Abstract

Time-dependent model is presented to simulate random lasers in the presence of an inhomogeneous gain medium. PbSe quantum dots (QDs) with an arbitrary size distribution are treated as an inhomogeneous gain medium. By introducing inhomogeneity of the PbSe QDs in polarization, rate, and Maxwell’s equations, our model is constructed for a one-dimensional disordered system. By employing the finite difference time-domain method, the governing equations are numerically solved and lasing spectra and spatial distribution of the electric field are calculated. The effect of increasing the pumping rate on the laser characteristics is investigated. The results show that the number of lasing modes and their intensities increase with pumping rate. It is also demonstrated that the emission spectra depend on the standard deviation of the Gaussian distribution function. Increasing the standard deviation leads to reduction of the laser intensity.

© 2013 Optical Society of America

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2012 (2)

A. G. Ardakani, M. G. G. Ali, S. M. Mahdavi, and A. R. Bahrampour, “Mode analysis of fiber Bragg grating random lasers in the presence of mode competition,” Opt. Laser Technol. 44, 969–975 (2012).
[CrossRef]

A. G. Ardakani, A. R. Bahrampour, S. M. Mahdavi, and M. G. G. Ali, “Numerical study of random lasing in three dimensional amplifying disordered media,” Opt. Commun. 285, 1314–1322 (2012).
[CrossRef]

2011 (5)

C. Cheng, H. Jiang, D. Ma, and X. Cheng, “An optical fiber glass containing PbSe quantum dots,” Opt. Commun. 284, 4491–4495 (2011).
[CrossRef]

F.-F. Pang, J. Wang, X.-L. Zeng, Z.-Y. Chen, and T.-Y. Wang, “PbSe quantum dots for an evanescent wave excited fiber amplifier,” J. Shanghai Univ. 15, 119–122 (2011).
[CrossRef]

J. Heo, Z. Jiang, J. Xu, and P. Bhattacharya, “Coherent and directional emission at 1.55 μm from PbSe colloidal quantum dot electroluminescent device on silicon,” Opt. Express 19, 26394–26398 (2011).
[CrossRef]

Y. Chen, J. Herrnsdorf, B. Guilhabert, Y. Zhang, I. M. Watson, E. Gu, N. Laurand, and M. D. Dawson, “Colloidal quantum dot random laser,” Opt. Express 19, 2996–3003 (2011).
[CrossRef]

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B 84, 094204 (2011).
[CrossRef]

2010 (1)

2009 (6)

A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
[CrossRef]

H. Fujiwara, Y. Hamabata, and K. Sasaki, “Numerical analysis of resonant and lasing properties at a defect region within a random structure,” Opt. Express 17, 3970–3977 (2009).
[CrossRef]

J. Lu, J. Liu, H. Liu, K. Wang, and S. Wang, “Theoretical investigation on temporal properties of random lasers pumped by femtosecond-lasing pulses,” Opt. Commun. 282, 2104–2109 (2009).
[CrossRef]

R. Frank, A. Lubatsch, and J. Kroha, “Light transport and localization in diffusive random lasers,” J. Opt. A 11, 114012 (2009).
[CrossRef]

C. Jiang, “Ultrabroadband gain characteristics of a quantum-dot-doped fiber amplifier,” IEEE J. Sel. Top. Quantum Electron. 15, 140–144 (2009).
[CrossRef]

H. Liu, J. Liu, J. Lu, and K. Wang, “Spectral time evolution of polarized modes under local pumping in a two-dimensional random medium,” J. Opt. A 11, 065202 (2009).
[CrossRef]

2008 (3)

J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
[CrossRef]

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

C. Cheng, “A multiquantum-dot-doped fiber amplifier with characteristics of broadband, flat gain, and low noise,” J. Lightwave Technol. 26, 1404–1410 (2008).
[CrossRef]

2007 (2)

C. Cheng and H. Zhang, “Characteristics of bandwidth, gain and noise of a PbSe quantum dot-doped fiber amplifier,” Opt. Commun. 277, 372–378 (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]

2006 (2)

2005 (2)

2004 (2)

R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85, 1289–1291 (2004).
[CrossRef]

J. M. Pietryga, R. D. Schaller, D. Werder, M. H. Stewart, V. I. Klimov, and J. A. Hollingsworth, “Pushing the band gap envelope:  mid-infrared emitting colloidal PbSe quantum dots,” J. Am. Chem. Soc. 126, 11752–11753 (2004).
[CrossRef]

2003 (1)

J. S. Steckel, S. Coe-Sullivan, V. Bulovic, and M. G. Bawendi, “1.3 um to 1.55 um tunable electroluminescence from PbSe quantum dots embedded within an organic device,” Adv. Mater. 15, 1862–1866 (2003).
[CrossRef]

2002 (3)

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

X. Y. Jiang and C. M. Soukoulis, “Localized random lasing modes and a path for observing localization,” Phys. Rev. E 65, 025601 (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]

2000 (3)

D. Wiersma, “The smallest random laser,” Nature 406, 132–135 (2000).
[CrossRef]

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

H. Cao, J. Y. Xu, and D. Z. Zhang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

1999 (1)

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)

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]

1996 (1)

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[CrossRef]

1995 (1)

N. M. Lawandy and R. M. Balachandra, “Random laser?” Nature 373, 204–204 (1995).
[CrossRef]

1994 (1)

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

1986 (1)

V. M. Markushev, V. F. Zolim, and C. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
[CrossRef]

1968 (1)

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

Ali, M. G. G.

A. G. Ardakani, M. G. G. Ali, S. M. Mahdavi, and A. R. Bahrampour, “Mode analysis of fiber Bragg grating random lasers in the presence of mode competition,” Opt. Laser Technol. 44, 969–975 (2012).
[CrossRef]

A. G. Ardakani, A. R. Bahrampour, S. M. Mahdavi, and M. G. G. Ali, “Numerical study of random lasing in three dimensional amplifying disordered media,” Opt. Commun. 285, 1314–1322 (2012).
[CrossRef]

Ardakani, A. G.

A. G. Ardakani, A. R. Bahrampour, S. M. Mahdavi, and M. G. G. Ali, “Numerical study of random lasing in three dimensional amplifying disordered media,” Opt. Commun. 285, 1314–1322 (2012).
[CrossRef]

A. G. Ardakani, M. G. G. Ali, S. M. Mahdavi, and A. R. Bahrampour, “Mode analysis of fiber Bragg grating random lasers in the presence of mode competition,” Opt. Laser Technol. 44, 969–975 (2012).
[CrossRef]

Askari, A. A.

A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
[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]

Bahrampour, A. R.

A. G. Ardakani, A. R. Bahrampour, S. M. Mahdavi, and M. G. G. Ali, “Numerical study of random lasing in three dimensional amplifying disordered media,” Opt. Commun. 285, 1314–1322 (2012).
[CrossRef]

A. G. Ardakani, M. G. G. Ali, S. M. Mahdavi, and A. R. Bahrampour, “Mode analysis of fiber Bragg grating random lasers in the presence of mode competition,” Opt. Laser Technol. 44, 969–975 (2012).
[CrossRef]

A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
[CrossRef]

Balachandra, R. M.

N. M. Lawandy and R. M. Balachandra, “Random laser?” Nature 373, 204–204 (1995).
[CrossRef]

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

Bawendi, M. G.

J. S. Steckel, S. Coe-Sullivan, V. Bulovic, and M. G. Bawendi, “1.3 um to 1.55 um tunable electroluminescence from PbSe quantum dots embedded within an organic device,” Adv. Mater. 15, 1862–1866 (2003).
[CrossRef]

Bhattacharya, P.

J. Heo, Z. Jiang, J. Xu, and P. Bhattacharya, “Coherent and directional emission at 1.55 μm from PbSe colloidal quantum dot electroluminescent device on silicon,” Opt. Express 19, 26394–26398 (2011).
[CrossRef]

J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
[CrossRef]

Boeglin, A.

Briskina, C. M.

V. M. Markushev, V. F. Zolim, and C. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
[CrossRef]

Bulovic, V.

J. S. Steckel, S. Coe-Sullivan, V. Bulovic, and M. G. Bawendi, “1.3 um to 1.55 um tunable electroluminescence from PbSe quantum dots embedded within an organic device,” Adv. Mater. 15, 1862–1866 (2003).
[CrossRef]

Cao, H.

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

H. Cao, J. Y. Xu, and D. Z. Zhang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (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]

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]

Cauchi, S.

Cavalcanti, S. B.

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B 84, 094204 (2011).
[CrossRef]

Chang, R. P. 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]

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]

Chen, Y.

Chen, Z.

Chen, Z.-Y.

F.-F. Pang, J. Wang, X.-L. Zeng, Z.-Y. Chen, and T.-Y. Wang, “PbSe quantum dots for an evanescent wave excited fiber amplifier,” J. Shanghai Univ. 15, 119–122 (2011).
[CrossRef]

Cheng, C.

C. Cheng, H. Jiang, D. Ma, and X. Cheng, “An optical fiber glass containing PbSe quantum dots,” Opt. Commun. 284, 4491–4495 (2011).
[CrossRef]

C. Cheng, “A multiquantum-dot-doped fiber amplifier with characteristics of broadband, flat gain, and low noise,” J. Lightwave Technol. 26, 1404–1410 (2008).
[CrossRef]

C. Cheng and H. Zhang, “Characteristics of bandwidth, gain and noise of a PbSe quantum dot-doped fiber amplifier,” Opt. Commun. 277, 372–378 (2007).
[CrossRef]

Cheng, X.

C. Cheng, H. Jiang, D. Ma, and X. Cheng, “An optical fiber glass containing PbSe quantum dots,” Opt. Commun. 284, 4491–4495 (2011).
[CrossRef]

Coe-Sullivan, S.

J. S. Steckel, S. Coe-Sullivan, V. Bulovic, and M. G. Bawendi, “1.3 um to 1.55 um tunable electroluminescence from PbSe quantum dots embedded within an organic device,” Adv. Mater. 15, 1862–1866 (2003).
[CrossRef]

Cregut, O.

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]

Dawson, M. D.

Dorkenoo, K. D.

dos Santos, R. R.

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B 84, 094204 (2011).
[CrossRef]

Frank, R.

R. Frank, A. Lubatsch, and J. Kroha, “Light transport and localization in diffusive random lasers,” J. Opt. A 11, 114012 (2009).
[CrossRef]

Fujiwara, H.

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]

Gindre, D.

Gomes, A. S. L.

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

Gu, E.

Guilhabert, B.

Guo, H.

Hamabata, Y.

Heo, J.

J. Heo, Z. Jiang, J. Xu, and P. Bhattacharya, “Coherent and directional emission at 1.55 μm from PbSe colloidal quantum dot electroluminescent device on silicon,” Opt. Express 19, 26394–26398 (2011).
[CrossRef]

J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
[CrossRef]

Herrnsdorf, J.

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]

Hollingsworth, J. A.

J. M. Pietryga, R. D. Schaller, D. Werder, M. H. Stewart, V. I. Klimov, and J. A. Hollingsworth, “Pushing the band gap envelope:  mid-infrared emitting colloidal PbSe quantum dots,” J. Am. Chem. Soc. 126, 11752–11753 (2004).
[CrossRef]

Hoogland, S.

Howard, I.

Ilic, R.

J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
[CrossRef]

Jiang, C.

C. Jiang, “Ultrabroadband gain characteristics of a quantum-dot-doped fiber amplifier,” IEEE J. Sel. Top. Quantum Electron. 15, 140–144 (2009).
[CrossRef]

Jiang, H.

C. Cheng, H. Jiang, D. Ma, and X. Cheng, “An optical fiber glass containing PbSe quantum dots,” Opt. Commun. 284, 4491–4495 (2011).
[CrossRef]

Jiang, X.

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

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]

Jiang, Z.

Klein, S.

Klimov, V. I.

J. M. Pietryga, R. D. Schaller, D. Werder, M. H. Stewart, V. I. Klimov, and J. A. Hollingsworth, “Pushing the band gap envelope:  mid-infrared emitting colloidal PbSe quantum dots,” J. Am. Chem. Soc. 126, 11752–11753 (2004).
[CrossRef]

Kroha, J.

R. Frank, A. Lubatsch, and J. Kroha, “Light transport and localization in diffusive random lasers,” J. Opt. A 11, 114012 (2009).
[CrossRef]

Lagendijk, A.

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[CrossRef]

Laurand, N.

Lawandy, N. M.

N. M. Lawandy and R. M. Balachandra, “Random laser?” Nature 373, 204–204 (1995).
[CrossRef]

N. M. Lawandy, R. M. Balachandra, 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,” J. Exp. Theor. Phys. 26, 835–840 (1968).

Levina, L.

Liu, H.

H. Liu, J. Liu, J. Lu, and K. Wang, “Spectral time evolution of polarized modes under local pumping in a two-dimensional random medium,” J. Opt. A 11, 065202 (2009).
[CrossRef]

J. Lu, J. Liu, H. Liu, K. Wang, and S. Wang, “Theoretical investigation on temporal properties of random lasers pumped by femtosecond-lasing pulses,” Opt. Commun. 282, 2104–2109 (2009).
[CrossRef]

Liu, J.

H. Liu, J. Liu, J. Lu, and K. Wang, “Spectral time evolution of polarized modes under local pumping in a two-dimensional random medium,” J. Opt. A 11, 065202 (2009).
[CrossRef]

J. Lu, J. Liu, H. Liu, K. Wang, and S. Wang, “Theoretical investigation on temporal properties of random lasers pumped by femtosecond-lasing pulses,” Opt. Commun. 282, 2104–2109 (2009).
[CrossRef]

C. Wang and J. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A 353, 269–272 (2006).
[CrossRef]

Lius, Z. D.

Y. M. Xie and Z. D. Lius, “A new physical model on lasing in active random media,” Phys. Lett. A 341, 339–344(2005).
[CrossRef]

Lu, J.

J. Lu, J. Liu, H. Liu, K. Wang, and S. Wang, “Theoretical investigation on temporal properties of random lasers pumped by femtosecond-lasing pulses,” Opt. Commun. 282, 2104–2109 (2009).
[CrossRef]

H. Liu, J. Liu, J. Lu, and K. Wang, “Spectral time evolution of polarized modes under local pumping in a two-dimensional random medium,” J. Opt. A 11, 065202 (2009).
[CrossRef]

Lubatsch, A.

R. Frank, A. Lubatsch, and J. Kroha, “Light transport and localization in diffusive random lasers,” J. Opt. A 11, 114012 (2009).
[CrossRef]

Ma, D.

C. Cheng, H. Jiang, D. Ma, and X. Cheng, “An optical fiber glass containing PbSe quantum dots,” Opt. Commun. 284, 4491–4495 (2011).
[CrossRef]

Mahdavi, S. M.

A. G. Ardakani, A. R. Bahrampour, S. M. Mahdavi, and M. G. G. Ali, “Numerical study of random lasing in three dimensional amplifying disordered media,” Opt. Commun. 285, 1314–1322 (2012).
[CrossRef]

A. G. Ardakani, M. G. G. Ali, S. M. Mahdavi, and A. R. Bahrampour, “Mode analysis of fiber Bragg grating random lasers in the presence of mode competition,” Opt. Laser Technol. 44, 969–975 (2012).
[CrossRef]

Markushev, V. M.

V. M. Markushev, V. F. Zolim, and C. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
[CrossRef]

Mogilevtsev, D.

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B 84, 094204 (2011).
[CrossRef]

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]

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]

Oliveira, L. E.

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B 84, 094204 (2011).
[CrossRef]

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]

Pang, F.

Pang, F.-F.

F.-F. Pang, J. Wang, X.-L. Zeng, Z.-Y. Chen, and T.-Y. Wang, “PbSe quantum dots for an evanescent wave excited fiber amplifier,” J. Shanghai Univ. 15, 119–122 (2011).
[CrossRef]

Pietryga, J. M.

J. M. Pietryga, R. D. Schaller, D. Werder, M. H. Stewart, V. I. Klimov, and J. A. Hollingsworth, “Pushing the band gap envelope:  mid-infrared emitting colloidal PbSe quantum dots,” J. Am. Chem. Soc. 126, 11752–11753 (2004).
[CrossRef]

Pinheiro, F. A.

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B 84, 094204 (2011).
[CrossRef]

Polson, R. C.

R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85, 1289–1291 (2004).
[CrossRef]

Rahimi, L.

A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
[CrossRef]

Rooholamini, H.

A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
[CrossRef]

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]

Sargent, E. H.

Sasaki, K.

Sauvain, E.

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

Schaller, R. D.

J. M. Pietryga, R. D. Schaller, D. Werder, M. H. Stewart, V. I. Klimov, and J. A. Hollingsworth, “Pushing the band gap envelope:  mid-infrared emitting colloidal PbSe quantum dots,” J. Am. Chem. Soc. 126, 11752–11753 (2004).
[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]

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

Seelig, E. W.

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]

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

Steckel, J. S.

J. S. Steckel, S. Coe-Sullivan, V. Bulovic, and M. G. Bawendi, “1.3 um to 1.55 um tunable electroluminescence from PbSe quantum dots embedded within an organic device,” Adv. Mater. 15, 1862–1866 (2003).
[CrossRef]

Stewart, M. H.

J. M. Pietryga, R. D. Schaller, D. Werder, M. H. Stewart, V. I. Klimov, and J. A. Hollingsworth, “Pushing the band gap envelope:  mid-infrared emitting colloidal PbSe quantum dots,” J. Am. Chem. Soc. 126, 11752–11753 (2004).
[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]

Sukhovatkin, V.

Sun, X.

Topolancik, J.

J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
[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]

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]

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

Vardeny, Z. V.

R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85, 1289–1291 (2004).
[CrossRef]

Vollmer, F.

J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
[CrossRef]

Wang, C.

C. Wang and J. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A 353, 269–272 (2006).
[CrossRef]

Wang, J.

F.-F. Pang, J. Wang, X.-L. Zeng, Z.-Y. Chen, and T.-Y. Wang, “PbSe quantum dots for an evanescent wave excited fiber amplifier,” J. Shanghai Univ. 15, 119–122 (2011).
[CrossRef]

F. Pang, X. Sun, H. Guo, J. Yan, J. Wang, X. Zeng, Z. Chen, and T. Wang, “A PbS quantum dots fiber amplifier excited by evanescent wave,” Opt. Express 18, 14024–14030 (2010).
[CrossRef]

Wang, K.

H. Liu, J. Liu, J. Lu, and K. Wang, “Spectral time evolution of polarized modes under local pumping in a two-dimensional random medium,” J. Opt. A 11, 065202 (2009).
[CrossRef]

J. Lu, J. Liu, H. Liu, K. Wang, and S. Wang, “Theoretical investigation on temporal properties of random lasers pumped by femtosecond-lasing pulses,” Opt. Commun. 282, 2104–2109 (2009).
[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]

Wang, S.

J. Lu, J. Liu, H. Liu, K. Wang, and S. Wang, “Theoretical investigation on temporal properties of random lasers pumped by femtosecond-lasing pulses,” Opt. Commun. 282, 2104–2109 (2009).
[CrossRef]

Wang, T.

Wang, T.-Y.

F.-F. Pang, J. Wang, X.-L. Zeng, Z.-Y. Chen, and T.-Y. Wang, “PbSe quantum dots for an evanescent wave excited fiber amplifier,” J. Shanghai Univ. 15, 119–122 (2011).
[CrossRef]

Watson, I. M.

Werder, D.

J. M. Pietryga, R. D. Schaller, D. Werder, M. H. Stewart, V. I. Klimov, and J. A. Hollingsworth, “Pushing the band gap envelope:  mid-infrared emitting colloidal PbSe quantum dots,” J. Am. Chem. Soc. 126, 11752–11753 (2004).
[CrossRef]

Wiersma, D.

D. Wiersma, “The smallest random laser,” Nature 406, 132–135 (2000).
[CrossRef]

Wiersma, D. S.

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[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]

Xie, Y. M.

Y. M. Xie and Z. D. Lius, “A new physical model on lasing in active random media,” Phys. Lett. A 341, 339–344(2005).
[CrossRef]

Xu, J.

J. Heo, Z. Jiang, J. Xu, and P. Bhattacharya, “Coherent and directional emission at 1.55 μm from PbSe colloidal quantum dot electroluminescent device on silicon,” Opt. Express 19, 26394–26398 (2011).
[CrossRef]

J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
[CrossRef]

Xu, J. Y.

H. Cao, J. Y. Xu, and D. Z. Zhang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

Yan, J.

Yang, J.

J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics (Saunders College Publishing, 1991).

Zeng, X.

Zeng, X.-L.

F.-F. Pang, J. Wang, X.-L. Zeng, Z.-Y. Chen, and T.-Y. Wang, “PbSe quantum dots for an evanescent wave excited fiber amplifier,” J. Shanghai Univ. 15, 119–122 (2011).
[CrossRef]

Zhang, D. Z.

H. Cao, J. Y. Xu, and D. Z. Zhang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

Zhang, H.

C. Cheng and H. Zhang, “Characteristics of bandwidth, gain and noise of a PbSe quantum dot-doped fiber amplifier,” Opt. Commun. 277, 372–378 (2007).
[CrossRef]

Zhang, Y.

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, T.

J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
[CrossRef]

Zolim, V. F.

V. M. Markushev, V. F. Zolim, and C. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
[CrossRef]

Adv. Mater. (1)

J. S. Steckel, S. Coe-Sullivan, V. Bulovic, and M. G. Bawendi, “1.3 um to 1.55 um tunable electroluminescence from PbSe quantum dots embedded within an organic device,” Adv. Mater. 15, 1862–1866 (2003).
[CrossRef]

Appl. Phys. Lett. (3)

J. Yang, J. Heo, T. Zhu, J. Xu, J. Topolancik, F. Vollmer, R. Ilic, and P. Bhattacharya, “Enhanced photoluminescence from embedded PbSe colloidal quantum dots in silicon-based random photonic crystal microcavities,” Appl. Phys. Lett. 92, 261110 (2008).
[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]

R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85, 1289–1291 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C. Jiang, “Ultrabroadband gain characteristics of a quantum-dot-doped fiber amplifier,” IEEE J. Sel. Top. Quantum Electron. 15, 140–144 (2009).
[CrossRef]

J. Am. Chem. Soc. (1)

J. M. Pietryga, R. D. Schaller, D. Werder, M. H. Stewart, V. I. Klimov, and J. A. Hollingsworth, “Pushing the band gap envelope:  mid-infrared emitting colloidal PbSe quantum dots,” J. Am. Chem. Soc. 126, 11752–11753 (2004).
[CrossRef]

J. Exp. Theor. Phys. (1)

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

J. Lightwave Technol. (1)

J. Opt. A (2)

H. Liu, J. Liu, J. Lu, and K. Wang, “Spectral time evolution of polarized modes under local pumping in a two-dimensional random medium,” J. Opt. A 11, 065202 (2009).
[CrossRef]

R. Frank, A. Lubatsch, and J. Kroha, “Light transport and localization in diffusive random lasers,” J. Opt. A 11, 114012 (2009).
[CrossRef]

J. Shanghai Univ. (1)

F.-F. Pang, J. Wang, X.-L. Zeng, Z.-Y. Chen, and T.-Y. Wang, “PbSe quantum dots for an evanescent wave excited fiber amplifier,” J. Shanghai Univ. 15, 119–122 (2011).
[CrossRef]

Nature (3)

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

N. M. Lawandy and R. M. Balachandra, “Random laser?” Nature 373, 204–204 (1995).
[CrossRef]

D. Wiersma, “The smallest random laser,” Nature 406, 132–135 (2000).
[CrossRef]

Opt. Commun. (6)

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]

A. R. Bahrampour, H. Rooholamini, L. Rahimi, and A. A. Askari, “An inhomogeneous theoretical model for analysis of PbSe quantum-dot-doped fiber amplifier,” Opt. Commun. 282, 4449–4454 (2009).
[CrossRef]

C. Cheng, H. Jiang, D. Ma, and X. Cheng, “An optical fiber glass containing PbSe quantum dots,” Opt. Commun. 284, 4491–4495 (2011).
[CrossRef]

C. Cheng and H. Zhang, “Characteristics of bandwidth, gain and noise of a PbSe quantum dot-doped fiber amplifier,” Opt. Commun. 277, 372–378 (2007).
[CrossRef]

J. Lu, J. Liu, H. Liu, K. Wang, and S. Wang, “Theoretical investigation on temporal properties of random lasers pumped by femtosecond-lasing pulses,” Opt. Commun. 282, 2104–2109 (2009).
[CrossRef]

A. G. Ardakani, A. R. Bahrampour, S. M. Mahdavi, and M. G. G. Ali, “Numerical study of random lasing in three dimensional amplifying disordered media,” Opt. Commun. 285, 1314–1322 (2012).
[CrossRef]

Opt. Express (6)

Opt. Laser Technol. (1)

A. G. Ardakani, M. G. G. Ali, S. M. Mahdavi, and A. R. Bahrampour, “Mode analysis of fiber Bragg grating random lasers in the presence of mode competition,” Opt. Laser Technol. 44, 969–975 (2012).
[CrossRef]

Phys. Lett. A (2)

Y. M. Xie and Z. D. Lius, “A new physical model on lasing in active random media,” Phys. Lett. A 341, 339–344(2005).
[CrossRef]

C. Wang and J. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A 353, 269–272 (2006).
[CrossRef]

Phys. Rev. B (2)

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

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B 84, 094204 (2011).
[CrossRef]

Phys. Rev. E (2)

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[CrossRef]

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

Phys. Rev. Lett. (4)

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

H. Cao, J. Y. Xu, and D. Z. Zhang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

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

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]

Sov. J. Quantum Electron. (1)

V. M. Markushev, V. F. Zolim, and C. M. Briskina, “Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders,” Sov. J. Quantum Electron. 16, 281–283 (1986).
[CrossRef]

Other (1)

A. Yariv, Optical Electronics (Saunders College Publishing, 1991).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of 1D RL in which the blue and white layers simulate the inhomogeneous gain medium (PbSe QDs) and dielectric layer (TiO2), respectively.

Fig. 2.
Fig. 2.

(a) Emission and absorption cross section for PbSe QDs with R¯=5.5nm [24]. (b) Schematic of the energy levels of PbSe QDs. Absorption and nonradiative and radiative transitions are presented by dotted lines, thin solid lines, and bold solid lines, respectively [24].

Fig. 3.
Fig. 3.

Spectral intensity in arbitrary units versus wavelength for different values of pumping rates: (a) Pr=1×1014s1, (b) Pr=1×1016s1, and (c) Pr=1×1018s1.

Fig. 4.
Fig. 4.

Spatial distribution of the electric field in the random system for different values of pumping rates: (a) Pr=1×1014s1, (b) Pr=1×1016s1, and (c) Pr=1×1018s1. (d) Spectrum corresponding to the Fourier transform of the field amplitude of the passive medium.

Fig. 5.
Fig. 5.

Spectral intensity in arbitrary units versus wavelength for different values of standard deviation: (a) D=0.3nm, (b) D=0.4nm, (c) D=0.5nm, and (d) D=0.6nm.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

σe,ainh(ν)=0σe,ah(ν,R)P(R)dR,
σe,ah(ν,R)=Δν2π[(Δν/2)2+(νν0,e,a(R))2].
dn3(R,x,t)dt=Prn1(R,x,t)n3(R,x,t)τ32,
dn2(R,x,t)dt=n2(R,x,t)(1τ21+F)+n3(R,x,t)τ32+E(x,t)ω0(R)dPtransition(R,x,t)dt+Fn2qe(R,x,t),
dn1(R,x,t)dt=n1(R,x,t)(Pr+F)+n2(R,x,t)τ21E(x,t)ω0(R)dPtransition(R,x,t)dt+Fn1qe(R,x,t).
d2Ptransition(R,x,t)dt2+Δω0dPtransition(R,x,t)dt+ω0,a2Ptransition(R,x,t)=ka(R)Δna(R,x,t)E(x,t),
d2Ptransition(R,x,t)dt2+Δω0dPtransition(R,x,t)dt+ω0,e2Ptransition(R,x,t)=ke(R)Δne(R,x,t)E(x,t),
E(x,t)x=μ0H(x,t)t,
H(x,t)x=ε0εr(x)E(x,t)t+0Ptransition(R,x,t)tdR.
εr(x)={εgfor active layerεdfor dielectric layer.
P(R)=1D2πexp((RR¯)22D2).
n2(R,x,t)n1(R,x,t)=(Prτ211)P(R)Nq1+Pr(τ32τ21).

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