Abstract

Harmonic mode locking in lasers with slow gain relaxation times requires fast intensity-dependent loss (fast loss) to equalize the pulse energies. A practical method to obtain fast loss is to use self-phase modulation and spectral filtering (SPM+F). We show that in a frequency modulation mode-locked laser SPM+F produces a fast loss only when the cavity dispersion is anomalous. In the absence of SPM the dispersion creates a gain imbalance between the pulsing modes in the upchirped and downchirped modulation cycles, which causes one mode to dominate over the other.

© 1996 Optical Society of America

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References

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  1. G. T. Harvey, L. F. Mollenauer, Opt. Lett. 18, 107 (1993).
    [CrossRef] [PubMed]
  2. C. R. Doerr, H. A. Haus, E. P. Ippen, M. Shirasaki, K. Tamura, Opt. Lett. 19, 31 (1994).
    [CrossRef] [PubMed]
  3. C. R. Doerr, H. A. Haus, E. P. Ippen, Opt. Lett. 19, 1958 (1994).
  4. M. Nakazawa, K. Tamura, E. Yoshida, Electron. Lett. 32, 461 (1996).
    [CrossRef]
  5. M. Nakazawa, E. Yoshida, K. Tamura, Electron. Lett. 32, 1285 (1996).
    [CrossRef]
  6. D. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 694 (1970).
    [CrossRef]
  7. D. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 709 (1970).
    [CrossRef]
  8. H. A. Haus, Waves And Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N. J., 1984).

1996

M. Nakazawa, K. Tamura, E. Yoshida, Electron. Lett. 32, 461 (1996).
[CrossRef]

M. Nakazawa, E. Yoshida, K. Tamura, Electron. Lett. 32, 1285 (1996).
[CrossRef]

1994

1993

1970

D. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 694 (1970).
[CrossRef]

D. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 709 (1970).
[CrossRef]

Doerr, C. R.

Harvey, G. T.

Haus, H. A.

Ippen, E. P.

Kuizenga, D.

D. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 694 (1970).
[CrossRef]

D. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 709 (1970).
[CrossRef]

Mollenauer, L. F.

Nakazawa, M.

M. Nakazawa, K. Tamura, E. Yoshida, Electron. Lett. 32, 461 (1996).
[CrossRef]

M. Nakazawa, E. Yoshida, K. Tamura, Electron. Lett. 32, 1285 (1996).
[CrossRef]

Shirasaki, M.

Siegman, A. E.

D. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 709 (1970).
[CrossRef]

D. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 694 (1970).
[CrossRef]

Tamura, K.

M. Nakazawa, K. Tamura, E. Yoshida, Electron. Lett. 32, 461 (1996).
[CrossRef]

M. Nakazawa, E. Yoshida, K. Tamura, Electron. Lett. 32, 1285 (1996).
[CrossRef]

C. R. Doerr, H. A. Haus, E. P. Ippen, M. Shirasaki, K. Tamura, Opt. Lett. 19, 31 (1994).
[CrossRef] [PubMed]

Yoshida, E.

M. Nakazawa, K. Tamura, E. Yoshida, Electron. Lett. 32, 461 (1996).
[CrossRef]

M. Nakazawa, E. Yoshida, K. Tamura, Electron. Lett. 32, 1285 (1996).
[CrossRef]

Electron. Lett.

M. Nakazawa, K. Tamura, E. Yoshida, Electron. Lett. 32, 461 (1996).
[CrossRef]

M. Nakazawa, E. Yoshida, K. Tamura, Electron. Lett. 32, 1285 (1996).
[CrossRef]

IEEE J. Quantum Electron

D. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 694 (1970).
[CrossRef]

D. Kuizenga, A. E. Siegman, IEEE J. Quantum Electron. QE-6, 709 (1970).
[CrossRef]

Opt. Lett.

Other

H. A. Haus, Waves And Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N. J., 1984).

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Figures (3)

Fig. 1
Fig. 1

Harmonic FM mode locking without SPM for Dn = 0, ±0.1. Thin slanted lines show chirp (shown only for the t = 0–25 time window). The entire time axis corresponds to one full round trip in the laser. The power axis is 1.4 power units/division. The chirp axis is 5.6 frequency units/division. Unlabeled ticks for the top trace mark zero.

Fig. 2
Fig. 2

Harmonic FM mode locking with SPM for Dn = 0, ±0.1 and κ = 0.1. Thin slanted lines show chirp (shown only for the t = 0–25 time window). The entire time axis corresponds to one full round trip in the laser. The power axis is 2 power units/division. The chirp axis is 5.6 frequency units/division. Unlabeled ticks for the top trace mark zero. Labels of 0.5× correspond only to the power.

Fig. 3
Fig. 3

Detail of pulses from Figs. 2 and 3. Long-dashed curves, top and bottom (Dn = 0, κ = 0); dotted curve, bottom (Dn = +0.1, κ = 0); solid curves, bottom (Dn = +0.1, κ = 0.1); dotted curves, top (Dn = −0.1, κ = 0); solid curve, top (Dn = −0.1, κ = 0.1).

Equations (12)

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[ ( - j D n + f 0 ω f 2 ) d 2 d t 2 + g i - l + j ψ - j 2 p i Φ ω m 2 t 2 ] × a i = 0 ,
g i = g 0 1 + E T E sat ,
a i = A i exp ( - Q i t 2 ) ,
g i - l + j ψ - 2 ( - j D n + f 0 ω f 2 ) Q i = 0 ,
4 Q i 2 ( - j D n + f 0 ω f 2 ) - j 2 p i Φ ω m 2 = 0.
Q i 2 = j p i Φ ω m 2 8 ( - j D n + f 0 ω f 2 ) .
g i = l + ζ Φ ( cos  σ + sin  σ ) l u i             ( p i = + 1 ) ,
g i = l + ζ Φ ( cos  σ - sin  σ ) l d i             ( p i = - 1 ) ,
ζ Φ = 1 2 { Φ ω m 2 [ D n 2 + ( f 0 / ω f 2 ) 2 ] 1 / 2 } 1 / 2 ,
σ = 1 2 tan - 1 ( D n ω f 2 f 0 ) .
g i = l + ζ ( Φ + κ eff A i 2 ) 1 / 2 ( cos  σ + sin  σ ) l u i             ( p i = + 1 ) ,
g i = l + ζ ( Φ - κ eff A i 2 ) 1 / 2 ( cos  σ - sin  σ ) l d i             ( p i = - 1 ) ,

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