CrossRef]

Deych, L. I.

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

Dutra, S. M.

S. M. Dutra and G. Nienhuis, "Quantized mode of a leaky cavity," Phys. Rev. A 62, 063805 (2000).
[CrossRef]

Frolov, S. V.

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

Ge, L.

H. E. Türeci, A. D. Stone, and L. Ge, "Theory of the spatial structure of non-linear lasing modes," http://arxiv.org/PSlowbarcache/cond-mat/pdf/0610/0610229v1.pdf.

Hackenbroich, G.

G. Hackenbroich, "Statistical theory of multimode random lasers," J. Phys. A 38, 10537-10543 (2005).
[CrossRef]

Ho, S. T.

S. H. Chang, H. Cao, and S. T. Ho, "Cavity formation and light propagation in partially ordered and completely random one-dimensional systems," IEEE J. Quantum Electron. 39, 364-374 (2003).
[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]

Jiang, X. Y.

X. Y. Jiang and C. M. Soukoulis, "Localized random lasing modes and a path for observing localization," Phys. Rev. E 65, 025601 (2002).
[CrossRef]

X. Y. Jiang and C. M. Soukoulis, "Symmetry between absorption and amplification in disordered media," Phys. Rev. B 59, R9007-R9010 (1999).
[CrossRef]

Kogelnik, H.

H. Kogelnik and C. V. Shank, "Coupled-wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327-2335 (1972).
[CrossRef]

Kottos, T.

T. Kottos, "Statistics of resonances and delay times in random media: beyond random matrix theory," J. Phys. A 38, 10761-10786 (2005).
[CrossRef]

Lagendijk, A.

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

Letokhov, V. S.

V. S. Letokhov, "Quantum statistics of multi-mode radiation from an ensemble of atoms," Sov. Phys. JETP 26, 1246-1251 (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, R025601 (2002).
[CrossRef]

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

Liu, C.

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

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]

Misirpashaev, T. Sh.

T. Sh. Misirpashaev and C. W. J. Beenakker, "Lasing threshold and mode competition in chaotic cavities," Phys. Rev. A 57, 2041-2045 (1998).
[CrossRef]

Mosk, A. P.

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

Nienhuis, G.

S. M. Dutra and G. Nienhuis, "Quantized mode of a leaky cavity," Phys. Rev. A 62, 063805 (2000).
[CrossRef]

Patra, M.

M. Patra, "Decay rate distributions of disordered slabs and application to random lasers," Phys. Rev. E 67, 016603 (2003).
[CrossRef]

Polson, R. C.

R. C. Polson and Z. V. Vardeny, "Organic random lasers in the weak-scattering regime," Phys. Rev. B 71, 045205 (2005).
[CrossRef]

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]

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, C. Liu, and R. P. H. Chang, "Investigation of random lasers with resonant feedback," Phys. Rev. A 64, 063808 (2001).
[CrossRef]

Sebbah, P.

C. Vanneste, P. Sebbah, and H. Cao, "Lasing with coherent feedback in the diffusive regime," 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]

Shank, C. V.

H. Kogelnik and C. V. Shank, "Coupled-wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327-2335 (1972).
[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]

Soukoulis, C. M.

X. Y. Jiang and C. M. Soukoulis, "Localized random lasing modes and a path for observing localization," Phys. Rev. E 65, 025601 (2002).
[CrossRef]

X. Y. Jiang and C. M. Soukoulis, "Symmetry between absorption and amplification in disordered media," Phys. Rev. B 59, R9007-R9010 (1999).
[CrossRef]

Stone, A. D.

H. E. Türeci, A. D. Stone, and B. Collier, "Self-consistent multimode lasing theory for complex or random lasing media," Phys. Rev. A 74, 043822 (2006).
[CrossRef]

H. E. Türeci, A. D. Stone, and L. Ge, "Theory of the spatial structure of non-linear lasing modes," http://arxiv.org/PSlowbarcache/cond-mat/pdf/0610/0610229v1.pdf.

Türeci, H. E.

H. E. Türeci, A. D. Stone, and B. Collier, "Self-consistent multimode lasing theory for complex or random lasing media," Phys. Rev. A 74, 043822 (2006).
[CrossRef]

H. E. Türeci, A. D. Stone, and L. Ge, "Theory of the spatial structure of non-linear lasing modes," http://arxiv.org/PSlowbarcache/cond-mat/pdf/0610/0610229v1.pdf.

van der Molen, K. L.

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 coherent feedback in the diffusive regime," 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.

R. C. Polson and Z. V. Vardeny, "Organic random lasers in the weak-scattering regime," Phys. Rev. B 71, 045205 (2005).
[CrossRef]

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

Wu, X.

X. Wu, 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. Burin, "Absorption-induced confinement of lasing modes in diffusive random medium," Opt. Lett. 30, 2430-2432 (2005).
[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, R025601 (2002).
[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]

Yamilov, A.

X. Wu, 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. Burin, "Absorption-induced confinement of lasing modes in diffusive random medium," Opt. Lett. 30, 2430-2432 (2005).
[CrossRef] [PubMed]

Yoshino, K.

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

Zakhidov, A. A.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. A. Zakhidov, and R. H. Baughman, "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]

IEEE J. Quantum Electron. (1)

S. H. Chang, H. Cao, and S. T. Ho, "Cavity formation and light propagation in partially ordered and completely random one-dimensional systems," IEEE J. Quantum Electron. 39, 364-374 (2003).
[CrossRef]

J. Appl. Phys. (1)

H. Kogelnik and C. V. Shank, "Coupled-wave theory of distributed feedback lasers," J. Appl. Phys. 43, 2327-2335 (1972).
[CrossRef]

J. Phys. A (2)

G. Hackenbroich, "Statistical theory of multimode random lasers," J. Phys. A 38, 10537-10543 (2005).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a), (b): Transmission T through a 1D random structure with n d = 2.0 , 1.05 as a function of vacuum wave vector k 0 . (c) Frequencies k 0 r and normalized decay rates k 0 i k 0 i of the quasi modes in the random systems with n d = 2.0 (solid squares) and n d = 1.05 (open circles), compared with the frequencies k 0 and normalized threshold gain k i k i of lasing modes in the same systems with n d = 2.0 (plus signs) and n d = 1.05 (crosses) under uniform excitation. (d) Normalized frequency spacing Δ k 0 r Δ k 0 r of neighboring quasi modes in the random systems with n d = 2.0 (solid squares) and n d = 1.05 (open circles), compared with the normalized frequency spacing Δ k 0 Δ k 0 of neighboring lasing modes in the same systems with n d = 2.0 (plus signs) and n d = 1.05 (crosses) under uniform excitation.

Fig. 2
Fig. 2

Spatial intensity distributions of quasi modes (black solid curve) and the corresponding lasing modes in the presence of global gain (red dashed curve) or local gain (blue dotted curve). The pumped region is between the two vertical lines, L p = 11.87 μ m . (a) For the mode marked A in Fig. 1a, λ = 646 nm , n d = 2.0 . (b) For the mode marked B in Fig. 1b, λ = 549 nm , n d = 1.05 .

Fig. 3
Fig. 3

(a) Normalized threshold gain k i k i versus the frequency k 0 of lasing modes in the random systems with n d = 2.0 (solid squares) and n d = 1.05 (open circles) under local excitation (between the two vertical lines in Fig. 2). (b) Normalized frequency spacing Δ k 0 Δ k 0 of neighboring lasing modes in the systems with n d = 2.0 (solid squares) and n d = 1.05 (open circles) under local excitation.

Fig. 4
Fig. 4

Threshold gain k i k i of lasing modes in the (original) random system of length 24.1 μ m with local excitation in the central region of length 11.87 μ m (solid squares), compared with the threshold gain of lasing modes in the reduced system of length 11.87 μ m under uniform excitation (open circles) and the threshold gain of lasing modes in the homogeneous medium with n eff under local excitation in the region of length 11.87 μ m . (a) n d = 2.0 , n eff = 1.3361 ; (b) n d = 1.05 , n eff = 1.0168 .

Equations (1)

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( p 1 q 1 ) = M ( p 0 q 0 ) ,

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