Abstract

We study the effect of cavity topology on the nonlinear dynamics of additive-pulse mode-locked (APM) lasers configured in the Fabry–Perot and Michelson geometries. In experiments the Fabry–Perot laser often exhibits such behaviors as period doubling and quasiperiodicity as the nonlinearity is increased, whereas the Michelson APM (M-APM) exhibits none of these effects. Numerical studies confirm that the M-APM appears to be more resistant to such behavior and thus is more tolerant to excessive nonlinearity in the control cavity. Using the concepts of intensity- and phase-dependent two-beam and multiple-beam interference, we obtain a general empirical rule connecting cavity topology to pulse train instabilities for fast saturable absorber mode-locked lasers employing coupled cavities.

© 1998 Optical Society of America

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1997 (1)

U. Morgner and F. Mitschke, Phys. Rev. A 55, 3124 (1997).
[CrossRef]

1996 (2)

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsässer, E. Göbel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef] [PubMed]

U. Morgner, U. Rolefs, and F. Mitschke, Opt. Lett. 21, 1265 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (4)

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

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

L. A. Melnikov, Bull. Russ. Acad. Sci. 58, 155 (1994).

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

1993 (2)

1991 (4)

1989 (4)

1986 (3)

F. M. Mitschke and L. F. Mollenauer, IEEE J. Quantum Electron. QE-22, 2242 (1986).
[CrossRef]

F. Salin, P. Grangier, G. Roger, and A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

F. Oulette and M. Piche, Opt. Commun. 60, 99 (1986).
[CrossRef]

1985 (1)

K. Ikeda and M. Mizuno, IEEE J. Quantum Electron. QE-21, 1429 (1985).
[CrossRef]

Agrawal, G. P.

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

Bolton, S. R.

Brun, A.

F. Salin, P. Grangier, G. Roger, and A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

Chemla, D. S.

Crust, D. W.

Doerr, C. R.

Duling III, I. N.

Elsässer, W.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsässer, E. Göbel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef] [PubMed]

Fischer, I.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsässer, E. Göbel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef] [PubMed]

Göbel, E.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsässer, E. Göbel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef] [PubMed]

Grangier, P.

F. Salin, P. Grangier, G. Roger, and A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

Grant, R. S.

Hall, K. L.

Haus, H. A.

Ikeda, K.

K. Ikeda and M. Mizuno, IEEE J. Quantum Electron. QE-21, 1429 (1985).
[CrossRef]

Ippen, E. P.

Jaspert, D.

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

Kean, P. N.

Langford, N.

Lenstra, D.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsässer, E. Göbel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef] [PubMed]

Levine, A. M.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsässer, E. Göbel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef] [PubMed]

Liu, L. Y.

Mark, J.

Melnikov, L. A.

L. A. Melnikov, Bull. Russ. Acad. Sci. 58, 155 (1994).

Mitschke, F.

U. Morgner and F. Mitschke, Phys. Rev. A 55, 3124 (1997).
[CrossRef]

U. Morgner, U. Rolefs, and F. Mitschke, Opt. Lett. 21, 1265 (1996).
[CrossRef] [PubMed]

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

Mitschke, F. M.

F. M. Mitschke and L. F. Mollenauer, IEEE J. Quantum Electron. QE-22, 2242 (1986).
[CrossRef]

Mizuno, M.

K. Ikeda and M. Mizuno, IEEE J. Quantum Electron. QE-21, 1429 (1985).
[CrossRef]

Mollenauer, L. F.

F. M. Mitschke and L. F. Mollenauer, IEEE J. Quantum Electron. QE-22, 2242 (1986).
[CrossRef]

Morgner, U.

Nelson, L. E.

Oulette, F.

F. Oulette and M. Piche, Opt. Commun. 60, 99 (1986).
[CrossRef]

Piche, M.

F. Oulette and M. Piche, Opt. Commun. 60, 99 (1986).
[CrossRef]

Pinto, J. F.

Pollock, C. R.

Roger, G.

F. Salin, P. Grangier, G. Roger, and A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

Rolefs, U.

Ryan, A. T.

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

Salin, F.

F. Salin, P. Grangier, G. Roger, and A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

Shirasaki, M.

Sibbett, W.

Steinmeyer, G.

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

Sucha, G.

Tamura, K.

Tsang, T.

van Tartwijk, G. H. M.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsässer, E. Göbel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef] [PubMed]

Weiss, S.

Yakymyshyn, C. P.

Zhu, X.

Bull. Russ. Acad. Sci. (1)

L. A. Melnikov, Bull. Russ. Acad. Sci. 58, 155 (1994).

IEEE J. Quantum Electron. (3)

K. Ikeda and M. Mizuno, IEEE J. Quantum Electron. QE-21, 1429 (1985).
[CrossRef]

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

F. M. Mitschke and L. F. Mollenauer, IEEE J. Quantum Electron. QE-22, 2242 (1986).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (3)

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

F. Oulette and M. Piche, Opt. Commun. 60, 99 (1986).
[CrossRef]

R. S. Grant and W. Sibbett, Opt. Commun. 86, 177 (1991).
[CrossRef]

Opt. Lett. (10)

Phys. Rev. A (1)

U. Morgner and F. Mitschke, Phys. Rev. A 55, 3124 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsässer, E. Göbel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef] [PubMed]

F. Salin, P. Grangier, G. Roger, and A. Brun, Phys. Rev. Lett. 56, 1132 (1986).
[CrossRef] [PubMed]

Other (2)

G. Sucha, S. R. Bolton, and D. S. Chemla, in Conference on Lasers and Electro-Optics, Vol. 7 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CThI16, p. 329.

J. Cormier, M. Morin, and M. Piche, in Nonlinear Dynamics in Optical Systems, N. B. Abraham, E. M. Garmire, and P. Mandel, eds., Vol. 7 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1990), p. 354.

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of the Fabry–Perot APM (FP-APM) laser cavity. The main cavity contains the gain (NaCl), a birefringent tuner plate (BTP), and an output coupler (OC). The control cavity contains 10 cm of single-mode fiber (SMF), and a 50% beam splitter (BS). The cavity length is adjusted by means of an end mirror (M2), which is mounted on a piezoelectric transducer (PZT). (b) Michelson APM (M-APM) laser cavity.

Fig. 2
Fig. 2

Pulse trains from the FP-APM laser under (a) normal mode-locking conditions (Pfib<80 mW) and (b) period-doubled mode-locking conditions (Pfib>80 mW); (c) antiphased, period-doubled pulse trains from main and control cavities of the Fabry–Perot during P2 mode locking, indicating energy exchange between cavities.

Fig. 3
Fig. 3

Bifurcation diagrams of output pulse energy versus nonlinearity for (a) FP-APM (b) M-APM configurations. Pulse intensity profiles are shown at various points on the bifurcation curve. Values for the Fabry–Perot are g0=0.7, r=0.707, γ=0.707, and ϕ0=-2.5; values for the Michelson are g0=1.0, r=0.707, γ=0.707, and ϕ0=-2.0.

Fig. 4
Fig. 4

Pulse intensity profiles for the the FP-APM laser: (a) simulated pulse solutions for P2 mode locking by using values of n2*L=0.085 kW-1, g0=0.7, r=0.707, γ=0.707, and ϕ0=-2.5; (b) calculated intensity autocorrelations of pulses in (a) averaged over both pulses; (c) experimental autocorrelation during period-doubled mode locking. For the M-APM: (d) simulated pulse intensity solution for values of n2*L=0.076 kW-1, g0=1.0, r=0.707, γ=0.89, and ϕ0=-2.0; (e) resulting intensity autocorrelation; (f) experimental autocorrelation at high power (Pfib=100 mW).

Fig. 5
Fig. 5

Cascade plots of pulse intensity profiles for (a) FP-APM and (b) M-APM lasers with increasing nonlinearity (back to front). Both upper- and lower-branch solutions are shown. Values for the Fabry–Perot are g0=0.7, r=0.707, γ=0.707, and ϕ0=-2.5; for the Michelson the values are g0=1.0, r2=0.50, γ=0.707, and ϕ0=-2.0.

Fig. 6
Fig. 6

Coupled-cavity, Figure-8 lasers that are topologically equivalent to (a) the Fabry–Perot and (b) Michelson configurations.

Equations (15)

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a1N(t)=GˆBˆb1N(t),
a2N(t)=γPˆ(γb2N(t))=γ2b2N(t)×exp{i[ϕ0+n2*LP0|γb2N(t)|2]},
b1N+1(t)=ra1N(t)+ta2N(t),
b2N+1(t)=ta1N(t)-ra2N(t),
Pˆ(b2N)=b2Nexp{i[ϕ0+n2*LP0|b2N|2]}.
a1N(t)=GˆBˆb1N-1(t),
a2N(t)=Pˆ(γb2N(t))=γb2N(t)exp{i[ϕ0+n2*LP0|γ2b2N(t)|2]},
b1N(t)=r2a1N(t)+ta2N(t),
b2N(t)=ta1N(t),
d1N+1(t)=rta1N(t)-ra2N(t).
Emain=P0ΔTi|b1i|2=(0.1nJ)i|b1i|2,
b1N+1=r2GˆBˆb1N+tPˆ(γtGˆBˆb1N-1).
b1N+1=rGˆBˆb1N+tγ2Pˆb2N,
b2N+1=tGˆBˆb1N-rγ2Pˆb2N.
b2N+1=(tGˆBˆ rt+rγ2Pˆ)b2N+tGˆBˆ γ2t Pˆb2N-1.

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