Abstract

We have recently predicted (R. Weill, B. Fischer and O. Gat, Phys. Rev. Lett. 104, 173901, 2010) condensation of light in actively mode locked lasers when the laser power increases, or the noise, that takes the role of temperature, decreases. The condensate is characterized by strong light pulses due to the dominance of the lowest eigenmode (“ground state”) power. Here, we experimentally demonstrate, for the first time, light mode condensation transition in an actively mode-locked fiber laser. Following the theoretical prediction, the condensation is obtained for modulations that have a power law dependence on time with exponents smaller than 2. The laser light system is strictly one dimensional, a special opportunity in experimental physics. We also discuss experimental schemes for condensation in two- and three-dimensional laser systems.

© 2010 OSA

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  1. E. A. Cornell and C. E. Wieman, “The Bose-Einstein condensate,” Sci. Am. 278(3), 40–45 (1998).
    [CrossRef]
  2. A. J. Leggett, “Bose-Einstein condensation in the alkali gases: some fundamental concepts,” Rev. Mod. Phys. 73(2), 307–356 (2001).
    [CrossRef]
  3. V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A 44(11), 7439–7441 (1991).
    [CrossRef] [PubMed]
  4. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett. 95(26), 263901 (2005).
    [CrossRef]
  5. 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]
  6. 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]
  7. O. Gat, A. Gordon, and B. Fischer, “Light-mode locking: a new class of solvable statistical physics systems,” N. J. Phys. 7, 151 (2005).
    [CrossRef]
  8. 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]
  9. A. Gordon, B. Vodonos, V. Smulakovski, and B. Fischer, “Melting and freezing of light pulses and modes in mode-locked lasers,” Opt. Express 11(25), 3418–3424 (2003).
    [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. A. Gordon and B. Fischer, “Statistical-mechanics theory of active mode locking with noise,” Opt. Lett. 29(9), 1022–1024 (2004).
    [CrossRef] [PubMed]
  13. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1173–1185 (2000).
    [CrossRef]
  14. F. Rana, R. J. Ram, and H. A. Haus, “Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation,” IEEE J. Quantum Electron. 40(1), 41–56 (2004).
    [CrossRef]
  15. R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett. 104(17), 173901 (2010).
    [CrossRef] [PubMed]

2010

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

2008

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]

2005

O. Gat, A. Gordon, and B. Fischer, “Light-mode locking: a new class of solvable statistical physics systems,” N. 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]

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

2004

A. Gordon and B. Fischer, “Statistical-mechanics theory of active mode locking with noise,” Opt. Lett. 29(9), 1022–1024 (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]

F. Rana, R. J. Ram, and H. A. Haus, “Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation,” IEEE J. Quantum Electron. 40(1), 41–56 (2004).
[CrossRef]

2003

A. Gordon, B. Vodonos, V. Smulakovski, and B. Fischer, “Melting and freezing of light pulses and modes in mode-locked lasers,” Opt. Express 11(25), 3418–3424 (2003).
[CrossRef] [PubMed]

2002

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]

2001

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

2000

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

1998

E. A. Cornell and C. E. Wieman, “The Bose-Einstein condensate,” Sci. Am. 278(3), 40–45 (1998).
[CrossRef]

1991

V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A 44(11), 7439–7441 (1991).
[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. A 44(11), 7439–7441 (1991).
[CrossRef] [PubMed]

Bekker, 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]

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]

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]

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.

E. A. Cornell and C. E. Wieman, “The Bose-Einstein condensate,” Sci. Am. 278(3), 40–45 (1998).
[CrossRef]

Fischer, B.

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]

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

A. Gordon and B. Fischer, “Statistical-mechanics theory of active mode locking with noise,” Opt. Lett. 29(9), 1022–1024 (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. Express 11(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.

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, 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,” N. J. Phys. 7, 151 (2005).
[CrossRef]

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]

Gordon, A.

O. Gat, A. Gordon, and B. Fischer, “Light-mode locking: a new class of solvable statistical physics systems,” N. 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]

A. Gordon and B. Fischer, “Statistical-mechanics theory of active mode locking with noise,” Opt. Lett. 29(9), 1022–1024 (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. Express 11(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]

Haus, H. A.

F. Rana, R. J. Ram, and H. A. Haus, “Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation,” IEEE J. Quantum Electron. 40(1), 41–56 (2004).
[CrossRef]

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

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]

Kleppner, D.

V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A 44(11), 7439–7441 (1991).
[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.

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]

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]

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]

Ram, R. J.

F. Rana, R. J. Ram, and H. A. Haus, “Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation,” IEEE J. Quantum Electron. 40(1), 41–56 (2004).
[CrossRef]

Rana, F.

F. Rana, R. J. Ram, and H. A. Haus, “Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation,” IEEE J. Quantum Electron. 40(1), 41–56 (2004).
[CrossRef]

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]

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]

Smulakovski, V.

A. Gordon, B. Vodonos, V. Smulakovski, and B. Fischer, “Melting and freezing of light pulses and modes in mode-locked lasers,” Opt. Express 11(25), 3418–3424 (2003).
[CrossRef] [PubMed]

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]

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. Express 11(25), 3418–3424 (2003).
[CrossRef] [PubMed]

Weill, R.

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

Wieman, C. E.

E. A. Cornell and C. E. Wieman, “The Bose-Einstein condensate,” Sci. Am. 278(3), 40–45 (1998).
[CrossRef]

IEEE J. Quantum Electron.

F. Rana, R. J. Ram, and H. A. Haus, “Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation,” IEEE J. Quantum Electron. 40(1), 41–56 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

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

N. J. Phys.

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

Opt. Express

A. Gordon, B. Vodonos, V. Smulakovski, and B. Fischer, “Melting and freezing of light pulses and modes in mode-locked lasers,” Opt. Express 11(25), 3418–3424 (2003).
[CrossRef] [PubMed]

Opt. Lett.

A. Gordon and B. Fischer, “Statistical-mechanics theory of active mode locking with noise,” Opt. Lett. 29(9), 1022–1024 (2004).
[CrossRef] [PubMed]

Phys. Rev. A

V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A 44(11), 7439–7441 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett.

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

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]

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]

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

Rev. Mod. Phys.

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

Sci. Am.

E. A. Cornell and C. E. Wieman, “The Bose-Einstein condensate,” Sci. Am. 278(3), 40–45 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Actively mode-locked laser: The Experimental setup of the mode-locked ring fiber laser with electro-optic modulator and an external noise source. EDF, erbium-doped fiber; ASE, amplified spontaneous emission.

Fig. 2
Fig. 2

Theoretical calculation of the AML condensation, following Ref. 4: Graph of the power in the first eigenmode p 0 / P versus the normalized overall laser cavity power P / P C ( η = 1 ) , showing sharp transitions for η = 1 / 2 ,     1 , and gradual changes for η = 2 ,       4 . The calculation is done for N = 106.

Fig. 3
Fig. 3

Experiment showing the condensation: The dependence on the overall laser cavity power normalized by P C ( η = 1 ) 6.7 p J of: (a) The measured normalized pulse peak power, and (b) the pulse energy, given by the peak power multiplied by the width of the lowest eigenmode for each η taken from the calculation that was found to match the experimental values in Fig. 4. It measures the first eigenmode occupancy. We can see the similarity to the theoretical graphs in Fig. 2, with a sharp transition for η = 1 / 2 ,     1 , and a gradual slow growth for η = 2 ,     4 . The solid lines are the theoretical fits to the experimental results, numerically calculated from the waveforms and eigenfunctions expansion for N = 1000.

Fig. 4
Fig. 4

Measured output light waveforms: Shown for η = 1 / 2 ,     1 ,     2 ,     4 at three power levels marked in Fig. 3: (A) P / P C ( η = 1 ) 0.4 , (B) P / P C ( η = 1 ) 0.8 , and (C) P / P C ( η = 1 ) 1.95 . The condensation is seen through the transition from low-amplitude noisy waveforms to high peak power pulses with ~1ns widths for η = 1 / 2 ,     1 . The cavity roundtrip time is t R = 641 . 8 n s e c . Note the different power scale in the vertical axis for the various total cavity power.

Equations (3)

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

P = | ψ | 2 d t t R = T ε 0 g + T 0 M ρ ( ε ) d ε ε + ε 0 g       ,
ρ ( ε ) = C η N M ( ε M ) 1 η 1 2     ,                     C η = 1 4 π 0 1 d s 1 s η       ,
O ^ ( t , y , z ) = ( γ g i γ d ) 2 t 2 + ( γ 1 + i γ 2 ) 2 V x ( t ) V ( y , z )     ,

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