Abstract

A passively mode-locked dual-core fiber ring laser, similar to that first proposed by Winful and Walton [ Opt. Lett. 17, 1688 ( 1992)], is numerically simulated, incorporating losses and higher-order effects. Ultrashort hyperbolic secantlike pulses with negligible chirp are generated by this laser. The laser operation is robust but not self-starting; lasing action is found even when stimulated Raman scattering and changes in the cavity length are included. The pulse amplitude, phase, and pulse spectrum are discussed.

© 1995 Optical Society of America

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References

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  1. L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
    [CrossRef]
  2. K. Nakagawa, S. Nishi, and E. Yoneda, J. Lightwave Technol. 9, 198 (1991).
    [CrossRef]
  3. H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
    [CrossRef]
  4. S. M. Jensen, IEEE J. Quantum Electron. 18, 1580 (1982)
    [CrossRef]
  5. H. G. Winful and D. T. Walton, Opt. Lett. 17, 1688 (1992).
    [CrossRef] [PubMed]
  6. S. L. Doty, Y. J. Oh, J. W. Haus, and R. L. Fork, presented at OSA Annual Meeting, Dallas, Texas, October 2–7, 1994; paper ML4.
  7. J. Kanka, Opt. Lett. 19, 1873 (1994).
    [CrossRef] [PubMed]
  8. P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, Opt. Lett. 11, 464 (1986).
    [CrossRef] [PubMed]
  9. D. Anderson and M. Lisak, Phys. Rev. A 27, 1393 (1983).
    [CrossRef]
  10. F. M. Mitschke and L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
    [CrossRef] [PubMed]
  11. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]
  12. See, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989), Chap. 2 and references therein.
  13. G. P. Agrawal, Phys. Rev. A 44, 7493 (1991).
    [CrossRef] [PubMed]
  14. K. J. Blow and D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
    [CrossRef]
  15. S. L. Doty, J. W. Haus, YunJe Oh, and R. L. Fork, Phys. Rev. E 51, 709 (1995).
    [CrossRef]
  16. Ref. 12, Chap. 4.

Agrawal, G. P.

G. P. Agrawal, Phys. Rev. A 44, 7493 (1991).
[CrossRef] [PubMed]

See, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989), Chap. 2 and references therein.

Anderson, D.

D. Anderson and M. Lisak, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

Blow, K. J.

K. J. Blow and D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

Chen, H. H.

P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, Opt. Lett. 11, 464 (1986).
[CrossRef] [PubMed]

Doty, S. L.

S. L. Doty, J. W. Haus, YunJe Oh, and R. L. Fork, Phys. Rev. E 51, 709 (1995).
[CrossRef]

S. L. Doty, Y. J. Oh, J. W. Haus, and R. L. Fork, presented at OSA Annual Meeting, Dallas, Texas, October 2–7, 1994; paper ML4.

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

Fork, R. L.

S. L. Doty, Y. J. Oh, J. W. Haus, and R. L. Fork, presented at OSA Annual Meeting, Dallas, Texas, October 2–7, 1994; paper ML4.

S. L. Doty, J. W. Haus, YunJe Oh, and R. L. Fork, Phys. Rev. E 51, 709 (1995).
[CrossRef]

Gordon, J. P.

J. P. Gordon, Opt. Lett. 11, 662 (1986).
[CrossRef] [PubMed]

Haus, H. A.

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

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

Haus, J. W.

S. L. Doty, J. W. Haus, YunJe Oh, and R. L. Fork, Phys. Rev. E 51, 709 (1995).
[CrossRef]

S. L. Doty, Y. J. Oh, J. W. Haus, and R. L. Fork, presented at OSA Annual Meeting, Dallas, Texas, October 2–7, 1994; paper ML4.

Ippen, E. P.

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

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron. 18, 1580 (1982)
[CrossRef]

Kanka, J.

J. Kanka, Opt. Lett. 19, 1873 (1994).
[CrossRef] [PubMed]

Lee, Y. C.

P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, Opt. Lett. 11, 464 (1986).
[CrossRef] [PubMed]

Lisak, M.

D. Anderson and M. Lisak, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

Menyuk, C. R.

P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, Opt. Lett. 11, 464 (1986).
[CrossRef] [PubMed]

Mitschke, F. M.

F. M. Mitschke and L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
[CrossRef] [PubMed]

Mollenauer, L. F.

F. M. Mitschke and L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
[CrossRef] [PubMed]

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

Nakagawa, K.

K. Nakagawa, S. Nishi, and E. Yoneda, J. Lightwave Technol. 9, 198 (1991).
[CrossRef]

Nishi, S.

K. Nakagawa, S. Nishi, and E. Yoneda, J. Lightwave Technol. 9, 198 (1991).
[CrossRef]

Oh, Y. J.

S. L. Doty, Y. J. Oh, J. W. Haus, and R. L. Fork, presented at OSA Annual Meeting, Dallas, Texas, October 2–7, 1994; paper ML4.

Oh, YunJe

S. L. Doty, J. W. Haus, YunJe Oh, and R. L. Fork, Phys. Rev. E 51, 709 (1995).
[CrossRef]

Tamura, K.

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

Wai, P. K. A.

P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, Opt. Lett. 11, 464 (1986).
[CrossRef] [PubMed]

Walton, D. T.

H. G. Winful and D. T. Walton, Opt. Lett. 17, 1688 (1992).
[CrossRef] [PubMed]

Winful, H. G.

H. G. Winful and D. T. Walton, Opt. Lett. 17, 1688 (1992).
[CrossRef] [PubMed]

Wood, D.

K. J. Blow and D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

Yoneda, E.

K. Nakagawa, S. Nishi, and E. Yoneda, J. Lightwave Technol. 9, 198 (1991).
[CrossRef]

Other

L. F. Mollenauer, S. G. Evangelides, and H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

K. Nakagawa, S. Nishi, and E. Yoneda, J. Lightwave Technol. 9, 198 (1991).
[CrossRef]

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

S. M. Jensen, IEEE J. Quantum Electron. 18, 1580 (1982)
[CrossRef]

H. G. Winful and D. T. Walton, Opt. Lett. 17, 1688 (1992).
[CrossRef] [PubMed]

S. L. Doty, Y. J. Oh, J. W. Haus, and R. L. Fork, presented at OSA Annual Meeting, Dallas, Texas, October 2–7, 1994; paper ML4.

J. Kanka, Opt. Lett. 19, 1873 (1994).
[CrossRef] [PubMed]

P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, Opt. Lett. 11, 464 (1986).
[CrossRef] [PubMed]

D. Anderson and M. Lisak, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

F. M. Mitschke and L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
[CrossRef] [PubMed]

J. P. Gordon, Opt. Lett. 11, 662 (1986).
[CrossRef] [PubMed]

See, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989), Chap. 2 and references therein.

G. P. Agrawal, Phys. Rev. A 44, 7493 (1991).
[CrossRef] [PubMed]

K. J. Blow and D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

S. L. Doty, J. W. Haus, YunJe Oh, and R. L. Fork, Phys. Rev. E 51, 709 (1995).
[CrossRef]

Ref. 12, Chap. 4.

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Figures (12)

Fig. 1
Fig. 1

Schematic of the dual-core ring laser geometry. The active core has a 4-dB gain per dispersion length and 10% of the energy is coupled out of the cavity. The parameters used to simulate mode-locked lasing operation are discussed in the text.

Fig. 2
Fig. 2

Initial seed pulse shape and phase. The pulse has a hyperbolic-secant shape, whose height is larger than a single soliton energy. The phase is initially constant.

Fig. 3
Fig. 3

Soliton pulse shape and the phase after one pass around the ring cavity. Note the change of the time scale and the narrowing of the pulse. The phase is strongly distorted as a result of the strong change of the self-phase modulation.

Fig. 4
Fig. 4

Pulse shape and phase after five passes around the cavity. The SRS parameter is τR = 0.01. The linear slope of the phase change corresponds to a frequency shift of roughly −4 in the scaled units.

Fig. 5
Fig. 5

Spectral changes in the pulse after successive passes around the cavity; τR = 0.

Fig. 6
Fig. 6

Spectra of the pulse for successive passes around the ring cavity for τR = 0.01.

Fig. 7
Fig. 7

Energy of a pulse versus the round trip number for τR = 0.01.

Fig. 8
Fig. 8

Pulse maximum in time and frequency regimes versus the number of round trips. τR = 0.01.

Fig. 9
Fig. 9

Steady-state pulse width in time and frequency regimes versus values of τR.

Fig. 10
Fig. 10

Pulse width in time and frequency regimes versus the gain bandwidth parameter T2.

Fig. 11
Fig. 11

Steady–state (a) pulse shape and phase as well as (b) pulse spectrum, when only self-steepening is taken into account. s = 0.05.

Fig. 12
Fig. 12

Steady–state (a) pulse shape and phase and (b) pulse spectrum found by including relevant loss mechanisms with values τR = 0.01, s = 0.05, and δ = 0.03.

Equations (6)

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i u z + 1 2 2 u T 2 + v + u 2 u = i 2 μ u + i d 2 2 u T 2 + τ R u u 2 T + i δ 3 u T 3 - i s ( u 2 u ) T , i v z + 1 2 2 v T 2 + u + v 2 v = 0.
μ = g 0 L D ,             d = g 0 L D T 2 2 T 0 2 ,
τ R = T R T 0 ,
δ = β 3 6 β 2 T 0 ,
s = 2 ω 0 T 0 ,
u ( z = 0 , T ) = u 0 sech ( T ) ,             v ( z = 0 , T ) = 0.

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