Abstract

We report numerical studies on temperature-tunable, multiple-scattering media with gain. We describe Monte Carlo simulations that model the behavior of such a system through a three-dimensional random walk of light in a temperature-dependent disordered medium with amplification. We compare the results of our model with previous experimental results on a disordered dielectric for which the scattering strength could be tuned by changing the external temperature. The agreement between the numerical and experimental results enables us to predict the spectral features of the emission from the tunable random laser under various conditions. Results obtained from new experimental data are consistent with the predictions of the simulations.

© 2004 Optical Society of America

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  1. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, San Diego, Calif., 1995).
  2. G. L. J. A. Rikken and B. A. van Tiggelen, “Observation of magneto-transverse light diffusion,” Nature 381, 54–55 (1996).
    [CrossRef]
  3. A. Sparenberg, G. L. J. A. Rikken, and B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–760 (1997).
    [CrossRef]
  4. F. Scheffold and G. Maret, “Universal conductance fluctuations of light,” Phys. Rev. Lett. 81, 5800–5803 (1998).
    [CrossRef]
  5. Y. Kuga and A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 1, 831–835 (1984).
    [CrossRef]
  6. M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
    [CrossRef] [PubMed]
  7. P. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
    [CrossRef] [PubMed]
  8. P. W. Anderson, “The question of classical localization: a theory of white paint?,” Philos. Mag. B 52, 505–509 (1985).
    [CrossRef]
  9. Sajeev John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef] [PubMed]
  10. V. S. Letokhov, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 26, 835–840 (1968).
  11. 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]
  12. S. John and G. Pang, “Theory of lasing in a multiple-scattering medium,” Phys. Rev. A 54, 3642–3652 (1996).
    [CrossRef] [PubMed]
  13. D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
    [CrossRef]
  14. G. A. Berger, M. Kempe, and A. Z. Genack, “Dynamics of stimulated emission from random media,” Phys. Rev. E 56, 6118–6122 (1997).
    [CrossRef]
  15. S. Mujumdar and H. Ramachandran, “Spectral features of emissions from random amplifying media,” Opt. Commun. 176, 31–41 (2000).
    [CrossRef]
  16. 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]
  17. Xunya Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70–73 (2000).
    [CrossRef] [PubMed]
  18. C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).
    [CrossRef]
  19. A. Yu. Zyuzin, “Transmission fluctuations and spectral rigidity of lasing states in a random amplifying medium,” Phys. Rev. E 51, 5274–5278 (1995).
    [CrossRef]
  20. K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
    [CrossRef]
  21. S. Chandrasekhar, Liquid Crystals (Cambridge University, Cambridge, UK, 1977).
  22. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford, New York, 1993).
  23. D. S. Wiersma, M. Colocci, R. Righini, and F. Aliev, “Temperature-controlled light diffusion in random media,” Phys. Rev. B 64, 144208 (2001).
    [CrossRef]
  24. D. S. Wiersma and S. Cavalieri, “A temperature-tunable random laser,” Nature 414, 708–709 (2001).
    [CrossRef] [PubMed]
  25. D. S. Wiersma and S. Cavalieri, “Temperature-controlled random laser action in liquid crystal infiltrated systems,” Phys. Rev. E 66, 056612 (2002).
    [CrossRef]

2002

D. S. Wiersma and S. Cavalieri, “Temperature-controlled random laser action in liquid crystal infiltrated systems,” Phys. Rev. E 66, 056612 (2002).
[CrossRef]

2001

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

D. S. Wiersma, M. Colocci, R. Righini, and F. Aliev, “Temperature-controlled light diffusion in random media,” Phys. Rev. B 64, 144208 (2001).
[CrossRef]

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

2000

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

S. Mujumdar and H. Ramachandran, “Spectral features of emissions from random amplifying media,” Opt. Commun. 176, 31–41 (2000).
[CrossRef]

1999

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]

K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[CrossRef]

1998

F. Scheffold and G. Maret, “Universal conductance fluctuations of light,” Phys. Rev. Lett. 81, 5800–5803 (1998).
[CrossRef]

1997

A. Sparenberg, G. L. J. A. Rikken, and B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–760 (1997).
[CrossRef]

G. A. Berger, M. Kempe, and A. Z. Genack, “Dynamics of stimulated emission from random media,” Phys. Rev. E 56, 6118–6122 (1997).
[CrossRef]

1996

S. John and G. Pang, “Theory of lasing in a multiple-scattering medium,” Phys. Rev. A 54, 3642–3652 (1996).
[CrossRef] [PubMed]

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

G. L. J. A. Rikken and B. A. van Tiggelen, “Observation of magneto-transverse light diffusion,” Nature 381, 54–55 (1996).
[CrossRef]

1995

A. Yu. Zyuzin, “Transmission fluctuations and spectral rigidity of lasing states in a random amplifying medium,” Phys. Rev. E 51, 5274–5278 (1995).
[CrossRef]

1994

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]

1987

Sajeev John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

1985

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

P. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

P. W. Anderson, “The question of classical localization: a theory of white paint?,” Philos. Mag. B 52, 505–509 (1985).
[CrossRef]

1984

1968

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

Aliev, F.

D. S. Wiersma, M. Colocci, R. Righini, and F. Aliev, “Temperature-controlled light diffusion in random media,” Phys. Rev. B 64, 144208 (2001).
[CrossRef]

Anderson, P. W.

P. W. Anderson, “The question of classical localization: a theory of white paint?,” Philos. Mag. B 52, 505–509 (1985).
[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]

Berger, G. A.

G. A. Berger, M. Kempe, and A. Z. Genack, “Dynamics of stimulated emission from random media,” Phys. Rev. E 56, 6118–6122 (1997).
[CrossRef]

Busch, K.

K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[CrossRef]

Cao, 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]

Cavalieri, S.

D. S. Wiersma and S. Cavalieri, “Temperature-controlled random laser action in liquid crystal infiltrated systems,” Phys. Rev. E 66, 056612 (2002).
[CrossRef]

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

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]

Colocci, M.

D. S. Wiersma, M. Colocci, R. Righini, and F. Aliev, “Temperature-controlled light diffusion in random media,” Phys. Rev. B 64, 144208 (2001).
[CrossRef]

Genack, A. Z.

G. A. Berger, M. Kempe, and A. Z. Genack, “Dynamics of stimulated emission from random media,” Phys. Rev. E 56, 6118–6122 (1997).
[CrossRef]

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]

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]

Ishimaru, A.

Jiang, Xunya

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

John, S.

K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (1999).
[CrossRef]

S. John and G. Pang, “Theory of lasing in a multiple-scattering medium,” Phys. Rev. A 54, 3642–3652 (1996).
[CrossRef] [PubMed]

John, Sajeev

Sajeev John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Kempe, M.

G. A. Berger, M. Kempe, and A. Z. Genack, “Dynamics of stimulated emission from random media,” Phys. Rev. E 56, 6118–6122 (1997).
[CrossRef]

Kuga, Y.

Lagendijk, A.

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

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

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).

Maret, G.

F. Scheffold and G. Maret, “Universal conductance fluctuations of light,” Phys. Rev. Lett. 81, 5800–5803 (1998).
[CrossRef]

P. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

Mujumdar, S.

S. Mujumdar and H. Ramachandran, “Spectral features of emissions from random amplifying media,” Opt. Commun. 176, 31–41 (2000).
[CrossRef]

Pang, G.

S. John and G. Pang, “Theory of lasing in a multiple-scattering medium,” Phys. Rev. A 54, 3642–3652 (1996).
[CrossRef] [PubMed]

Ramachandran, H.

S. Mujumdar and H. Ramachandran, “Spectral features of emissions from random amplifying media,” Opt. Commun. 176, 31–41 (2000).
[CrossRef]

Righini, R.

D. S. Wiersma, M. Colocci, R. Righini, and F. Aliev, “Temperature-controlled light diffusion in random media,” Phys. Rev. B 64, 144208 (2001).
[CrossRef]

Rikken, G. L. J. A.

A. Sparenberg, G. L. J. A. Rikken, and B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–760 (1997).
[CrossRef]

G. L. J. A. Rikken and B. A. van Tiggelen, “Observation of magneto-transverse light diffusion,” Nature 381, 54–55 (1996).
[CrossRef]

Sauvain, E.

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

Scheffold, F.

F. Scheffold and G. Maret, “Universal conductance fluctuations of light,” Phys. Rev. Lett. 81, 5800–5803 (1998).
[CrossRef]

Sebbah, P.

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, 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.

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

Sparenberg, A.

A. Sparenberg, G. L. J. A. Rikken, and B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–760 (1997).
[CrossRef]

van Albada, M. P.

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

van Tiggelen, B. A.

A. Sparenberg, G. L. J. A. Rikken, and B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–760 (1997).
[CrossRef]

G. L. J. A. Rikken and B. A. van Tiggelen, “Observation of magneto-transverse light diffusion,” Nature 381, 54–55 (1996).
[CrossRef]

Vanneste, C.

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).
[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 and S. Cavalieri, “Temperature-controlled random laser action in liquid crystal infiltrated systems,” Phys. Rev. E 66, 056612 (2002).
[CrossRef]

D. S. Wiersma, M. Colocci, R. Righini, and F. Aliev, “Temperature-controlled light diffusion in random media,” Phys. Rev. B 64, 144208 (2001).
[CrossRef]

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

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

Wolf, P.

P. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[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]

Zyuzin, A. Yu.

A. Yu. Zyuzin, “Transmission fluctuations and spectral rigidity of lasing states in a random amplifying medium,” Phys. Rev. E 51, 5274–5278 (1995).
[CrossRef]

J. Opt. Soc. Am. A

Nature

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

G. L. J. A. Rikken and B. A. van Tiggelen, “Observation of magneto-transverse light diffusion,” Nature 381, 54–55 (1996).
[CrossRef]

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]

Opt. Commun.

S. Mujumdar and H. Ramachandran, “Spectral features of emissions from random amplifying media,” Opt. Commun. 176, 31–41 (2000).
[CrossRef]

Philos. Mag. B

P. W. Anderson, “The question of classical localization: a theory of white paint?,” Philos. Mag. B 52, 505–509 (1985).
[CrossRef]

Phys. Rev. A

S. John and G. Pang, “Theory of lasing in a multiple-scattering medium,” Phys. Rev. A 54, 3642–3652 (1996).
[CrossRef] [PubMed]

Phys. Rev. B

D. S. Wiersma, M. Colocci, R. Righini, and F. Aliev, “Temperature-controlled light diffusion in random media,” Phys. Rev. B 64, 144208 (2001).
[CrossRef]

Phys. Rev. E

D. S. Wiersma and S. Cavalieri, “Temperature-controlled random laser action in liquid crystal infiltrated systems,” Phys. Rev. E 66, 056612 (2002).
[CrossRef]

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

G. A. Berger, M. Kempe, and A. Z. Genack, “Dynamics of stimulated emission from random media,” Phys. Rev. E 56, 6118–6122 (1997).
[CrossRef]

A. Yu. Zyuzin, “Transmission fluctuations and spectral rigidity of lasing states in a random amplifying medium,” Phys. Rev. E 51, 5274–5278 (1995).
[CrossRef]

Phys. Rev. Lett.

K. Busch and S. John, “Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum,” Phys. Rev. Lett. 83, 967–970 (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]

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

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

Sajeev John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

P. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

A. Sparenberg, G. L. J. A. Rikken, and B. A. van Tiggelen, “Observation of photonic magnetoresistance,” Phys. Rev. Lett. 79, 757–760 (1997).
[CrossRef]

F. Scheffold and G. Maret, “Universal conductance fluctuations of light,” Phys. Rev. Lett. 81, 5800–5803 (1998).
[CrossRef]

Sov. Phys. JETP

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

Other

S. Chandrasekhar, Liquid Crystals (Cambridge University, Cambridge, UK, 1977).

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford, New York, 1993).

P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, San Diego, Calif., 1995).

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Figures (7)

Fig. 1
Fig. 1

Narrowing of the emission as a function of pump energy seen in the simulations. Above 0.06 mJ, the system reaches its threshold and the bandwidth falls rapidly. At an operating pump energy of 0.12 mJ, the bandwidth at 27.3 °C is 23 nm. At 27.3 °C, D=7230 m2/s, as measured in experiments.25

Fig. 2
Fig. 2

Calculated variation of emission bandwidth as a function of the diffusion constant. The bandwidth steadily decreases with decreasing diffusion constant. The inset shows the variation of the diffusion constant with temperature measured in the experiments on the sample SK11+7CB+DCM with overall dye concentration of 1.1 mM.25 Above 42.5 °C, the diffusion constant diverges as the glass matrix and the liquid crystal are nearly index-matched.

Fig. 3
Fig. 3

(a) Spectral profiles as seen in the simulations at two different temperatures: curve I, T>43.2 °C; curve II, T=28.6 °C. Curve II is narrower by a factor of ∼2. Operating pump energy, 0.12 mJ. (b) Experimentally observed spectral profiles of the emission at two different temperatures: curve I, T=75.2 °C; curve II, T=35 °C. Curve II is scaled down by a factor of 10 and is narrower by about a factor of 2.5. Operating pump intensity, 4.5 mJ. The concentration of the dye in both experiments and simulations was 1.1 mM.

Fig. 4
Fig. 4

(a) Variation of emission bandwidth with temperature as seen in the numerical simulations. Above 43.2 °C the bandwidth is 55 nm and narrows by a factor of 2 to 27 nm at a temperature of 27 °C. The narrowing is rapid at ∼43 °C, agreeing with the experimental observations. The isotropic–nematic phase transition carries the system above threshold at temperatures below 43 °C. (b) Experimentally observed variation of the emission bandwidth. Above 43 °C, the emission is primarily broadband. The bandwidth starts collapsing from 73.4 nm at 45.4 °C to 29.8 nm at 30.8 °C after which it decreases slowly to ∼27 nm.

Fig. 5
Fig. 5

(a) Maximum intensity of the simulated random laser with temperature. At temperatures above 43.2 °C the intensity remains low, and the random laser is in an OFF state. Below 30 °C the random laser is in the ON state and lases with a high peak intensity. (b) Peak intensity of emission observed in the experiments as a function of temperature.

Fig. 6
Fig. 6

(a) Bandwidth of emission versus temperature when the dye concentration in the sample is doubled to 2.2 mM, as seen in the simulations. The consequent reduction in the gain length results in spectral narrowing up to 20 nm, as compared with 28 nm in the case of a dye concentration of 1.1 mM. The range of tunability is from 53 nm to 20 nm. (b) Peak intensity of emission with temperature. The variation in intensity is larger compared with the case of 1.1-mM dye concentration.

Fig. 7
Fig. 7

(a) Experimental observation of emission bandwidth with temperature from a sample with an overall dye concentration of 2.2 mM. At low temperatures the bandwidth narrows to 21 nm compared with 28 nm in the earlier sample. (See Fig. 5.) The range of tunability is also changed to 69–21 nm compared with 53–20 nm, consistent with the simulations. (b) Observed peak intensity versus temperature.

Equations (7)

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

Lcr=π(g/3)1/2.
α(λ)=exp{[σem(λ)N1-σabs(λ)N0]ltot}.
xi+1=xi+pi,
|pi|=- ln ,
p(z)N1(z).
Ii=j=j1jn exp{[σem(λ)N1,j-σabs(λ)N0,j]wj sec θi},
j=j1jnwj sec θi=l

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