Abstract

Generation of self-similar parabolic pulse is analytically and numerically demonstrated by designing parabolic index normal dispersion decreasing fiber (NDDF) amplifiers. The pulse transmission is extensively studied for NDDFs in presence of physical gain as well as virtual gain induced by two different dispersion profiles corresponding to two different physical gain coefficients. Here, we introduce the virtual gain arising from the unavoidable spatial nonlinear variation, which helps to obtain the self-similar parabolic pulses at smaller optimum length in comparison to NDDF with constant nonlinearity. The output power profiles resemble with a perfect parabolic shape giving rise to self-similar pulses with very small misfit parameters. Pulse propagation in presence of spatial gain variation is also studied. To avoid fabrication difficulties, we propose equivalent staircase dispersion profiles consisting of a number of constant dispersion fibers (CDFs), which are simple to manufacture and show performances excellently close to that of the proposed NDDF.

© 2009 IEEE

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  1. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84, 6010-6013 (2000).
  2. J. M. Dudley, C. Finot, D. J. Richardson, G. Millot, "Self-similarity in ultrafast nonlinear optics," Nat. Phys. 3, 597-603 (2007).
  3. A. Ruehl, O. Prochnow, D. Wandt, D. Kracht, B. Burgoyne, N. Godbout, S. Lacroix, "Dynamics of parabolic pulses in ultrafast fiber laser," Opt. Lett. 31, 2734-2736 (2006).
  4. K. R. Tamura, H. Kubota, M. Nakazawa, "Fundamentals of stable continuum generation at high repetition rates," IEEE J. Quantum Electron. 36, 773-778 (2000).
  5. C. Finot, G. Millot, S. Pitois, C. Billet, J. M. Dudley, "Numerical and experimental study of parabolic pulses generated via Raman amplification in standard optical fibers," IEEE J. Sel. Topics Quantum. Electron. 10, 1211-1218 (2004).
  6. C. Finot, F. Parmigiani, P. Petropoulos, D. J. Richardson, "Parabolic pulse evolution in normally dispersive fiber amplifiers preceding the similariton formation regime," Opt. Exp. 14, 3161-3170 (2006).
  7. T. Hirooka, M. Nakazawa, "Parabolic pulse generation by use of a dispersion-decreasing fiber with normal group-velocity dispersion," Opt. Lett. 29, 498-500 (2004).
  8. A. I. Latkin, S. K. Turitsyn, A. A. Sysoliatin, "Theory of parabolic pulse generation in tapered fiber," Opt. Lett. 32, 331-333 (2007).
  9. N. Vukovic, N. G. R. Broderick, F. Poletti, "Parabolic pulse generation using tapered microstructured optical fibres," Adv. Nonlinear Opt. 2008, 1-10 (2008).
  10. B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, J. M. Dudley, "Parabolic pulse generation in comb-like profiled dispersion decreasing fiber," Electron Lett. 42, 965-966 (2006).
  11. A. Y. Plotski, A. A. Sysoliatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, S. K. Turitsyn, "Experiments on the generation of parabolic pulses in fibers with length-varying normal chromatic dispersion," JETP Lett. 85, 319-322 (2007).
  12. S. Wabnitz, C. Finot, "Theory of parabolic pulse propagation in nonlinear dispersion-decreasing optical fiber amplifiers," J. Opt. Soc. Amer. B 25, 614-621 (2008).
  13. C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, S. Wabnitz, "Parabolic pulse generation with active or passive dispersion decreasing optical fibers," Opt. Exp. 15, 15824-15835 (2007).
  14. D. Ghosh, M. Basu, "Propagation of short soliton pulses through a parabolic index fiber with dispersion decreasing along length," Opt. Commun. 281, 3361-3368 (2008).
  15. C. Finot, L. Provost, P. Petropoulos, D. J. Richardson, "Parabolic pulse generation through passive nonlinear pulse reshaping in a normally dispersive two segment fiber device," Opt. Exp. 15, 852-864 (2007).
  16. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  17. G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2006).
  18. A. K. Ghatak, K. Thyagarajan, Introduction to Fiber Optics (Cambridge Univ., 2002).
  19. D. Marcuse, "," J. Opt. Soc. Am. 68, 103-109 (1978).
  20. D. Gupta, G. Kumar, K. Thyagarajan, "Nonlinear pulse propagation in dispersion decreasing fibers," Opt. Commun. 237, 309-317 (2004).
  21. V. I. Kruglov, A. C. Peacock, J. M. Dudley, J. D. Harvey, "Self-similar propagation of high-power parabolic pulses in optical fiber amplifiers," Opt. Lett. 25, 1753-1755 (2000).
  22. 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. Amer. B 19, 461-469 (2002).

2008

N. Vukovic, N. G. R. Broderick, F. Poletti, "Parabolic pulse generation using tapered microstructured optical fibres," Adv. Nonlinear Opt. 2008, 1-10 (2008).

S. Wabnitz, C. Finot, "Theory of parabolic pulse propagation in nonlinear dispersion-decreasing optical fiber amplifiers," J. Opt. Soc. Amer. B 25, 614-621 (2008).

D. Ghosh, M. Basu, "Propagation of short soliton pulses through a parabolic index fiber with dispersion decreasing along length," Opt. Commun. 281, 3361-3368 (2008).

2007

C. Finot, L. Provost, P. Petropoulos, D. J. Richardson, "Parabolic pulse generation through passive nonlinear pulse reshaping in a normally dispersive two segment fiber device," Opt. Exp. 15, 852-864 (2007).

C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, S. Wabnitz, "Parabolic pulse generation with active or passive dispersion decreasing optical fibers," Opt. Exp. 15, 15824-15835 (2007).

A. Y. Plotski, A. A. Sysoliatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, S. K. Turitsyn, "Experiments on the generation of parabolic pulses in fibers with length-varying normal chromatic dispersion," JETP Lett. 85, 319-322 (2007).

J. M. Dudley, C. Finot, D. J. Richardson, G. Millot, "Self-similarity in ultrafast nonlinear optics," Nat. Phys. 3, 597-603 (2007).

A. I. Latkin, S. K. Turitsyn, A. A. Sysoliatin, "Theory of parabolic pulse generation in tapered fiber," Opt. Lett. 32, 331-333 (2007).

2006

A. Ruehl, O. Prochnow, D. Wandt, D. Kracht, B. Burgoyne, N. Godbout, S. Lacroix, "Dynamics of parabolic pulses in ultrafast fiber laser," Opt. Lett. 31, 2734-2736 (2006).

C. Finot, F. Parmigiani, P. Petropoulos, D. J. Richardson, "Parabolic pulse evolution in normally dispersive fiber amplifiers preceding the similariton formation regime," Opt. Exp. 14, 3161-3170 (2006).

B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, J. M. Dudley, "Parabolic pulse generation in comb-like profiled dispersion decreasing fiber," Electron Lett. 42, 965-966 (2006).

2004

D. Gupta, G. Kumar, K. Thyagarajan, "Nonlinear pulse propagation in dispersion decreasing fibers," Opt. Commun. 237, 309-317 (2004).

C. Finot, G. Millot, S. Pitois, C. Billet, J. M. Dudley, "Numerical and experimental study of parabolic pulses generated via Raman amplification in standard optical fibers," IEEE J. Sel. Topics Quantum. Electron. 10, 1211-1218 (2004).

T. Hirooka, M. Nakazawa, "Parabolic pulse generation by use of a dispersion-decreasing fiber with normal group-velocity dispersion," Opt. Lett. 29, 498-500 (2004).

2002

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. Amer. B 19, 461-469 (2002).

2000

V. I. Kruglov, A. C. Peacock, J. M. Dudley, J. D. Harvey, "Self-similar propagation of high-power parabolic pulses in optical fiber amplifiers," Opt. Lett. 25, 1753-1755 (2000).

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

K. R. Tamura, H. Kubota, M. Nakazawa, "Fundamentals of stable continuum generation at high repetition rates," IEEE J. Quantum Electron. 36, 773-778 (2000).

1978

D. Marcuse, "," J. Opt. Soc. Am. 68, 103-109 (1978).

Adv. Nonlinear Opt.

N. Vukovic, N. G. R. Broderick, F. Poletti, "Parabolic pulse generation using tapered microstructured optical fibres," Adv. Nonlinear Opt. 2008, 1-10 (2008).

Electron Lett.

B. Kibler, C. Billet, P. A. Lacourt, R. Ferriere, L. Larger, J. M. Dudley, "Parabolic pulse generation in comb-like profiled dispersion decreasing fiber," Electron Lett. 42, 965-966 (2006).

IEEE J. Quantum Electron.

K. R. Tamura, H. Kubota, M. Nakazawa, "Fundamentals of stable continuum generation at high repetition rates," IEEE J. Quantum Electron. 36, 773-778 (2000).

IEEE J. Sel. Topics Quantum. Electron.

C. Finot, G. Millot, S. Pitois, C. Billet, J. M. Dudley, "Numerical and experimental study of parabolic pulses generated via Raman amplification in standard optical fibers," IEEE J. Sel. Topics Quantum. Electron. 10, 1211-1218 (2004).

J. Opt. Soc. Am.

D. Marcuse, "," J. Opt. Soc. Am. 68, 103-109 (1978).

J. Opt. Soc. Amer. B

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. Amer. B 19, 461-469 (2002).

S. Wabnitz, C. Finot, "Theory of parabolic pulse propagation in nonlinear dispersion-decreasing optical fiber amplifiers," J. Opt. Soc. Amer. B 25, 614-621 (2008).

JETP Lett.

A. Y. Plotski, A. A. Sysoliatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, S. K. Turitsyn, "Experiments on the generation of parabolic pulses in fibers with length-varying normal chromatic dispersion," JETP Lett. 85, 319-322 (2007).

Nat. Phys.

J. M. Dudley, C. Finot, D. J. Richardson, G. Millot, "Self-similarity in ultrafast nonlinear optics," Nat. Phys. 3, 597-603 (2007).

Opt. Commun.

D. Gupta, G. Kumar, K. Thyagarajan, "Nonlinear pulse propagation in dispersion decreasing fibers," Opt. Commun. 237, 309-317 (2004).

D. Ghosh, M. Basu, "Propagation of short soliton pulses through a parabolic index fiber with dispersion decreasing along length," Opt. Commun. 281, 3361-3368 (2008).

Opt. Exp.

C. Finot, L. Provost, P. Petropoulos, D. J. Richardson, "Parabolic pulse generation through passive nonlinear pulse reshaping in a normally dispersive two segment fiber device," Opt. Exp. 15, 852-864 (2007).

C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, S. Wabnitz, "Parabolic pulse generation with active or passive dispersion decreasing optical fibers," Opt. Exp. 15, 15824-15835 (2007).

C. Finot, F. Parmigiani, P. Petropoulos, D. J. Richardson, "Parabolic pulse evolution in normally dispersive fiber amplifiers preceding the similariton formation regime," Opt. Exp. 14, 3161-3170 (2006).

Opt. Lett.

Phys. Rev. Lett.

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

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2006).

A. K. Ghatak, K. Thyagarajan, Introduction to Fiber Optics (Cambridge Univ., 2002).

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