Abstract

We propose an optical amplifier composed of fibers with varying normal group velocity dispersion (GVD) for picosecond pulse amplification. The analytical analysis defines the optimal axial distribution of dispersion that results in shaping of the parabolic pulses with controllable chirp. The proposed cascaded all-fiber pulse amplifier employs fiber gain segments with exponential increase of normal dispersion separated by the passive fiber sections with decreasing normal GVD. The cascaded amplifier allows us to prevent an excessive broadening of the pulse spectrum and, therefore, offers an attractive potential for energy scaling of similariton pulses.

© 2013 Optical Society of America

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References

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  1. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
    [CrossRef]
  2. J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, “High-power ultrafast fiber laser systems,” IEEE J. Sel. Top. Quantum Electron. 12, 233–244 (2006).
    [CrossRef]
  3. S. Zhou, F. Wise, and D. G. Ouzounov, “Divided-pulse amplification of ultrashort pulses,” Opt. Lett. 32, 871–873 (2007).
    [CrossRef]
  4. L. J. Kong, L. M. Zhao, S. Lefrancois, D. G. Ouzounov, C. X. Yang, and F. W. Wise, “Generation of megawatt peak power picosecond pulses from a divided-pulse fiber amplifier,” Opt. Lett. 37, 253–255 (2012).
    [CrossRef]
  5. T. Eidam, J. Rothhardt, F. Stutzki, F. Jansen, S. Hädrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Fiber chirped-pulse amplification system emitting 3.8 GW peak power,” Opt. Express 19, 255–260 (2011).
    [CrossRef]
  6. 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]
  7. G. Chang, H. G. Winful, A. Galvanauskas, and T. B. Norris, “Incoherent selfsimilarities of the coupled amplified nonlinear Schrödinger equations,” Phys. Rev. E 73, 016616 (2006).
    [CrossRef]
  8. J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).
    [CrossRef]
  9. T. Hirooka and M. Nakazava, “Parabolic pulse generation by use of a dispersion-decreasing fibre with normal group-velocity dispersion,” Opt. Lett. 29, 498–500 (2004).
    [CrossRef]
  10. A. Latkin, S. K. Turitsyn, and A. Sysoliatin, “Theory of parabolic pulse generation in tapered fiber,” Opt. Lett. 32, 331–333 (2007).
    [CrossRef]
  11. A. Yu. Plotskii, A. A. Sysolyatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, and S. K. Turitsyn, “Experiments of generation of parabolic pulses in fibers with length-varying normal chromatic dispersion,” JETP Lett. 85, 319–322 (2007).
    [CrossRef]
  12. V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).
    [CrossRef]
  13. S. Kraus and M. Lucki, “Dispersion compensating photonic crystal fiber with enhanced properties achieved by modified core geometry,” Adv. Electric. Electron. Eng. 10, 101–105 (2012).
  14. D. C. Zografopoulos, C. Vázquez, E. E. Kriezis, and T. V. Yioultsis, “Dual-core photonic crystal fibers for tunable polarization mode dispersion compensation,” Opt. Express 19, 21680–21691 (2011).
    [CrossRef]
  15. J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
    [CrossRef]
  16. G. P. Agraval, Nonlinear Fiber Optics (Academic, 1995).
  17. U. G. Akhmetshin, V. A. Bogatyrev, A. K. Senatorov, A. A. Sysolyatin, and M. G. Shalygin, “New single-mode fibres with the flat spectral dependence of the chromatic dispersion varying over the fibre length,” Quantum Electron. 33, 265–267 (2003).
    [CrossRef]
  18. A. A. Sysoliatin, U. G. Akhmetshin, S. V. Muraviev, and A. V. Kirsanov, “Stable continuum generation in fibers with varying dispersion,” Laser Phys. 15, 1288–1291 (2005).
  19. A. A. Sysolyatin and D. A. Nolan, “Optical signal processing in dispersion varying fibres,” J. Nonlinear Opt. Phys. Mater. 16, 171–184 (2007).
    [CrossRef]

2012 (2)

S. Kraus and M. Lucki, “Dispersion compensating photonic crystal fiber with enhanced properties achieved by modified core geometry,” Adv. Electric. Electron. Eng. 10, 101–105 (2012).

L. J. Kong, L. M. Zhao, S. Lefrancois, D. G. Ouzounov, C. X. Yang, and F. W. Wise, “Generation of megawatt peak power picosecond pulses from a divided-pulse fiber amplifier,” Opt. Lett. 37, 253–255 (2012).
[CrossRef]

2011 (2)

2007 (5)

A. Latkin, S. K. Turitsyn, and A. Sysoliatin, “Theory of parabolic pulse generation in tapered fiber,” Opt. Lett. 32, 331–333 (2007).
[CrossRef]

S. Zhou, F. Wise, and D. G. Ouzounov, “Divided-pulse amplification of ultrashort pulses,” Opt. Lett. 32, 871–873 (2007).
[CrossRef]

A. A. Sysolyatin and D. A. Nolan, “Optical signal processing in dispersion varying fibres,” J. Nonlinear Opt. Phys. Mater. 16, 171–184 (2007).
[CrossRef]

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).
[CrossRef]

A. Yu. Plotskii, A. A. Sysolyatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, and S. K. Turitsyn, “Experiments of generation of parabolic pulses in fibers with length-varying normal chromatic dispersion,” JETP Lett. 85, 319–322 (2007).
[CrossRef]

2006 (2)

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, “High-power ultrafast fiber laser systems,” IEEE J. Sel. Top. Quantum Electron. 12, 233–244 (2006).
[CrossRef]

G. Chang, H. G. Winful, A. Galvanauskas, and T. B. Norris, “Incoherent selfsimilarities of the coupled amplified nonlinear Schrödinger equations,” Phys. Rev. E 73, 016616 (2006).
[CrossRef]

2005 (2)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).
[CrossRef]

A. A. Sysoliatin, U. G. Akhmetshin, S. V. Muraviev, and A. V. Kirsanov, “Stable continuum generation in fibers with varying dispersion,” Laser Phys. 15, 1288–1291 (2005).

2004 (1)

2003 (1)

U. G. Akhmetshin, V. A. Bogatyrev, A. K. Senatorov, A. A. Sysolyatin, and M. G. Shalygin, “New single-mode fibres with the flat spectral dependence of the chromatic dispersion varying over the fibre length,” Quantum Electron. 33, 265–267 (2003).
[CrossRef]

2002 (1)

J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
[CrossRef]

2000 (1)

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]

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Agraval, G. P.

G. P. Agraval, Nonlinear Fiber Optics (Academic, 1995).

Akhmetshin, U. G.

A. A. Sysoliatin, U. G. Akhmetshin, S. V. Muraviev, and A. V. Kirsanov, “Stable continuum generation in fibers with varying dispersion,” Laser Phys. 15, 1288–1291 (2005).

U. G. Akhmetshin, V. A. Bogatyrev, A. K. Senatorov, A. A. Sysolyatin, and M. G. Shalygin, “New single-mode fibres with the flat spectral dependence of the chromatic dispersion varying over the fibre length,” Quantum Electron. 33, 265–267 (2003).
[CrossRef]

Auguste, J. L.

J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
[CrossRef]

Blondy, J. M.

J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
[CrossRef]

Bogatyrev, V. A.

U. G. Akhmetshin, V. A. Bogatyrev, A. K. Senatorov, A. A. Sysolyatin, and M. G. Shalygin, “New single-mode fibres with the flat spectral dependence of the chromatic dispersion varying over the fibre length,” Quantum Electron. 33, 265–267 (2003).
[CrossRef]

Carstens, H.

Chang, G.

G. Chang, H. G. Winful, A. Galvanauskas, and T. B. Norris, “Incoherent selfsimilarities of the coupled amplified nonlinear Schrödinger equations,” Phys. Rev. E 73, 016616 (2006).
[CrossRef]

Dudley, J. M.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).
[CrossRef]

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]

Dussardier, B.

J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
[CrossRef]

Eidam, T.

Fermann, M. E.

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]

Finot, C.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).
[CrossRef]

Galvanauskas, A.

G. Chang, H. G. Winful, A. Galvanauskas, and T. B. Norris, “Incoherent selfsimilarities of the coupled amplified nonlinear Schrödinger equations,” Phys. Rev. E 73, 016616 (2006).
[CrossRef]

Hädrich, S.

Harper, P.

A. Yu. Plotskii, A. A. Sysolyatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, and S. K. Turitsyn, “Experiments of generation of parabolic pulses in fibers with length-varying normal chromatic dispersion,” JETP Lett. 85, 319–322 (2007).
[CrossRef]

Harrison, J.

A. Yu. Plotskii, A. A. Sysolyatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, and S. K. Turitsyn, “Experiments of generation of parabolic pulses in fibers with length-varying normal chromatic dispersion,” JETP Lett. 85, 319–322 (2007).
[CrossRef]

Harvey, J. D.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).
[CrossRef]

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]

Hirooka, T.

Jansen, F.

Jauregui, C.

Jindal, R.

J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
[CrossRef]

Khopin, V. F.

A. Yu. Plotskii, A. A. Sysolyatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, and S. K. Turitsyn, “Experiments of generation of parabolic pulses in fibers with length-varying normal chromatic dispersion,” JETP Lett. 85, 319–322 (2007).
[CrossRef]

Kirsanov, A. V.

A. A. Sysoliatin, U. G. Akhmetshin, S. V. Muraviev, and A. V. Kirsanov, “Stable continuum generation in fibers with varying dispersion,” Laser Phys. 15, 1288–1291 (2005).

Kong, L. J.

Kraus, S.

S. Kraus and M. Lucki, “Dispersion compensating photonic crystal fiber with enhanced properties achieved by modified core geometry,” Adv. Electric. Electron. Eng. 10, 101–105 (2012).

Kriezis, E. E.

Kruglov, V. I.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).
[CrossRef]

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]

Latkin, A.

Latkin, A. I.

A. Yu. Plotskii, A. A. Sysolyatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, and S. K. Turitsyn, “Experiments of generation of parabolic pulses in fibers with length-varying normal chromatic dispersion,” JETP Lett. 85, 319–322 (2007).
[CrossRef]

Lefrancois, S.

Limpert, J.

Lucki, M.

S. Kraus and M. Lucki, “Dispersion compensating photonic crystal fiber with enhanced properties achieved by modified core geometry,” Adv. Electric. Electron. Eng. 10, 101–105 (2012).

Marcou, J.

J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
[CrossRef]

Maury, J.

J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
[CrossRef]

Millot, G.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).
[CrossRef]

Monnom, G.

J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
[CrossRef]

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Muraviev, S. V.

A. A. Sysoliatin, U. G. Akhmetshin, S. V. Muraviev, and A. V. Kirsanov, “Stable continuum generation in fibers with varying dispersion,” Laser Phys. 15, 1288–1291 (2005).

Nakazava, M.

Nolan, D. A.

A. A. Sysolyatin and D. A. Nolan, “Optical signal processing in dispersion varying fibres,” J. Nonlinear Opt. Phys. Mater. 16, 171–184 (2007).
[CrossRef]

Norris, T. B.

G. Chang, H. G. Winful, A. Galvanauskas, and T. B. Norris, “Incoherent selfsimilarities of the coupled amplified nonlinear Schrödinger equations,” Phys. Rev. E 73, 016616 (2006).
[CrossRef]

Ouzounov, D. G.

Pal, B. P.

J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
[CrossRef]

Peacock, A. C.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).
[CrossRef]

Plotskii, A. Yu.

A. Yu. Plotskii, A. A. Sysolyatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, and S. K. Turitsyn, “Experiments of generation of parabolic pulses in fibers with length-varying normal chromatic dispersion,” JETP Lett. 85, 319–322 (2007).
[CrossRef]

Richardson, D. J.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).
[CrossRef]

Roser, F.

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, “High-power ultrafast fiber laser systems,” IEEE J. Sel. Top. Quantum Electron. 12, 233–244 (2006).
[CrossRef]

Rothhardt, J.

Schreiber, T.

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, “High-power ultrafast fiber laser systems,” IEEE J. Sel. Top. Quantum Electron. 12, 233–244 (2006).
[CrossRef]

Senatorov, A. K.

U. G. Akhmetshin, V. A. Bogatyrev, A. K. Senatorov, A. A. Sysolyatin, and M. G. Shalygin, “New single-mode fibres with the flat spectral dependence of the chromatic dispersion varying over the fibre length,” Quantum Electron. 33, 265–267 (2003).
[CrossRef]

Shalygin, M. G.

U. G. Akhmetshin, V. A. Bogatyrev, A. K. Senatorov, A. A. Sysolyatin, and M. G. Shalygin, “New single-mode fibres with the flat spectral dependence of the chromatic dispersion varying over the fibre length,” Quantum Electron. 33, 265–267 (2003).
[CrossRef]

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Stutzki, F.

Sysoliatin, A.

Sysoliatin, A. A.

A. A. Sysoliatin, U. G. Akhmetshin, S. V. Muraviev, and A. V. Kirsanov, “Stable continuum generation in fibers with varying dispersion,” Laser Phys. 15, 1288–1291 (2005).

Sysolyatin, A. A.

A. A. Sysolyatin and D. A. Nolan, “Optical signal processing in dispersion varying fibres,” J. Nonlinear Opt. Phys. Mater. 16, 171–184 (2007).
[CrossRef]

A. Yu. Plotskii, A. A. Sysolyatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, and S. K. Turitsyn, “Experiments of generation of parabolic pulses in fibers with length-varying normal chromatic dispersion,” JETP Lett. 85, 319–322 (2007).
[CrossRef]

U. G. Akhmetshin, V. A. Bogatyrev, A. K. Senatorov, A. A. Sysolyatin, and M. G. Shalygin, “New single-mode fibres with the flat spectral dependence of the chromatic dispersion varying over the fibre length,” Quantum Electron. 33, 265–267 (2003).
[CrossRef]

Thomsen, B. C.

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]

Thyagarajan, K.

J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
[CrossRef]

Tunnermann, A.

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, “High-power ultrafast fiber laser systems,” IEEE J. Sel. Top. Quantum Electron. 12, 233–244 (2006).
[CrossRef]

Tünnermann, A.

Turitsyn, S. K.

A. Latkin, S. K. Turitsyn, and A. Sysoliatin, “Theory of parabolic pulse generation in tapered fiber,” Opt. Lett. 32, 331–333 (2007).
[CrossRef]

A. Yu. Plotskii, A. A. Sysolyatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, and S. K. Turitsyn, “Experiments of generation of parabolic pulses in fibers with length-varying normal chromatic dispersion,” JETP Lett. 85, 319–322 (2007).
[CrossRef]

Vázquez, C.

Winful, H. G.

G. Chang, H. G. Winful, A. Galvanauskas, and T. B. Norris, “Incoherent selfsimilarities of the coupled amplified nonlinear Schrödinger equations,” Phys. Rev. E 73, 016616 (2006).
[CrossRef]

Wise, F.

Wise, F. W.

Yang, C. X.

Yioultsis, T. V.

Zhao, L. M.

Zhou, S.

Zografopoulos, D. C.

Adv. Electric. Electron. Eng. (1)

S. Kraus and M. Lucki, “Dispersion compensating photonic crystal fiber with enhanced properties achieved by modified core geometry,” Adv. Electric. Electron. Eng. 10, 101–105 (2012).

IEEE J. Sel. Top. Quantum Electron. (1)

J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, “High-power ultrafast fiber laser systems,” IEEE J. Sel. Top. Quantum Electron. 12, 233–244 (2006).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

A. A. Sysolyatin and D. A. Nolan, “Optical signal processing in dispersion varying fibres,” J. Nonlinear Opt. Phys. Mater. 16, 171–184 (2007).
[CrossRef]

JETP Lett. (1)

A. Yu. Plotskii, A. A. Sysolyatin, A. I. Latkin, V. F. Khopin, P. Harper, J. Harrison, and S. K. Turitsyn, “Experiments of generation of parabolic pulses in fibers with length-varying normal chromatic dispersion,” JETP Lett. 85, 319–322 (2007).
[CrossRef]

Laser Phys. (1)

A. A. Sysoliatin, U. G. Akhmetshin, S. V. Muraviev, and A. V. Kirsanov, “Stable continuum generation in fibers with varying dispersion,” Laser Phys. 15, 1288–1291 (2005).

Nat. Phys. (1)

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).
[CrossRef]

Opt. Commun. (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Opt. Express (2)

Opt. Fiber Technol. (1)

J. L. Auguste, J. M. Blondy, J. Maury, J. Marcou, B. Dussardier, G. Monnom, R. Jindal, K. Thyagarajan, and B. P. Pal, “Conception, realization, and characterization of a very high negative chromatic dispersion fiber,” Opt. Fiber Technol. 8, 89–105 (2002).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. E (2)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).
[CrossRef]

G. Chang, H. G. Winful, A. Galvanauskas, and T. B. Norris, “Incoherent selfsimilarities of the coupled amplified nonlinear Schrödinger equations,” Phys. Rev. E 73, 016616 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

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]

Quantum Electron. (1)

U. G. Akhmetshin, V. A. Bogatyrev, A. K. Senatorov, A. A. Sysolyatin, and M. G. Shalygin, “New single-mode fibres with the flat spectral dependence of the chromatic dispersion varying over the fibre length,” Quantum Electron. 33, 265–267 (2003).
[CrossRef]

Other (1)

G. P. Agraval, Nonlinear Fiber Optics (Academic, 1995).

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Figures (9)

Fig. 1.
Fig. 1.

Axial profile of GVD derived from Eq. (12) for amplifier with parameters D0=1027s2/m, α0=1023s2, and g=(0.25,0.5,1)m1 corresponding to curves from 1 to 3, respectively.

Fig. 2.
Fig. 2.

Evolution of instantaneous pulse frequency Δω(t) and amplitude envelope |u(t)|2 in the amplifier with increasing distribution of GVD corresponding to profile 2 in Fig. 1. Pulse propagation distances in the amplifier of z=15, 19, and 23 m correspond to the blue solid curves 1–3, respectively. Red dashed curves show the asymptotic parabolic solution of Eq. (1).

Fig. 3.
Fig. 3.

Pulse spectrum evolution in the amplifier with increasing distribution of GVD corresponding to profile 2 in Fig. 1. Pulse propagation distances in the amplifier of z=15, 19, and 23 m are presented by curves 1 (blue), 2 (green), and 3 (red), respectively. The central black curve shows the spectrum of the input Gaussian pulse.

Fig. 4.
Fig. 4.

GVD profiles calculated using Eq. (14) for D0=5·1026s2/m. Chirp values α0 (1, 1.5, 2, 3, 5, 10, and 20) ×1023s2 correspond to curves 1–7, respectively.

Fig. 5.
Fig. 5.

GVD profile of amplification cascade used in numerical simulation. Red lines (I, III) with increasing GVD indicate the amplifier stages, and blue curves (II, IV) show the passive DDFs.

Fig. 6.
Fig. 6.

(a) Instantaneous frequency and pulse amplitude after propagation through the first cascade element. The black curve is the input pulse. (b) Evolution of instantaneous frequency and pulse amplitude after propagation through the cascade: after the 1, first (red); 2, second (green); and 3, third (blue) elements; and 4, at the cascade output (orange). Dotted line is the asymptotic behavior of instantaneous frequency Δω=2α0t, α0=2·1023s2.

Fig. 7.
Fig. 7.

Spectrum evolution of pulse propagating through the cascaded amplifier: after the 1, first (red); 2, second (green); and 3, third (blue) elements; and 4, at the cascade output (orange). Central black curve is the input pulse spectrum.

Fig. 8.
Fig. 8.

Pulse compression at the output of the cascaded system.

Fig. 9.
Fig. 9.

Characteristics of the pulse passed three amplifying cascades (1, blue) and an amplifier with uniform GVD and gain (2, red). The length, the average gain, and the GVD are taken to be equal for both cases. (a) pulse spectrum and (b) instantaneous frequency and pulse envelope. Asymptotics of the instantaneous frequency are shown by dashed lines: (1) Δω=2α0t, α0=2·1023s2 and (2) Δω=2α¯t, α¯=4.03·1023s2.

Equations (22)

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uziD(z)22ut2+iR(z)|u|2u=γ(z)2u,
γ(z)=g(z)(Sm/z)/Sm,
Sm(z)=2π0|U(r,z)|2rdr,
ξ=0zd(z)dz,
AξiD022At2+iR0|A|2A=Γ(ξ)2A.
Γ(ξ)=gd(ξ)d(ξ)d(ξ)+r(ξ)r(ξ)Sm(ξ)Sm(ξ).
Γ(ξ)=gd(ξ)d(ξ).
D=D0exp(gz),
A(t,ξ)=A(ξ)G(t,ξ)exp[i(φ(ξ)+α(ξ)t2)],
G(t,ξ)={1t2/τs2(ξ),tτs(ξ),0,t>τs(ξ),
A(ξ)=12(ΓE0R0D0/2)1/3exp(Γξ3),τs(ξ)=6R0D0/2ΓA0exp(Γξ3),φ(ξ)=φ0+3R0A022Γexp(2Γξ3).
α0=Γ/6D0.
Δω1τs2+α02τs2α0τs
DzgD+6α0D2=0,
D(z)=gD0exp(gz)g+6α0D0(exp(gz)1).
u0(t)=P0exp(t2/2t02)
uas(t,z)=A0exp(gz/2)1t2/τs2(z)(1+(6α0D0/g)(exp(gz)1))1/6,τs(z)=A0α0R02D0(1+6α0D0g(exp(gz)1))1/3,A0=12(6α0E02D0/R0)1/3.
D(z)=D01+6α0D0z,
DII(z)=D0II1+Γz.
DII=D0II1+6·2·1023D0II(zL1).
DIV=D0IV1+6·1024D0IV(zL3)
D¯=1L3{0L1DI(z)dz+L1L2DII(z)dz+L2L3DIII(z)dz}=4.3·1027s2/m.

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