Abstract

We present a first experimental demonstration of melting of light pulses and freezing of lightwave modes by applying external noise which acts like temperature, verifying our recent theoretical prediction (Gordon and Fischer [1]). The experiment was performed in a fiber laser passively mode-locked by nonlinear rotation of polarization. The first order phase transition was observed directly in time domain and also by measurement of the quartic order parameter (RF power).

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. A. Gordon and B. Fischer, �??Phase Transition Theory of Many-Mode Ordering and Pulse Formation in Lasers,�?? Phys. Rev. Lett. 89, 103901, (2002).
    [CrossRef] [PubMed]
  2. H. A. Haus, �??Mode-Locking of Lasers,�?? IEEE J. Sel. Top. Quant. 6, 1173 (2000).
    [CrossRef]
  3. H. Haken and H. Ohno, �??Theory of Ultra-Short Laser Pulses�??, Opt. Commun. 16, 205 (1976).
    [CrossRef]
  4. H. A. Haus, �??Parameter Ranges for CW Passive Mode Locking,�?? IEEE J. Quantum Electron. 12, 169 (1976).
    [CrossRef]
  5. H. Haken and H. Ohno, �??Onset of ultrashort laser pulses: first or second order phase transition?,�?? Opt. Commun. 26, 117 (1978).
    [CrossRef]
  6. H. Haken, Synergetics, 2-nd ed., Springler-Verlag, Berlin Heidelberg New-York (1978).
    [CrossRef]
  7. E. P. Ippen, L. Y. Liu and H. A. Haus, �??Self-Starting Condition for Additive-Pulse Mode-Locked Lasers,�?? Opt. Lett. 15, 183 (1990).
    [CrossRef] [PubMed]
  8. C. J. Chen, P. K. A. Wai and C. R. Menyuk, �??Self-Starting of Passively Mode-Locked Lasers with Fast Saturable Absorbers,�?? Opt. Lett. 20 (4), 350 (1995).
    [CrossRef] [PubMed]
  9. F. Fontana, M. Begotti, E. M. Pessina and L. A. Lugiato, �??Maxwell-Bloch ML Instabilities in Erbium-Doped Fiber Lasers,�?? Opt. Commun. 114, 89 (1995).
    [CrossRef]
  10. M. A. Marioni and A. A. Hnilo, �??Self-Starting of Self Mode-Locking Ti:Sapphire Lasers. Description with a Poincare Map,�?? Opt. Commun. 147, 89 (1998).
    [CrossRef]
  11. T. Kapitula, J. N. Kutz, Björn Sandstede, �??Stability of Pulses in the Master Mode-Locking Equation,�?? J. Opt. Soc. Am. B 19, 740, (2002).
    [CrossRef]
  12. F. Krausz, T. Brabec and Ch. Spilmann, �??Self-Starting of Passive Mode Locking,�?? Opt. Lett. 16, 235 (1991).
    [CrossRef] [PubMed]
  13. H. A. Haus and E. P. Ippen, �??Self-Starting of Passively Mode-Locked Lasers,�?? Opt. Lett. 16, 1331 (1991).
    [CrossRef] [PubMed]
  14. J. Herrmann, �??Starting dynamic, self-starting condition and mode-locking threshold in passive, coupled-cavity or Kerr-lens mode-locked solid-state lasers,�?? Opt. Commun. 98, 111 (1993).
    [CrossRef]
  15. V. DeGiorgio and M. O. Scully, �??Analogy between the Laser Threshold Region and a Second-Order Phase Transition,�?? Phys. Rev. A 2, 1170 (1970).
    [CrossRef]
  16. H. A. Haus and A. Mecozzi, �??Noise os Mode-Locked Lasers,�?? IEEE J. Quantum Electron. 29, 983 (1993).
    [CrossRef]
  17. H. E. Stanley, Introduction to phase transitions and critical phenomena, Oxford University Press, NY and Oxford (1971).
  18. A. Gordon and B Fischer, �??Phase transition theory of pulse formation in passively mode-locked lasers with dispersion and Kerr nonlinearity,�?? Opt. Commun 223, 151 (2003).
    [CrossRef]
  19. A. Gordon and B. Fischer, �??Inhibition of modulation instability in lasers by noise,�?? Opt. Lett. 28, 1326 (2003).
    [CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

H. A. Haus, �??Parameter Ranges for CW Passive Mode Locking,�?? IEEE J. Quantum Electron. 12, 169 (1976).
[CrossRef]

H. A. Haus and A. Mecozzi, �??Noise os Mode-Locked Lasers,�?? IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

IEEE J. Sel. Top. Quant. (1)

H. A. Haus, �??Mode-Locking of Lasers,�?? IEEE J. Sel. Top. Quant. 6, 1173 (2000).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun (1)

A. Gordon and B Fischer, �??Phase transition theory of pulse formation in passively mode-locked lasers with dispersion and Kerr nonlinearity,�?? Opt. Commun 223, 151 (2003).
[CrossRef]

Opt. Commun. (5)

J. Herrmann, �??Starting dynamic, self-starting condition and mode-locking threshold in passive, coupled-cavity or Kerr-lens mode-locked solid-state lasers,�?? Opt. Commun. 98, 111 (1993).
[CrossRef]

H. Haken and H. Ohno, �??Theory of Ultra-Short Laser Pulses�??, Opt. Commun. 16, 205 (1976).
[CrossRef]

H. Haken and H. Ohno, �??Onset of ultrashort laser pulses: first or second order phase transition?,�?? Opt. Commun. 26, 117 (1978).
[CrossRef]

F. Fontana, M. Begotti, E. M. Pessina and L. A. Lugiato, �??Maxwell-Bloch ML Instabilities in Erbium-Doped Fiber Lasers,�?? Opt. Commun. 114, 89 (1995).
[CrossRef]

M. A. Marioni and A. A. Hnilo, �??Self-Starting of Self Mode-Locking Ti:Sapphire Lasers. Description with a Poincare Map,�?? Opt. Commun. 147, 89 (1998).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (1)

V. DeGiorgio and M. O. Scully, �??Analogy between the Laser Threshold Region and a Second-Order Phase Transition,�?? Phys. Rev. A 2, 1170 (1970).
[CrossRef]

Phys. Rev. Lett. (1)

A. Gordon and B. Fischer, �??Phase Transition Theory of Many-Mode Ordering and Pulse Formation in Lasers,�?? Phys. Rev. Lett. 89, 103901, (2002).
[CrossRef] [PubMed]

Other (2)

H. E. Stanley, Introduction to phase transitions and critical phenomena, Oxford University Press, NY and Oxford (1971).

H. Haken, Synergetics, 2-nd ed., Springler-Verlag, Berlin Heidelberg New-York (1978).
[CrossRef]

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 (5)

Fig. 1.
Fig. 1.

Two regimes of a many-mode laser, illustrated in the spectral domain (on the left, where the length and angle of the arrow represent amplitudes and phases (phasors) of the electric field of the optical modes (“particles”) respectively) and in the time domain (on the right). In the ordered state (phase) the modes are correlated (locked), and add up to form a pulse (upper pictures). In the disordered state (lower pictures) the non-correlated modes add up to a noisy “continuous” light.

Fig. 2.
Fig. 2.

Experimental configuration of the PML fiber laser system. It consists of an Erbium doped fiber amplifier (EDFA) pumped by a 980 nm laser source through a WDM coupler, an isolator that assures oscillations in one direction only, while the polarization controllers (PC), long fiber span (SMF) and the polarizer provide the saturable absorber [2]. The external noise source for the tunable noise (“temperature”) is constructed from filtered amplified spontaneous emission (ASE) source, high power EDFA and variable optical attenuator (VOA).

Fig. 3.
Fig. 3.

The temporal waveform (light intensity as a function of time) of the laser as a function of the “temperature” (noise) showing the melting of pulses as the temperature is increased and passes the transition temperature Tc . Numerical simulation (a) and experiment (b, c) shown in a small range (b) and a larger range (c) of time and tempetature. In the experiment, in addition to the clear phase transition, one can witness in (c) the gradual disappearance of additional pulses per period upon “heating”.

Fig. 4.
Fig. 4.

Theoretical and experimental plots of the order parameter Q vs. the optical noise T (“temperature”). The theoretical curve (a) was obtained by a Monte-Carlo simulation of the Gibbs distribution (squares), by a direct simulation of the equations of motion (crosses) and by mean field theory (lines) [1]. Here the temperature is normalized by the square of the light power P. The experimental results in (b) were measured by an RF power meter (for a pumping current of 30mA). One can see the discontinuity (“latent heat”) in the order parameter with the predicted phase transition of the first kind.

Fig. 5.
Fig. 5.

More experimental plots of the order parameter Q vs. the optical noise T (“temperature”) measured by an RF power meter. In (a–b) we find again the typical discontinuity in the order parameter for different laser pumping currents (of 40 and 70 mA, respectively). In (c) there is a second large discontinuity, and in (d) a gradual (diffused) transition that is actually a cascade of small discontinuities (its lower part is seen in the zoomed inset), associated with the build-up of additional pulses in the cavity.

Equations (1)

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

e / T ,

Metrics