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Passive Nonlinear Pulse Reshaping in Optical Fibers

Igor A. Sukhoivanov1, Oleksiy V. Shulika1,*, Sergii O. Iakushev2,

Jose A. Andrade Lucio1, and Gabriel Ramos Ortiz3 1 University of Guanajuato, Mexico

2 Kharkiv National University of Radio Electronics, Ukraine 3 Centro de Investigaciónes en Óptica, México

*e-mail: i.sukhoivanov@ieee.org

ABSTRACT Needs of science and industry for compact laser sources with ultra-broad spectrum or specially shaped pulse waveforms can be satisfied on fiber-optic platform. Here we address transformation of ultrashort optical pulses in a variety of optical fibers aiming synthesis of specially shaped pulses and single-pulse flat-top supercontinuum. Results are discussed in the context of possible applications and experimental implementations. Keywords: fiber-optic sources, nonlinear pulse shaping, triangular optical pulses, single-pulse flat-top

supercontinuum, all-normal dispersion photonic crystal fibers, microstructured optical fibers.

1. INTRODUCTION

Ultrashort optical pulses of special waveforms are very important in a number of all-optical signal processing applications [1]. In order to fulfil requirements of telecommunications, the compact fiber-based techniques for producing of special pulse waveforms from Gaussian or secant pulses delivered by modern ultrafast lasers are required. H. Wang et al. [2] have discussed conditions of chirped Gaussian pulse reshaping towards triangular waveform in the normally dispersive optical fiber. However, triangular pulse shape is achieved only within the narrow range of the fiber lengths, and during subsequent pulse propagation in a fiber the triangular pulse shape is destroyed. Here we propose another approach allowing preserving the triangular waveform, and discuss nonlinear pulse reshaping in single-mode optical fibers depending on pulse and fiber features, in terms of normalized parameters: soliton number, pulse chirp, normalized propagation distance.

Another very interesting case of passive nonlinear reshaping, which we report here, is generation of supercontinuum (SC) in all-normal dispersion photonic crystal fibers (ANDi PCFs) which exhibit convex dispersion profiles lying completely in the normal dispersion region. Pumping near the flattened top of such ANDi PCF provides generation of single-pulse and octave-spanning SC [3]. As compared to the traditional SC generation in anomalous dispersion region, in the last case a highly coherent, flat-top spectrum can be generated preserving a single pulse waveform in the temporal domain, which is rather beneficial for applications.

2. ULTRASHORT PULSE RESHAPING TOWARDS TRIANGULAR WAVEFORM

Recently we have shown that passive nonlinear reshaping in normal dispersive fiber could provide formation of parabolic pulses in the steady-state regime, when z is larger than dispersion length DL [4]. Here we show that

applying another initial conditions we can obtain also triangular pulses in the steady-state regime which preserve its triangular shape during long propagation in the fiber.

The evolution of an ultrashort pulse during its propagation in a normal-dispersion optical fiber with Kerr nonlinearity is studied by solving nonlinear Schrödinger equation. Figure 1 shows the evolution of the misfit parameter M versus normalized length ξ for initial unchirped Gaussian and secant pulse shapes for different values of soliton order N. Misfit parameter M shows the deviation from ideal triangular profile; it is considered that pulse is close enough to the triangular waveform when M < 0.04.

Figure 1. Evolution of the misfit parameter M versus normalized length ξ for initial

Gaussian (a) secant (b) pulse shapes.

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Figure 1 shows that triangular pulse shape can be achieved both from Gaussian and secant initial pulses. Condition for Gaussian pulse is N > 7, whereas for secant pulse N > 3. These conditions provide formation of triangular pulses which preserve triangular shape during the propagation in the fiber as Fig. 1 shows. Using these results we have calculated actual pulse shapes obtained from initial Gaussian and secant pulses after propagation in conventional single mode fiber Thorlabs 780HP, which has normal dispersion at 800 nm. From Fig. 2 one can see that pulse shape indeed is close to the triangular waveform, moreover the chirp of the pulses is perfectly linear.

Figure 2. Triangular pulses produced in the Thorlabs 780HP fiber. a) temporal intensity and chirp (green curve) for triangular pulse generated at the fiber length 1.4527 m from initial Gaussian pulse ( 07, 2.39 nJ,FWHM 200 fsN E= = = ); b) temporal intensity and chirp (green curve) for triangular pulse generated at the fiber length 1.9435 m from initial secant pulse ( fs 200FWHM,nJ 101.2,6 0 === EN ).

3. PULSE RESHAPING TOWARDS SINGLE-PULSE FLAT-TOP SUPERCONTINUUM

Here we discuss SC generation in the ANDi PCFs designed for pumping at 800 nm by Ti:Sapphire lasers [5]. Figure 3 shows the simulation results of SC generation in the designed ANDi PCF using 10 cm fiber’s piece and initial Gaussian pulses with different pulse energy and duration. Figure 3a shows that during SC generation single pulse shape remains in this fiber. Figure 3b shows that the best flatness of the SC spectrum is achieved for smaller pulse energy – 5 nJ and larger pulse duration – 100 fs. However, spectral width in this case is smaller ~572 nm. If we increase initial pulse energy up to 10 nJ, spectral width is increased up to 710 nm corresponding to ~1.3 octave. Spectral width is also increased up to 711 nm, if we use initial pulses with smaller duration (50 fs).

Figure 3. Supercontinuum generation in ANDi PCF of 10 cm length for different pulse energies and durations: a) – pulse profiles in temporal domain; b) – corresponding pulse spectra.

Thus, increasing the initial pulse energy or application of shorter initial pulses allows obtaining wider spectral width. However, the price for that is worse spectral flatness. Additional spectral broadening is accompanied by the depletion of central part of the spectrum, such that a dip appears at the pumping wavelength.

Spectral changes appearing during the shifting of the incident pulse wavelength are shown in Fig. 4. We can see that pumping far away from the top of the dispersion curve leads to strong asymmetry of the SC. At 700 nm red part of the spectrum is amplified, whereas the blue spectral part is depleted. The opposite picture appears at 900 nm. One can see that observable spectral asymmetry still exists for 750 and 850 nm pumping. Thus, we suppose that the optimal pump wavelength range for obtaining of SC spectra with a good flatness in the designed ANDi PCF is ~ 760 nm 840 nmpλ< < .

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Figure 4. Supercontinuum spectra generated in ANDi PCF of 10 cm length for different pump wave-lengths. In all cases initial pulse energy is 5 nJ, pulse duration is 100 fs.

4. CONCLUSIONS

To conclude, we have discussed nonlinear pulse reshaping towards triangular waveform and supercontinuum generation in normal dispersion optical fibers. Conditions for triangular pulse formation in the steady-state regime have been presented. The conditions of maximal spectral broadening while keeping the good spectral flatness in specially designed ANDi PCF have been presented as well.

ACKNOWLEDGEMENTS

The work reported here was partially supported by SEP/PROMEP (project UGTO-PTC-371) and the University of Guanajuato (projects DAIP-334/13 and DAIP-192/13).

REFERENCES

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19, 3775–3787 (2011). [4] S.O. Iakushev, O.V. Shulika, and I.A. Sukhoivanov, Opt. Commun. 285(21-22), 4493-4499 (2012). [5] I.A. Sukhoivanov, S.O. Iakushev, O.V. Shulika, A. Díez, and M. Andrés, Opt. Express, vol. 21, no. 15,

pp. 17769-17785 (2013).