Abstract

We present a numerical study of lasing modes in diffusive random media with local pumping. The reabsorption of emitted light suppresses the feedback from the unpumped part of the sample and effectively reduces the system size. The lasing modes are dramatically different from the quasi modes of the passive system (without gain or absorption). Even if all the quasi modes of a passive diffusive system are extended across the entire sample, the lasing modes are still confined in the pumped volume with an exponential tail outside it. The reduction of effective system volume by absorption broadens the distribution of decay rates of quasi modes and facilitates the occurrence of discrete lasing peaks.

© 2005 Optical Society of America

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  1. H. Cao, Waves Random Media 13, R1 (2003).
    [CrossRef]
  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, Phys. Rev. Lett. 84, 5584 (2000).
    [CrossRef] [PubMed]
  3. X. Jiang and C. M. Soukoulis, Phys. Rev. Lett. 85, 70 (2000).
    [CrossRef] [PubMed]
  4. P. Sebbah and C. Vanneste, Phys. Rev. Lett. 87, 183903 (2001).
    [CrossRef]
  5. A. L. Burin, M. A. Ratner, H. Cao, and R. P.H. Chang, Phys. Rev. Lett. 87, 215503 (2001).
    [CrossRef]
  6. S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughman, Phys. Rev. B 59, R5284 (1999).
    [CrossRef]
  7. Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, C. Liu, and R. P.H. Chang, Phys. Rev. A 64, 063808 (2001).
    [CrossRef]
  8. R. C. Polson, A. Chipouline, and Z. V. Vardeny, Adv. Mater. (Weinheim) 13, 760 (2001).
    [CrossRef]
  9. H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, Phys. Rev. E 66, R025601 (2002).
    [CrossRef]
  10. V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 89, 016802 (2002).
    [CrossRef]
  11. R. C. Polson, M. E. Raikh, and Z. V. Vardeny, C. R. Acad. Sci. Ser IV Phys., Astrophys. 3, 500 (2002).
  12. A. D. Mirlin, Phys. Rep. 326, 259 (2000).
    [CrossRef]
  13. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2000).
  14. M. C.W. van Rossum and Th. M. Nieuvenhuizen, Rev. Mod. Phys. 71, 313 (1999).
    [CrossRef]
  15. S. H. Chang, “FDTD modeling of light propagation and correlations in active random media,” Ph.D. dissertation (Department of Electrical and Computer Engineering, Northwestern University, 2003).
  16. A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, Phys. Rev. Lett. 90, 203903 (2003).
    [CrossRef]
  17. A. L. Burin, H. Cao, and M. A. Ratner, Physica B 338, 112 (2003).
    [CrossRef]
  18. M. Patra, Phys. Rev. E 67, 016603 (2003).
    [CrossRef]
  19. A. Yamilov and H. Cao, Phys. Rev. A 69, 031803 (2004).
    [CrossRef]

2004

A. Yamilov and H. Cao, Phys. Rev. A 69, 031803 (2004).
[CrossRef]

2003

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef]

A. L. Burin, H. Cao, and M. A. Ratner, Physica B 338, 112 (2003).
[CrossRef]

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

H. Cao, Waves Random Media 13, R1 (2003).
[CrossRef]

2002

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, Phys. Rev. E 66, R025601 (2002).
[CrossRef]

V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 89, 016802 (2002).
[CrossRef]

R. C. Polson, M. E. Raikh, and Z. V. Vardeny, C. R. Acad. Sci. Ser IV Phys., Astrophys. 3, 500 (2002).

2001

P. Sebbah and C. Vanneste, Phys. Rev. Lett. 87, 183903 (2001).
[CrossRef]

A. L. Burin, M. A. Ratner, H. Cao, and R. P.H. Chang, Phys. Rev. Lett. 87, 215503 (2001).
[CrossRef]

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, C. Liu, and R. P.H. Chang, Phys. Rev. A 64, 063808 (2001).
[CrossRef]

R. C. Polson, A. Chipouline, and Z. V. Vardeny, Adv. Mater. (Weinheim) 13, 760 (2001).
[CrossRef]

2000

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P.H. Chang, Phys. Rev. Lett. 84, 5584 (2000).
[CrossRef] [PubMed]

X. Jiang and C. M. Soukoulis, Phys. Rev. Lett. 85, 70 (2000).
[CrossRef] [PubMed]

A. D. Mirlin, Phys. Rep. 326, 259 (2000).
[CrossRef]

1999

M. C.W. van Rossum and Th. M. Nieuvenhuizen, Rev. Mod. Phys. 71, 313 (1999).
[CrossRef]

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughman, Phys. Rev. B 59, R5284 (1999).
[CrossRef]

Apalkov, V. M.

V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 89, 016802 (2002).
[CrossRef]

Baughman, R. H.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughman, Phys. Rev. B 59, R5284 (1999).
[CrossRef]

Burin, A. L.

A. L. Burin, H. Cao, and M. A. Ratner, Physica B 338, 112 (2003).
[CrossRef]

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, Phys. Rev. E 66, R025601 (2002).
[CrossRef]

A. L. Burin, M. A. Ratner, H. Cao, and R. P.H. Chang, Phys. Rev. Lett. 87, 215503 (2001).
[CrossRef]

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, C. Liu, and R. P.H. Chang, Phys. Rev. A 64, 063808 (2001).
[CrossRef]

Cao, H.

A. Yamilov and H. Cao, Phys. Rev. A 69, 031803 (2004).
[CrossRef]

A. L. Burin, H. Cao, and M. A. Ratner, Physica B 338, 112 (2003).
[CrossRef]

H. Cao, Waves Random Media 13, R1 (2003).
[CrossRef]

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, Phys. Rev. E 66, R025601 (2002).
[CrossRef]

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, C. Liu, and R. P.H. Chang, Phys. Rev. A 64, 063808 (2001).
[CrossRef]

A. L. Burin, M. A. Ratner, H. Cao, and R. P.H. Chang, Phys. Rev. Lett. 87, 215503 (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, Phys. Rev. Lett. 84, 5584 (2000).
[CrossRef] [PubMed]

Chabanov, A. A.

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef]

Chang, R. P.H.

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, C. Liu, and R. P.H. Chang, Phys. Rev. A 64, 063808 (2001).
[CrossRef]

A. L. Burin, M. A. Ratner, H. Cao, and R. P.H. Chang, Phys. Rev. Lett. 87, 215503 (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, Phys. Rev. Lett. 84, 5584 (2000).
[CrossRef] [PubMed]

Chang, S. H.

S. H. Chang, “FDTD modeling of light propagation and correlations in active random media,” Ph.D. dissertation (Department of Electrical and Computer Engineering, Northwestern University, 2003).

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, Phys. Rev. Lett. 84, 5584 (2000).
[CrossRef] [PubMed]

Chipouline, A.

R. C. Polson, A. Chipouline, and Z. V. Vardeny, Adv. Mater. (Weinheim) 13, 760 (2001).
[CrossRef]

Frolov, S. V.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughman, Phys. Rev. B 59, R5284 (1999).
[CrossRef]

Genack, A. Z.

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2000).

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, Phys. Rev. Lett. 84, 5584 (2000).
[CrossRef] [PubMed]

Jiang, X.

X. Jiang and C. M. Soukoulis, Phys. Rev. Lett. 85, 70 (2000).
[CrossRef] [PubMed]

Ling, Y.

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, Phys. Rev. E 66, R025601 (2002).
[CrossRef]

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, C. Liu, and R. P.H. Chang, 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, 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, Phys. Rev. Lett. 84, 5584 (2000).
[CrossRef] [PubMed]

Mirlin, A. D.

A. D. Mirlin, Phys. Rep. 326, 259 (2000).
[CrossRef]

Nieuvenhuizen, Th. M.

M. C.W. van Rossum and Th. M. Nieuvenhuizen, Rev. Mod. Phys. 71, 313 (1999).
[CrossRef]

Patra, M.

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

Polson, R. C.

R. C. Polson, M. E. Raikh, and Z. V. Vardeny, C. R. Acad. Sci. Ser IV Phys., Astrophys. 3, 500 (2002).

R. C. Polson, A. Chipouline, and Z. V. Vardeny, Adv. Mater. (Weinheim) 13, 760 (2001).
[CrossRef]

Raikh, M. E.

R. C. Polson, M. E. Raikh, and Z. V. Vardeny, C. R. Acad. Sci. Ser IV Phys., Astrophys. 3, 500 (2002).

V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 89, 016802 (2002).
[CrossRef]

Ratner, M. A.

A. L. Burin, H. Cao, and M. A. Ratner, Physica B 338, 112 (2003).
[CrossRef]

A. L. Burin, M. A. Ratner, H. Cao, and R. P.H. Chang, Phys. Rev. Lett. 87, 215503 (2001).
[CrossRef]

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, C. Liu, and R. P.H. Chang, Phys. Rev. A 64, 063808 (2001).
[CrossRef]

Sebbah, P.

P. Sebbah and C. Vanneste, 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, Phys. Rev. Lett. 84, 5584 (2000).
[CrossRef] [PubMed]

Shapiro, B.

V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 89, 016802 (2002).
[CrossRef]

Soukoulis, C. M.

X. Jiang and C. M. Soukoulis, Phys. Rev. Lett. 85, 70 (2000).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2000).

van Rossum, M. C.W.

M. C.W. van Rossum and Th. M. Nieuvenhuizen, Rev. Mod. Phys. 71, 313 (1999).
[CrossRef]

Vanneste, C.

P. Sebbah and C. Vanneste, Phys. Rev. Lett. 87, 183903 (2001).
[CrossRef]

Vardeny, Z. V.

R. C. Polson, M. E. Raikh, and Z. V. Vardeny, C. R. Acad. Sci. Ser IV Phys., Astrophys. 3, 500 (2002).

R. C. Polson, A. Chipouline, and Z. V. Vardeny, Adv. Mater. (Weinheim) 13, 760 (2001).
[CrossRef]

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughman, Phys. Rev. B 59, R5284 (1999).
[CrossRef]

Xu, J. Y.

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, 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, Phys. Rev. Lett. 84, 5584 (2000).
[CrossRef] [PubMed]

Yamilov, A.

A. Yamilov and H. Cao, Phys. Rev. A 69, 031803 (2004).
[CrossRef]

Yoshino, K.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughman, Phys. Rev. B 59, R5284 (1999).
[CrossRef]

Zakhidov, A.

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughman, Phys. Rev. B 59, R5284 (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, Phys. Rev. Lett. 84, 5584 (2000).
[CrossRef] [PubMed]

Zhang, Z. Q.

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef]

Adv. Mater. (Weinheim)

R. C. Polson, A. Chipouline, and Z. V. Vardeny, Adv. Mater. (Weinheim) 13, 760 (2001).
[CrossRef]

C. R. Acad. Sci. Ser IV Phys., Astrophys.

R. C. Polson, M. E. Raikh, and Z. V. Vardeny, C. R. Acad. Sci. Ser IV Phys., Astrophys. 3, 500 (2002).

Phys. Rep.

A. D. Mirlin, Phys. Rep. 326, 259 (2000).
[CrossRef]

Phys. Rev. A

Y. Ling, H. Cao, A. L. Burin, M. A. Ratner, C. Liu, and R. P.H. Chang, Phys. Rev. A 64, 063808 (2001).
[CrossRef]

A. Yamilov and H. Cao, Phys. Rev. A 69, 031803 (2004).
[CrossRef]

Phys. Rev. B

S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughman, Phys. Rev. B 59, R5284 (1999).
[CrossRef]

Phys. Rev. E

H. Cao, Y. Ling, J. Y. Xu, and A. L. Burin, Phys. Rev. E 66, R025601 (2002).
[CrossRef]

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

Phys. Rev. Lett.

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef]

V. M. Apalkov, M. E. Raikh, and B. Shapiro, Phys. Rev. Lett. 89, 016802 (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, Phys. Rev. Lett. 84, 5584 (2000).
[CrossRef] [PubMed]

X. Jiang and C. M. Soukoulis, Phys. Rev. Lett. 85, 70 (2000).
[CrossRef] [PubMed]

P. Sebbah and C. Vanneste, Phys. Rev. Lett. 87, 183903 (2001).
[CrossRef]

A. L. Burin, M. A. Ratner, H. Cao, and R. P.H. Chang, Phys. Rev. Lett. 87, 215503 (2001).
[CrossRef]

Physica B

A. L. Burin, H. Cao, and M. A. Ratner, Physica B 338, 112 (2003).
[CrossRef]

Rev. Mod. Phys.

M. C.W. van Rossum and Th. M. Nieuvenhuizen, Rev. Mod. Phys. 71, 313 (1999).
[CrossRef]

Waves Random Media

H. Cao, Waves Random Media 13, R1 (2003).
[CrossRef]

Other

S. H. Chang, “FDTD modeling of light propagation and correlations in active random media,” Ph.D. dissertation (Department of Electrical and Computer Engineering, Northwestern University, 2003).

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2000).

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Figures (2)

Fig. 1
Fig. 1

Spatial intensity distribution of (a) the quasi mode with the longest lifetime in a passive diffusive system, (b) the (first) lasing mode with gain inside the circular region near the center and no absorption outside it, (c) the (first) lasing mode with gain inside the circular region near the center and absorption outside it, (d) the (first) lasing mode with random medium beyond one l p (dashed circle) removed.

Fig. 2
Fig. 2

Radial dependence of the angularly integrated intensities of the modes shown in Fig. 1: (a) is compared with the diffusive mode profile; the tail of (c) is fitted with an exponential decay; the falloff of (d) outside the random medium is compared with r 1 .

Equations (1)

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σ ( ω ) = σ 0 2 1 + i ( ω ω 0 ) T 2 + σ 0 2 1 + i ( ω + ω 0 ) T 2 .

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