Abstract

We present a generic route to classical light condensation (LC) in linear photonic mode systems, such as cw lasers, with different grounds from regular Bose-Einstein condensation (BEC). LC is based on weighting the modes in a noisy environment (spontaneous emission, etc.) in a loss-gain scale, rather than in photon energy. It is characterized by a sharp transition from a multi- to single-mode oscillation. The study uses a linear multivariate Langevin formulation which gives a mode occupation hierarchy that functions like Bose-Einstein statistics. Condensation occurs when the spectral filtering has near the lowest-loss mode a power law dependence with exponent smaller than 1. We then discuss how condensation can occur in photon systems, its relation to lasing and the difficulties to observe regular photon-BEC in laser cavities. We raise the possibility that experiments on photon condensation in optical cavities fall in a classical LC or lasing category rather than being a thermal-quantum BEC phenomenon.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science269(5221), 198–201 (1995).
    [CrossRef] [PubMed]
  2. A. J. Leggett, “Bose-Einstein condensation in the alkali gases: Some fundamental concepts,” Rev. Mod. Phys.73(2), 307–356 (2001).
    [CrossRef]
  3. J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature468(7323), 545–548 (2010).
    [CrossRef] [PubMed]
  4. J. Klaers, F. Vewinger, and M. Weitz, “Thermalization of a two-dimensional photonic gas in a white wall photon box,” Nat. Phys.6(7), 512–515 (2010).
    [CrossRef]
  5. H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science298(5591), 199–202 (2002).
    [CrossRef] [PubMed]
  6. R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science316(5827), 1007–1010 (2007).
    [CrossRef] [PubMed]
  7. S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature443(7110), 430–433 (2006).
    [CrossRef] [PubMed]
  8. R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express18(16), 16520–16525 (2010).
    [CrossRef] [PubMed]
  9. R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett.104(17), 173901 (2010).
    [CrossRef] [PubMed]
  10. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett.95(26), 263901 (2005).
    [CrossRef] [PubMed]
  11. C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett.101(14), 143901 (2008).
    [CrossRef] [PubMed]
  12. A. Fratalocchi, “Mode-locked lasers: light condensation,” Nat. Photonics4(8), 502–503 (2010).
    [CrossRef]
  13. A. Gordon and B. Fischer, “Phase transition theory of many-mode ordering and pulse formation in lasers,” Phys. Rev. Lett.89(10), 103901 (2002).
    [CrossRef] [PubMed]
  14. O. Gat, A. Gordon, and B. Fischer, “Solution of a statistical mechanics model for pulse formation in lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70, 046108 (2004).
    [CrossRef] [PubMed]
  15. O. Gat, A. Gordon, and B. Fischer, “Light-mode locking: a new class of solvable statistical physics systems,” New J. Phys.7, 151 (2005).
    [CrossRef]
  16. B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, “Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway,” Phys. Rev. Lett.93(15), 153901 (2004).
    [CrossRef] [PubMed]
  17. A. Gordon, B. Vodonos, V. Smulakovski, and B. Fischer, “Melting and freezing of light pulses and modes in mode-locked lasers,” Opt. Express11(25), 3418–3424 (2003).
    [CrossRef] [PubMed]
  18. A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105(1), 013905 (2010).
    [CrossRef] [PubMed]
  19. R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett.95(1), 013903 (2005).
    [CrossRef] [PubMed]
  20. V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A44(11), 7439–7441 (1991).
    [CrossRef] [PubMed]
  21. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron.6(6), 1173–1185 (2000).
    [CrossRef]
  22. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993), Ch.6.
  23. A. E. Siegman, Lasers (University Science Books, 1986).
  24. D. A. Sawicki and R. S. Knox, “Universal relationship between optical emission and absorption of complex systems: An alternative approach,” Phys. Rev. A54(6), 4837–4841 (1996).
    [CrossRef] [PubMed]

2010 (6)

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature468(7323), 545–548 (2010).
[CrossRef] [PubMed]

J. Klaers, F. Vewinger, and M. Weitz, “Thermalization of a two-dimensional photonic gas in a white wall photon box,” Nat. Phys.6(7), 512–515 (2010).
[CrossRef]

R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express18(16), 16520–16525 (2010).
[CrossRef] [PubMed]

R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett.104(17), 173901 (2010).
[CrossRef] [PubMed]

A. Fratalocchi, “Mode-locked lasers: light condensation,” Nat. Photonics4(8), 502–503 (2010).
[CrossRef]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105(1), 013905 (2010).
[CrossRef] [PubMed]

2008 (1)

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett.101(14), 143901 (2008).
[CrossRef] [PubMed]

2007 (1)

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science316(5827), 1007–1010 (2007).
[CrossRef] [PubMed]

2006 (1)

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature443(7110), 430–433 (2006).
[CrossRef] [PubMed]

2005 (3)

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett.95(26), 263901 (2005).
[CrossRef] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett.95(1), 013903 (2005).
[CrossRef] [PubMed]

O. Gat, A. Gordon, and B. Fischer, “Light-mode locking: a new class of solvable statistical physics systems,” New J. Phys.7, 151 (2005).
[CrossRef]

2004 (2)

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, “Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway,” Phys. Rev. Lett.93(15), 153901 (2004).
[CrossRef] [PubMed]

O. Gat, A. Gordon, and B. Fischer, “Solution of a statistical mechanics model for pulse formation in lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70, 046108 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (2)

A. Gordon and B. Fischer, “Phase transition theory of many-mode ordering and pulse formation in lasers,” Phys. Rev. Lett.89(10), 103901 (2002).
[CrossRef] [PubMed]

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science298(5591), 199–202 (2002).
[CrossRef] [PubMed]

2001 (1)

A. J. Leggett, “Bose-Einstein condensation in the alkali gases: Some fundamental concepts,” Rev. Mod. Phys.73(2), 307–356 (2001).
[CrossRef]

2000 (1)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron.6(6), 1173–1185 (2000).
[CrossRef]

1996 (1)

D. A. Sawicki and R. S. Knox, “Universal relationship between optical emission and absorption of complex systems: An alternative approach,” Phys. Rev. A54(6), 4837–4841 (1996).
[CrossRef] [PubMed]

1995 (1)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science269(5221), 198–201 (1995).
[CrossRef] [PubMed]

1991 (1)

V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A44(11), 7439–7441 (1991).
[CrossRef] [PubMed]

Anderson, M. H.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science269(5221), 198–201 (1995).
[CrossRef] [PubMed]

Angelani, L.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett.101(14), 143901 (2008).
[CrossRef] [PubMed]

Bagnato, V.

V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A44(11), 7439–7441 (1991).
[CrossRef] [PubMed]

Balili, R.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science316(5827), 1007–1010 (2007).
[CrossRef] [PubMed]

Bekker, A.

R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express18(16), 16520–16525 (2010).
[CrossRef] [PubMed]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105(1), 013905 (2010).
[CrossRef] [PubMed]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, “Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway,” Phys. Rev. Lett.93(15), 153901 (2004).
[CrossRef] [PubMed]

Bloch, J.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science298(5591), 199–202 (2002).
[CrossRef] [PubMed]

Connaughton, C.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett.95(26), 263901 (2005).
[CrossRef] [PubMed]

Conti, C.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett.101(14), 143901 (2008).
[CrossRef] [PubMed]

Cornell, E. A.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science269(5221), 198–201 (1995).
[CrossRef] [PubMed]

Demidov, V. E.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature443(7110), 430–433 (2006).
[CrossRef] [PubMed]

Demokritov, S. O.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature443(7110), 430–433 (2006).
[CrossRef] [PubMed]

Deng, H.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science298(5591), 199–202 (2002).
[CrossRef] [PubMed]

Dzyapko, O.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature443(7110), 430–433 (2006).
[CrossRef] [PubMed]

Ensher, J. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science269(5221), 198–201 (1995).
[CrossRef] [PubMed]

Fischer, B.

R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express18(16), 16520–16525 (2010).
[CrossRef] [PubMed]

R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett.104(17), 173901 (2010).
[CrossRef] [PubMed]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105(1), 013905 (2010).
[CrossRef] [PubMed]

O. Gat, A. Gordon, and B. Fischer, “Light-mode locking: a new class of solvable statistical physics systems,” New J. Phys.7, 151 (2005).
[CrossRef]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett.95(1), 013903 (2005).
[CrossRef] [PubMed]

O. Gat, A. Gordon, and B. Fischer, “Solution of a statistical mechanics model for pulse formation in lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70, 046108 (2004).
[CrossRef] [PubMed]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, “Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway,” Phys. Rev. Lett.93(15), 153901 (2004).
[CrossRef] [PubMed]

A. Gordon, B. Vodonos, V. Smulakovski, and B. Fischer, “Melting and freezing of light pulses and modes in mode-locked lasers,” Opt. Express11(25), 3418–3424 (2003).
[CrossRef] [PubMed]

A. Gordon and B. Fischer, “Phase transition theory of many-mode ordering and pulse formation in lasers,” Phys. Rev. Lett.89(10), 103901 (2002).
[CrossRef] [PubMed]

Fratalocchi, A.

A. Fratalocchi, “Mode-locked lasers: light condensation,” Nat. Photonics4(8), 502–503 (2010).
[CrossRef]

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett.101(14), 143901 (2008).
[CrossRef] [PubMed]

Gat, O.

R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett.104(17), 173901 (2010).
[CrossRef] [PubMed]

R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express18(16), 16520–16525 (2010).
[CrossRef] [PubMed]

O. Gat, A. Gordon, and B. Fischer, “Light-mode locking: a new class of solvable statistical physics systems,” New J. Phys.7, 151 (2005).
[CrossRef]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett.95(1), 013903 (2005).
[CrossRef] [PubMed]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, “Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway,” Phys. Rev. Lett.93(15), 153901 (2004).
[CrossRef] [PubMed]

O. Gat, A. Gordon, and B. Fischer, “Solution of a statistical mechanics model for pulse formation in lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70, 046108 (2004).
[CrossRef] [PubMed]

Gordon, A.

O. Gat, A. Gordon, and B. Fischer, “Light-mode locking: a new class of solvable statistical physics systems,” New J. Phys.7, 151 (2005).
[CrossRef]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett.95(1), 013903 (2005).
[CrossRef] [PubMed]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, “Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway,” Phys. Rev. Lett.93(15), 153901 (2004).
[CrossRef] [PubMed]

O. Gat, A. Gordon, and B. Fischer, “Solution of a statistical mechanics model for pulse formation in lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70, 046108 (2004).
[CrossRef] [PubMed]

A. Gordon, B. Vodonos, V. Smulakovski, and B. Fischer, “Melting and freezing of light pulses and modes in mode-locked lasers,” Opt. Express11(25), 3418–3424 (2003).
[CrossRef] [PubMed]

A. Gordon and B. Fischer, “Phase transition theory of many-mode ordering and pulse formation in lasers,” Phys. Rev. Lett.89(10), 103901 (2002).
[CrossRef] [PubMed]

Hartwell, V.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science316(5827), 1007–1010 (2007).
[CrossRef] [PubMed]

Haus, H. A.

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron.6(6), 1173–1185 (2000).
[CrossRef]

Hillebrands, B.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature443(7110), 430–433 (2006).
[CrossRef] [PubMed]

Josserand, C.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett.95(26), 263901 (2005).
[CrossRef] [PubMed]

Klaers, J.

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature468(7323), 545–548 (2010).
[CrossRef] [PubMed]

J. Klaers, F. Vewinger, and M. Weitz, “Thermalization of a two-dimensional photonic gas in a white wall photon box,” Nat. Phys.6(7), 512–515 (2010).
[CrossRef]

Kleppner, D.

V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A44(11), 7439–7441 (1991).
[CrossRef] [PubMed]

Knox, R. S.

D. A. Sawicki and R. S. Knox, “Universal relationship between optical emission and absorption of complex systems: An alternative approach,” Phys. Rev. A54(6), 4837–4841 (1996).
[CrossRef] [PubMed]

Leggett, A. J.

A. J. Leggett, “Bose-Einstein condensation in the alkali gases: Some fundamental concepts,” Rev. Mod. Phys.73(2), 307–356 (2001).
[CrossRef]

Leonetti, M.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett.101(14), 143901 (2008).
[CrossRef] [PubMed]

Levit, B.

R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express18(16), 16520–16525 (2010).
[CrossRef] [PubMed]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105(1), 013905 (2010).
[CrossRef] [PubMed]

Matthews, M. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science269(5221), 198–201 (1995).
[CrossRef] [PubMed]

Melkov, G. A.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature443(7110), 430–433 (2006).
[CrossRef] [PubMed]

Pfeiffer, L.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science316(5827), 1007–1010 (2007).
[CrossRef] [PubMed]

Picozzi, A.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett.95(26), 263901 (2005).
[CrossRef] [PubMed]

Pomeau, Y.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett.95(26), 263901 (2005).
[CrossRef] [PubMed]

Rica, S.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett.95(26), 263901 (2005).
[CrossRef] [PubMed]

Rosen, A.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105(1), 013905 (2010).
[CrossRef] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett.95(1), 013903 (2005).
[CrossRef] [PubMed]

Ruocco, G.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett.101(14), 143901 (2008).
[CrossRef] [PubMed]

Santori, C.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science298(5591), 199–202 (2002).
[CrossRef] [PubMed]

Sawicki, D. A.

D. A. Sawicki and R. S. Knox, “Universal relationship between optical emission and absorption of complex systems: An alternative approach,” Phys. Rev. A54(6), 4837–4841 (1996).
[CrossRef] [PubMed]

Schmitt, J.

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature468(7323), 545–548 (2010).
[CrossRef] [PubMed]

Serga, A. A.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature443(7110), 430–433 (2006).
[CrossRef] [PubMed]

Slavin, A. N.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature443(7110), 430–433 (2006).
[CrossRef] [PubMed]

Smulakovski, V.

Smulakovsky, V.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105(1), 013905 (2010).
[CrossRef] [PubMed]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, “Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway,” Phys. Rev. Lett.93(15), 153901 (2004).
[CrossRef] [PubMed]

Snoke, D.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science316(5827), 1007–1010 (2007).
[CrossRef] [PubMed]

Vewinger, F.

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature468(7323), 545–548 (2010).
[CrossRef] [PubMed]

J. Klaers, F. Vewinger, and M. Weitz, “Thermalization of a two-dimensional photonic gas in a white wall photon box,” Nat. Phys.6(7), 512–515 (2010).
[CrossRef]

Vodonos, B.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, “Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway,” Phys. Rev. Lett.93(15), 153901 (2004).
[CrossRef] [PubMed]

A. Gordon, B. Vodonos, V. Smulakovski, and B. Fischer, “Melting and freezing of light pulses and modes in mode-locked lasers,” Opt. Express11(25), 3418–3424 (2003).
[CrossRef] [PubMed]

Weihs, G.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science298(5591), 199–202 (2002).
[CrossRef] [PubMed]

Weill, R.

R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express18(16), 16520–16525 (2010).
[CrossRef] [PubMed]

R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett.104(17), 173901 (2010).
[CrossRef] [PubMed]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105(1), 013905 (2010).
[CrossRef] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett.95(1), 013903 (2005).
[CrossRef] [PubMed]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, “Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway,” Phys. Rev. Lett.93(15), 153901 (2004).
[CrossRef] [PubMed]

Weitz, M.

J. Klaers, F. Vewinger, and M. Weitz, “Thermalization of a two-dimensional photonic gas in a white wall photon box,” Nat. Phys.6(7), 512–515 (2010).
[CrossRef]

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature468(7323), 545–548 (2010).
[CrossRef] [PubMed]

West, K.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science316(5827), 1007–1010 (2007).
[CrossRef] [PubMed]

Wieman, C. E.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science269(5221), 198–201 (1995).
[CrossRef] [PubMed]

Yamamoto, Y.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science298(5591), 199–202 (2002).
[CrossRef] [PubMed]

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

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron.6(6), 1173–1185 (2000).
[CrossRef]

Nat. Photonics (1)

A. Fratalocchi, “Mode-locked lasers: light condensation,” Nat. Photonics4(8), 502–503 (2010).
[CrossRef]

Nat. Phys. (1)

J. Klaers, F. Vewinger, and M. Weitz, “Thermalization of a two-dimensional photonic gas in a white wall photon box,” Nat. Phys.6(7), 512–515 (2010).
[CrossRef]

Nature (2)

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature443(7110), 430–433 (2006).
[CrossRef] [PubMed]

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature468(7323), 545–548 (2010).
[CrossRef] [PubMed]

New J. Phys. (1)

O. Gat, A. Gordon, and B. Fischer, “Light-mode locking: a new class of solvable statistical physics systems,” New J. Phys.7, 151 (2005).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (2)

V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A44(11), 7439–7441 (1991).
[CrossRef] [PubMed]

D. A. Sawicki and R. S. Knox, “Universal relationship between optical emission and absorption of complex systems: An alternative approach,” Phys. Rev. A54(6), 4837–4841 (1996).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

O. Gat, A. Gordon, and B. Fischer, “Solution of a statistical mechanics model for pulse formation in lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70, 046108 (2004).
[CrossRef] [PubMed]

Phys. Rev. Lett. (7)

A. Gordon and B. Fischer, “Phase transition theory of many-mode ordering and pulse formation in lasers,” Phys. Rev. Lett.89(10), 103901 (2002).
[CrossRef] [PubMed]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett.105(1), 013905 (2010).
[CrossRef] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett.95(1), 013903 (2005).
[CrossRef] [PubMed]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, and B. Fischer, “Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway,” Phys. Rev. Lett.93(15), 153901 (2004).
[CrossRef] [PubMed]

R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett.104(17), 173901 (2010).
[CrossRef] [PubMed]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett.95(26), 263901 (2005).
[CrossRef] [PubMed]

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett.101(14), 143901 (2008).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

A. J. Leggett, “Bose-Einstein condensation in the alkali gases: Some fundamental concepts,” Rev. Mod. Phys.73(2), 307–356 (2001).
[CrossRef]

Science (3)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science269(5221), 198–201 (1995).
[CrossRef] [PubMed]

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science298(5591), 199–202 (2002).
[CrossRef] [PubMed]

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science316(5827), 1007–1010 (2007).
[CrossRef] [PubMed]

Other (2)

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993), Ch.6.

A. E. Siegman, Lasers (University Science Books, 1986).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Spectral filtering: (a) Power law function with γ ˜ =1 and η=0.8 . (b), (c) Cut structures (solid line) obtained for example from sections of Gaussian (can be exponential etc.) filtering spectra (combined frequency dependent losses/absorption and gain). They can result from various frequency cutoff mechanisms, such as the far apart longitudinal mode separation in microcavity lasers [3,4]. The cuts lowest loss ( ε 0 ) mode at Ω ˜ =±1 are redefined to be at Ω ˜ =0 .

Fig. 2
Fig. 2

Light spectra, in a semi-logarithmic scale, obtained by Eqs. (4) and 5: (a) For the power law dependence spectral filtering example (Fig. 1a), with γ ˜ =1 and η=0.8 . The various graphs correspond (from bottom to top) to μg ε 0 =0.4,0.2,0.1,0 , and respectively to P/ P c =0.23,0.3,0.4,1 . In the cut examples (the high and low pass filters in Fig. 1b) the spectra have only the right or left of Ω=0 sides. (b) For the exponential spectral filtering given by Eq. (5), with the above μ s, γ e =1 and β ˜ =1.5 . In both figures, the three lower graphs correspond to non-condensate states, and the upper one to condensation. At and beyond the condensation transition, μ=0 ,and the spectrum stays as in the top graph, except for the lowest-loss mode p 0 at Ω=0 that grows upon further pumping (not shown here, but given in Fig. 4).

Fig. 3
Fig. 3

Normalized “chemical potential” μ=(g ε 0 ) as a function of the overall normalized laser power P/ P c for γ ˜ =1 , η=0.8 and ε N =1 .

Fig. 4
Fig. 4

Condensation transition: Normalized lowest mode power p 0 / P C as a function of the overall normalized laser power for γ ˜ =1 , η=0.8 and ε N =1 . Above the phase transition ( P P C ) all the excess power goes to p 0 - the condensation state.

Equations (7)

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

d a m dτ =(g ε m ) a m + Γ m ,
< Γ m (τ) Γ n * (τ')>=2Tδ( ττ' ) δ mn
< Γ m (τ)>=0
P= m p m = m < a m a * m > = m T ε m g T ε 0 g +T 0 ε N ρ(ε)dε ε+ ε 0 g
ρ(ε)= V d (2π) d d d kδ(ε γ|Ω | η )( C d η γ ξ+1 ) ε ξ
p( Ω ˜ )= C d T ε( Ω ˜ )+ ε 0 g
p( Ω ˜ )= C d T γ e ( e β ˜ | Ω ˜ | 1)+( ε 0 g)

Metrics