Abstract

The Haus–Mecozzi theory of timing jitter and amplitude fluctuations of a self-starting additive-pulse mode-locked fiber ring laser operating in the negative group-velocity regime is reviewed. Experimental results confirm the theoretical predictions. The measured timing jitter has two physical origins. One is amplified spontaneous emission (quantum noise). The other is the amplitude fluctuation that is due to the pump source. The jitter is due mainly to the amplified spontaneous emission and is thus quantum limited.

© 1996 Optical Society of America

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  1. D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201 (1986).
    [CrossRef]
  2. H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983 (1993).
    [CrossRef]
  3. D. E. Spence, J. M. Dudley, K. Lamb, W. E. Sleat, and W. Sibbett, “Nearly quantum-limited timing jitter in a self-mode-locked Ti:sapphire laser,” Opt. Lett. 19, 481 (1994).
    [CrossRef] [PubMed]
  4. K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fiber ring laser,” Electron. Lett. 28, 2226 (1992).
    [CrossRef]
  5. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
    [CrossRef]
  6. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8, 2068 (1991).
    [CrossRef]
  7. E. P. Ippen, H. A. Haus, and L. Y. Liu, “Additive pulse mode locking,” J. Opt. Soc. Am. B 6, 1736 (1989).
    [CrossRef]
  8. H. A. Haus, E. P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200 (1994).
    [CrossRef]
  9. S. M. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806 (1992).
    [CrossRef]
  10. D. U. Noske, N. Pandit, and J. R. Taylor, “Source of spectral and temporal instability in soliton fiber lasers,” Opt. Lett. 17, 1515 (1992).
    [CrossRef] [PubMed]
  11. M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469 (1994).
    [CrossRef]
  12. J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 9, 91 (1992).
    [CrossRef]
  13. A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode locked lasers,” Appl. Phys. B 39, 201 (1986).
    [CrossRef]
  14. U. Keller, C. E. Soccolich, G. Sucha, M. N. Islam, and M. Wegener, “Noise characterization of femtosecond color-center lasers,” Opt. Lett. 15, 974 (1990).
    [CrossRef] [PubMed]
  15. G. T. Harvey, M. S. Heutmaker, P. R. Smith, M. C. Nuss, U. Keller, and J. A. Valdmanis, “Timing jitter and pump-induced amplitude modulation in the colliding pulse mode-locked (CPM) laser,” IEEE J. Quantum Electron. 27, 295 (1991).
    [CrossRef]
  16. S. B. Darack, D. R. Dykaar, and G. T. Harvey, “Timing-jitter stabilization of a colliding-pulse mode-locked laser by active control of the cavity length,” Opt. Lett. 16, 1677 (1991).
    [CrossRef] [PubMed]
  17. D. E. Spence, J. M. Evans, W. E. Sleat, and W. Sibbett, “Regeneratively initiated self-mode-locked Ti:sapphire laser,” Opt. Lett. 16, 1762 (1991).
    [CrossRef] [PubMed]
  18. D. R. Walker, D. W. Crust, W. E. Sleat, and W. Sibbett, “Reduction of phase noise in passively mode-locked lasers,” IEEE J. Quantum Electron. 28, 289 (1992).
    [CrossRef]
  19. J. Son, J. V. Rudd, and J. F. Whitaker, “Noise characterization of a self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 733 (1992).
    [CrossRef] [PubMed]
  20. J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  21. H. A. Haus, “Quantum noise in a solitonlike repeater system,” J. Opt. Soc. Am. B 8, 1122 (1991).
    [CrossRef]

1994 (3)

D. E. Spence, J. M. Dudley, K. Lamb, W. E. Sleat, and W. Sibbett, “Nearly quantum-limited timing jitter in a self-mode-locked Ti:sapphire laser,” Opt. Lett. 19, 481 (1994).
[CrossRef] [PubMed]

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469 (1994).
[CrossRef]

1993 (1)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

1992 (7)

S. M. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806 (1992).
[CrossRef]

D. U. Noske, N. Pandit, and J. R. Taylor, “Source of spectral and temporal instability in soliton fiber lasers,” Opt. Lett. 17, 1515 (1992).
[CrossRef] [PubMed]

K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fiber ring laser,” Electron. Lett. 28, 2226 (1992).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 9, 91 (1992).
[CrossRef]

D. R. Walker, D. W. Crust, W. E. Sleat, and W. Sibbett, “Reduction of phase noise in passively mode-locked lasers,” IEEE J. Quantum Electron. 28, 289 (1992).
[CrossRef]

J. Son, J. V. Rudd, and J. F. Whitaker, “Noise characterization of a self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 733 (1992).
[CrossRef] [PubMed]

1991 (5)

1990 (1)

1989 (1)

1986 (3)

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201 (1986).
[CrossRef]

J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11, 665 (1986).
[CrossRef] [PubMed]

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode locked lasers,” Appl. Phys. B 39, 201 (1986).
[CrossRef]

Crust, D. W.

D. R. Walker, D. W. Crust, W. E. Sleat, and W. Sibbett, “Reduction of phase noise in passively mode-locked lasers,” IEEE J. Quantum Electron. 28, 289 (1992).
[CrossRef]

Darack, S. B.

Dennis, M. L.

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469 (1994).
[CrossRef]

Dudley, J. M.

Duling, I. N.

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469 (1994).
[CrossRef]

Dykaar, D. R.

Evans, J. M.

Finch, A.

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode locked lasers,” Appl. Phys. B 39, 201 (1986).
[CrossRef]

Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8, 2068 (1991).
[CrossRef]

Gordon, J. P.

Harvey, G. T.

S. B. Darack, D. R. Dykaar, and G. T. Harvey, “Timing-jitter stabilization of a colliding-pulse mode-locked laser by active control of the cavity length,” Opt. Lett. 16, 1677 (1991).
[CrossRef] [PubMed]

G. T. Harvey, M. S. Heutmaker, P. R. Smith, M. C. Nuss, U. Keller, and J. A. Valdmanis, “Timing jitter and pump-induced amplitude modulation in the colliding pulse mode-locked (CPM) laser,” IEEE J. Quantum Electron. 27, 295 (1991).
[CrossRef]

Haus, H. A.

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fiber ring laser,” Electron. Lett. 28, 2226 (1992).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8, 2068 (1991).
[CrossRef]

H. A. Haus, “Quantum noise in a solitonlike repeater system,” J. Opt. Soc. Am. B 8, 1122 (1991).
[CrossRef]

E. P. Ippen, H. A. Haus, and L. Y. Liu, “Additive pulse mode locking,” J. Opt. Soc. Am. B 6, 1736 (1989).
[CrossRef]

J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11, 665 (1986).
[CrossRef] [PubMed]

Heutmaker, M. S.

G. T. Harvey, M. S. Heutmaker, P. R. Smith, M. C. Nuss, U. Keller, and J. A. Valdmanis, “Timing jitter and pump-induced amplitude modulation in the colliding pulse mode-locked (CPM) laser,” IEEE J. Quantum Electron. 27, 295 (1991).
[CrossRef]

Ippen, E. P.

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fiber ring laser,” Electron. Lett. 28, 2226 (1992).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8, 2068 (1991).
[CrossRef]

E. P. Ippen, H. A. Haus, and L. Y. Liu, “Additive pulse mode locking,” J. Opt. Soc. Am. B 6, 1736 (1989).
[CrossRef]

Islam, M. N.

Kean, P. N.

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode locked lasers,” Appl. Phys. B 39, 201 (1986).
[CrossRef]

Keller, U.

G. T. Harvey, M. S. Heutmaker, P. R. Smith, M. C. Nuss, U. Keller, and J. A. Valdmanis, “Timing jitter and pump-induced amplitude modulation in the colliding pulse mode-locked (CPM) laser,” IEEE J. Quantum Electron. 27, 295 (1991).
[CrossRef]

U. Keller, C. E. Soccolich, G. Sucha, M. N. Islam, and M. Wegener, “Noise characterization of femtosecond color-center lasers,” Opt. Lett. 15, 974 (1990).
[CrossRef] [PubMed]

Kelly, S. M.

S. M. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806 (1992).
[CrossRef]

Lamb, K.

Liu, L. Y.

Mecozzi, A.

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

Noske, D. U.

Nuss, M. C.

G. T. Harvey, M. S. Heutmaker, P. R. Smith, M. C. Nuss, U. Keller, and J. A. Valdmanis, “Timing jitter and pump-induced amplitude modulation in the colliding pulse mode-locked (CPM) laser,” IEEE J. Quantum Electron. 27, 295 (1991).
[CrossRef]

Pandit, N.

Rudd, J. V.

Sibbett, W.

D. E. Spence, J. M. Dudley, K. Lamb, W. E. Sleat, and W. Sibbett, “Nearly quantum-limited timing jitter in a self-mode-locked Ti:sapphire laser,” Opt. Lett. 19, 481 (1994).
[CrossRef] [PubMed]

D. R. Walker, D. W. Crust, W. E. Sleat, and W. Sibbett, “Reduction of phase noise in passively mode-locked lasers,” IEEE J. Quantum Electron. 28, 289 (1992).
[CrossRef]

D. E. Spence, J. M. Evans, W. E. Sleat, and W. Sibbett, “Regeneratively initiated self-mode-locked Ti:sapphire laser,” Opt. Lett. 16, 1762 (1991).
[CrossRef] [PubMed]

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode locked lasers,” Appl. Phys. B 39, 201 (1986).
[CrossRef]

Sleat, W. E.

Smith, P. R.

G. T. Harvey, M. S. Heutmaker, P. R. Smith, M. C. Nuss, U. Keller, and J. A. Valdmanis, “Timing jitter and pump-induced amplitude modulation in the colliding pulse mode-locked (CPM) laser,” IEEE J. Quantum Electron. 27, 295 (1991).
[CrossRef]

Soccolich, C. E.

Son, J.

Spence, D. E.

Sucha, G.

Tamura, K.

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fiber ring laser,” Electron. Lett. 28, 2226 (1992).
[CrossRef]

Taylor, J. R.

Valdmanis, J. A.

G. T. Harvey, M. S. Heutmaker, P. R. Smith, M. C. Nuss, U. Keller, and J. A. Valdmanis, “Timing jitter and pump-induced amplitude modulation in the colliding pulse mode-locked (CPM) laser,” IEEE J. Quantum Electron. 27, 295 (1991).
[CrossRef]

von der Linde, D.

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201 (1986).
[CrossRef]

Walker, D. R.

D. R. Walker, D. W. Crust, W. E. Sleat, and W. Sibbett, “Reduction of phase noise in passively mode-locked lasers,” IEEE J. Quantum Electron. 28, 289 (1992).
[CrossRef]

Wegener, M.

Whitaker, J. F.

Zhu, X.

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode locked lasers,” Appl. Phys. B 39, 201 (1986).
[CrossRef]

Appl. Phys. B (2)

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39, 201 (1986).
[CrossRef]

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode locked lasers,” Appl. Phys. B 39, 201 (1986).
[CrossRef]

Electron. Lett. (2)

S. M. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806 (1992).
[CrossRef]

K. Tamura, H. A. Haus, and E. P. Ippen, “Self-starting additive pulse mode-locked erbium fiber ring laser,” Electron. Lett. 28, 2226 (1992).
[CrossRef]

IEEE J. Quantum Electron. (6)

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469 (1994).
[CrossRef]

G. T. Harvey, M. S. Heutmaker, P. R. Smith, M. C. Nuss, U. Keller, and J. A. Valdmanis, “Timing jitter and pump-induced amplitude modulation in the colliding pulse mode-locked (CPM) laser,” IEEE J. Quantum Electron. 27, 295 (1991).
[CrossRef]

D. R. Walker, D. W. Crust, W. E. Sleat, and W. Sibbett, “Reduction of phase noise in passively mode-locked lasers,” IEEE J. Quantum Electron. 28, 289 (1992).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Lett. (7)

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Figures (10)

Fig. 1
Fig. 1

Schematic of the all-fiber ring laser. WDM, wavelength-division multiplexing.

Fig. 2
Fig. 2

Effect of finite integration time on timing jitter. T=0.1 s, τp=0.39 µs.

Fig. 3
Fig. 3

Experimental setup.

Fig. 4
Fig. 4

Optical spectrum of the laser spectrum.

Fig. 5
Fig. 5

Harmonic 0 of the rf spectrum.

Fig. 6
Fig. 6

Timing jitter structures that are due to pump noise and to white noise for harmonic 35.

Fig. 7
Fig. 7

Fitting for harmonic 35.

Fig. 8
Fig. 8

Fitting for harmonic 25.

Fig. 9
Fig. 9

Timing jitter that is due to white noise. Jitter, 27 ppm.

Fig. 10
Fig. 10

Theoretically predicted quantum jitter and experimental data for harmonic 35.

Tables (1)

Tables Icon

Table 1 Summary of Different Timing Jitter Values

Equations (38)

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TRaT=-l+g1-1Ωgt+1Ωg22t2+jD2t2+(γ-jδ)|a|2a+TRS(t,T).
a(t,T)=[as(t-t0)+Δa(t-t0,T)]
×exp-jδ2A02TTR,
TRTΔa(t-t0,T)=g-l+jδ2A02+gΩg2+j|D|2t2+2(γ-jδ)as2(t-t0)Δa+(γ-jδ)as2Δa*-gs1-1Ωgt+1Ωg22t2as(t)2τA02×dtas(t)(Δa+Δa*)+TRS(t,T),
gs=g0PsTR2τA021+2τA02PsTR2.
w0=as2(t)dt=2A02τ.
TRTΔw=-2gs+83γA02-23gΩg2δ|D|A02Δw+TRSw(T),
TRTΔθ=-δA02Δww0+TRSθ(T),
TRTΔp=-43gΩg2τ2Δp+TRSp(T),
TRTΔt=-2|D|Δp-gsΩgΔww0+TRSt(T).
f(Ω)=1T0 dT exp(-jΩT)f(T),
f(T)=T02π dΩ exp(jΩT)f(Ω),
1τw=--2gs+83γA02-23gΩg2δ|D|A021TR,
1τp=43gΩg2τ21TR.
|Δw(Ω)|2=|Sw(Ω)|2(Ω2+1/τw2),
|Δp(Ω)|2=|Sp(Ω)|2(Ω2+1/τp2),
|Δt(Ω)|2=4D2TR2Ω2|Sp(Ω)|2(Ω2+1/τp2)+gs2Ω2Ωg2TR2|Δw(Ω)|2w02+|St(Ω)|2Ω2.
|Δθ(Ω)|2=(δA02)2TR2Ω2|Sw(Ω)|2(Ω2+1/τw2)+|Sθ(Ω)|2Ω2.
ik(T)=A1+Δww0exp(-jkΩ0Δt),
ik(T)=A1+Δw(T)w0[1-jkΩ0Δt(T)].
|ik(Ω)|2=A22πδ(Ω)+1w02|Δw(Ω)|2+k2Ω02|Δt(Ω)|2+jkΩ0[Δt*(Ω)Δw(Ω)-Δt(Ω)Δw*(Ω)].
Δp(t)=exp(-t/τp)0tSp(t)exp(t/τp)dt,
Δt(t)=-2|D|TR0t exp(-t/τp)dt×0tSp(t)exp(t/τp)dt.
4D2TR2k2Ω020Texp(jΩt)dt0Texp(jΩt)dt×0texp(-t/τp)dt0texp(-t/τp)dt×0texp(tIV/τp)Sp(tIV)dtIV0texp(tV/τp)Sp(tV)dtV.
R=4D2TR2k2Ω02Dpp-τp4T2+2τp2Ω2+τp2TΩ2+[cos(ΩT)τpΩ-sin(ΩT)]τp2(1+τp2Ω2)Ω3-τp3Ω2+τp5(τp2Ω2+5)4[(τp2Ω2-1)2+4(τp2Ω2)],
R=4D2TR2k2Ω02Dppτp2T36-τp3T22+τp4T2+τp54,
(Δw)rms2=12π-+|Δw(Ω)|2dΩ,
(Δt)rms2=12π-+|Δt(Ω)|2dΩ.
 PJΩdΩΔΩresP0=(2πk)2ΔtT2,
Sqn(T,t)Sqn*(T,t)=θ2gTRhνδ(T-T)δ(t-t),
Si,qn(T)Sh,qn(T)=Di,qnδi,hδ(T-T),
Dw,qn=4w0θ2gTRhν,
Dθ,qn=43w01+π212θ2gTRhν,
Dp,qn=23w0τ2θ2gTRhν,
Dt,qn=π2τ23w0θ2gTRhν.
|Δt(T+T0)-Δt(T0)2|
=4D2TR2Dp,qnτp3Tτp-1+exp(-T/τp),
|Δt(T+T0)-Δt(T0)2|=4D2TR2Dp,qnτp2T.

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