Abstract

We report the complete characterization of the self-similar scaling of parabolic pulse similaritons in an optical fiber amplifier. High dynamic range frequency resolved optical gating allows the direct observation of the evolution of a hyperbolic secant-like input pulse to an asymptotic amplifier similariton, and reveals the presence of intermediate asymptotic wings about the parabolic pulse core. These results are used to optimize additional self-similar propagation in highly-nonlinear fiber and subsequent compression in hollow-core photonic bandgap fiber.

© 2005 Optical Society of America

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References

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  1. See for example: P. L. Sachdev, Self-Similarity and Beyond: Exact Solutions of Nonlinear Problems, Chapman and Hall (CRC Press), London (2000); G. I. Barenblatt, Scaling, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge (2003).
  2. D. Anderson, M. Desaix, M. Karlson, M. Lisak, and M.L. Quiroga-Teixeiro, �??Wave-breaking-free pulses in nonlinear-optical fibers,�?? J. Opt. Soc. Am. B 10, 1185-1190 (1993).
    [CrossRef]
  3. K. Tamura and M. Nakazawa, �??Pulse compression by nonlinear pulse evolution with reduced optical wave breaking in erbium-doped fiber amplifiers,�?? Opt. Lett. 21, 68-70 (1996)
    [CrossRef] [PubMed]
  4. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, �??Self-similar propagation and amplification of parabolic pulses in optical fibers,�?? Phys. Rev. Lett. 84, 6010-6013 (2000).
    [CrossRef] [PubMed]
  5. V. I. Kruglov, A. C. Peacock, J. M. Dudley, and J. D. Harvey, �??Self-similar propagation of high-power parabolic pulses in optical fiber amplifiers,�?? Opt. Lett. 25, 1753-1755 (2000).
    [CrossRef]
  6. V. I. Kruglov, A. C. Peacock, J. D. Harvey, J. M. Dudley, �??Self-similar propagation of parabolic pulses in normal dispersion fiber amplifiers,�?? J. Opt. Soc. Am. B 19, 461-469 (2002).
    [CrossRef]
  7. S. Boscolo, S. K. Turitsyn, V. Y. Novokshenov, and J. H. B. Nijhof, �??Self-similar parabolic optical solitary waves,�?? Theor. and Math. Phys. 133, 1647-1656 (2002).
    [CrossRef]
  8. J. H. V. Price, W. Belardi, T. M. Monro, A. Malinowski, A. Piper, D. J. Richardson, �??Soliton transmission and supercontinuum generation in holey fiber using a diode pumped Ytterbium fiber source,�?? Opt. Express 10, 382-387 (2002). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-8-382">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-8-382</a>
    [PubMed]
  9. J. Limpert, T. Schreiber, T. Clausnitzer, K. Zöllner, H. J. Fuchs, E. -B. Kley, H. Zellmer, and A. Tünnermann, �??High-power femtosecond Yb-doped fiber amplifier,�?? Opt. Express 10, 628-638 (2002). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-628">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-628</a>
    [PubMed]
  10. A. Malinowski, A. Piper, J. H. V. Price, K. Furusawa, Y. Jeong, J. Nilsson and D. J. Richardson �??Ultrashort-pulse Yb3+-fiber-based laser and amplifier system producing > 25 W average power,�?? Opt. Lett. 29, 2073-2075 (2004).
    [CrossRef] [PubMed]
  11. J. W. Nicholson, A. D. Yablon, P. S. Westbrook, K. S. Feder and M. F. Yan, �??High power, single mode, all-fiber source of femtosecond pulses at 1550 nm and its use in supercontinuum generation,�?? Opt. Express 12, 3025-3034 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-3025">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-3025</a>
    [CrossRef] [PubMed]
  12. Y. Ozeki, K. Taira, K. Aiso, Y. Takushima and K. Kikuchi, �??Highly flat super-continuum generation from 2 ps pulses using 1 km-long erbium-doped fibre amplifier,�?? Electron. Lett. 38, 1642-1643 (2004).
    [CrossRef]
  13. C. Finot, G. Millot, C. Billet, and J. M. Dudley, �??Experimental generation of parabolic pulses via Raman amplification in optical fiber�??, Opt. Express 11, 1547-1552 (2003). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1547">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1547</a>
    [CrossRef] [PubMed]
  14. C. Finot, G. Millot, and J. M. Dudley, �??Asymptotic characteristics of parabolic similariton pulses in optical fiber amplifiers,�?? Opt. Lett. 29, 2533-2535 (2004).
    [CrossRef] [PubMed]
  15. C. Finot and G. Millot, �??Synthesis of optical pulses by use of similaritons�??, Opt. Express 12, 5104-5109 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5104">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5104</a>
    [CrossRef] [PubMed]
  16. C. J. S. de Matos, S. V. Popov, A. B. Rulkov, J. R. Taylor, J. Broeng, T. P. Hansen and V. P. Gapontsev, �??All-fiber format compression of frequency-chirped pulses in air-guiding photonic crystal fibers,�?? Phys. Rev. Lett. 93 / 103901 (2004).
    [CrossRef] [PubMed]
  17. D. N. Fittinghoff and M. Munroe, �??Noise: Its effects and Suppression�?? in Frequency Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, R. Trebino, Kluwer Academic Publishers chapter 9, 179-201 (2000).
    [CrossRef]

Electron Lett.

Y. Ozeki, K. Taira, K. Aiso, Y. Takushima and K. Kikuchi, �??Highly flat super-continuum generation from 2 ps pulses using 1 km-long erbium-doped fibre amplifier,�?? Electron. Lett. 38, 1642-1643 (2004).
[CrossRef]

Frequency Resolved Optical Gating: The M

D. N. Fittinghoff and M. Munroe, �??Noise: Its effects and Suppression�?? in Frequency Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, R. Trebino, Kluwer Academic Publishers chapter 9, 179-201 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

J. H. V. Price, W. Belardi, T. M. Monro, A. Malinowski, A. Piper, D. J. Richardson, �??Soliton transmission and supercontinuum generation in holey fiber using a diode pumped Ytterbium fiber source,�?? Opt. Express 10, 382-387 (2002). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-8-382">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-8-382</a>
[PubMed]

J. Limpert, T. Schreiber, T. Clausnitzer, K. Zöllner, H. J. Fuchs, E. -B. Kley, H. Zellmer, and A. Tünnermann, �??High-power femtosecond Yb-doped fiber amplifier,�?? Opt. Express 10, 628-638 (2002). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-628">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-628</a>
[PubMed]

J. W. Nicholson, A. D. Yablon, P. S. Westbrook, K. S. Feder and M. F. Yan, �??High power, single mode, all-fiber source of femtosecond pulses at 1550 nm and its use in supercontinuum generation,�?? Opt. Express 12, 3025-3034 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-3025">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-3025</a>
[CrossRef] [PubMed]

C. Finot, G. Millot, C. Billet, and J. M. Dudley, �??Experimental generation of parabolic pulses via Raman amplification in optical fiber�??, Opt. Express 11, 1547-1552 (2003). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1547">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1547</a>
[CrossRef] [PubMed]

C. Finot and G. Millot, �??Synthesis of optical pulses by use of similaritons�??, Opt. Express 12, 5104-5109 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5104">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5104</a>
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. Lett.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, �??Self-similar propagation and amplification of parabolic pulses in optical fibers,�?? Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

C. J. S. de Matos, S. V. Popov, A. B. Rulkov, J. R. Taylor, J. Broeng, T. P. Hansen and V. P. Gapontsev, �??All-fiber format compression of frequency-chirped pulses in air-guiding photonic crystal fibers,�?? Phys. Rev. Lett. 93 / 103901 (2004).
[CrossRef] [PubMed]

Theor. and Math. Phys.

S. Boscolo, S. K. Turitsyn, V. Y. Novokshenov, and J. H. B. Nijhof, �??Self-similar parabolic optical solitary waves,�?? Theor. and Math. Phys. 133, 1647-1656 (2002).
[CrossRef]

Other

See for example: P. L. Sachdev, Self-Similarity and Beyond: Exact Solutions of Nonlinear Problems, Chapman and Hall (CRC Press), London (2000); G. I. Barenblatt, Scaling, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge (2003).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Numerical simulations of parabolic pulse evolution in a normal dispersion amplifier as described in the text. (b) Corresponding experimental results obtained from FROG measurements. (c) Experimental results using a logarithmic intensity scale to illustrate the temporal broadening and the growth of intermediate asymptotic wings. (d) Experimental results using a logarithmic intensity scale to illustrate the associated spectral evolution.

Fig. 2.
Fig. 2.

(a) Experiment (solid line) and simulation (dashed line) after 7 m propagation, showing intensity (left axis) and chirp (right axis). The shading distinguishes the parabolic pulse core and intermediate asymptotic wings. (b) Transition between the core and wing regions. (c) Experimental results (circles) and best straight line fit (solid line) showing the exponential decrease in the relative energy in the intermediate asymptotic wings with propagation.

Fig. 3.
Fig. 3.

Pulse Spectra and intensity and chirp characteristics from (a) the 10 m Er3+ amplifier and (b) after 10 m additional self-similar propagation in HNLF. The spectral intensities (top) are shown using a linear scale whilst the temporal intensities (bottom) use a logarithmic scale. (c) and (d) show pulse characteristics after photonic bandgap fiber compression using linear (top) and logarithmic (bottom) scales. The solid line in (c) corresponds to the experimental compression of the pulse shown in (b) whilst the dashed line shows the ideal Fourier transform limit. The experimental results in (d) show the non-optimal case using 15 m of HNLF.

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