Abstract

A semi-analytic tool is developed for investigating pulse dynamics in mode-locked lasers. It provides a set of rate equations for pulse energy, width, and chirp, whose solutions predict how these pulse parameters evolve from one round trip to the next and how they approach their final steady-state values. An actively mode-locked laser is investigated using this technique and the results are in excellent agreement with numerical simulations and previous analytical studies.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. D. J. Kuizenga and A. E. Siegman, �??FM and AM Mode Locking of the Homogeneous Laser�??Part I: Theory,�?? IEEE J. Quantum Electron. QE-6, 694-708 (1970).
    [CrossRef]
  2. S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov �??Averaged description of wave beams in linear and nonlinear media (the method of moments),�?? Radiophys. Quantum Electron. 14, 1062-1070 (1971).
    [CrossRef]
  3. C. J. McKinstrie, �??Effects of filtering on Gordon-Haus timing jitter in dispersion-managed systems,�?? J. Opt. Soc. Am. B 19, 1275-1285 (2002).
    [CrossRef]
  4. J. Santhanam and G. P. Agrawal, �??Raman-induced spectral shifts in optical fibers: general theory based on the moment method,�?? Opt. Commun. 222, 413-420 (2003).
    [CrossRef]
  5. H. A. Haus and Y. Silberberg, �??Laser Mode Locking with Addition of Nonliner Index,�?? IEEE J. Quantum Electron. QE-22, 325-331 (1986).
    [CrossRef]
  6. G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic Press, New York, 2001).
  7. F. X. Kärtner, D. Kopf, and U. Keller, �??Solitary-pulse stabilization and shortening in actively mode-locked lasers,�?? J. Opt. Soc. Am. B 12, 486-496 (1995).
    [CrossRef]

IEEE J. Quantum Electron.

H. A. Haus and Y. Silberberg, �??Laser Mode Locking with Addition of Nonliner Index,�?? IEEE J. Quantum Electron. QE-22, 325-331 (1986).
[CrossRef]

D. J. Kuizenga and A. E. Siegman, �??FM and AM Mode Locking of the Homogeneous Laser�??Part I: Theory,�?? IEEE J. Quantum Electron. QE-6, 694-708 (1970).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

J. Santhanam and G. P. Agrawal, �??Raman-induced spectral shifts in optical fibers: general theory based on the moment method,�?? Opt. Commun. 222, 413-420 (2003).
[CrossRef]

Radiophys. Quantum Electron.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov �??Averaged description of wave beams in linear and nonlinear media (the method of moments),�?? Radiophys. Quantum Electron. 14, 1062-1070 (1971).
[CrossRef]

Other

G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic Press, New York, 2001).

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 (2)

Fig. 1.
Fig. 1.

Changes in pulse energy, width, and chirp over multiple round trips assuming a Gaussian pulse in the normal dispersion regime (top row) and an autosoliton shape in the anomalous-dispersion region (bottom row). The energy scale has been magnified to illustrate that the oscillatory behavior persists for more than 1000 round trips.

Fig. 2.
Fig. 2.

Steady-state pulse width and chirp as functions of β̄2 (left column) and nonlinear parameter γ̄ (right column). Dispersion is normal for the top row and anomalous for the bottom row. The discrete markers come from solving Eq. (1) while the solid lines come from solving Eqs. (14)(16).

Equations (18)

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

T R A T + i 2 ( β ̅ 2 + i g ̅ T 2 2 ) L R 2 A t 2 = i γ ̅ L R A 2 A + 1 2 ( g ̅ α ̅ ) L R A + M ( A , t ) ,
P ave = 1 T m T m 2 T m 2 A ( t , z ) 2 dt .
A ( T , t ) = a [ sech ( t τ ) ] 1 + i q exp [ i ϕ ( T ) ] ,
A ( T , t ) = a [ exp ( t 2 2 τ 2 ) ] 1 + i q exp [ i ϕ ( T ) ] .
E ( T ) = A ( T , t ) 2 d t ,
τ 2 ( T ) = 2 C 1 E t 2 A ( T , t ) 2 d t ,
q ( T ) = i E t [ A * A t A A * t ] d t ,
d E d T = [ A * A t + A A * t ] d t ,
τ d τ d T = 1 2 E d E d T τ 2 + 1 C 1 E t 2 [ A * A t + A A * t ] d t ,
dq d T = 1 E d E d T q + i E t [ T ( A * A t ) T ( A A * t ) ] d t .
T R E d E d T = ( g ̅ α ̅ ) L R C 0 g ̅ T 2 2 L R 2 τ 2 ( 1 + q 2 ) 1 2 C 1 Δ A M ω m 2 τ 2 ,
2 τ T R d T = ( 2 β ̅ 2 L R C 1 ) q + C 2 g ̅ T 2 2 L R ( C 3 q 2 ) C 4 Δ A M ω m 2 τ 4 ,
τ 2 T R d q d T = C 0 β ̅ 2 L R ( 1 + q 2 ) C 5 g ̅ T 2 2 L R ( 1 + q 2 ) q + C 6 γ ̅ L R E τ 2 π C 1 Δ A M ω m 2 τ 4 q ,
g ̅ s s = ( α ̅ + Δ A M ω 2 τ s s 2 2 C 5 L R ) [ 1 T 2 2 2 τ s s 2 ( 1 + q s s 2 ) ] 1 ,
τ s s = ( C 4 Δ A M ω m 2 L R ) 1 4 [ ( 2 β ̅ 2 C 1 ) q s s + C 2 g ̅ s s T 2 2 ( C 3 q s s 2 ) ] 1 4 ,
q s s = d ± [ d 2 + C 3 + C 6 γ ̅ E τ s s ( C 5 β ̅ 2 2 π ) ] 1 2 ,
d = 1 2 β ̅ 2 [ ( 1 + C 3 ) g ̅ s s T 2 2 + ( C 1 C 5 C 4 C 2 ) Δ A M ω m 2 τ s s 4 L R ] .
τ s s = ( g ̅ L R Δ A M ) 1 4 T 2 ω m .

Metrics