Abstract

We have observed period doubling and quasi-periodicity in an additive-pulse mode-locked F-center laser. Experiments show that period doubling is often present even though standard diagnostics such as pulse autocorrelations and spectra give no indication of it. Numerical simulations show that the period doubling is associated with strong pulse reshaping.

© 1995 Optical Society of America

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References

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  1. L. Y. Liu, “Additive pulse modelocking,” Ph.D. dissertation (MIT, Cambridge, Mass., 1990).
  2. X. Zhu, P. N. Kean, W. Sibbett, IEEE J. Quantum Electron. 25, 2445 (1989).
    [CrossRef]
  3. U. Keller, C. E. Soccolich, G. Sucha, M. N. Islam, M. Wegener, Opt. Lett. 15, 974 (1990).
    [CrossRef] [PubMed]
  4. K. Ikeda, M. Mizuno, IEEE J. Quantum Electron. QE-21, 2445 (1985).
  5. A. T. Ryan, G. P. Agrawal, IEEE J. Quantum Electron. 30, 668 (1994).
    [CrossRef]
  6. M. E. Fermann, IMRA America, Inc., 1044 Woodridge Avenue, Ann Arbor, Michigan 48105 (personal communication, 1994).
  7. C. P. Yakymyshyn, J. F. Pinto, C. R. Pollock, Opt. Lett. 14, 621 (1989).
    [CrossRef] [PubMed]
  8. G. Sucha, Opt. Lett. 16, 922 (1991).
    [CrossRef] [PubMed]
  9. E. P. Ippen, H. A. Haus, L. Y. Liu, J. Opt. Soc. Am. B 6, 1736 (1989).
    [CrossRef]
  10. K. Naganuma, Y. Sakai, Opt. Lett. 19, 487 (1994).
    [CrossRef] [PubMed]
  11. D. Dangoisse, P. Glorieux, D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
    [CrossRef] [PubMed]
  12. G. Steinmeyer, D. Jaspert, F. Mitschke, Opt. Commun. 104, 379 (1994).
    [CrossRef]

1994 (3)

A. T. Ryan, G. P. Agrawal, IEEE J. Quantum Electron. 30, 668 (1994).
[CrossRef]

G. Steinmeyer, D. Jaspert, F. Mitschke, Opt. Commun. 104, 379 (1994).
[CrossRef]

K. Naganuma, Y. Sakai, Opt. Lett. 19, 487 (1994).
[CrossRef] [PubMed]

1991 (1)

1990 (1)

1989 (3)

1986 (1)

D. Dangoisse, P. Glorieux, D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
[CrossRef] [PubMed]

1985 (1)

K. Ikeda, M. Mizuno, IEEE J. Quantum Electron. QE-21, 2445 (1985).

Agrawal, G. P.

A. T. Ryan, G. P. Agrawal, IEEE J. Quantum Electron. 30, 668 (1994).
[CrossRef]

Dangoisse, D.

D. Dangoisse, P. Glorieux, D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
[CrossRef] [PubMed]

Fermann, M. E.

M. E. Fermann, IMRA America, Inc., 1044 Woodridge Avenue, Ann Arbor, Michigan 48105 (personal communication, 1994).

Glorieux, P.

D. Dangoisse, P. Glorieux, D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
[CrossRef] [PubMed]

Haus, H. A.

Hennequin, D.

D. Dangoisse, P. Glorieux, D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
[CrossRef] [PubMed]

Ikeda, K.

K. Ikeda, M. Mizuno, IEEE J. Quantum Electron. QE-21, 2445 (1985).

Ippen, E. P.

Islam, M. N.

Jaspert, D.

G. Steinmeyer, D. Jaspert, F. Mitschke, Opt. Commun. 104, 379 (1994).
[CrossRef]

Kean, P. N.

X. Zhu, P. N. Kean, W. Sibbett, IEEE J. Quantum Electron. 25, 2445 (1989).
[CrossRef]

Keller, U.

Liu, L. Y.

E. P. Ippen, H. A. Haus, L. Y. Liu, J. Opt. Soc. Am. B 6, 1736 (1989).
[CrossRef]

L. Y. Liu, “Additive pulse modelocking,” Ph.D. dissertation (MIT, Cambridge, Mass., 1990).

Mitschke, F.

G. Steinmeyer, D. Jaspert, F. Mitschke, Opt. Commun. 104, 379 (1994).
[CrossRef]

Mizuno, M.

K. Ikeda, M. Mizuno, IEEE J. Quantum Electron. QE-21, 2445 (1985).

Naganuma, K.

Pinto, J. F.

Pollock, C. R.

Ryan, A. T.

A. T. Ryan, G. P. Agrawal, IEEE J. Quantum Electron. 30, 668 (1994).
[CrossRef]

Sakai, Y.

Sibbett, W.

X. Zhu, P. N. Kean, W. Sibbett, IEEE J. Quantum Electron. 25, 2445 (1989).
[CrossRef]

Soccolich, C. E.

Steinmeyer, G.

G. Steinmeyer, D. Jaspert, F. Mitschke, Opt. Commun. 104, 379 (1994).
[CrossRef]

Sucha, G.

Wegener, M.

Yakymyshyn, C. P.

Zhu, X.

X. Zhu, P. N. Kean, W. Sibbett, IEEE J. Quantum Electron. 25, 2445 (1989).
[CrossRef]

IEEE J. Quantum Electron. (3)

K. Ikeda, M. Mizuno, IEEE J. Quantum Electron. QE-21, 2445 (1985).

A. T. Ryan, G. P. Agrawal, IEEE J. Quantum Electron. 30, 668 (1994).
[CrossRef]

X. Zhu, P. N. Kean, W. Sibbett, IEEE J. Quantum Electron. 25, 2445 (1989).
[CrossRef]

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

Opt. Commun. (1)

G. Steinmeyer, D. Jaspert, F. Mitschke, Opt. Commun. 104, 379 (1994).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

D. Dangoisse, P. Glorieux, D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
[CrossRef] [PubMed]

Other (2)

M. E. Fermann, IMRA America, Inc., 1044 Woodridge Avenue, Ann Arbor, Michigan 48105 (personal communication, 1994).

L. Y. Liu, “Additive pulse modelocking,” Ph.D. dissertation (MIT, Cambridge, Mass., 1990).

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Figures (4)

Fig. 1
Fig. 1

Schematic of APM laser. The main cavity contains mirror M1, the gain (NaCl), the birefringent tuner plate (BTP), and the output coupler (OC). The control cavity contains 10 cm of single-mode fiber (SMF), a 55% beam splitter (BS), and end mirror M2, which is mounted on a piezoelectric transducer (PZT) for fine adjustment of the cavity-length mismatch. Pulse amplitudes a1 and b1 (main cavity) and a2 and b2 (control cavity) are also shown.

Fig. 2
Fig. 2

Pulse train during (a) normal mode locking, (b) period-doubled mode locking, and (c) quasi-periodic mode locking.

Fig. 3
Fig. 3

Birfurcation diagram generated by simulations of laser output pulse energy versus fiber nonlinearity, n2, for an APM laser with a 45% output coupler (r = 0.8367), a 55% beam splitter (γ = 0.7416), and phase bias Φ0 = −2.5.

Fig. 4
Fig. 4

(a) Calculated pulse intensity profiles |b1(t)|2 and |b2(t)|2 for both the upper-branch pulses (shaded curves) and the lower-branch pulses (dotted curves) in the main and the control cavities for n2 = 2.8. (b) The measured pulse trains in the main and the control cavities.

Equations (4)

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a 1 N ( t ) = G ^ B ^ b 1 N ( t ) ,
a 2 N ( t ) = γ 2 b 2 N ( t ) exp { i [ Φ 0 + γ 2 n 2 b 2 N ( t ) 2 ] } ,
b 1 N + 1 ( t ) = r a 1 N ( t ) + 1 - r 2 a 2 N ( t ) ,
b 2 N + 1 ( t ) = 1 - r 2 a 1 N ( t ) - r a 2 N ( t ) ,

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