### Abstract

Self-phase modulation (SPM) in optical fibre is ordinarily associated with spectral broadening of an ultra-short optical pulse. However, for appropriate initial conditions of the input pulse, SPM can result in significant spectral compression. Indeed, SPM causes spectral compression or broadening depending on the initial frequency modulation (chirp) of the pulse electric field. Specifically, a pulse with a negative chirp, such as that imparted by an anomalously dispersive element, is compressed by the effects of SPM [1]. This method of spectral compression has been reported for various parameters and system configurations.

In this contribution, we review our recent results and advances in the area. Firstly, we provide insight into the influence of the temporal intensity profile of the initial pulse on the spectral dynamics of the nonlinear propagation in fibre. In particular, we emphasise that spectral narrowing does not occur for any initial pulse shape, and that there are significant differences between the propagation of parabolic, Gaussian, super-Gaussian or triangular pulses, which we elucidate with the aid of a time-frequency analysis [2]. The main limitation of SPM-driven spectral compression in the nonlinearity-dominant regime of propagation is the presence of residual side lobes in the compressed spectrum that result from the mismatch between the initial linear chirp of the pulse and the SPM-induced nonlinear chirp. Hence we discuss several strategies to overcome this limitation. We demonstrate that the use of pre-shaped input pulses with a parabolic waveform can achieve spectral compression to the Fourier transform limit owing to the fact that for such pulses the cancellation of the linear and nonlinear phases can be made complete [3]. We show that the intensity level of the side lobes in the compressed spectrum of pulses with standard temporal intensity profiles (such as Gaussian or hyperbolic secant shapes) can be efficiently reduced by an additional sinusoidal modulation of the temporal phase applied to the pulse [4]. Another strategy to enhance the quality of the compressed pulse spectrum is to select a dispersive nonlinear regime of propagation in which the combined action of normal group-velocity dispersion and SPM results in a deformation of the temporal profile of the pulse tending to acquire a rectangular shape while nearly complete compensation of the pulse chirp occurs [5]. Lastly, we unveil the rather good stability of the spectral compression process against amplitude fluctuations and optical signal-to-noise degradation of the seed pulses. We therefore evaluate the capability of the process of being used in the context of optical regeneration of intensity-modulated signals by describing an optical power limiting scheme that combines nonlinear spectral compression with centred optical bandpass filtering [6].

References

[1] M. Oberthaler, R.A. Höpfel. Spectral narrowing of ultrashort laser pulses by self-phase modulation in optical fibers. Appl. Phys. Lett. 63 (1993), 1017–1019.

[2] S. Boscolo, F. Chaussard, E. Andresen, H. Rigneault, C. Finot. Impact of initial pulse shape on the nonlinear spectral compression in optical fibre. (2017), Submitted.

[3] E.R. Andresen, C. Finot, D. Oron, H. Rigneault. Spectral analog of the Gouy phase shift. Phys. Rev. Lett. 110 (2013), 143902.

[4] S. Boscolo, L.Kh. Mouradian, C. Finot. Enhanced nonlinear spectral compression in fiber by external sinusoidal phase modulation. J. Opt. 18 (2016), 105504 (7pp).

[5] C. Finot, S. Boscolo. Design rules for nonlinear spectral compression in optical fibers. J. Opt. Soc. Amer. B 33 (2016), 760–767.

[6] S. Boscolo, J. Fatome, C. Finot. Impact of amplitude jitter and signal-tonoise ratio on the nonlinear spectral compression in optical fibres. Opt. Commun. 389 (2017), 197–202.

In this contribution, we review our recent results and advances in the area. Firstly, we provide insight into the influence of the temporal intensity profile of the initial pulse on the spectral dynamics of the nonlinear propagation in fibre. In particular, we emphasise that spectral narrowing does not occur for any initial pulse shape, and that there are significant differences between the propagation of parabolic, Gaussian, super-Gaussian or triangular pulses, which we elucidate with the aid of a time-frequency analysis [2]. The main limitation of SPM-driven spectral compression in the nonlinearity-dominant regime of propagation is the presence of residual side lobes in the compressed spectrum that result from the mismatch between the initial linear chirp of the pulse and the SPM-induced nonlinear chirp. Hence we discuss several strategies to overcome this limitation. We demonstrate that the use of pre-shaped input pulses with a parabolic waveform can achieve spectral compression to the Fourier transform limit owing to the fact that for such pulses the cancellation of the linear and nonlinear phases can be made complete [3]. We show that the intensity level of the side lobes in the compressed spectrum of pulses with standard temporal intensity profiles (such as Gaussian or hyperbolic secant shapes) can be efficiently reduced by an additional sinusoidal modulation of the temporal phase applied to the pulse [4]. Another strategy to enhance the quality of the compressed pulse spectrum is to select a dispersive nonlinear regime of propagation in which the combined action of normal group-velocity dispersion and SPM results in a deformation of the temporal profile of the pulse tending to acquire a rectangular shape while nearly complete compensation of the pulse chirp occurs [5]. Lastly, we unveil the rather good stability of the spectral compression process against amplitude fluctuations and optical signal-to-noise degradation of the seed pulses. We therefore evaluate the capability of the process of being used in the context of optical regeneration of intensity-modulated signals by describing an optical power limiting scheme that combines nonlinear spectral compression with centred optical bandpass filtering [6].

References

[1] M. Oberthaler, R.A. Höpfel. Spectral narrowing of ultrashort laser pulses by self-phase modulation in optical fibers. Appl. Phys. Lett. 63 (1993), 1017–1019.

[2] S. Boscolo, F. Chaussard, E. Andresen, H. Rigneault, C. Finot. Impact of initial pulse shape on the nonlinear spectral compression in optical fibre. (2017), Submitted.

[3] E.R. Andresen, C. Finot, D. Oron, H. Rigneault. Spectral analog of the Gouy phase shift. Phys. Rev. Lett. 110 (2013), 143902.

[4] S. Boscolo, L.Kh. Mouradian, C. Finot. Enhanced nonlinear spectral compression in fiber by external sinusoidal phase modulation. J. Opt. 18 (2016), 105504 (7pp).

[5] C. Finot, S. Boscolo. Design rules for nonlinear spectral compression in optical fibers. J. Opt. Soc. Amer. B 33 (2016), 760–767.

[6] S. Boscolo, J. Fatome, C. Finot. Impact of amplitude jitter and signal-tonoise ratio on the nonlinear spectral compression in optical fibres. Opt. Commun. 389 (2017), 197–202.

Original language | English |
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Title of host publication | Book of Abstracts of the Conference: Physics and Mathematics of Nonlinear Phenomena: 50 years of IST (PMNP 2017) |

Place of Publication | Lecce (Italy) |

Pages | 60-61 |

Number of pages | 2 |

Publication status | Published - 24 Jun 2017 |

Event | Physics and Mathematics of Nonlinear Phenomena: 50 years of IST - Ecoresort Le Sirene, Gallipoli (Lecce), Italy Duration: 17 Jun 2017 → 24 Jun 2017 http://pmnp.unisalento.it |

### Conference

Conference | Physics and Mathematics of Nonlinear Phenomena: 50 years of IST |
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Abbreviated title | PMNP 2017 |

Country | Italy |

City | Gallipoli (Lecce) |

Period | 17/06/17 → 24/06/17 |

Internet address |

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### Cite this

Boscolo, S. A., & Finot, C. (2017). Spectral compression by self-phase modulation in optical fibres. In

*Book of Abstracts of the Conference: Physics and Mathematics of Nonlinear Phenomena: 50 years of IST (PMNP 2017)*(pp. 60-61).