Abstract

Simulations on three-dimensional random lasers were performed by finite-difference time-domain integration of Maxwell’s equations combined with rate-equations providing gain. We investigated the frequency-dependent emission polarization of random lasers in the far-field of the sample and characterized the influence of anisotropic pumping in orthogonal polarizations. Under weak scattering, the polarization states of random lasing modes were random for isotropic pumping and linear under anisotropic pumping. These findings are in accordance with recent experimental observations. A crossover was observed towards very strong scattering, in which the scattering destroys the pump-induced polarization-anisotropy of the random lasing modes and randomizes (scrambles) the mode-polarization.

© 2013 Optical Society of America

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    [CrossRef] [PubMed]
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2013 (2)

S. Knitter, M. Kues, and C. Fallnich, “Spectro-polarimetric signature of a random laser,” Phys. Rev. A88, 013839 (2013).
[CrossRef]

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photonics7, 197–204 (2013).
[CrossRef]

2012 (5)

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]

R. El-Dardiry, R. Mooiweer, and A. Lagendijk, “Experimental phase diagram for random laser spectra,” New J. Phys.14, 113031 (2012).
[CrossRef]

S. Knitter, M. Kues, and C. Fallnich, “Emission polarization of random lasers in organic dye solutions.” Opt. Lett.37, 3621–3623 (2012).
[CrossRef] [PubMed]

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett.109, 033903 (2012).
[CrossRef] [PubMed]

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics6, 355–359 (2012).
[CrossRef]

2011 (4)

Y. Liu, J.-S. Liu, and K.-J. Wang, “A method to control the polarization of random terahertz lasing in two-dimensional disordered ruby medium,” Chin. Phys. B20, 094205 (2011).
[CrossRef]

M. Leonetti, C. Conti, and C. Lopez, “The mode-locking transition of random lasers,” Nat. Photonics5, 615–617 (2011).
[CrossRef]

R. El-Dardiry, S. Faez, and A. Lagendijk, “Classification of light sources and their interaction with active and passive environments,” Phys. Rev. A.83, 031801(R) (2011).
[CrossRef]

R. G. S. El-Dardiry and A. Lagendijk, “Tuning random lasers by engineered absorption,” Appl. Phys. Lett.98, 161106 (2011).
[CrossRef]

2009 (2)

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

H. Liu, J. Liu, J. Lü, Q. Zhang, and K. Wang, “The research on polarization states with local pumping in two-dimensional active random medium,” Opt. Commun.282, 1004–1008 (2009).
[CrossRef]

2008 (2)

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys.4, 359–367 (2008).
[CrossRef]

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys.4, 794–798 (2008).
[CrossRef]

2007 (2)

U. M. Scheven, “Intrinsic dispersivity of randomly packed monodisperse spheres,” Phys. Rev. Lett.99, 054502 (2007).
[CrossRef] [PubMed]

K. van der Molen, R. Tjerkstra, A. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett.98, 143901 (2007).
[CrossRef] [PubMed]

2006 (3)

X. Wu, W. Fang, A. Yamilov, A. A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A74, 053812 (2006).
[CrossRef]

C. Wang and J. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A353, 269–272 (2006).
[CrossRef]

V. Markushev, M. Ryzhkov, and C. Briskina, “Characteristic properties of ZnO random laser pumped by nanosecond pulses,” Appl. Phys. B84, 333–337 (2006).
[CrossRef]

2005 (2)

M. Xu and R. Alfano, “Random walk of polarized light in turbid media,” Phys. Rev. Lett.95, 213901 (2005).
[CrossRef] [PubMed]

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A Math. Gen.38, 10497–10535 (2005).
[CrossRef]

2004 (1)

N. Ghosh, A. Pradhan, P. Gupta, S. Gupta, V. Jaiswal, and R. Singh, “Depolarization of light in a multiply scattering medium: Effect of the refractive index of a scatterer,” Phys. Rev. E70, 066607 (2004).
[CrossRef]

2002 (1)

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B66, 144202 (2002).
[CrossRef]

2001 (1)

A. Kim and M. Moscoso, “Influence of the relative refractive index on the depolarization of multiply scattered waves,” Phys. Rev. E64, 026612 (2001).
[CrossRef]

2000 (2)

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

H. Cao, J. Y. Xu, D. Z. Zhang, S. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett.84, 5584–5587 (2000).
[CrossRef] [PubMed]

1999 (1)

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82, 2278–2281 (1999).
[CrossRef]

1994 (1)

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E49, 1767–1770 (1994).
[CrossRef]

1985 (1)

W. S. Jodrey and E. M. Tory, “Computer simulation of close random packing of equal spheres,” Phys. Rev. A32, 2347–2351 (1985).
[CrossRef] [PubMed]

1978 (1)

A. Penzkofer and W. Falkenstein, “Theoretical investigation of amplified spontaneous emission with picosecond light pulses in dye solutions,” Opt. Quantum Electron.10, 399–423 (1978).
[CrossRef]

1975 (1)

T. Vincenty, “Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations,” Surv. Rev.23, 88–93 (1975).

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.14, 302–307 (1966).
[CrossRef]

Alfano, R.

M. Xu and R. Alfano, “Random walk of polarized light in turbid media,” Phys. Rev. Lett.95, 213901 (2005).
[CrossRef] [PubMed]

Ali, M. G. 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]

Andreasen, J.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett.109, 033903 (2012).
[CrossRef] [PubMed]

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

Asatryan, A. A.

X. Wu, W. Fang, A. Yamilov, A. A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A74, 053812 (2006).
[CrossRef]

Bachelard, N.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett.109, 033903 (2012).
[CrossRef] [PubMed]

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]

Bicout, D.

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E49, 1767–1770 (1994).
[CrossRef]

Botten, L. C.

X. Wu, W. Fang, A. Yamilov, A. A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A74, 053812 (2006).
[CrossRef]

Briskina, C.

V. Markushev, M. Ryzhkov, and C. Briskina, “Characteristic properties of ZnO random laser pumped by nanosecond pulses,” Appl. Phys. B84, 333–337 (2006).
[CrossRef]

Brosseau, C.

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E49, 1767–1770 (1994).
[CrossRef]

Cao, H.

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics6, 355–359 (2012).
[CrossRef]

X. Wu, W. Fang, A. Yamilov, A. A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A74, 053812 (2006).
[CrossRef]

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A Math. Gen.38, 10497–10535 (2005).
[CrossRef]

H. Cao, J. Y. Xu, D. Z. Zhang, S. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett.84, 5584–5587 (2000).
[CrossRef] [PubMed]

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82, 2278–2281 (1999).
[CrossRef]

Chabanov, A. A. A.

X. Wu, W. Fang, A. Yamilov, A. A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A74, 053812 (2006).
[CrossRef]

Chang, R.

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82, 2278–2281 (1999).
[CrossRef]

Chang, R. P.

H. Cao, J. Y. Xu, D. Z. Zhang, S. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett.84, 5584–5587 (2000).
[CrossRef] [PubMed]

Chang, S.

H. Cao, J. Y. Xu, D. Z. Zhang, S. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett.84, 5584–5587 (2000).
[CrossRef] [PubMed]

Choma, M. A.

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics6, 355–359 (2012).
[CrossRef]

Christodoulides, D. N.

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photonics7, 197–204 (2013).
[CrossRef]

Conti, C.

M. Leonetti, C. Conti, and C. Lopez, “The mode-locking transition of random lasers,” Nat. Photonics5, 615–617 (2011).
[CrossRef]

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys.4, 794–798 (2008).
[CrossRef]

Drexhage, K.

F. Schäfer and K. Drexhage, Dye Lasers, Topics in Applied Physics (Springer, 1973).

El-Dardiry, R.

R. El-Dardiry, R. Mooiweer, and A. Lagendijk, “Experimental phase diagram for random laser spectra,” New J. Phys.14, 113031 (2012).
[CrossRef]

R. El-Dardiry, S. Faez, and A. Lagendijk, “Classification of light sources and their interaction with active and passive environments,” Phys. Rev. A.83, 031801(R) (2011).
[CrossRef]

El-Dardiry, R. G. S.

R. G. S. El-Dardiry and A. Lagendijk, “Tuning random lasers by engineered absorption,” Appl. Phys. Lett.98, 161106 (2011).
[CrossRef]

Faez, S.

R. El-Dardiry, S. Faez, and A. Lagendijk, “Classification of light sources and their interaction with active and passive environments,” Phys. Rev. A.83, 031801(R) (2011).
[CrossRef]

Falkenstein, W.

A. Penzkofer and W. Falkenstein, “Theoretical investigation of amplified spontaneous emission with picosecond light pulses in dye solutions,” Opt. Quantum Electron.10, 399–423 (1978).
[CrossRef]

Fallnich, C.

S. Knitter, M. Kues, and C. Fallnich, “Spectro-polarimetric signature of a random laser,” Phys. Rev. A88, 013839 (2013).
[CrossRef]

S. Knitter, M. Kues, and C. Fallnich, “Emission polarization of random lasers in organic dye solutions.” Opt. Lett.37, 3621–3623 (2012).
[CrossRef] [PubMed]

Fang, W.

X. Wu, W. Fang, A. Yamilov, A. A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A74, 053812 (2006).
[CrossRef]

Fratalocchi, A.

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys.4, 794–798 (2008).
[CrossRef]

Ghosh, N.

N. Ghosh, A. Pradhan, P. Gupta, S. Gupta, V. Jaiswal, and R. Singh, “Depolarization of light in a multiply scattering medium: Effect of the refractive index of a scatterer,” Phys. Rev. E70, 066607 (2004).
[CrossRef]

Gigan, S.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett.109, 033903 (2012).
[CrossRef] [PubMed]

Gupta, P.

N. Ghosh, A. Pradhan, P. Gupta, S. Gupta, V. Jaiswal, and R. Singh, “Depolarization of light in a multiply scattering medium: Effect of the refractive index of a scatterer,” Phys. Rev. E70, 066607 (2004).
[CrossRef]

Gupta, S.

N. Ghosh, A. Pradhan, P. Gupta, S. Gupta, V. Jaiswal, and R. Singh, “Depolarization of light in a multiply scattering medium: Effect of the refractive index of a scatterer,” Phys. Rev. E70, 066607 (2004).
[CrossRef]

Ho, S.

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82, 2278–2281 (1999).
[CrossRef]

Ho, S. T.

H. Cao, J. Y. Xu, D. Z. Zhang, S. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett.84, 5584–5587 (2000).
[CrossRef] [PubMed]

Jaiswal, V.

N. Ghosh, A. Pradhan, P. Gupta, S. Gupta, V. Jaiswal, and R. Singh, “Depolarization of light in a multiply scattering medium: Effect of the refractive index of a scatterer,” Phys. Rev. E70, 066607 (2004).
[CrossRef]

Jiang, X.

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

Jodrey, W. S.

W. S. Jodrey and E. M. Tory, “Computer simulation of close random packing of equal spheres,” Phys. Rev. A32, 2347–2351 (1985).
[CrossRef] [PubMed]

Kim, A.

A. Kim and M. Moscoso, “Influence of the relative refractive index on the depolarization of multiply scattered waves,” Phys. Rev. E64, 026612 (2001).
[CrossRef]

Knitter, S.

S. Knitter, M. Kues, and C. Fallnich, “Spectro-polarimetric signature of a random laser,” Phys. Rev. A88, 013839 (2013).
[CrossRef]

S. Knitter, M. Kues, and C. Fallnich, “Emission polarization of random lasers in organic dye solutions.” Opt. Lett.37, 3621–3623 (2012).
[CrossRef] [PubMed]

Kues, M.

S. Knitter, M. Kues, and C. Fallnich, “Spectro-polarimetric signature of a random laser,” Phys. Rev. A88, 013839 (2013).
[CrossRef]

S. Knitter, M. Kues, and C. Fallnich, “Emission polarization of random lasers in organic dye solutions.” Opt. Lett.37, 3621–3623 (2012).
[CrossRef] [PubMed]

Lagendijk, A.

R. El-Dardiry, R. Mooiweer, and A. Lagendijk, “Experimental phase diagram for random laser spectra,” New J. Phys.14, 113031 (2012).
[CrossRef]

R. El-Dardiry, S. Faez, and A. Lagendijk, “Classification of light sources and their interaction with active and passive environments,” Phys. Rev. A.83, 031801(R) (2011).
[CrossRef]

R. G. S. El-Dardiry and A. Lagendijk, “Tuning random lasers by engineered absorption,” Appl. Phys. Lett.98, 161106 (2011).
[CrossRef]

K. van der Molen, R. Tjerkstra, A. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett.98, 143901 (2007).
[CrossRef] [PubMed]

Leonetti, M.

M. Leonetti, C. Conti, and C. Lopez, “The mode-locking transition of random lasers,” Nat. Photonics5, 615–617 (2011).
[CrossRef]

Liu, H.

H. Liu, J. Liu, J. Lü, Q. Zhang, and K. Wang, “The research on polarization states with local pumping in two-dimensional active random medium,” Opt. Commun.282, 1004–1008 (2009).
[CrossRef]

Liu, J.

H. Liu, J. Liu, J. Lü, Q. Zhang, and K. Wang, “The research on polarization states with local pumping in two-dimensional active random medium,” Opt. Commun.282, 1004–1008 (2009).
[CrossRef]

C. Wang and J. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A353, 269–272 (2006).
[CrossRef]

Liu, J.-S.

Y. Liu, J.-S. Liu, and K.-J. Wang, “A method to control the polarization of random terahertz lasing in two-dimensional disordered ruby medium,” Chin. Phys. B20, 094205 (2011).
[CrossRef]

Liu, X.

H. Cao, J. Y. Xu, D. Z. Zhang, S. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett.84, 5584–5587 (2000).
[CrossRef] [PubMed]

Liu, Y.

Y. Liu, J.-S. Liu, and K.-J. Wang, “A method to control the polarization of random terahertz lasing in two-dimensional disordered ruby medium,” Chin. Phys. B20, 094205 (2011).
[CrossRef]

Lopez, C.

M. Leonetti, C. Conti, and C. Lopez, “The mode-locking transition of random lasers,” Nat. Photonics5, 615–617 (2011).
[CrossRef]

Lü, J.

H. Liu, J. Liu, J. Lü, Q. Zhang, and K. Wang, “The research on polarization states with local pumping in two-dimensional active random medium,” Opt. Commun.282, 1004–1008 (2009).
[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]

Markushev, V.

V. Markushev, M. Ryzhkov, and C. Briskina, “Characteristic properties of ZnO random laser pumped by nanosecond pulses,” Appl. Phys. B84, 333–337 (2006).
[CrossRef]

Martinez, A.

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E49, 1767–1770 (1994).
[CrossRef]

Mooiweer, R.

R. El-Dardiry, R. Mooiweer, and A. Lagendijk, “Experimental phase diagram for random laser spectra,” New J. Phys.14, 113031 (2012).
[CrossRef]

Moscoso, M.

A. Kim and M. Moscoso, “Influence of the relative refractive index on the depolarization of multiply scattered waves,” Phys. Rev. E64, 026612 (2001).
[CrossRef]

Mosk, A.

K. van der Molen, R. Tjerkstra, A. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett.98, 143901 (2007).
[CrossRef] [PubMed]

Noginov, M.

M. Noginov, Solid-State Random Lasers, Springer Series in Optical Sciences (Springer, 2005).

Penzkofer, A.

A. Penzkofer and W. Falkenstein, “Theoretical investigation of amplified spontaneous emission with picosecond light pulses in dye solutions,” Opt. Quantum Electron.10, 399–423 (1978).
[CrossRef]

Pradhan, A.

N. Ghosh, A. Pradhan, P. Gupta, S. Gupta, V. Jaiswal, and R. Singh, “Depolarization of light in a multiply scattering medium: Effect of the refractive index of a scatterer,” Phys. Rev. E70, 066607 (2004).
[CrossRef]

Redding, B.

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics6, 355–359 (2012).
[CrossRef]

Ryzhkov, M.

V. Markushev, M. Ryzhkov, and C. Briskina, “Characteristic properties of ZnO random laser pumped by nanosecond pulses,” Appl. Phys. B84, 333–337 (2006).
[CrossRef]

Schäfer, F.

F. Schäfer and K. Drexhage, Dye Lasers, Topics in Applied Physics (Springer, 1973).

Scheven, U. M.

U. M. Scheven, “Intrinsic dispersivity of randomly packed monodisperse spheres,” Phys. Rev. Lett.99, 054502 (2007).
[CrossRef] [PubMed]

Schmitt, J.

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E49, 1767–1770 (1994).
[CrossRef]

Sebbah, P.

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett.109, 033903 (2012).
[CrossRef] [PubMed]

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B66, 144202 (2002).
[CrossRef]

Seelig, E.

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82, 2278–2281 (1999).
[CrossRef]

Seelig, E. W.

H. Cao, J. Y. Xu, D. Z. Zhang, S. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett.84, 5584–5587 (2000).
[CrossRef] [PubMed]

Segev, M.

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photonics7, 197–204 (2013).
[CrossRef]

Silberberg, Y.

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photonics7, 197–204 (2013).
[CrossRef]

Singh, R.

N. Ghosh, A. Pradhan, P. Gupta, S. Gupta, V. Jaiswal, and R. Singh, “Depolarization of light in a multiply scattering medium: Effect of the refractive index of a scatterer,” Phys. Rev. E70, 066607 (2004).
[CrossRef]

Soukoulis, C. M.

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

Tjerkstra, R.

K. van der Molen, R. Tjerkstra, A. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett.98, 143901 (2007).
[CrossRef] [PubMed]

Tory, E. M.

W. S. Jodrey and E. M. Tory, “Computer simulation of close random packing of equal spheres,” Phys. Rev. A32, 2347–2351 (1985).
[CrossRef] [PubMed]

van de Hulst, H.

H. van de Hulst, Light Scattering by Small Particles, Structure of Matter Series (Dover, 1957).

van der Molen, K.

K. van der Molen, R. Tjerkstra, A. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett.98, 143901 (2007).
[CrossRef] [PubMed]

Vanneste, C.

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B66, 144202 (2002).
[CrossRef]

Vincenty, T.

T. Vincenty, “Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations,” Surv. Rev.23, 88–93 (1975).

Wang, C.

C. Wang and J. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A353, 269–272 (2006).
[CrossRef]

Wang, K.

H. Liu, J. Liu, J. Lü, Q. Zhang, and K. Wang, “The research on polarization states with local pumping in two-dimensional active random medium,” Opt. Commun.282, 1004–1008 (2009).
[CrossRef]

Wang, K.-J.

Y. Liu, J.-S. Liu, and K.-J. Wang, “A method to control the polarization of random terahertz lasing in two-dimensional disordered ruby medium,” Chin. Phys. B20, 094205 (2011).
[CrossRef]

Wang, Q.

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82, 2278–2281 (1999).
[CrossRef]

Wiersma, D. S.

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys.4, 359–367 (2008).
[CrossRef]

Wu, X.

X. Wu, W. Fang, A. Yamilov, A. A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A74, 053812 (2006).
[CrossRef]

Xu, J. Y.

H. Cao, J. Y. Xu, D. Z. Zhang, S. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett.84, 5584–5587 (2000).
[CrossRef] [PubMed]

Xu, M.

M. Xu and R. Alfano, “Random walk of polarized light in turbid media,” Phys. Rev. Lett.95, 213901 (2005).
[CrossRef] [PubMed]

Yamilov, A.

X. Wu, W. Fang, A. Yamilov, A. A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A74, 053812 (2006).
[CrossRef]

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.14, 302–307 (1966).
[CrossRef]

Zhang, D. Z.

H. Cao, J. Y. Xu, D. Z. Zhang, S. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett.84, 5584–5587 (2000).
[CrossRef] [PubMed]

Zhang, Q.

H. Liu, J. Liu, J. Lü, Q. Zhang, and K. Wang, “The research on polarization states with local pumping in two-dimensional active random medium,” Opt. Commun.282, 1004–1008 (2009).
[CrossRef]

Zhao, Y.

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82, 2278–2281 (1999).
[CrossRef]

Appl. Phys. B (1)

V. Markushev, M. Ryzhkov, and C. Briskina, “Characteristic properties of ZnO random laser pumped by nanosecond pulses,” Appl. Phys. B84, 333–337 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

R. G. S. El-Dardiry and A. Lagendijk, “Tuning random lasers by engineered absorption,” Appl. Phys. Lett.98, 161106 (2011).
[CrossRef]

Chin. Phys. B (1)

Y. Liu, J.-S. Liu, and K.-J. Wang, “A method to control the polarization of random terahertz lasing in two-dimensional disordered ruby medium,” Chin. Phys. B20, 094205 (2011).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.14, 302–307 (1966).
[CrossRef]

J. Lightwave Technol. (1)

J. Phys. A Math. Gen. (1)

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A Math. Gen.38, 10497–10535 (2005).
[CrossRef]

Nat. Photonics (3)

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics6, 355–359 (2012).
[CrossRef]

M. Leonetti, C. Conti, and C. Lopez, “The mode-locking transition of random lasers,” Nat. Photonics5, 615–617 (2011).
[CrossRef]

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photonics7, 197–204 (2013).
[CrossRef]

Nat. Phys. (2)

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys.4, 794–798 (2008).
[CrossRef]

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys.4, 359–367 (2008).
[CrossRef]

New J. Phys. (1)

R. El-Dardiry, R. Mooiweer, and A. Lagendijk, “Experimental phase diagram for random laser spectra,” New J. Phys.14, 113031 (2012).
[CrossRef]

Opt. Commun. (2)

H. Liu, J. Liu, J. Lü, Q. Zhang, and K. Wang, “The research on polarization states with local pumping in two-dimensional active random medium,” Opt. Commun.282, 1004–1008 (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. Lett. (1)

Opt. Quantum Electron. (1)

A. Penzkofer and W. Falkenstein, “Theoretical investigation of amplified spontaneous emission with picosecond light pulses in dye solutions,” Opt. Quantum Electron.10, 399–423 (1978).
[CrossRef]

Phys. Lett. A (1)

C. Wang and J. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A353, 269–272 (2006).
[CrossRef]

Phys. Rev. A (3)

X. Wu, W. Fang, A. Yamilov, A. A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A74, 053812 (2006).
[CrossRef]

S. Knitter, M. Kues, and C. Fallnich, “Spectro-polarimetric signature of a random laser,” Phys. Rev. A88, 013839 (2013).
[CrossRef]

W. S. Jodrey and E. M. Tory, “Computer simulation of close random packing of equal spheres,” Phys. Rev. A32, 2347–2351 (1985).
[CrossRef] [PubMed]

Phys. Rev. A. (1)

R. El-Dardiry, S. Faez, and A. Lagendijk, “Classification of light sources and their interaction with active and passive environments,” Phys. Rev. A.83, 031801(R) (2011).
[CrossRef]

Phys. Rev. B (1)

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B66, 144202 (2002).
[CrossRef]

Phys. Rev. E (3)

D. Bicout, C. Brosseau, A. Martinez, and J. Schmitt, “Depolarization of multiply scattered waves by spherical diffusers: Influence of the size parameter,” Phys. Rev. E49, 1767–1770 (1994).
[CrossRef]

A. Kim and M. Moscoso, “Influence of the relative refractive index on the depolarization of multiply scattered waves,” Phys. Rev. E64, 026612 (2001).
[CrossRef]

N. Ghosh, A. Pradhan, P. Gupta, S. Gupta, V. Jaiswal, and R. Singh, “Depolarization of light in a multiply scattering medium: Effect of the refractive index of a scatterer,” Phys. Rev. E70, 066607 (2004).
[CrossRef]

Phys. Rev. Lett. (7)

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

N. Bachelard, J. Andreasen, S. Gigan, and P. Sebbah, “Taming random lasers through active spatial control of the pump,” Phys. Rev. Lett.109, 033903 (2012).
[CrossRef] [PubMed]

H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett.82, 2278–2281 (1999).
[CrossRef]

H. Cao, J. Y. Xu, D. Z. Zhang, S. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett.84, 5584–5587 (2000).
[CrossRef] [PubMed]

K. van der Molen, R. Tjerkstra, A. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett.98, 143901 (2007).
[CrossRef] [PubMed]

U. M. Scheven, “Intrinsic dispersivity of randomly packed monodisperse spheres,” Phys. Rev. Lett.99, 054502 (2007).
[CrossRef] [PubMed]

M. Xu and R. Alfano, “Random walk of polarized light in turbid media,” Phys. Rev. Lett.95, 213901 (2005).
[CrossRef] [PubMed]

Surv. Rev. (1)

T. Vincenty, “Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations,” Surv. Rev.23, 88–93 (1975).

Other (3)

F. Schäfer and K. Drexhage, Dye Lasers, Topics in Applied Physics (Springer, 1973).

H. van de Hulst, Light Scattering by Small Particles, Structure of Matter Series (Dover, 1957).

M. Noginov, Solid-State Random Lasers, Springer Series in Optical Sciences (Springer, 2005).

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Figures (6)

Fig. 1
Fig. 1

(a) Mean integrated spectral intensity as a function of the pump rate. (b) Spectral intensity: distinct modes occurred at different frequencies for a pump rate of 1ps−1.

Fig. 2
Fig. 2

Spectra for three different initial conditions for a pump rate of p = 10ps−1: (a) and (b) for two different spatial positions of the exciting pulse (1 μm separation) and (c) for noise-perturbed rate equations.

Fig. 3
Fig. 3

Polarization states of single random lasing modes projected onto the Poincaré sphere with (a) amplification in x-, (b) equal amplification in x- and y- and (c) amplification in the y-direction. States on the positive-S1 hemisphere of the Poincaré sphere are marked with blue dots and states on the negative-S1 hemisphere are marked with red dots to avoid ambiguity in the two-dimensional projection. The polarization states cluster around the pump polarization induced by anisotropic amplification and are randomly distributed over the sphere under isotropic amplification. (d) The coverage of modes was almost isotropic over a large range of α = 25...65° and strictly localized for α = 0...15° and α = 75...90°.

Fig. 4
Fig. 4

Polarization of random lasing modes in a glycerol solvent projected on the Poincaré sphere: (a) under linear and (b) under circular pump polarization (view in S1-direction). Red squares indicate the pump polarization. For details see Ref. [12]

Fig. 5
Fig. 5

(a) Integrated spectral intensity in x- and y-polarization, normalized to intensity in both polarization channels for each α. Red-full and blue-dashed lines guide the eye. For anisotropic pumping (α = 0° and 90°), the random lasing emission is polarized only in the direction of the pump. For isotropic pumping in the x- and y- direction simultaneously (α = 45°), modes develop into both polarization directions. The emission spectra are different for pumping in (b) x- and (d) y-direction. The emission spectrum under (c) isotropic pumping is linearly independent of the two anisotropic cases.

Fig. 6
Fig. 6

Average great circle distance of random lasing modes and the linear pump polarization on the Poincaré sphere for different refractive indices. The dashed-blue line guides the eye. Strong scattering (on the right side of the vertical dashed line) facilitated a wide spread of modes on the Poincaré sphere. The mean free path was calculated from Eqs. (8) and (9).

Equations (19)

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

S 0 = | E ˜ x | 2 + | E ˜ y | 2 ,
S 1 = | E ˜ x | 2 | E ˜ y | 2 ,
S 2 = 2 Re ( E ˜ x * E ˜ y ) ,
S 3 = 2 Im ( E ˜ x * E ˜ y ) .
p x = p cos 2 ( α )
and p y = p sin 2 ( α ) ,
Δ s ( S 1 , S 2 ) = arctan ( ( cos ϕ 1 sin Λ ) 2 + ( cos ϕ 2 sin ϕ 1 sin ϕ 2 cos ϕ 1 cos Λ ) 2 sin ϕ 2 sin ϕ 1 + cos ϕ 2 cos ϕ 1 cos Λ )
l s ( n p ) = ( ρ σ ) 1
σ ( n ) = 128 3 π 5 r p 6 ( n p 2 1 ) 2 λ 4 ( n p 2 + 2 ) 2
E ( r , t ) = 0 ,
H ( r , t ) = 0 ,
t D ( r , t ) = × H ( r , t ) ,
t H ( r , t ) = 1 ε 0 μ 0 × E ( r , t ) ,
E ( r , t ) = [ D ( r , t ) P ( r , t ) ] / ε 0 ε r ( r ) ,
t N 3 i ( r , t ) = p i N 0 i ( r , t ) N 3 i ( r , t ) τ 32 ,
t N 2 i ( r , t ) = N 3 i ( r , t ) τ 32 + E i ( r , t ) ω a t P i ( r , t ) N 2 i ( r , t ) τ 21 ,
t N 1 i ( r , t ) = N 2 i ( r , t ) τ 21 E i ( r , t ) ω a t P i ( r , t ) N 1 i ( r , t ) τ 10 ,
t N 0 i ( r , t ) = i p i N 0 i ( r , t ) + i N 1 i ( r , t ) τ 10
2 t 2 P i ( r , t ) + Δ ω a t P i ( r , t ) + ω a 2 P i ( r , t ) = 6 π ε 0 c 3 ω a 2 Δ N i ( r , t ) E i ( r , t ) ,

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