Abstract

We propose a feedback technique for obtaining stable mode-locked operation in lasers that would normally exhibit Q switching. Using the Haus model with population dynamics, we examine numerically the case in which the intensity is monitored by a slow detector and fed back to the pump power after electronic derivation. This approach allows elimination of Q switching in all situations considered, in particular, in lasers with a long upper-state lifetime.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Haus, IEEE J. Quantum Electron. 12, 169 (1976).
    [Crossref]
  2. F. X. Kärtner, L. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, Opt. Eng. 34, 2024 (1995).
    [Crossref]
  3. C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, J. Opt. Soc. Am. 16, 46 (1999).
  4. F. Krausz, IEEE J. Quantum Electron. 28, 2097 (1992).
    [Crossref]
  5. S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993).
    [Crossref] [PubMed]
  6. Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
    [Crossref] [PubMed]
  7. K. Pyragas, F. Lange, and A. Kittel, Phys. Rev. E 61, 3271 (2000).
    [Crossref]
  8. E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
    [Crossref] [PubMed]
  9. The perturbations are small in the sense that, in the absence of noise, they tend to zero when the desired state is reached. This zero limit is a major consequence of the fact that the desired state exists (in an unstable form here).
  10. H. Haus, J. Fujimoto, and E. Ippen, J. Opt. Soc. Am. B 8, 2068 (1991).
    [Crossref]
  11. A. Dunlop, W. Firth, D. Heatley, and E. Wright, Opt. Lett. 21, 770 (1996).
    [Crossref] [PubMed]
  12. Note that, as in previous work,1 we do not take into account the term -iNEθ on the right-hand side of Eq.  (1). This simplification results in neglect of the change of cavity length induced by the presence of the active medium.
  13. F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Quantum Electron. 4, 159 (1998).
  14. The important point is that, at the Q-switch frequency, we introduce a π/2 phase shift between the detected signal IT and the correction.5,6 Other forms of feedback with this property should a priori be possible.
  15. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  16. T. R. Schibli, U. Morgner, and F. X. Kärtner, Opt. Lett. 26, 148 (2001).
    [Crossref]

2001 (1)

2000 (1)

K. Pyragas, F. Lange, and A. Kittel, Phys. Rev. E 61, 3271 (2000).
[Crossref]

1999 (1)

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, J. Opt. Soc. Am. 16, 46 (1999).

1998 (1)

F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Quantum Electron. 4, 159 (1998).

1996 (1)

1995 (1)

F. X. Kärtner, L. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, Opt. Eng. 34, 2024 (1995).
[Crossref]

1993 (1)

S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993).
[Crossref] [PubMed]

1992 (2)

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

F. Krausz, IEEE J. Quantum Electron. 28, 2097 (1992).
[Crossref]

1991 (1)

1990 (1)

E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
[Crossref] [PubMed]

1976 (1)

H. Haus, IEEE J. Quantum Electron. 12, 169 (1976).
[Crossref]

Aus der Au, J.

F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Quantum Electron. 4, 159 (1998).

Bielawski, S.

S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993).
[Crossref] [PubMed]

Bouazaoui, M.

S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993).
[Crossref] [PubMed]

Brovelli, L.

F. X. Kärtner, L. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, Opt. Eng. 34, 2024 (1995).
[Crossref]

Calasso, I.

F. X. Kärtner, L. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, Opt. Eng. 34, 2024 (1995).
[Crossref]

Derozier, D.

S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993).
[Crossref] [PubMed]

Dunlop, A.

Firth, W.

Fujimoto, J.

Gills, Z.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

Glorieux, P.

S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993).
[Crossref] [PubMed]

Grebogi, C.

E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
[Crossref] [PubMed]

Haus, H.

Heatley, D.

Hönninger, C.

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, J. Opt. Soc. Am. 16, 46 (1999).

Ippen, E.

Iwata, C.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

Kamp, M.

F. X. Kärtner, L. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, Opt. Eng. 34, 2024 (1995).
[Crossref]

Kärtner, F. X.

T. R. Schibli, U. Morgner, and F. X. Kärtner, Opt. Lett. 26, 148 (2001).
[Crossref]

F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Quantum Electron. 4, 159 (1998).

F. X. Kärtner, L. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, Opt. Eng. 34, 2024 (1995).
[Crossref]

Keller, U.

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, J. Opt. Soc. Am. 16, 46 (1999).

F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Quantum Electron. 4, 159 (1998).

F. X. Kärtner, L. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, Opt. Eng. 34, 2024 (1995).
[Crossref]

Kittel, A.

K. Pyragas, F. Lange, and A. Kittel, Phys. Rev. E 61, 3271 (2000).
[Crossref]

Kopf, D.

F. X. Kärtner, L. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, Opt. Eng. 34, 2024 (1995).
[Crossref]

Krausz, F.

F. Krausz, IEEE J. Quantum Electron. 28, 2097 (1992).
[Crossref]

Lange, F.

K. Pyragas, F. Lange, and A. Kittel, Phys. Rev. E 61, 3271 (2000).
[Crossref]

Morgner, U.

Morier-Genoud, F.

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, J. Opt. Soc. Am. 16, 46 (1999).

Moser, M.

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, J. Opt. Soc. Am. 16, 46 (1999).

Ott, E.

E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
[Crossref] [PubMed]

Paschotta, R.

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, J. Opt. Soc. Am. 16, 46 (1999).

Pyragas, K.

K. Pyragas, F. Lange, and A. Kittel, Phys. Rev. E 61, 3271 (2000).
[Crossref]

Roy, R.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

Schibli, T. R.

Schwartz, I. B.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Triandaf, I.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

Wright, E.

Yorke, J. A.

E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (3)

H. Haus, IEEE J. Quantum Electron. 12, 169 (1976).
[Crossref]

F. Krausz, IEEE J. Quantum Electron. 28, 2097 (1992).
[Crossref]

F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Quantum Electron. 4, 159 (1998).

J. Opt. Soc. Am. (1)

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, J. Opt. Soc. Am. 16, 46 (1999).

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

Opt. Eng. (1)

F. X. Kärtner, L. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, Opt. Eng. 34, 2024 (1995).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993).
[Crossref] [PubMed]

Phys. Rev. E (1)

K. Pyragas, F. Lange, and A. Kittel, Phys. Rev. E 61, 3271 (2000).
[Crossref]

Phys. Rev. Lett. (2)

E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
[Crossref] [PubMed]

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

Other (4)

The perturbations are small in the sense that, in the absence of noise, they tend to zero when the desired state is reached. This zero limit is a major consequence of the fact that the desired state exists (in an unstable form here).

Note that, as in previous work,1 we do not take into account the term -iNEθ on the right-hand side of Eq.  (1). This simplification results in neglect of the change of cavity length induced by the presence of the active medium.

The important point is that, at the Q-switch frequency, we introduce a π/2 phase shift between the detected signal IT and the correction.5,6 Other forms of feedback with this property should a priori be possible.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 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 (3)

Fig. 1
Fig. 1

Suppression of QS in the model [Eqs.  (1) and (2)] when feedback control is applied (right), starting from a situation of QSML (left). The gray scale corresponds to the field intensity (white corresponds to high intensities). This figure can be interpreted as a stroboscopic view of the pulse profile, Eθ (vertical section), at each cavity round trip (horizontal scale). Nonlinear loss parameter a=0.01. Only the part in which the pulse is present θ/γ0,270 ps is represented.

Fig. 2
Fig. 2

Pulse duration (FWHM) versus nonlinear loss parameter a, predicted for a Nd:YLF laser. With feedback (β=-8.5, solid curve), stable ML operation occurs along the whole curve. Without feedback (β=0, squares), Q-switch instabilities appear for a>aQ=0.003, and ML fails for a>0.028. For QSML, the duration of the maximum-intensity pulses is represented.

Fig. 3
Fig. 3

Stability regions of the ML state versus cutoff frequency ωC and feedback gain β. Other parameters are the same as in Fig.  1.

Equations (8)

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

ET=-1+kE2E+NE+Eθθ-iDEθθ,
NT=γA-1+L-10LE2dθN,
AT=A01+βITT,
IT=L-10LEθ,T2dθ.
kE2=a/1+bE2.
uT=ωG-u+v,
vT=ωD-v+βIT,
NT=γA-1N0-A+1N-NL-10LE2dθ.

Metrics