Abstract

Optical pulse generation and compression have been numerically studied in anomalous dispersion decreasing fibers. We show that evolution of modulation instability (MI) observed with chirped wave packets in tapered fibers produces the mechanism for generation of ultrashort pulses with high repetition rates. The role of MI and Raman self-scattering has been also discussed. The simulations show that pulse chirping enhances self-Raman scattering at early stages of pulse propagation and improves compression of the generated pulses. It is also shown that the presence of amplitude and frequency modulation of the seed wave provide essential impact on the pulse train formation. The new method for increasing the pulse train repetition rate through frequency modulation of the seed wave has been proposed.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013 (1)

2012 (4)

W. H. Renninger, A. Chong, and F. W. Wise, “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 389–398 (2012).
[CrossRef]

A. V. Zhukov, I. O. Zolotovskii, O. G. Okhotnikov, D. I. Sementsov, A. A. Sysolyatin, and I. O. Yavtushenko, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous active optical waveguide,” Opt. Spectrosc. 113, 75–80 (2012).
[CrossRef]

I. O. Zolotovskii, D. A. Korobko, O. G. Okhotnikov, A. A. Sysolyatin, and A. A. Fotiadi, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous, anomalous group velocity dispersion fibre amplifier,” Quantum Electron. 42, 828–833 (2012).
[CrossRef]

E. J. Saarinen, A. Rantamäki, A. Chamorovskiy, and O. G. Okhotnikov, “200 GHz 1 W semiconductor disc laser emitting 800 fs pulses,” Electron. Lett. 48, 1355–1357 (2012).
[CrossRef]

2010 (2)

M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. J. Phys. Special Top. 185, 135–144 (2010).
[CrossRef]

I. O. Zolotovskii, D. I. Sementsov, A. K. Senatorov, A. A. Sysolyatin, and M. S. Yavtushenko, “Dynamics of similariton pulses in length-inhomogeneous active fibres,” Quantum Electron. 40, 229 (2010).
[CrossRef]

2009 (2)

2008 (3)

2007 (6)

S. A. Ponomarenko and G. P. Agrawal, “Optical similaritons in nonlinear waveguides,” Opt. Lett. 32, 1659–1661 (2007).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

I. O. Zolotovskii and D. I. Sementsov, “Formation of the amplification regime of quasi-soliton pulses in waveguides with longitudinally inhomogeneous cross sections, Opt. Spectrosc. 102, 594–598 (2007).
[CrossRef]

C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, and S. Wabnitz, “Parabolic pulse generation with active or passive dispersion decreasing optical fibers,” Opt. Express 15, 85824–85835 (2007).

J. M. Dudley, C. Finot, D. Richardson, and G. Millot, “Self-similarity and scaling phenomena in nonlinear ultrafast optics,” Nat. Phys. 3, 597 (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]

2005 (2)

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).

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]

2004 (2)

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Comment on exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 92, 199401 (2004).
[CrossRef]

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]

2003 (2)

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]

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
[CrossRef]

2001 (3)

W. Xu, S. Zhang, W. Chen, A. Luo, and S. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

N. Akhmediev, “Déjà vu in optics,” Nature 413, 267–268 (2001).
[CrossRef]

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37, 587–594 (2001).
[CrossRef]

2000 (2)

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).
[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]

1996 (1)

1994 (1)

E. A. Swanson and S. R. Chinn, “23 GHz and 123 GHz soliton pulse generation using two CW lasers and standard single-mode fiber,” IEEE Photon. Technol. Lett. 6, 796 (1994).
[CrossRef]

1993 (1)

S. V. Chernikov, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “114 Gbit/s soliton train generation through Raman self-scattering of a dual frequency beat signal in dispersion decreasing optical fiber,” Appl. Phys. Lett. 63, 293–295 (1993).
[CrossRef]

1991 (1)

1990 (2)

1989 (1)

1986 (1)

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef]

Agrawal, G.

Agrawal, G. P.

Akhmediev, N.

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]

Barenblatt, G. I.

G. I. Barenblatt, Scaling, Self-similarity and Intermediate Asymptotics: Dimensional Analysis (Cambridge University, 1996).

Barviau, B.

C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, and S. Wabnitz, “Parabolic pulse generation with active or passive dispersion decreasing optical fibers,” Opt. Express 15, 85824–85835 (2007).

Belyaeva, T. L.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Comment on exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 92, 199401 (2004).
[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]

Chamorovskiy, A.

E. J. Saarinen, A. Rantamäki, A. Chamorovskiy, and O. G. Okhotnikov, “200 GHz 1 W semiconductor disc laser emitting 800 fs pulses,” Electron. Lett. 48, 1355–1357 (2012).
[CrossRef]

Chen, W.

W. Xu, S. Zhang, W. Chen, A. Luo, and S. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Chernikov, S. V.

Chinn, S. R.

E. A. Swanson and S. R. Chinn, “23 GHz and 123 GHz soliton pulse generation using two CW lasers and standard single-mode fiber,” IEEE Photon. Technol. Lett. 6, 796 (1994).
[CrossRef]

Chong, A.

W. H. Renninger, A. Chong, and F. W. Wise, “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 389–398 (2012).
[CrossRef]

Dianov, E. M.

Dias, F.

Dudley, J. M.

M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. J. Phys. Special Top. 185, 135–144 (2010).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).
[CrossRef]

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

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37, 587–594 (2001).
[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]

Erkintalo, M.

M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. J. Phys. Special Top. 185, 135–144 (2010).
[CrossRef]

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.

S. Wabnitz and C. Finot, “Theory of parabolic pulse propagation in nonlinear dispersion decreasing optical fiber amplifiers, J. Opt. Soc. Am. B 25, 614–621 (2008).
[CrossRef]

C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, and S. Wabnitz, “Parabolic pulse generation with active or passive dispersion decreasing optical fibers,” Opt. Express 15, 85824–85835 (2007).

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

Fotiadi, A. A.

I. O. Zolotovskii, D. A. Korobko, O. G. Okhotnikov, A. A. Sysolyatin, and A. A. Fotiadi, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous, anomalous group velocity dispersion fibre amplifier,” Quantum Electron. 42, 828–833 (2012).
[CrossRef]

Genty, G.

M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. J. Phys. Special Top. 185, 135–144 (2010).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).
[CrossRef]

Guryanov, A.

C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, and S. Wabnitz, “Parabolic pulse generation with active or passive dispersion decreasing optical fibers,” Opt. Express 15, 85824–85835 (2007).

Gutty, F.

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37, 587–594 (2001).
[CrossRef]

Haboucha, A.

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]

Hasegawa, A.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Comment on exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 92, 199401 (2004).
[CrossRef]

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).
[CrossRef]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef]

Hirooka, T.

Jalali, B.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Kibler, B.

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).

Komarov, A.

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Korobko, D. A.

I. O. Zolotovskii, D. A. Korobko, O. G. Okhotnikov, A. A. Sysolyatin, and A. A. Fotiadi, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous, anomalous group velocity dispersion fibre amplifier,” Quantum Electron. 42, 828–833 (2012).
[CrossRef]

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]

Laming, R. I.

S. V. Chernikov, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “114 Gbit/s soliton train generation through Raman self-scattering of a dual frequency beat signal in dispersion decreasing optical fiber,” Appl. Phys. Lett. 63, 293–295 (1993).
[CrossRef]

Li, Q.

Liu, S.

W. Xu, S. Zhang, W. Chen, A. Luo, and S. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Luo, A.

W. Xu, S. Zhang, W. Chen, A. Luo, and S. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Mamyshev, P. V.

Millot, G.

C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, and S. Wabnitz, “Parabolic pulse generation with active or passive dispersion decreasing optical fibers,” Opt. Express 15, 85824–85835 (2007).

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

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
[CrossRef]

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37, 587–594 (2001).
[CrossRef]

Moores, J. D.

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.

Nakkeeran, K.

Nithyanandan, K.

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]

Okhotnikov, O. G.

I. O. Zolotovskii, D. A. Korobko, O. G. Okhotnikov, A. A. Sysolyatin, and A. A. Fotiadi, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous, anomalous group velocity dispersion fibre amplifier,” Quantum Electron. 42, 828–833 (2012).
[CrossRef]

E. J. Saarinen, A. Rantamäki, A. Chamorovskiy, and O. G. Okhotnikov, “200 GHz 1 W semiconductor disc laser emitting 800 fs pulses,” Electron. Lett. 48, 1355–1357 (2012).
[CrossRef]

A. V. Zhukov, I. O. Zolotovskii, O. G. Okhotnikov, D. I. Sementsov, A. A. Sysolyatin, and I. O. Yavtushenko, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous active optical waveguide,” Opt. Spectrosc. 113, 75–80 (2012).
[CrossRef]

Payne, D. N.

S. V. Chernikov, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “114 Gbit/s soliton train generation through Raman self-scattering of a dual frequency beat signal in dispersion decreasing optical fiber,” Appl. Phys. Lett. 63, 293–295 (1993).
[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]

Pitois, S.

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
[CrossRef]

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37, 587–594 (2001).
[CrossRef]

Ponomarenko, S. A.

Porsezian, K.

Prokhorov, A. M.

Raja, Jayakantha

Rantamäki, A.

E. J. Saarinen, A. Rantamäki, A. Chamorovskiy, and O. G. Okhotnikov, “200 GHz 1 W semiconductor disc laser emitting 800 fs pulses,” Electron. Lett. 48, 1355–1357 (2012).
[CrossRef]

Renninger, W. H.

W. H. Renninger, A. Chong, and F. W. Wise, “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 389–398 (2012).
[CrossRef]

Richardson, D.

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

Richardson, D. J.

S. V. Chernikov, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “114 Gbit/s soliton train generation through Raman self-scattering of a dual frequency beat signal in dispersion decreasing optical fiber,” Appl. Phys. Lett. 63, 293–295 (1993).
[CrossRef]

Ropers, C.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Saarinen, E. J.

E. J. Saarinen, A. Rantamäki, A. Chamorovskiy, and O. G. Okhotnikov, “200 GHz 1 W semiconductor disc laser emitting 800 fs pulses,” Electron. Lett. 48, 1355–1357 (2012).
[CrossRef]

Sanchez, F.

Sementsov, D. I.

A. V. Zhukov, I. O. Zolotovskii, O. G. Okhotnikov, D. I. Sementsov, A. A. Sysolyatin, and I. O. Yavtushenko, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous active optical waveguide,” Opt. Spectrosc. 113, 75–80 (2012).
[CrossRef]

I. O. Zolotovskii, D. I. Sementsov, A. K. Senatorov, A. A. Sysolyatin, and M. S. Yavtushenko, “Dynamics of similariton pulses in length-inhomogeneous active fibres,” Quantum Electron. 40, 229 (2010).
[CrossRef]

I. O. Zolotovskii and D. I. Sementsov, “Formation of the amplification regime of quasi-soliton pulses in waveguides with longitudinally inhomogeneous cross sections, Opt. Spectrosc. 102, 594–598 (2007).
[CrossRef]

Senatorov, A. K.

I. O. Zolotovskii, D. I. Sementsov, A. K. Senatorov, A. A. Sysolyatin, and M. S. Yavtushenko, “Dynamics of similariton pulses in length-inhomogeneous active fibres,” Quantum Electron. 40, 229 (2010).
[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]

Senthilnathan, K.

Serkin, V. N.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Comment on exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 92, 199401 (2004).
[CrossRef]

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).
[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]

Solli, D. R.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Swanson, E. A.

E. A. Swanson and S. R. Chinn, “23 GHz and 123 GHz soliton pulse generation using two CW lasers and standard single-mode fiber,” IEEE Photon. Technol. Lett. 6, 796 (1994).
[CrossRef]

Sysoliatin, A.

C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, and S. Wabnitz, “Parabolic pulse generation with active or passive dispersion decreasing optical fibers,” Opt. Express 15, 85824–85835 (2007).

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. V. Zhukov, I. O. Zolotovskii, O. G. Okhotnikov, D. I. Sementsov, A. A. Sysolyatin, and I. O. Yavtushenko, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous active optical waveguide,” Opt. Spectrosc. 113, 75–80 (2012).
[CrossRef]

I. O. Zolotovskii, D. A. Korobko, O. G. Okhotnikov, A. A. Sysolyatin, and A. A. Fotiadi, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous, anomalous group velocity dispersion fibre amplifier,” Quantum Electron. 42, 828–833 (2012).
[CrossRef]

I. O. Zolotovskii, D. I. Sementsov, A. K. Senatorov, A. A. Sysolyatin, and M. S. Yavtushenko, “Dynamics of similariton pulses in length-inhomogeneous active fibres,” Quantum Electron. 40, 229 (2010).
[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]

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]

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[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]

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef]

Vasantha, R.

Wabnitz, S.

S. Wabnitz and C. Finot, “Theory of parabolic pulse propagation in nonlinear dispersion decreasing optical fiber amplifiers, J. Opt. Soc. Am. B 25, 614–621 (2008).
[CrossRef]

C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, and S. Wabnitz, “Parabolic pulse generation with active or passive dispersion decreasing optical fibers,” Opt. Express 15, 85824–85835 (2007).

Wai, P. K. A.

Wise, F. W.

W. H. Renninger, A. Chong, and F. W. Wise, “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 389–398 (2012).
[CrossRef]

Xu, W.

W. Xu, S. Zhang, W. Chen, A. Luo, and S. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Yavtushenko, I. O.

A. V. Zhukov, I. O. Zolotovskii, O. G. Okhotnikov, D. I. Sementsov, A. A. Sysolyatin, and I. O. Yavtushenko, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous active optical waveguide,” Opt. Spectrosc. 113, 75–80 (2012).
[CrossRef]

Yavtushenko, M. S.

I. O. Zolotovskii, D. I. Sementsov, A. K. Senatorov, A. A. Sysolyatin, and M. S. Yavtushenko, “Dynamics of similariton pulses in length-inhomogeneous active fibres,” Quantum Electron. 40, 229 (2010).
[CrossRef]

Zhang, S.

W. Xu, S. Zhang, W. Chen, A. Luo, and S. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Zhukov, A. V.

A. V. Zhukov, I. O. Zolotovskii, O. G. Okhotnikov, D. I. Sementsov, A. A. Sysolyatin, and I. O. Yavtushenko, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous active optical waveguide,” Opt. Spectrosc. 113, 75–80 (2012).
[CrossRef]

Zolotovskii, I. O.

A. V. Zhukov, I. O. Zolotovskii, O. G. Okhotnikov, D. I. Sementsov, A. A. Sysolyatin, and I. O. Yavtushenko, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous active optical waveguide,” Opt. Spectrosc. 113, 75–80 (2012).
[CrossRef]

I. O. Zolotovskii, D. A. Korobko, O. G. Okhotnikov, A. A. Sysolyatin, and A. A. Fotiadi, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous, anomalous group velocity dispersion fibre amplifier,” Quantum Electron. 42, 828–833 (2012).
[CrossRef]

I. O. Zolotovskii, D. I. Sementsov, A. K. Senatorov, A. A. Sysolyatin, and M. S. Yavtushenko, “Dynamics of similariton pulses in length-inhomogeneous active fibres,” Quantum Electron. 40, 229 (2010).
[CrossRef]

I. O. Zolotovskii and D. I. Sementsov, “Formation of the amplification regime of quasi-soliton pulses in waveguides with longitudinally inhomogeneous cross sections, Opt. Spectrosc. 102, 594–598 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

S. V. Chernikov, E. M. Dianov, D. J. Richardson, R. I. Laming, and D. N. Payne, “114 Gbit/s soliton train generation through Raman self-scattering of a dual frequency beat signal in dispersion decreasing optical fiber,” Appl. Phys. Lett. 63, 293–295 (1993).
[CrossRef]

Electron. Lett. (1)

E. J. Saarinen, A. Rantamäki, A. Chamorovskiy, and O. G. Okhotnikov, “200 GHz 1 W semiconductor disc laser emitting 800 fs pulses,” Electron. Lett. 48, 1355–1357 (2012).
[CrossRef]

Eur. J. Phys. Special Top. (1)

M. Erkintalo, G. Genty, and J. M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. J. Phys. Special Top. 185, 135–144 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. M. Dudley, F. Gutty, S. Pitois, and G. Millot, “Complete characterization of THz pulse trains generated from nonlinear processes in optical fibers,” IEEE J. Quantum Electron. 37, 587–594 (2001).
[CrossRef]

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

W. H. Renninger, A. Chong, and F. W. Wise, “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 18, 389–398 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

E. A. Swanson and S. R. Chinn, “23 GHz and 123 GHz soliton pulse generation using two CW lasers and standard single-mode fiber,” IEEE Photon. Technol. Lett. 6, 796 (1994).
[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]

J. Opt. Soc. Am. B (5)

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. Richardson, and G. Millot, “Self-similarity and scaling phenomena in nonlinear ultrafast optics,” Nat. Phys. 3, 597 (2007).
[CrossRef]

Nature (2)

N. Akhmediev, “Déjà vu in optics,” Nature 413, 267–268 (2001).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[CrossRef]

Opt. Commun. (2)

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun. 226, 415–422 (2003).
[CrossRef]

W. Xu, S. Zhang, W. Chen, A. Luo, and S. Liu, “Modulation instability of femtosecond pulses in dispersion-decreasing fibers,” Opt. Commun. 199, 355–360 (2001).
[CrossRef]

Opt. Express (2)

C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, and S. Wabnitz, “Parabolic pulse generation with active or passive dispersion decreasing optical fibers,” Opt. Express 15, 85824–85835 (2007).

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).
[CrossRef]

Opt. Lett. (7)

Opt. Spectrosc. (2)

I. O. Zolotovskii and D. I. Sementsov, “Formation of the amplification regime of quasi-soliton pulses in waveguides with longitudinally inhomogeneous cross sections, Opt. Spectrosc. 102, 594–598 (2007).
[CrossRef]

A. V. Zhukov, I. O. Zolotovskii, O. G. Okhotnikov, D. I. Sementsov, A. A. Sysolyatin, and I. O. Yavtushenko, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous active optical waveguide,” Opt. Spectrosc. 113, 75–80 (2012).
[CrossRef]

Phys. Rev. E (1)

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]

Phys. Rev. Lett. (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]

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).
[CrossRef]

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Comment on exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 92, 199401 (2004).
[CrossRef]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef]

Quantum Electron. (3)

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]

I. O. Zolotovskii, D. I. Sementsov, A. K. Senatorov, A. A. Sysolyatin, and M. S. Yavtushenko, “Dynamics of similariton pulses in length-inhomogeneous active fibres,” Quantum Electron. 40, 229 (2010).
[CrossRef]

I. O. Zolotovskii, D. A. Korobko, O. G. Okhotnikov, A. A. Sysolyatin, and A. A. Fotiadi, “Dynamics of frequency-modulated soliton-like pulses in a longitudinally inhomogeneous, anomalous group velocity dispersion fibre amplifier,” Quantum Electron. 42, 828–833 (2012).
[CrossRef]

Other (2)

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Springer, 2007).

G. I. Barenblatt, Scaling, Self-similarity and Intermediate Asymptotics: Dimensional Analysis (Cambridge University, 1996).

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Figures (9)

Fig. 1.
Fig. 1.

Anomalous dispersion decreasing profiles for Eq. (8). The decreasing factor is μ=(0.5,1,2,5)km1 (1-4), |β20|=5·1026s2/m.

Fig. 2.
Fig. 2.

Numerical simulation of pulse evolution in exponentially DDF. (a) Envelopes and (b) spectra of the input seed sech2-pulses with the duration τ0=2ps (1, blue), τ0=4ps (2, red); spectra of unchirped seed pulse: solid curve, with ideal initial chirp α0 [exact self-similar solutions in Eq. (7)]: dashed curve. (c) Envelopes and (d) spectra of the DDF output pulses with the initial duration τ0=2ps (1, blue), τ0=4ps (2, red), unchirped input pulse: solid curve, exact self-similar solutions in Eq. (8) with ideal initial chirp α0: dashed curve.

Fig. 3.
Fig. 3.

Numerical simulation of pulse evolution in exponentially DDF. (a) Envelopes and (b) spectra of the input pulses: chirped sech2-pulses with the duration τ0=4ps. (1, blue curves) Exact self-similar solutions in Eq. (7) with ideal chirp α0 (dashed), and with chirp equal to a half of the ideal value α=α0/2=1022s2 (solid); chirp-free sech2 pulse (2, cyan); Gaussian pulse with the same FWHM duration–(3, red curves) chirp-free pulse (solid), with chirp α0 (dashed). (c) Envelopes and (d) spectra of the DDF output pulses for chirped sech2-pulse seed with the duration τ0=4ps. (1, blue curves) Seed with ideal initial chirp α0 (dashed), and seed with initial chirp equal to a half of the ideal value α=α0/2=1022s2 (solid); chirp-free sech2 pulse seed signal (2, cyan curve); Gaussian seed pulse with the same FWHM duration–(3, red curves) chirp-free seed pulse (solid), seed signal with chirp α0 (dashed).

Fig. 4.
Fig. 4.

(a) Pulse train generated in anomalous DDF from modulated continuous-wave u(t,0)=P0(0.98+0.02·cos(t/τ0)), τ0=2ps. (b) The same, but with initial frequency modulation u(t,0)=P0(0.98+0.02·cos(t/τ0))exp(iαt2), α=1.5·1022s2, τ0=2ps.

Fig. 5.
Fig. 5.

(a) Time dependence of instantaneous frequency and pulse train obtained from propagation of the modulated continuous wave with power of Pin=|u(t,0)|2 in 1600 m long anomalous DDF (profile No. 3, Fig. 1). (b) The same, but with additional frequency modulation of the continuous wave α=1.5·1022s2.

Fig. 6.
Fig. 6.

Shape of the pulses generated from a continuous amplitude-modulated wave in anomalous DDF (green, I: without initial frequency modulation; II: with chirped seed signal). Pulses of the same input peak power after propagation over anomalous DDF [compare with Fig. 1(c)]; (1, blue): chirp-free sech2 seed pulse with τ0=2ps, dashed line is an envelope derived from the exact solution in Eq. (7); (2, red): the envelope of the output pulse generated through high-depth harmonic modulation in Eq. (14).

Fig. 7.
Fig. 7.

Evolution of the envelope (a) and spectrum (b) of single sech2 seed pulse with the duration τ0=1.5ps (blue, solid line) and τ0=2ps (red, dashed line) accounting the effect of Raman intrapulse scattering. Plots 1 show the graphs for the input pulse, curves 2 and 3 show the pulse characteristics after propagating through DDF No. 3: 560 m (2) and 800 m (3).

Fig. 8.
Fig. 8.

Evolution of the envelope and instantaneous frequency of the input pulse [Eq. (16)] after propagation through anomalous DDF with length 0 m (a, a′), 640 m (b, b′), 800 m (c, c′), and 880 m (d, d′).

Fig. 9.
Fig. 9.

(a) Pulse train generated from the modulated pulse (16); the effect of Raman self-scattering is taken into account. (b) Spectrum evolution for the modulated pulse after propagation through 640 m (1, red), 800 m (2, green), and 880 m (3, blue) in anomalous DDF (profile No. 3, Fig. 1). Dashed line is the input pulse spectrum.

Equations (22)

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

uziβ2(z)22ut2+iγ|u|2u=g(z)2u,
Aξiβ2022At2+iγ|A|2A=geff(ξ)2A,
geff(ξ)=g(ξ)d(ξ)ξlnd(ξ)
geff(ξ)=2Q/(12Qξ),
A(t,ξ)=A012Qξsechtτexp(iα0t2aξ12Qξ).
τ02|β20|=1γ|A0|2.
d(z)=(1+2α0β200zd(y)dy)exp(0zg(y)dy).
β2(z)=β20G(z)exp(2α0β200zG(y)dy),
G(z)=exp(0zg(y)dy)
u(t,z)=|β20|/γτ0exp(μz/2)sech(t/τ0exp(μz))exp(iα0t2exp(μz)+iaμ(1exp(μz))).
β2(z)=β20exp(μz),μ=2α0|β20|.
u(t,z)=|β20|/γτ0exp(μz/2)F(t/τ0exp(μz),k)exp(iα0t2exp(μz)+ia(z)).
Lc=12α(z)β2(z)=12α0β20=1μ.
LNL(z)=Lβ(z)=τ02|β20|exp(μz).
u(t,z)=P0exp((t2τ0)2),τ01.059τ0,P0=|β20|γτ02.
g(Ω)=12|β2|ΩΩc2Ω2,Ωc2=4γP0|β2|.
Ωc2=4γP0|β20|exp(μz),Ωmax=Ωc2.
P0=|β20|γτ02
u(t,0)=P02(1+cos(t/τ0)).
uziβ2(z)22ut2+iγ(|u|2τR|u|2t)u=0,
u(t,0)=P0sech(t/τ)(1+δ·cos(Ωt))exp(iαt2),
Ω=23Ωmax0=232γP0|β20|=4.71·1011s1,τ=60ps28Ω,

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