Abstract

We employ a recently developed gain balance principle to study the problem of passive mode locking with a slow saturable absorber in the presence of noise and solitonic pulse compression. We calculate the compression of the chirped pulse under general conditions and show that there is a minimal achievable pulse width owing to stability requirements. We derive the slow-absorber mode locking parameter, which must exceed a pulse-width-dependent minimal value to sustain mode locking, and calculate the fraction of the total intracavity power that resides in the pulse. We show that choosing the system parameters in an attempt to achieve shorter pulses reduces the pulse power, which, in contrast to fast-absorber passive mode locking, can attain arbitrary small values. Finally, we discuss the modification of the continuum stability condition needed to account for the effect of noise.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. D. Jung, F. X. Kartner, L. R. Brovelli, M. Kamp, and U. Keller, Opt. Lett. 20, 1892 (1995).
    [CrossRef] [PubMed]
  2. F. X. Kartner, I. D. Jung, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 2, 540 (1996).
    [CrossRef]
  3. L. W. Shi, Y. H. Chen, B. Xu, Z. C. Wang, Y. H. Jiao, and Z. G. Wang, J. Phys. D 40, R307 (2007).
    [CrossRef]
  4. E. P. Ippen, Appl. Phys. B 58, 159 (1994).
    [CrossRef]
  5. F. X. Kartner and U. Keller, Opt. Lett. 20, 16 (1995).
    [CrossRef] [PubMed]
  6. F. X. Kartner, J. A. der Au, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 159 (1998).
    [CrossRef]
  7. N. N. Akhmediev, A. Ankiewicz, M. J. Lederer, and B. Luther-Davies, Opt. Lett. 23, 280 (1998).
    [CrossRef]
  8. R. Paschotta and U. Keller, Appl. Phys. B 73, 653 (2001).
    [CrossRef]
  9. H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
    [CrossRef]
  10. A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
    [CrossRef] [PubMed]
  11. A. Gordon, B. Vodonos, V. Smulakovski, and B. Fischer, Opt. Express 11, 3418 (2003).
    [CrossRef] [PubMed]
  12. O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
    [CrossRef]
  13. R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, Phys. Rev. Lett. 97, 013903 (2005).
    [CrossRef]
  14. A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, Opt. Express 14, 11142 (2006).
    [CrossRef] [PubMed]
  15. M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
    [CrossRef] [PubMed]

2007 (1)

L. W. Shi, Y. H. Chen, B. Xu, Z. C. Wang, Y. H. Jiao, and Z. G. Wang, J. Phys. D 40, R307 (2007).
[CrossRef]

2006 (2)

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, Opt. Express 14, 11142 (2006).
[CrossRef] [PubMed]

2005 (1)

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, Phys. Rev. Lett. 97, 013903 (2005).
[CrossRef]

2004 (1)

O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
[CrossRef]

2003 (1)

2002 (1)

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef] [PubMed]

2001 (1)

R. Paschotta and U. Keller, Appl. Phys. B 73, 653 (2001).
[CrossRef]

2000 (1)

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

1998 (2)

F. X. Kartner, J. A. der Au, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 159 (1998).
[CrossRef]

N. N. Akhmediev, A. Ankiewicz, M. J. Lederer, and B. Luther-Davies, Opt. Lett. 23, 280 (1998).
[CrossRef]

1996 (1)

F. X. Kartner, I. D. Jung, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 2, 540 (1996).
[CrossRef]

1995 (2)

1994 (1)

E. P. Ippen, Appl. Phys. B 58, 159 (1994).
[CrossRef]

Akhmediev, N. N.

Ankiewicz, A.

Brovelli, L. R.

Chen, Y. H.

L. W. Shi, Y. H. Chen, B. Xu, Z. C. Wang, Y. H. Jiao, and Z. G. Wang, J. Phys. D 40, R307 (2007).
[CrossRef]

der Au, J. A.

F. X. Kartner, J. A. der Au, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 159 (1998).
[CrossRef]

Fischer, B.

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, Opt. Express 14, 11142 (2006).
[CrossRef] [PubMed]

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, Phys. Rev. Lett. 97, 013903 (2005).
[CrossRef]

O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
[CrossRef]

A. Gordon, B. Vodonos, V. Smulakovski, and B. Fischer, Opt. Express 11, 3418 (2003).
[CrossRef] [PubMed]

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef] [PubMed]

Gat, O.

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, Opt. Express 14, 11142 (2006).
[CrossRef] [PubMed]

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, Phys. Rev. Lett. 97, 013903 (2005).
[CrossRef]

O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
[CrossRef]

Gordon, A.

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

A. Gordon, O. Gat, B. Fischer, and F. X. Kartner, Opt. Express 14, 11142 (2006).
[CrossRef] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, Phys. Rev. Lett. 97, 013903 (2005).
[CrossRef]

O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
[CrossRef]

A. Gordon, B. Vodonos, V. Smulakovski, and B. Fischer, Opt. Express 11, 3418 (2003).
[CrossRef] [PubMed]

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef] [PubMed]

Haus, H. A.

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

Ippen, E. P.

E. P. Ippen, Appl. Phys. B 58, 159 (1994).
[CrossRef]

Jiao, Y. H.

L. W. Shi, Y. H. Chen, B. Xu, Z. C. Wang, Y. H. Jiao, and Z. G. Wang, J. Phys. D 40, R307 (2007).
[CrossRef]

Jung, I. D.

F. X. Kartner, I. D. Jung, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 2, 540 (1996).
[CrossRef]

I. D. Jung, F. X. Kartner, L. R. Brovelli, M. Kamp, and U. Keller, Opt. Lett. 20, 1892 (1995).
[CrossRef] [PubMed]

Kamp, M.

Kartner, F. X.

Katz, M.

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

Keller, U.

R. Paschotta and U. Keller, Appl. Phys. B 73, 653 (2001).
[CrossRef]

F. X. Kartner, J. A. der Au, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 159 (1998).
[CrossRef]

F. X. Kartner, I. D. Jung, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 2, 540 (1996).
[CrossRef]

I. D. Jung, F. X. Kartner, L. R. Brovelli, M. Kamp, and U. Keller, Opt. Lett. 20, 1892 (1995).
[CrossRef] [PubMed]

F. X. Kartner and U. Keller, Opt. Lett. 20, 16 (1995).
[CrossRef] [PubMed]

Lederer, M. J.

Luther-Davies, B.

Paschotta, R.

R. Paschotta and U. Keller, Appl. Phys. B 73, 653 (2001).
[CrossRef]

Rosen, A.

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, Phys. Rev. Lett. 97, 013903 (2005).
[CrossRef]

Shi, L. W.

L. W. Shi, Y. H. Chen, B. Xu, Z. C. Wang, Y. H. Jiao, and Z. G. Wang, J. Phys. D 40, R307 (2007).
[CrossRef]

Smulakovski, V.

Vodonos, B.

Wang, Z. C.

L. W. Shi, Y. H. Chen, B. Xu, Z. C. Wang, Y. H. Jiao, and Z. G. Wang, J. Phys. D 40, R307 (2007).
[CrossRef]

Wang, Z. G.

L. W. Shi, Y. H. Chen, B. Xu, Z. C. Wang, Y. H. Jiao, and Z. G. Wang, J. Phys. D 40, R307 (2007).
[CrossRef]

Weill, R.

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, Phys. Rev. Lett. 97, 013903 (2005).
[CrossRef]

Xu, B.

L. W. Shi, Y. H. Chen, B. Xu, Z. C. Wang, Y. H. Jiao, and Z. G. Wang, J. Phys. D 40, R307 (2007).
[CrossRef]

Appl. Phys. B (2)

E. P. Ippen, Appl. Phys. B 58, 159 (1994).
[CrossRef]

R. Paschotta and U. Keller, Appl. Phys. B 73, 653 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (3)

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

F. X. Kartner, J. A. der Au, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 159 (1998).
[CrossRef]

F. X. Kartner, I. D. Jung, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 2, 540 (1996).
[CrossRef]

J. Phys. D (1)

L. W. Shi, Y. H. Chen, B. Xu, Z. C. Wang, Y. H. Jiao, and Z. G. Wang, J. Phys. D 40, R307 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. E (1)

O. Gat, A. Gordon, and B. Fischer, Phys. Rev. E 70, 046108 (2004).
[CrossRef]

Phys. Rev. Lett. (3)

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, Phys. Rev. Lett. 97, 013903 (2005).
[CrossRef]

M. Katz, O. Gat, A. Gordon, and B. Fischer, Phys. Rev. Lett. 97, 113902 (2006).
[CrossRef] [PubMed]

A. Gordon and B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[CrossRef] [PubMed]

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 (1)

Fig. 1
Fig. 1

Top, the pulse power fraction, as a function of the inverse of the mode-locking parameter M 1 , which defines an effective noise power, and r, the ratio of the minimal pulse width to the pulse width defined by the soliton effects. The pulse ceases to exist when M < M min . Note the maximal power limit for r > 1 . Bottom, the normalized net-gain value that determines the continuum stability condition.

Equations (8)

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

ψ ̇ = ( γ g + i γ d ) 2 ψ z 2 + i γ k | ψ | 2 ψ ( q q 0 ) ψ + g ψ ,
q = q 0 q 0 W s 0 z | ψ | 2 d z + q 0 2 ( 1 W s 0 z | ψ | 2 d z ) 2 .
( 2 β 2 ) γ g 3 β γ d = ϵ g s L p 2 8 ,
( 2 β 2 ) γ d + 3 β γ g = γ k P L L p 2 .
g = ϵ γ ̃ g 2 β ̃ γ d ( α l p ) 2 x 2 x g s 2 .
L p - min = ( 2 3 γ g g s ) 1 2 .
ψ ̇ c = ( γ g + i γ d ) 2 ψ c z 2 + g ψ c + x g s e z τ ψ c + Γ .
2 M ( x r x 2 ) ( 1 x ) 2 = 1 ,

Metrics