Abstract

Passively mode-locked lasers with intracavity weakly birefringent fiber are theoretically analyzed based on two coupled complex one-dimensional Ginzburg–Landau equations. The model includes fiber birefringence, spectral filtering, saturable gain, and saturable loss. Phase-locked soliton solutions are found for small amounts of birefringence and several types of soliton with periodic polarization evolution for higher amounts of birefringence. Numerical simulations show qualitative agreement with experimental results.

© 1998 Optical Society of America

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1998 (1)

1997 (3)

S. T. Cundiff, B. C. Collings, and W. H. Knox, Opt. Express 1, 12 (1997); www.osa.org .
[CrossRef] [PubMed]

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, N. Kutz, J. E. Cunningham, W. Y. Jan, and W. H. Knox, IEEE J. Sel. Topics Quantum Electron. 3, 1065 (1997).
[CrossRef]

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

1996 (1)

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

1995 (1)

1994 (3)

N. N. Akhmediev, A. V. Buryak, and J. M. Soto-Crespo, Opt. Commun. 112, 278 (1994).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

C.-J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 19, 198 (1994).
[CrossRef]

1993 (1)

1992 (1)

D. U. Noske, N. Pandit, and J. R. Taylor, Electron. Lett. 28, 2185 (1992).
[CrossRef]

1991 (5)

Akhmediev, N. N.

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

N. N. Akhmediev, A. V. Buryak, J. M. Soto-Crespo, and D. R. Andersen, J. Opt. Soc. Am. B 12, 434 (1995).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and J. M. Soto-Crespo, Opt. Commun. 112, 278 (1994).
[CrossRef]

N. N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman & Hall, New York, 1997).

Andersen, D. R.

Ankiewicz, A.

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

N. N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman & Hall, New York, 1997).

Belanger, P. A.

Bergman, K.

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, N. Kutz, J. E. Cunningham, W. Y. Jan, and W. H. Knox, IEEE J. Sel. Topics Quantum Electron. 3, 1065 (1997).
[CrossRef]

Buryak, A. V.

N. N. Akhmediev, A. V. Buryak, J. M. Soto-Crespo, and D. R. Andersen, J. Opt. Soc. Am. B 12, 434 (1995).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and J. M. Soto-Crespo, Opt. Commun. 112, 278 (1994).
[CrossRef]

Chen, C.-J.

Chen, H. H.

Collings, B. C.

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, N. Kutz, J. E. Cunningham, W. Y. Jan, and W. H. Knox, IEEE J. Sel. Topics Quantum Electron. 3, 1065 (1997).
[CrossRef]

S. T. Cundiff, B. C. Collings, and W. H. Knox, Opt. Express 1, 12 (1997); www.osa.org .
[CrossRef] [PubMed]

Cundiff, S. T.

S. T. Cundiff, B. C. Collings, and W. H. Knox, Opt. Express 1, 12 (1997); www.osa.org .
[CrossRef] [PubMed]

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, N. Kutz, J. E. Cunningham, W. Y. Jan, and W. H. Knox, IEEE J. Sel. Topics Quantum Electron. 3, 1065 (1997).
[CrossRef]

Cunningham, J. E.

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, N. Kutz, J. E. Cunningham, W. Y. Jan, and W. H. Knox, IEEE J. Sel. Topics Quantum Electron. 3, 1065 (1997).
[CrossRef]

Duling, I. N.

Fermann, M. E.

Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, J. Opt. Soc. Am. B 10, 2068 (1991).
[CrossRef]

Haberl, F.

Haus, H. A.

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, J. Opt. Soc. Am. B 10, 2068 (1991).
[CrossRef]

Hofer, M.

Ippen, E. P.

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, J. Opt. Soc. Am. B 10, 2068 (1991).
[CrossRef]

Jan, W. Y.

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, N. Kutz, J. E. Cunningham, W. Y. Jan, and W. H. Knox, IEEE J. Sel. Topics Quantum Electron. 3, 1065 (1997).
[CrossRef]

Jones, D. J.

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

Jung, I. D.

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

Kärtner, F. X.

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

Keller, U.

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

Knox, W. H.

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, N. Kutz, J. E. Cunningham, W. Y. Jan, and W. H. Knox, IEEE J. Sel. Topics Quantum Electron. 3, 1065 (1997).
[CrossRef]

S. T. Cundiff, B. C. Collings, and W. H. Knox, Opt. Express 1, 12 (1997); www.osa.org .
[CrossRef] [PubMed]

Kutz, N.

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, N. Kutz, J. E. Cunningham, W. Y. Jan, and W. H. Knox, IEEE J. Sel. Topics Quantum Electron. 3, 1065 (1997).
[CrossRef]

Lederer, M. J.

Luther-Davies, B.

Matsas, V. J.

Menyuk, C. R.

Nelson, L. E.

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

Newson, T. P.

Noske, D. U.

D. U. Noske, N. Pandit, and J. R. Taylor, Electron. Lett. 28, 2185 (1992).
[CrossRef]

Ober, M. H.

Pandit, N.

D. U. Noske, N. Pandit, and J. R. Taylor, Electron. Lett. 28, 2185 (1992).
[CrossRef]

Payne, D. N.

Richardson, D. J.

Schmidt, A. J.

Soto-Crespo, J. M.

N. N. Akhmediev, A. V. Buryak, J. M. Soto-Crespo, and D. R. Andersen, J. Opt. Soc. Am. B 12, 434 (1995).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, and J. M. Soto-Crespo, Opt. Commun. 112, 278 (1994).
[CrossRef]

Tamura, K.

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

Taylor, J. R.

D. U. Noske, N. Pandit, and J. R. Taylor, Electron. Lett. 28, 2185 (1992).
[CrossRef]

Tsuda, S.

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, N. Kutz, J. E. Cunningham, W. Y. Jan, and W. H. Knox, IEEE J. Sel. Topics Quantum Electron. 3, 1065 (1997).
[CrossRef]

Wai, P. K. A.

Appl. Phys. B (1)

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

Electron. Lett. (1)

D. U. Noske, N. Pandit, and J. R. Taylor, Electron. Lett. 28, 2185 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

IEEE J. Sel. Topics Quantum Electron. (2)

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

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, N. Kutz, J. E. Cunningham, W. Y. Jan, and W. H. Knox, IEEE J. Sel. Topics Quantum Electron. 3, 1065 (1997).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

N. N. Akhmediev, A. V. Buryak, and J. M. Soto-Crespo, Opt. Commun. 112, 278 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Other (1)

N. N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman & Hall, New York, 1997).

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Figures (3)

Fig. 1
Fig. 1

Amplitude profiles for the two components of the phase-locked solutions. Solid curve, ϕ; dashed curve, ψ.

Fig. 2
Fig. 2

Pulse energy Q versus γ for four qualitatively different types of soliton. The two polarization components are phase locked in the interval 0<γ<0.16 (upper dotted curve). The state of polarization is elliptical and can be represented by a dot on the Poincaré sphere that is close to the north or south pole. The periodic evolution of the state of polarization on the Poincaré sphere for other solutions is shown above each curve. In the case of the other three kinds of solution with lower values of Q, the state of polarization evolves periodically. In each sphere we show two trajectories that correspond to the two solutions for the limiting values of γ in their corresponding curves Qγ.

Fig. 3
Fig. 3

(a) Calculated PEF for phase-locked solitons and for the type  II periodic solitons in Fig.  2. (b) Experimentally observed PEF.

Equations (5)

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

iϕz+γϕ+D2ϕtt+ϕ2ϕ+Aψ2ϕ+Bψ2ϕ*=igQ1-δsϕ2ϕ+iβϕtt,  iψz-γψ+D2ψtt+ψ2ψ+Aϕ2ψ+Bϕ2ψ*=igQ2-δsψ2ψ+iβψtt,
gQi=g01+Qi/EL,
δst=-δs-δ0T1-ϒ2EAδs,
δst=δ0f-1t1T1-tftdt+1,
ft=exp-t1T1+ϒ2EAdt.

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