Abstract

We propose the use of self-defocusing nonlinearities to control nonlinear phase shifts in soliton fiber lasers. By analogy to dispersion management, we refer to this scheme as nonlinearity management. First we describe a map that can be regarded as a combination of nonlinearity management and dispersion management. The map is designed to support solitons in two segments of alternating sign of nonlinearity and dispersion. Analytical and numerical calculations demonstrate that this map can be essentially free of spectral-sideband generation. Suppressing the spectral sidebands should make possible pulse energies 100 times greater than those of existing soliton fiber lasers. We also discuss the less than ideal case of direct reduction of average nonlinearity by use of self-defocusing nonlinearity segments without optimizing dispersion. The second scheme has the advantage of easier implementation. Practical implementations with existing materials are discussed.

© 2002 Optical Society of America

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References

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  1. L. J. Qian, X. Liu, and F. W. Wise, “Femtosecond Kerr-lens mode locking with negative nonlinear phase shifts,” Opt. Lett. 24, 166–168 (1999).
    [CrossRef]
  2. X. Liu, L. Qian, and F. W. Wise, “High-energy pulse compression using negative phase shifts produced by the cascade χ(2)(2) nonlinearity,” Opt. Lett. 24, 1777–1779 (1999).
    [CrossRef]
  3. C. Pare, A. Villeneuve, and P.-A. Belanger, “Compensating for dispersion and the nonlinear Kerr effect without phase conjugation,” Opt. Lett. 21, 459–461 (1996).
    [CrossRef] [PubMed]
  4. C. Pare, A. Villeneuve, and S. LaRochelle, “Split compensation of dispersion and self-phase modulation in optical communication systems,” Opt. Commun. 160, 130–138 (1999).
    [CrossRef]
  5. M. Hofer, M. E. Fermann, F. Haberl, M. H. Ober, and A. J. Schmidt, “Mode locking with cross-phase and self-phase modulation,” Opt. Lett. 16, 502–504 (1991).
    [CrossRef] [PubMed]
  6. S. M. J. Kelly, “Characteristic side-band instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
    [CrossRef]
  7. B. A. Malomed, “Propagation of a soliton in a nonlinear waveguide with dissipation and pumping,” Opt. Commun. 61, 192–194 (1987).
    [CrossRef]
  8. K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Photonics Technol. Lett. 6, 697–699 (1994).
    [CrossRef]
  9. K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18, 1080–1082 (1993).
    [CrossRef] [PubMed]
  10. N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997), and references therein.
    [CrossRef]
  11. D. J. Jones, Y. Chen, H. A. Haus, and E. P. Ippen, “Resonant sideband generation in stretched-pulse fiber lasers,” Opt. Lett. 23, 1535–1537 (1998).
    [CrossRef]
  12. G. Lenz, K. Tamura, H. A. Haus, and E. P. Ippen, “All-solid state femtosecond source at 1.55 μm,” Opt. Lett. 20, 1289–1291 (1995).
    [CrossRef] [PubMed]
  13. L. E. Nelson, S. B. Fleischer, G. Lenz, and E. P. Ippen, “Efficient frequency doubling of a femtosecond fiber laser,” Opt. Lett. 21, 1759–1761 (1996).
    [CrossRef] [PubMed]
  14. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
    [CrossRef] [PubMed]
  15. R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949–1951 (1994).
    [CrossRef] [PubMed]
  16. X. Liu, F. Ö. Ilday, K. Beckwitt, and F. W. Wise, “Femtosecond nonlinear polarization evolution based on cascade quadratic nonlinearities,” Opt. Lett. 25, 1394–1396 (2000).
    [CrossRef]

2000 (1)

1999 (3)

1998 (1)

1997 (1)

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997), and references therein.
[CrossRef]

1996 (2)

1995 (1)

1994 (2)

R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949–1951 (1994).
[CrossRef] [PubMed]

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Photonics Technol. Lett. 6, 697–699 (1994).
[CrossRef]

1993 (1)

1992 (2)

1991 (1)

1987 (1)

B. A. Malomed, “Propagation of a soliton in a nonlinear waveguide with dissipation and pumping,” Opt. Commun. 61, 192–194 (1987).
[CrossRef]

Baek, Y.

Beckwitt, K.

Belanger, P.-A.

Chen, Y.

DeSalvo, R.

Doerr, C. R.

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Photonics Technol. Lett. 6, 697–699 (1994).
[CrossRef]

Doran, N. J.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997), and references therein.
[CrossRef]

Fermann, M. E.

Fleischer, S. B.

Forysiak, W.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997), and references therein.
[CrossRef]

Haberl, F.

Hagan, D. J.

Haus, H. A.

Hofer, M.

Ilday, F. Ö.

Ippen, E. P.

Jones, D. J.

Kelly, S. M. J.

S. M. J. Kelly, “Characteristic side-band instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[CrossRef]

Kim, D. Y.

Knox, F. M.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997), and references therein.
[CrossRef]

LaRochelle, S.

C. Pare, A. Villeneuve, and S. LaRochelle, “Split compensation of dispersion and self-phase modulation in optical communication systems,” Opt. Commun. 160, 130–138 (1999).
[CrossRef]

Lenz, G.

Liu, X.

Malomed, B. A.

B. A. Malomed, “Propagation of a soliton in a nonlinear waveguide with dissipation and pumping,” Opt. Commun. 61, 192–194 (1987).
[CrossRef]

Nelson, L. E.

Ober, M. H.

Pare, C.

C. Pare, A. Villeneuve, and S. LaRochelle, “Split compensation of dispersion and self-phase modulation in optical communication systems,” Opt. Commun. 160, 130–138 (1999).
[CrossRef]

C. Pare, A. Villeneuve, and P.-A. Belanger, “Compensating for dispersion and the nonlinear Kerr effect without phase conjugation,” Opt. Lett. 21, 459–461 (1996).
[CrossRef] [PubMed]

Qian, L.

Qian, L. J.

Schiek, R.

Schmidt, A. J.

Seibert, H.

Sheik-Bahae, M.

Smith, N. J.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997), and references therein.
[CrossRef]

Sohler, W.

Stegeman, G.

Stegeman, G. I.

Sundheimer, M. L.

Tamura, K.

Van Stryland, E. W.

Vanherzeele, H.

Villeneuve, A.

C. Pare, A. Villeneuve, and S. LaRochelle, “Split compensation of dispersion and self-phase modulation in optical communication systems,” Opt. Commun. 160, 130–138 (1999).
[CrossRef]

C. Pare, A. Villeneuve, and P.-A. Belanger, “Compensating for dispersion and the nonlinear Kerr effect without phase conjugation,” Opt. Lett. 21, 459–461 (1996).
[CrossRef] [PubMed]

Wise, F. W.

Electron. Lett. (1)

S. M. J. Kelly, “Characteristic side-band instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Photonics Technol. Lett. 6, 697–699 (1994).
[CrossRef]

J. Lightwave Technol. (1)

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997), and references therein.
[CrossRef]

Opt. Commun. (2)

B. A. Malomed, “Propagation of a soliton in a nonlinear waveguide with dissipation and pumping,” Opt. Commun. 61, 192–194 (1987).
[CrossRef]

C. Pare, A. Villeneuve, and S. LaRochelle, “Split compensation of dispersion and self-phase modulation in optical communication systems,” Opt. Commun. 160, 130–138 (1999).
[CrossRef]

Opt. Lett. (11)

M. Hofer, M. E. Fermann, F. Haberl, M. H. Ober, and A. J. Schmidt, “Mode locking with cross-phase and self-phase modulation,” Opt. Lett. 16, 502–504 (1991).
[CrossRef] [PubMed]

L. J. Qian, X. Liu, and F. W. Wise, “Femtosecond Kerr-lens mode locking with negative nonlinear phase shifts,” Opt. Lett. 24, 166–168 (1999).
[CrossRef]

X. Liu, L. Qian, and F. W. Wise, “High-energy pulse compression using negative phase shifts produced by the cascade χ(2)(2) nonlinearity,” Opt. Lett. 24, 1777–1779 (1999).
[CrossRef]

C. Pare, A. Villeneuve, and P.-A. Belanger, “Compensating for dispersion and the nonlinear Kerr effect without phase conjugation,” Opt. Lett. 21, 459–461 (1996).
[CrossRef] [PubMed]

K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18, 1080–1082 (1993).
[CrossRef] [PubMed]

D. J. Jones, Y. Chen, H. A. Haus, and E. P. Ippen, “Resonant sideband generation in stretched-pulse fiber lasers,” Opt. Lett. 23, 1535–1537 (1998).
[CrossRef]

G. Lenz, K. Tamura, H. A. Haus, and E. P. Ippen, “All-solid state femtosecond source at 1.55 μm,” Opt. Lett. 20, 1289–1291 (1995).
[CrossRef] [PubMed]

L. E. Nelson, S. B. Fleischer, G. Lenz, and E. P. Ippen, “Efficient frequency doubling of a femtosecond fiber laser,” Opt. Lett. 21, 1759–1761 (1996).
[CrossRef] [PubMed]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef] [PubMed]

R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949–1951 (1994).
[CrossRef] [PubMed]

X. Liu, F. Ö. Ilday, K. Beckwitt, and F. W. Wise, “Femtosecond nonlinear polarization evolution based on cascade quadratic nonlinearities,” Opt. Lett. 25, 1394–1396 (2000).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic of a generic soliton laser consisting of segments with self-focusing nonlinearity, anomalous dispersion, and amplitude modulation (AM).

Fig. 2
Fig. 2

Typical autocorrelation of the stretched-pulse laser in our laboratory. Inset, the corresponding spectrum.

Fig. 3
Fig. 3

Block diagram of the proposed laser consisting of fiber, compensator, and SA. We envisage a ring cavity for increased ease of self-starting. The sequence of the components in the diagram is the same as in the simulations.

Fig. 4
Fig. 4

Buildup of a solitary pulse from intracavity noise plotted for the proposed laser with zc,eff=1.

Fig. 5
Fig. 5

(a) Spectra (as offset from the carrier frequency) for effective map lengths of (top to bottom) zc,eff=10, 8, 6, 4, 2,1, 0.5, 0.1. (b) Plot of the frequency offset of the first sidebands for the proposed laser and the control simulation.

Fig. 6
Fig. 6

Results of simulations for full compensation (ξ=1/2): SSG is eliminated, and similar pulse duration is achieved at 10 times higher energy than in the soliton laser. The traces have been displaced horizontally for clarity.

Fig. 7
Fig. 7

Schematic of a fiber laser with reduced average nonlinearity.

Fig. 8
Fig. 8

Results of numerical simulations of a soliton fiber laser, showing the intensity profiles with increasing pulse energy and nonlinearity compensation. The intensity profiles are normalized and have been displaced vertically and horizontally for clarity.

Fig. 9
Fig. 9

Intensity profile and spectrum (as offset from the carrier frequency) of the proposed laser with zc,eff=0.1 compared with the same laser with 10% mismatch in the nonlinearity coefficient of the compensating segment.

Equations (7)

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

dudz-i12D(z)d2udt2=iΓ(z)|u|2u,
D(z)=Γ(z)=+10<z<ξzc-1ξzc<z<zc,
u=sech(t)exp[iδ(z)/2],
dudz-i12D(z)d2udt2=iΓ(z)|u|2u+gu,
m(z)dudz-i12d2udt2=iA2(z)|u|2u,
u=η sech[η(t-wz)]exp[iδ(z)(wt-kz)],
Δwn±1/τp[8nzs/(zc|2ξ-1|)-1]1/2.

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