Abstract

Specialty shape ultrashort optical pulses, and triangular pulses in particular, are of great interest in optical signal processing. Compact fiber-based techniques for producing the special pulse waveforms from Gaussian or secant pulses delivered by modern ultrafast lasers are in demand in telecommunications. Using the nonlinear Schrödinger equation in an extended form the transformation of ultrashort pulses in a fiber towards triangular shape is characterized by the misfit parameter under variety of incident pulse shapes, energies, and chirps. It is shown that short (1–2 m) conventional single mode fiber can be used for triangular pulse formation in the steady-state regime without any pre-chirping if femtosecond pulses are used for pumping. The pulses obtained are stable and demonstrate linear chirp. The ranges and combinations of the pulse parameters found here will serve as a guide for scheduling the experiments and implementation of various all-fiber schemes for optical signal processing.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2013 (1)

2012 (3)

S. Boscolo and C. Finot, “Nonlinear pulse shaping in fibers for pulse generation and optical processing,” Int. J. Optics 2012, 1–14 (2012).
[Crossref]

S. O. Iakushev, O. V. Shulika, and I. A. Sukhoivanov, “Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers,” Opt. Commun. 285, 4493–4499 (2012).
[Crossref]

S. Boscolo and S. K. Turitsyn, “Intermediate asymptotics in nonlinear optical systems,” Phys. Rev. A 85, 043811 (2012).
[Crossref]

2011 (4)

2010 (2)

H. Wang, A. I. Latkin, S. Boscolo, P. Harper, and S. K. Turitsyn, “Generation of triangular-shaped optical pulses in normally dispersive fibre,” J. Opt. 12, 0352051 (2010).
[Crossref]

A. M. Clarke, D. G. Williams, M. A. F. Roelens, and B. J. Eggleton, “Reconfigurable optical pulse generator employing a Fourier-domain programmable optical processor,” J. Lightwave Technol. 28, 97–103 (2010).
[Crossref]

2009 (4)

F. Parmigiani, M. Ibsen, P. Petropoulos, and D. J. Richardson, “Efficient all-optical wavelength conversion scheme based on a saw-tooth pulse shaper,” IEEE Photon. Technol. Lett. 21, 1837–1839 (2009).
[Crossref]

A. Zeytunyan, G. Yesayan, L. Mouradian, P. Kockaert, P. Emplit, F. Louradour, and A. Barthélémy, “Nonlinear-dispersive similariton of passive fiber,” J. Euro. Opt. Soc. - Rapid Pub. 4, 090091 (2009).
[Crossref]

F. Parmigiani, P. Petropoulos, M. Ibsen, P. J. Almeida, T. T. Ng, and D. J. Richardson, “Time domain add-drop multiplexing scheme snhanced using a saw-tooth pulse shaper,” Opt. Express 17, 8362–8369 (2009).
[Crossref] [PubMed]

A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Doubling of optical signals using triangular pulses,” J. Opt. Soc. Am. B 26, 1492–1496 (2009).
[Crossref]

2008 (2)

S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber systems,” IEEE J. Quantum Electron. 44, 1196–1203 (2008).
[Crossref]

T. Hirooka, M. Nakazawa, and K. Okamoto, “Bright and dark 40 GHz parabolic pulse generation using a picosecond optical pulse train and an arrayed waveguide grating,” Opt. Lett. 33, 1102–1104 (2008).
[Crossref] [PubMed]

2007 (1)

2001 (1)

2000 (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Scien. Instrum. 71, 1939–1960 (2000).
[Crossref]

1994 (1)

M. Karlsson, “Optical fiber-grating compressors utilizing long fibers,” Opt. Commun. 112, 48–54 (1994).
[Crossref]

1984 (1)

Agrawal, G. P.

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

Almeida, P. J.

Andrés, M.

Bale, B. B.

Barthélémy, A.

A. Zeytunyan, G. Yesayan, L. Mouradian, P. Kockaert, P. Emplit, F. Louradour, and A. Barthélémy, “Nonlinear-dispersive similariton of passive fiber,” J. Euro. Opt. Soc. - Rapid Pub. 4, 090091 (2009).
[Crossref]

Bhamber, R. S.

A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Doubling of optical signals using triangular pulses,” J. Opt. Soc. Am. B 26, 1492–1496 (2009).
[Crossref]

R. S. Bhamber, S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “All-optical TDM to WDM signal conversion and partial regeneration using XPM with triangular pulses,” in “Optical Communication, 2008. ECOC 2008. 34th European Conference on,” (Brussels, Begium, 2008).

Boscolo, S.

S. Boscolo and C. Finot, “Nonlinear pulse shaping in fibers for pulse generation and optical processing,” Int. J. Optics 2012, 1–14 (2012).
[Crossref]

S. Boscolo and S. K. Turitsyn, “Intermediate asymptotics in nonlinear optical systems,” Phys. Rev. A 85, 043811 (2012).
[Crossref]

B. B. Bale, S. Boscolo, K. Hammani, and C. Finot, “Effects of fourth-order fiber dispersion on ultrashort parabolic optical pulses in the normal dispersion regime,” J. Opt. Soc. Am. B 28, 2059–2065 (2011).
[Crossref]

H. Wang, A. I. Latkin, S. Boscolo, P. Harper, and S. K. Turitsyn, “Generation of triangular-shaped optical pulses in normally dispersive fibre,” J. Opt. 12, 0352051 (2010).
[Crossref]

A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Doubling of optical signals using triangular pulses,” J. Opt. Soc. Am. B 26, 1492–1496 (2009).
[Crossref]

S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber systems,” IEEE J. Quantum Electron. 44, 1196–1203 (2008).
[Crossref]

R. S. Bhamber, S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “All-optical TDM to WDM signal conversion and partial regeneration using XPM with triangular pulses,” in “Optical Communication, 2008. ECOC 2008. 34th European Conference on,” (Brussels, Begium, 2008).

Clarke, A. M.

Delfyett, P. J.

Díez, A.

Eggleton, B. J.

Ellis, A. D.

Emplit, P.

A. Zeytunyan, G. Yesayan, L. Mouradian, P. Kockaert, P. Emplit, F. Louradour, and A. Barthélémy, “Nonlinear-dispersive similariton of passive fiber,” J. Euro. Opt. Soc. - Rapid Pub. 4, 090091 (2009).
[Crossref]

Finot, C.

Hammani, K.

Harper, P.

H. Wang, A. I. Latkin, S. Boscolo, P. Harper, and S. K. Turitsyn, “Generation of triangular-shaped optical pulses in normally dispersive fibre,” J. Opt. 12, 0352051 (2010).
[Crossref]

Hirooka, T.

Iakushev, S. O.

I. A. Sukhoivanov, S. O. Iakushev, O. V. Shulika, A. Díez, and M. Andrés, “Femtosecond parabolic pulse shaping in normally dispersive optical fibers,” Opt. Express 21, 17769–17785 (2013).
[Crossref] [PubMed]

S. O. Iakushev, O. V. Shulika, and I. A. Sukhoivanov, “Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers,” Opt. Commun. 285, 4493–4499 (2012).
[Crossref]

Ibsen, M.

Karlsson, M.

M. Karlsson, “Optical fiber-grating compressors utilizing long fibers,” Opt. Commun. 112, 48–54 (1994).
[Crossref]

Kockaert, P.

A. Zeytunyan, G. Yesayan, L. Mouradian, P. Kockaert, P. Emplit, F. Louradour, and A. Barthélémy, “Nonlinear-dispersive similariton of passive fiber,” J. Euro. Opt. Soc. - Rapid Pub. 4, 090091 (2009).
[Crossref]

Latkin, A. I.

H. Wang, A. I. Latkin, S. Boscolo, P. Harper, and S. K. Turitsyn, “Generation of triangular-shaped optical pulses in normally dispersive fibre,” J. Opt. 12, 0352051 (2010).
[Crossref]

A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Doubling of optical signals using triangular pulses,” J. Opt. Soc. Am. B 26, 1492–1496 (2009).
[Crossref]

S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber systems,” IEEE J. Quantum Electron. 44, 1196–1203 (2008).
[Crossref]

R. S. Bhamber, S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “All-optical TDM to WDM signal conversion and partial regeneration using XPM with triangular pulses,” in “Optical Communication, 2008. ECOC 2008. 34th European Conference on,” (Brussels, Begium, 2008).

Louradour, F.

A. Zeytunyan, G. Yesayan, L. Mouradian, P. Kockaert, P. Emplit, F. Louradour, and A. Barthélémy, “Nonlinear-dispersive similariton of passive fiber,” J. Euro. Opt. Soc. - Rapid Pub. 4, 090091 (2009).
[Crossref]

Luo, B.

Mandridis, D.

Mouradian, L.

A. Zeytunyan, G. Yesayan, L. Mouradian, P. Kockaert, P. Emplit, F. Louradour, and A. Barthélémy, “Nonlinear-dispersive similariton of passive fiber,” J. Euro. Opt. Soc. - Rapid Pub. 4, 090091 (2009).
[Crossref]

Nakazawa, M.

Ng, T. T.

Nguyen, D.

Okamoto, K.

Pan, W.

Parmigiani, F.

F. Parmigiani, P. Petropoulos, M. Ibsen, P. J. Almeida, T. T. Ng, and D. J. Richardson, “Time domain add-drop multiplexing scheme snhanced using a saw-tooth pulse shaper,” Opt. Express 17, 8362–8369 (2009).
[Crossref] [PubMed]

F. Parmigiani, M. Ibsen, P. Petropoulos, and D. J. Richardson, “Efficient all-optical wavelength conversion scheme based on a saw-tooth pulse shaper,” IEEE Photon. Technol. Lett. 21, 1837–1839 (2009).
[Crossref]

Petropoulos, P.

Piracha, M. U.

Provost, L.

Ramachandran, S.

S. Ramachandran, Fiber Based Dispersion Compensation (Springer, 2007).
[Crossref]

Richardson, D. J.

Roelens, M. A. F.

Shank, C. V.

Shulika, O. V.

I. A. Sukhoivanov, S. O. Iakushev, O. V. Shulika, A. Díez, and M. Andrés, “Femtosecond parabolic pulse shaping in normally dispersive optical fibers,” Opt. Express 21, 17769–17785 (2013).
[Crossref] [PubMed]

S. O. Iakushev, O. V. Shulika, and I. A. Sukhoivanov, “Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers,” Opt. Commun. 285, 4493–4499 (2012).
[Crossref]

Stolen, R. H.

Sukhoivanov, I. A.

I. A. Sukhoivanov, S. O. Iakushev, O. V. Shulika, A. Díez, and M. Andrés, “Femtosecond parabolic pulse shaping in normally dispersive optical fibers,” Opt. Express 21, 17769–17785 (2013).
[Crossref] [PubMed]

S. O. Iakushev, O. V. Shulika, and I. A. Sukhoivanov, “Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers,” Opt. Commun. 285, 4493–4499 (2012).
[Crossref]

Tomlinson, A.

Turitsyn, S. K.

S. Boscolo and S. K. Turitsyn, “Intermediate asymptotics in nonlinear optical systems,” Phys. Rev. A 85, 043811 (2012).
[Crossref]

H. Wang, A. I. Latkin, S. Boscolo, P. Harper, and S. K. Turitsyn, “Generation of triangular-shaped optical pulses in normally dispersive fibre,” J. Opt. 12, 0352051 (2010).
[Crossref]

A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Doubling of optical signals using triangular pulses,” J. Opt. Soc. Am. B 26, 1492–1496 (2009).
[Crossref]

S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber systems,” IEEE J. Quantum Electron. 44, 1196–1203 (2008).
[Crossref]

R. S. Bhamber, S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “All-optical TDM to WDM signal conversion and partial regeneration using XPM with triangular pulses,” in “Optical Communication, 2008. ECOC 2008. 34th European Conference on,” (Brussels, Begium, 2008).

Verscheure, N.

N. Verscheure and C. Finot, “Pulse doubling and wavelength conversion through triangular nonlinear pulse re-shaping,” Electron. Lett. 47, 1194–1196 (2011).
[Crossref]

Wang, H.

H. Wang, A. I. Latkin, S. Boscolo, P. Harper, and S. K. Turitsyn, “Generation of triangular-shaped optical pulses in normally dispersive fibre,” J. Opt. 12, 0352051 (2010).
[Crossref]

Weiner, A. M.

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Scien. Instrum. 71, 1939–1960 (2000).
[Crossref]

Williams, D. G.

Yan, L.

Yao, S.

Ye, J.

Yesayan, G.

A. Zeytunyan, G. Yesayan, L. Mouradian, P. Kockaert, P. Emplit, F. Louradour, and A. Barthélémy, “Nonlinear-dispersive similariton of passive fiber,” J. Euro. Opt. Soc. - Rapid Pub. 4, 090091 (2009).
[Crossref]

Yi, A.

Zeytunyan, A.

A. Zeytunyan, G. Yesayan, L. Mouradian, P. Kockaert, P. Emplit, F. Louradour, and A. Barthélémy, “Nonlinear-dispersive similariton of passive fiber,” J. Euro. Opt. Soc. - Rapid Pub. 4, 090091 (2009).
[Crossref]

Zou, X.

Electron. Lett. (1)

N. Verscheure and C. Finot, “Pulse doubling and wavelength conversion through triangular nonlinear pulse re-shaping,” Electron. Lett. 47, 1194–1196 (2011).
[Crossref]

IEEE J. Quantum Electron. (1)

S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber systems,” IEEE J. Quantum Electron. 44, 1196–1203 (2008).
[Crossref]

IEEE Photon. Technol. Lett. (1)

F. Parmigiani, M. Ibsen, P. Petropoulos, and D. J. Richardson, “Efficient all-optical wavelength conversion scheme based on a saw-tooth pulse shaper,” IEEE Photon. Technol. Lett. 21, 1837–1839 (2009).
[Crossref]

Int. J. Optics (1)

S. Boscolo and C. Finot, “Nonlinear pulse shaping in fibers for pulse generation and optical processing,” Int. J. Optics 2012, 1–14 (2012).
[Crossref]

J. Euro. Opt. Soc. - Rapid Pub. (1)

A. Zeytunyan, G. Yesayan, L. Mouradian, P. Kockaert, P. Emplit, F. Louradour, and A. Barthélémy, “Nonlinear-dispersive similariton of passive fiber,” J. Euro. Opt. Soc. - Rapid Pub. 4, 090091 (2009).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. (1)

H. Wang, A. I. Latkin, S. Boscolo, P. Harper, and S. K. Turitsyn, “Generation of triangular-shaped optical pulses in normally dispersive fibre,” J. Opt. 12, 0352051 (2010).
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Commun. (2)

S. O. Iakushev, O. V. Shulika, and I. A. Sukhoivanov, “Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers,” Opt. Commun. 285, 4493–4499 (2012).
[Crossref]

M. Karlsson, “Optical fiber-grating compressors utilizing long fibers,” Opt. Commun. 112, 48–54 (1994).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. A (1)

S. Boscolo and S. K. Turitsyn, “Intermediate asymptotics in nonlinear optical systems,” Phys. Rev. A 85, 043811 (2012).
[Crossref]

Rev. Scien. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Scien. Instrum. 71, 1939–1960 (2000).
[Crossref]

Other (5)

R. S. Bhamber, S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “All-optical TDM to WDM signal conversion and partial regeneration using XPM with triangular pulses,” in “Optical Communication, 2008. ECOC 2008. 34th European Conference on,” (Brussels, Begium, 2008).

S. Ramachandran, Fiber Based Dispersion Compensation (Springer, 2007).
[Crossref]

Thorlabs, “Specification sheet: 780 HP – Single Mode Optical Fiber, 780 – 970 nm, ∅125 μm cladding (Rev. D, 2013-April-1, 6829-s01),” http://www.thorlabs.com/thorcat/6800/780HP-SpecSheet.pdf (2013). Accessed: 2014-June-27.

OFS, “TrueWave Ocean Fibers SRS,” http://ofsoptics.thomasnet-navigator.com/Asset/TrueWaveSRSFiber-121-web.pdf (2013). Accessed: 2014-June-27.

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

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Figures (9)

Fig. 1
Fig. 1 Evolution of the misfit parameter M versus normalized distance ξ for the temporal (a) and spectral (b) pulse shapes at N = 10 and C = −4, which corresponds to the case example of [16] shown there on Fig. 1. Black dashed lines correspond to the level M = 0.04. The insets in the figures show the enlarged areas of the minima where M < 0.04.
Fig. 2
Fig. 2 Normalized pulse temporal intensity (a), (b) and spectrum (c), (d) in the transient- state propagation (TSP) regime produced from chirped Gaussian pulse (N = 10, C = −4) at the distances ξ = 0.33 (the left column) and ξ = 0.42 (the right column), respectively. The right column corresponds to the case example of [16] shown there on Fig. 1. The insets located in the upper right corner show the value of misfit parameter M. Red curves show corresponding triangular fits.
Fig. 3
Fig. 3 Evolution of the misfit parameter M versus normalized distance ξ for the temporal (a) and spectral (b) pulse shapes in case of the initial unchirped Gaussian pulse.
Fig. 4
Fig. 4 Evolution of the misfit parameter M versus normalized distance ξ for the temporal (a) and spectral (b) pulse shapes in case of the initial unchirped secant hyperbolic pulse.
Fig. 5
Fig. 5 Evolution of the misfit parameter M versus ξ for temporal (a) and spectral (b) pulse shapes in case of the initial unchirped 3-rd order super-Gaussian pulse. Figures (c) and (d) shows the enlarged areas of the minima of M in the transient-state propagation (TSP) regime extracted from Fig. 5(a) and Fig. 5(b), respectively.
Fig. 6
Fig. 6 Evolution of the misfit parameter M versus ξ for temporal (a) and spectral (b) pulse shapes in case of the initial Gaussian pulse having N = 10. Figures (c) and (d) show the enlarged areas of the minima of M in the transient-state propagation (TSP) regime extracted from Fig. 6(a) and Fig. 6(b), respectively. Fig. 6(e) and Fig. 6(f) shows evolution of the misfit parameter M versus ξ for temporal and spectral pulse shapes, respectively, in case of the initial Gaussian pulse with N = 3.
Fig. 7
Fig. 7 Evolution of the misfit parameter M versus normalized distance ξ for the temporal (a) and spectral (b) pulse shapes in case of the initial secant hyperbolic pulse with N = 10 and various values of chirp.
Fig. 8
Fig. 8 Evolution of the misfit parameter M versus normalized distance ξ for the temporal (a) and spectral (b) pulse shapes in case of the initial super-Gaussian pulse with N = 10 and various values of chirp C. Fig. 8(c) and Fig. 8(d) show the enlarged areas of the minima in the transient-state propagation regime extracted from figures Fig. 8(a) Fig. 8(b), respectively.
Fig. 9
Fig. 9 Triangular pulses produced in the Thorlabs 780HP fiber. The left column shows results ((a) - temporal intensity and chirp (green curve), (c) - spectrum) for triangular pulse generated in the steady-state regime at the fiber length 1.4527 m (ξ = 4) from initial unchirped Gaussian pulse (N = 7, E0 = 2.39 nJ, FWHM=200 fs). Right column ((b), (d)) shows triangular pulse generated in the steady-state regime at the fiber length 1.9435 m (ξ = 6) from initial unchirped secant pulse (N = 6, E0 = 2.101 nJ, FWHM=200 fs). The insets located in the upper right corner show the amount of misfit parameter M. Red curves show corresponding triangular fits.

Tables (2)

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Table 1 Summary of the conditions for the formation of triangular pulses in a fiber.

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Table 2 Comparisons of contributions of the fourth order dispersion and Raman intrapulse scattering into distortion of triangular pulses in the Thorlabs 780HP fiber

Equations (7)

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A z = α 2 A i β 2 2 2 A T 2 + β 3 6 3 A T 3 + i γ | A | 2 A ,
β ( ω ) = n ˜ eff ω c = n 0 1 n ! n β ( ω 0 ) ω n ( ω ω 0 )
L D = T 0 2 | β 2 | , L NL = 1 γ P 0 , N = L D L NL , ξ = z L D .
M = ( | A | 2 | A Δ | 2 ) 2 T | A | 4 T .
A Δ ( T ) = { P Δ 1 | T T Δ 2.5 | , | T | T Δ 2.5 0 , otherwise
A chirp = A 0 exp ( i C T 2 2 T 0 2 ) ,
ω = ω 0 + C T T 0 2 .

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