Nonlinear pulse compression of picosecond
parabolic-like pulses synthesized with a long
period fiber grating filter

doi:10.1364/OE.17.007074

« Show journal navigation

Nonlinear pulse compression of picosecond parabolic-like pulses synthesized with a long period fiber grating filter

David Krcmarík, Radan Slavík, Yongwoo Park, and José Azaña »View Author Affiliations

Optics Express, Vol. 17, Issue 9, pp. 7074-7087 (2009)
http://dx.doi.org/10.1364/OE.17.007074

View Full Text Article

Acrobat PDF (348 KB)

Journal Search
Article Lookup

Article Tools

Citations

Alert me when this article is cited
Export Citation/Save

Full Text
Article Info
References (22)
Cited By
Figures (9)
Multimedia (1)
Metrics

Abstract

We demonstrate high quality pulse compression at high repetition rates by use of spectral broadening of short parabolic-like pulses in a normally-dispersive highly nonlinear fiber (HNLF) followed by linear dispersion compensation with a conventional SMF-28 fiber. The key contribution of this work is on the use of a simple and efficient long-period fiber grating (LPFG) filter for synthesizing the desired parabolic-like pulses from sech²-like input optical pulses; this all-fiber low-loss filter enables reducing significantly the required input pulse power as compared with the use of previous all-fiber pulse re-shaping solutions (e.g. fiber Bragg gratings). A detailed numerical analysis has been performed in order to optimize the system’s performance, including investigation of the optimal initial pulse shape to be launched into the HNLF fiber. We found that the pulse shape launched into the HNLF is critically important for suppressing the undesired wave breaking in the nonlinear spectral broadening process. The optimal shape is found to be independent on the parameters of normally dispersive HNLFs. In our experiments, 1.5-ps pulses emitted by a 10-GHz mode-locked laser are first reshaped into 3.2-ps parabolic-like pulses using our LPFG-based pulse reshaper. Flat spectrum broadening of the amplified initial parabolic-like pulses has been generated using propagation through a commercially-available HNLF. Pulses of 260 fs duration with satellite peak and pedestal suppression greater than 17 dB have been obtained after the linear dispersion compensation fiber. The generated pulses exhibit a 20-nm wide supercontinuum energy spectrum that has almost a square-like spectral profile with >85% of the pulse energy contained in its FWHM spectral bandwidth.

1. Introduction

High-repetition rate (>10 GHz) ultrashort (sub-picoseconds) optical pulses and/or signals with broadband spectral characteristics, are needed for many applications in present and future high-speed communications systems. For example, optical time domain multiplexed systems (OTDM) at clock rates up to 640 GHz are currently under intensive investigation [1

L. K. Oxenlowe, R. Slavík, M. Galili, H. C. H. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gb/s timing jitter-tolerant data processing using a long-period fiber-grating-based flat-top pulse shaper,” IEEE J. Sel. Top. in Quantum Electron. 14, 566–572 (2008).

]. At such clock rate, the single-bit time window is only 1.56 ps long, requiring the use of optical pulses with full width at half maximum (FWHM) time-widths <500 fs, low pulse pedestals and high satellite pulses suppression [1

]. However, commercially available high repetition rate (GHz-rate) laser pulsed sources provide pulses of ~1 to 5 ps, typically >1.5 ps, and thus are insufficient for OTDM applications with clock rates above 320 GHz. Another important application in which such ultrashort pulses are needed is ultrafast pulse shaping [2

F. Parmigiani, M. Ibsen, T. T. Ng, L. Provost, P. Petropoulos, and D. J. Richardson, “An efficient wavelength converter exploiting a grating based saw-tooth pulse shaper,” Photon. Technol. Lett. 20, 1461–1463 (2008).

, 3

R. Slavík, Y. Park, and J. Azaña, “Long period fiber grating-based filter for generation of picosecond and sub-picosecond transform-limited flat-top pulses,” Photon. Technol. Lett. 20, 806–808 (2008).

, 4

A. M. Wiener, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable femtosecond pulse shaping by use of amultielement liquid-crystal phase modulator,” Opt. Lett. 15, 326–328 (1990).

, 5

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, “Flexible pulse waveform generation using silica-waveguide-based spectrum synthesis circuit,” Electron. Lett. 40, 537–538 (2004).

] based on the use of linear optical filters (e.g. fiber Bragg gratings, FBGs [2

], long period fiber gratings, LPFGs [3

], pulse shapers with spatial light modulators [4

A. M. Wiener, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable femtosecond pulse shaping by use of amultielement liquid-crystal phase modulator,” Opt. Lett. 15, 326–328 (1990).

] or arrayed waveguide gratings, AWGs) [5

]). Linear pulse shaping techniques do not enable generating new spectral components – consequently, the re-shaped pulse cannot exhibit faster temporal features than those of the incident pulse. To give an example, in [6

F. Parmigiani, C. Finot, K. Mukasa, M. Ibsen, M. A. F. Roelens, P. Petropoulos, and D. J. Richardson, “Ultra-flat SPM-broadened spectra in a highly nonlinear fiber using parabolic pulses formed in a fiber Bragg grating,” Opt. Express 14, 7617–7622 (2006). [PubMed]

], a 10-ps flat-top pulse was generated from an input 2-ps pulse (with rising/falling edge steepness similar for the input and the shaped pulse). Thus, for obtaining sub-picosecond-scale shaped pulses, the incident pulse must be <<1 ps. It was shown recently that many shapes are of practical interest. Flat-top pulses have proven to be useful to increase the timing jitter tolerance in ultrafast nonlinear switching (up to 640 GHz using LPFG-based pulse shapers [1

]), saw-tooth and triangular-shaped pulses were demonstrated for improving various signal processing devices, e.g., for jitter tolerant OTDM demultiplexing [7

F. Parmigiani, T. T. Ng, M. Ibsen, P. Petropoulos, and D. J. Richardson, “Timing jitter tolerant OTDM demultiplexing using a saw-tooth pulse shaper,” presented at ECOC, Brussels, Belgium, 2008.

] or channel add/drop [8

A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Optical frequency conversion, pulse compression and signal copying using triangular pulses,” presented at ECOC, Brussels, Belgium, 2008, Paper Mo.3.F.4.

], parabolic-shaped pulses were demonstrated for a low-ripple supercontinuum generation and pulse compression [9

D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, “Wave-breaking-free pulses in nonlinear-optical fibers,” J. Opt. Soc. Am. B 10, 1185–1190 (1993).

], etc. For most of the mentioned applications (OTDM transmission and ultrafast pulse reshaping), transform-limited (unchirped) optical pulses are also highly desired.

Considering an input transform-limited picosecond-scale optical pulse, pulse compression techniques incorporating nonlinear spectral broadening are particularly attractive and have been used in a wide range of applications [10–13

M. Nakazawa, E. Yoshida, H. Kubota, and Y. Kimura, “Generation of a 170 fs, 10 GHz transform-limited pulse train at 1.55 μm using a dispersion-decreasing, erbium-doped active soliton compressor,” Electron. Lett. 30, 2038–2039 (1994).

]. Optical pulse propagation in a dispersive nonlinear medium strongly depends on a variety of factors, including the nonlinear medium chromatic dispersion and the group delay induced by the nonlinear phase shift. Thus, careful tailoring of these parameters is indispensable to fully optimize the temporal compression process leading to the formation of nearly transform-limited ultrashort pulses. Obviously, the use of all-fiber technologies is always advantageous, particularly for telecom-related applications. Nonlinear pulse compression in optical fibers has been previously demonstrated using dispersion decreasing fibers [10

, 11

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. Lett. 15, 15824–15835 (2007).

], higher order soliton compression [12

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. 8, 289–291 (1983). [PubMed]

] or self-similar parabolic pulses [13

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. 85, 6010–6013 (2003).

]. The first technique requires a specially-made dispersion decreasing fiber [10

, 11

], whereas higher order soliton compression requires properly chosen parameters and is strongly input power dependent [12

] – moreover, Raman scattering and two-photon absorption can be very limiting.

There were several reports showing theoretically [9

D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, “Wave-breaking-free pulses in nonlinear-optical fibers,” J. Opt. Soc. Am. B 10, 1185–1190 (1993).

], and experimentally [6

] that input optical pulses with parabolic temporal shapes are the best suited for subsequent pulse compression. Parabolic optical pulses propagate as self-similar entities, i.e. they maintain their temporal shape during propagation through a suitable nonlinear, normally-dispersive medium (by normal dispersion we refer to a positive slope of the group-delay curve as a function of the optical frequency). Moreover, they accumulate purely linear chirp, without the detrimental wave-breaking phenomenon, which subsequently enables a nearly optimal compression in a very simple fashion (e.g., using simple linear propagation through a suitable section of a standard SMF-28 fiber) [9

D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, “Wave-breaking-free pulses in nonlinear-optical fibers,” J. Opt. Soc. Am. B 10, 1185–1190 (1993).

]. The main task is how to obtain parabolic pulses at first. A few linear and nonlinear based techniques were proposed for this purpose. Linear techniques include filtering with (i) a specially-designed superstructured FBG (SSFBG) [6

], (ii) bulk-optics based interferometers using coherence synthesization [14

Y. Park, M. H. Asghari, T.-J. Ahn, and J. Azaña, “Transform-limited picosecond pulse shaping based on coherence synthesization,” Opt. Express 15, 9584–9599 (2007). [PubMed]

], or (iii) an all-fiber implementation of this latter concept using a pair of LPFGs [3

,15

R. Slavík, Y. Park, T. -J. Ahn, and J. Azaña, “Synthesis of picosecond parabolic pulses formed by a long period fiber grating structure and its application for flat-top supercontinuum generation,” presented at OFC/NFOEC, San Diego, CA, 2008, Paper OTuB4.

]. Nonlinear techniques for pulse shaping are based, e.g., on normally dispersive fiber [16

A. I. Latkin, S. Boscolo, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber,” presented at OFC/NFOEC, San Diego, CA, 2008, Paper OTuB7.

], dispersion decreasing fiber [11

], etc.

To our knowledge, experiments concerning pulse compression after obtaining broadband parabolic pulses were carried out only for the parabolic pulses generated with the SSFBGs [6

]. In this previous work, the initial 2-ps sech² pulses were first transformed into 10-ps parabolic pulses via linear spectral filtering and subsequently propagated along a normally-dispersive highly nonlinear fiber (HNLF) and SMF-28 (for linear dispersion compensation). The 10-ps duration was limited by the SSFBG fabrication constrains rather than by the input pulse duration – using a shorter input pulse would not lead to generation of a shorter parabolic pulse. The parabolic pulse duration is roughly limited by the round-trip time through the SSFBG that was approximately 1-mm long. Although the SSFBG-generated parabolic pulses were compressed down to 310 fs FWHM, the method had relatively low energetic budget due to two main reasons. First, the pulse reshaping process suffers from low energetic efficiency, as most of the spectral content of the input pulse is strongly attenuated by the SSFBG to obtain a relatively long (10-ps) pulse out of a relatively short (2-ps) pulse. Further, due to the relatively long shaped pulses used at the HNLF input, high average pulse power is required to trigger the desired nonlinear effects (e.g. pulse energy of 100 pJ at a repetition rate of 5 GHz was used in [6

]).

The parabolic pulse re-shaping process plays a very important role for obtaining a high-quality, ripple-free supercontinuum without spectral tails (responsible for wave breaking) by pulse propagation through the HNLF. Such a supercontinuum is also attractive for a range of applications, such as spectral slicing for WDM systems [6

,17

Y. Takushima and K. Kikuchi, “10-GHz, over 20-Channel Multiwavelength Pulse Source by Slicing Super-Continuum Spectrum Generated in Normal-Dispersion Fiber,” Photon. Technol. Lett. . 11, 322 (1999).

] or optical coherence tomography [18

I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001).

]. In [6

] a 29-nm almost ripple-free and wave-breaking-free supercontinuum was generated prior to the above-discussed pulse compression operation.

We have recently proposed an alternative technique for generation of parabolic pulses through linear reshaping of an input pulse using LPFG filters [15

]. It represents, similarly to SSFBG, an all-fiber solution with advantages like low insertion loss and ability to handle high powers. However, the LPFG-based method has several distinctive advantages. An LPFG filter operates in transmission (as opposed to SSFBG that generally operates in reflection) and it allows one to synthesize shorter pulses. For example, our previous LPFG-generated parabolic pulses were 2.2-ps long [15

] after reshaping from initial 1.3-ps pulses, compared to 10 ps using an SSFBG [6

] with initial 2-ps pulses. Moreover, the pulse re-shaping process presented here has energetic efficiency typically of ~70%), as only a small part of the spectral content of the input pulse is filtered out. This compares favorably to reshaping scheme used in [6

], where the initial 2-ps pulse spectrum was severely filtered out in order to get the 10-ps pulse spectrum (shorter parabolic pulses were not easily obtainable in [6

] due to the fabrication constrains associated with SSFBGs). However, this high energetic efficiency is achieved at the expense of a relatively higher deviation of the generated pulse shape with respect to an ideal parabolic, especially at the pulse edges. Thus, to fully evaluate the potential applicability of this recently proposed pulse re-shaping scheme for nonlinear pulse compression, a detailed theoretical and experimental analysis would be needed.

In this article we investigate in detail the suitability of the LPFG-based parabolic pulse shaping technique [15

] for pulse compression and supercontinuum generation. Our research is oriented according to the needs in the above mentioned applications, i.e. for implementing both an optical pulse source with the required features for 640-Gbit/s OTDM data transmission and an ultrafast input pulse source for sub-picosecond linear pulse re-shaping operations.

2. Theory: linear pulse shaping

The principle of the LPFG filters used for the considered pulse shaping may be understood by the simple theory reported in Ref. [14

Y. Park, M. H. Asghari, T.-J. Ahn, and J. Azaña, “Transform-limited picosecond pulse shaping based on coherence synthesization,” Opt. Express 15, 9584–9599 (2007). [PubMed]

] which is referred to as ‘temporal coherence synthesis’. In this method, time-delayed replicas of a transform-limited pulse are interfered constructively, which allows the superposition of the amplitude envelopes of the time-delayed individual pulses. As shown in Fig. 1(a), different pulse shapes can be synthesized at the output depending on the relative time delays among the different pulse replicas. In the practical implementation reported here, only two replicas of the input optical pulse are interfered. The studied device consists of two cascaded LPFGs that form an all-fiber Mach-Zehnder interferometer, MZI, Fig. 1(b). The input pulse energy is split into two parts by the first LPFG and propagates in different modes (core mode and one of the cladding modes) at different speeds till the second LPFG, where coherent interference of the two modes takes place. Such interferometer was demonstrated to be capable of synthesizing different shapes like flat-top [3

] and parabolic [15

] – details on the design of these pulse re-shaping operations may be found in [14

Y. Park, M. H. Asghari, T.-J. Ahn, and J. Azaña, “Transform-limited picosecond pulse shaping based on coherence synthesization,” Opt. Express 15, 9584–9599 (2007). [PubMed]

]. The inherent advantage of the LPFG implementation is that both interfering signals are carried within a single piece of fiber (the core mode and a cladding mode), which translates into a very robust operation. Its robustness was demonstrated in our previous experiments on generation of stable flat-top [3

] and parabolic [15

] optical pulses. Since the filter MZI is made by two LPFGs made with low polarization dependence [19

D. D. David, T. K. Gaylord, E. N. Glytsis, and S. C. Mettler, “CO2 laser-induced long-period fibre gratings: spectral characteristics, cladding modes and polarization independence,” Electron. Lett. 34, 1416–1417 (1998).

] the process is almost polarization-insensitive. Moreover due to a single-fiber implementation of the two branches of the MZI, the temperature influences the two interfering signals in a very similar manner and hence the whole device is expected to have low temperature sensitivity.

There are two parameters that can be controlled in such an interferometer: the relative MZI delay (adjusted here by the relative distance between the two concatenated LPFGs) and the coupling ratios (given by the LPFGs’ strengths). However, for obtaining a symmetric temporal waveform from a symmetric input pulse, the two LPFGs should provide 50% coupling [14

Y. Park, M. H. Asghari, T.-J. Ahn, and J. Azaña, “Transform-limited picosecond pulse shaping based on coherence synthesization,” Opt. Express 15, 9584–9599 (2007). [PubMed]

]. Thus, we have only one free parameter – the relative delay. The influence of the MZI delay on the generated waveform is shown in Fig. 2 considering a 1.5-ps FWHM sech² input pulse. The pulses are normalized to the pulse energy of 15 pJ which corresponds to an average power of 150 mW for a repetition rate of 10 GHz. For illustration purposes, parabolic fits are shown for each considered waveform, Fig. 2. The input sech² pulse differs considerably from the parabolic – its peak is sharper and it has large temporal tails, Fig. 2. For small values of the MZI delay, the pulse is getting only slightly broadened. However, for an MZI delay corresponding to 0.8 of the FWHM time-width of the input pulse (0.8xFWHM), the generated pulse peak fits perfectly the parabolic shape; however, significant temporal tails deviating from the ideal parabolic shape appear from about 40% of the peak intensity, Fig. 2, [14

Y. Park, M. H. Asghari, T.-J. Ahn, and J. Azaña, “Transform-limited picosecond pulse shaping based on coherence synthesization,” Opt. Express 15, 9584–9599 (2007). [PubMed]

, 15

]. Increasing the MZI delay to 1xFWHM, we obtain a flat-top pulse, Fig. 2, [3

, 14

Y. Park, M. H. Asghari, T.-J. Ahn, and J. Azaña, “Transform-limited picosecond pulse shaping based on coherence synthesization,” Opt. Express 15, 9584–9599 (2007). [PubMed]

]. When fitted with a parabolic function, we get a slight deviation both at the pulse top and at the temporal tails, even though the latter are notably reduced as compared to the previous case (0.8xFWHM) – the pulse temporal tails deviating from the ideal parabolic shape appear now from about 30% of the peak intensity, Fig. 2. Further increase in the MZI delay leads to a pulse that has a shallow minimum across its almost-flat-top part (e.g., for 1.3xFWHM), Fig. 2. For reasons that will become clear later, we entitle this latter shape as ‘optimal’. The spectral tails are further reduced compared to the previous case, Fig. 2. For further increase of the MZI delay (e.g., for 1.5xFWHM), a ‘double-pulse’ starts to appear and its parabolic fit is worsened as compared to the previous case, Fig. 2.

Fig. 1. (a) Examples of the temporal coherent synthesis concept. Here, dashed lines are time-delayed replicas of a transform-limited input pulse, and the solid lines are the synthesized waveform intensity (b) Pulse shaping device with two LPFG-based fiber interferometer: principle of coherent superposition of the core and cladding modes.

Fig. 2. Pulse shapes that can be synthesized with the used device (solid lines) from a 1.5-ps FWHM sech² pulse (violet) together with their parabolic fits (dashed). Black: parabolic pulse (relative inter-pulse delay = 0.8xFWHM), red: flat-top pulse (1xFWHM), green: optimal pulse (1.3xFWHM), and blue: double pulse (1.5xFWHM).

3. Theory: pulse propagation in HNLF

It is not straightforward to choose the shape that should give the best results in a nonlinear pulse propagation experiment in terms of its suitability for supercontinuum generation and subsequent pulse compression. For example, the parabolic-like pulse (0.8xFWHM) gives the best parabolic fit at its maximum, but suffers from significant temporal tails that are known to cause wave breaking [9

D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, “Wave-breaking-free pulses in nonlinear-optical fibers,” J. Opt. Soc. Am. B 10, 1185–1190 (1993).

]. The ‘optimal’ shape (around 1.3xFWHM), on the other hand, gives considerably smaller temporal tails, but differs significantly from the parabolic shape at its maximum, Fig. 2. Thus, in what follows, we perform simulations of nonlinear propagation of all possible shapes that can be generated with our device with the aim of finding the optimum input pulse shape. Further, we compare the performance that can be obtained using our device with that achievable using ideal parabolic pulses.

In our analysis, the quality of the pulse compression process was assessed by two main waveform factors: the temporal width of the compressed pulses and the suppression of satellite pulses (i.e. extinction ratio, hereafter ‘ER’, defined as the ratio of peak power amplitudes of the pulse and the most significant satellite pulse). Notice that the main aim of our simulations was to identify the system’s parameters that are required for optimizing the targeted pulse compression operation (i.e. leading to the generation of ~400-fs pulses). To allow direct comparison with the conducted experiments, the repetition rate was fixed to 10 GHz in all our calculations.

Propagation through HNLF was calculated using the generalized nonlinear Schrüdinger equation (GNLSE) [20

C. Finot, G. Millot, C. Billet, and J. M. Dudley, “Experimental generation of parabolic pulses via Raman amplification in optical fiber,” Opt. Express 11, 1547–1552 (2003). [PubMed]

\frac{\partial A (z, t)}{\partial z} + \frac{α}{2} A (z, t) - i \sum_{n = 1}^{\infty} \frac{i^{n} β_{n} \partial^{n}}{n!} \frac{\partial^{n}}{\partial t^{n}} A (z, t) = iγ (1 + \frac{i}{ω_{0}} \frac{\partial}{\partial t}) \times A (z, t) \int_{- \infty}^{\infty} g (t') {∣ A (z, t - t') ∣}^{2} dt'

(1)

where

g (t) = bδ (t) + (1 - b) g_{R} (t) .

(2)

The complex slowly varying envelope of the pulse is A(z,t), α is the attenuation factor (in our simulations, α=0.2 dB/km corresponding to 5×10^-5 m^-1), β_n is the n-th order dispersion, γ is the nonlinear coefficient, ω ₀ is the center frequency of the pulse, and z is the distance along the fiber. The function g(t) takes into account both the Kerr effects – bδ(t) and the Raman effects – (l-b)g_R(t), where b=0.82 gives the proportion between them, δ(t) is the Dirac function, and g_R(t) is the Raman response, which is computed according to:

g_{R} (t) = \frac{τ_{1}^{2} + τ_{2}^{2}}{τ_{1} τ_{2}^{2}} \exp (- \frac{t}{τ_{2}}) \sin (\frac{t}{τ_{1}}),

(3)

where τ₁ =12.2 fs and τ₂ =32 fs [21

K.J. Blow and D. Wood, “Theoretical description of Transient Stimulated Raman Scattering in Optical Fibers,” IEEE J. Quantum. Electron. 25, 2665–2673 (1989).

Theoretical simulations were based on the HNLF parameters obtained from the specifications of the used fiber – Tab. 1. For the linear pulse compression, SMF-28 with the following parameters was used: dispersion of 16.8 ps/(nm-km) (corresponding to -21.4 ps²/km) and dispersion slope of -0.4 – 0.1) ps/(nm²-km) (corresponding to -(0.3–0.62) ps³/km). The dispersion slope stated here was used in the calculations (for each case a different optimal dispersion slope was needed) whereas the dispersion slope in the table is obtained from the SMF-28 parameters.

Tab. 1: Parameters of the used fibers (experiment)

	HNLF	SMF-28
Dispersion @1550 nm (D)	-0.66 ps/(nm-km)	+16.78 ps/(nm-km)
Dispersion slope @1550 nm (S)	0.016 ps/(nm²-km)	0.0089 ps/(nm²-km)
Attenuation (α)	≤0.9 dB/km	0.2 dB/km
Nonlinear coefficient (γ)	11.8 W^-1 km^-1	2.5 W^-1 km^-1
Length (L)	500 m	20–30 m

The results of our theoretical analysis are shown in Fig. 3. The length of the compensating SMF was typically 20 m; the dispersion slope was chosen to provide the best compression performance and was within -(0.2–0.4) ps/(nm²-km) interval. First, we considered an ideal parabolic pulse [9

D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, “Wave-breaking-free pulses in nonlinear-optical fibers,” J. Opt. Soc. Am. B 10, 1185–1190 (1993).

]. We used 3.2-ps FWHM parabolic pulses – this duration was chosen in order to allow for direct comparison with the shaped pulses that can be generated in the experiment. The ER was calculated to be >20 dB for any input power >60 mW, Fig. 3. The duration of the compressed pulse decreased when increasing the input power down to 250 fs for average input power of 150 mW, Fig. 3. Subsequently, we analyzed the set-up in which no pulse shaping would be present, considering 1.5-ps FWHM sech² pulses at the input. The obtained ERs were low – typically <12 dB, Fig. 3, although we were able to get 250-fs pulses at a relatively low average power of 120 mW. For higher input power levels, the output pulse phase characteristics become seriously distorted, which did not allow for efficient pulse compression and thus the minimum pulse width increased, Fig. 3(a). We tested also a 1.5-ps FWHM Gaussian-shaped pulses and found results similar to those obtained with sech² pulses. Finally, we analyzed the set-up in which our pulse shaper provided different values of the MZI delay. The considered MZI delays varied from 0.5xFWHM (slightly broadened input pulse), to 1.5xFWHM (double-pulse). The best ERs were obtained for 1.2–1.3xFWHM MZI delays and were typically 17 dB – Fig. 3. For lower levels of pulse compression (e.g., to obtain 400-fs pulses suitable for 640-Gbit/s transmission), we concluded that 1.2xFWHM was the optimum value, whereas for higher levels of compression, 1.3xFWHM gives the best results in terms of ER, Fig. 3. For pulses synthesized with MZI delays considerably larger or smaller than the ‘optimal’ value (e.g. with 0.8xFWHM), the ER of the compressed pulses approached that obtained when using sech² input pulses. Further we made similar analysis with different parameters of the HNLF (particularly using fiber parameters stated in [6

] with two different nonlinear coefficients of γ=11.8 W^-1km^-1 and γ=19 W^-1km^-1). We have also tested different fiber length (500 m and 1 km). In all these simulations we found that MZI delay of 1.2–1.3xFWHM of the input pulse gives the best performance.

Hence, based on our conducted analysis, the ‘optimal’ pulse shape, among those that can be obtained with the proposed LPFG-based pulse re-shaper, is an almost flat-top shape with a shallow valley at its center. The generality of our deduction was confirmed for analyzing propagation through HNLF with different parameters detailed in the previous paragraph. We further investigated the 1.3xFWHM-generated pulse being the ‘optimal’ pulse shape – a movie that demonstrates the evolution of this ‘optimal’ pulse shape as it propagates along the simulated HNLF for an average input power of 150 mW is shown in Fig. 4(a) (Media 1). The pulse shape changes gradually and after 80 m, it evolves into a signal that is a close approximation of a parabolic pulse – the original shallow dip at its center is gradually filled in and finally approaches the parabolic shape while the tails keep similar to those of the input pulse shape. To allow for more rigorous evaluation, we performed parabolic fits of the pulse waveforms along the length of the HNLF and evaluated the error in terms of the standard deviation (SD) given as:

SD = \sqrt{\frac{\sum_{n = 1}^{2 \times N_{FWHM}} {∣ y (n) - y_{parabolic} (n) ∣}^{2}}{2 \times N_{FWHM}}},

(4)

where n is the pulse envelope sampling, y corresponds to the normalized pulse envelope, y_parabolic is the best-fitted parabolic pulse characteristics (giving the smallest SD), and N_FWHM is the number of the samples within the full width at half maximum of the pulse (we have used 2×N_FWHM in order to include into consideration most of the non-zero samples for a given waveform). We evaluated SD considering different input pulse shapes (synthesized with MZI with delay ranging from 0.8xFWHM to 1.5xFWHM) and different pulses positions along the HNLF fiber. The lowest SD values obtained along the HNLF were as follows: 5.5%, 4.3%, 2.9%, 3.1%, 4.3% for pulses synthesized with 0xFWHM (sech² pulse), 0.8xFWHM, 1xFWHM, 1.3xFWHM, and 1.5xFWHM MZI filter at positions 74 m, 112 m, 136 m, 78 m, and 96 m, respectively. Further, we analyzed the SD along the entire length of the HNLF for different input shapes and found that the average SD was 36%, 31%, 22%, 7%, 10% for pulses synthesized with 0xFWHM (sech² pulse), 0.8xFWHM, 1xFWHM, 1.3xFWHM, and 1.5xFWHM MZI filter, respectively. These results clearly confirm that the best resemblance to the ideal parabolic waveform in terms of SD along the HNLF is achieved when using the anticipated best-performing waveform, i.e. the waveform entitled as ‘optimal’ (using 1.3xFWHM). Thus, we suggest that in our configuration the SD is better predicting the performance (minimum obtained for 1.3xFWHM) than the simple resemblance of the generated pulses to the parabolic shape (best obtained for 0.8xFWHM).

Fig. 3. Comparison of different initial pulse shapes in terms of FWHM time-width (a) and ERs (b) of the compressed pulses as a function of the average power at the HNLF input; black solid – sech² (FWHM=1.5 ps), red dashed – ideal parabolic (FWHM=3.2 ps), green dotted – ‘optimal’ (delay 1.2xFWHM) for 640 Gbit/s systems, blue dash-doted – ‘optimal’ (delay 1.3xFWHM) for maximum compression.

Figure 4 shows the normalized temporal waveforms and corresponding spectral characteristics of the maximum-compressed pulses (FWHM~250 fs) obtained (i) by directly launching the 1.5-ps FWHM sech² pulses from the laser source into the HNLF; (ii) using ‘optimal pulses’ with an MZI delay of 1.3xFWHM (FWHM of the resulting parabolic-like pulse =3.2 ps); and (iii) launching ideal parabolic pulses, each with a FWHM=3.2 ps, at the HNLF input. Here, we can clearly appreciate a significant improvement in terms of the satellite pulses’ suppression when the pulses shaped with our device, instead of standard sech² pulses, are launched at the HNLF input.

Fig. 4. Maximally compressed output temporal pulse waveforms for different input pulse shapes (a) and their corresponding spectra (b); solid – sech², dashed – ideal parabolic (3.2 ps), dotted – ‘optimized’ (delay=1.3xFWHM); temporal evolution along the HNLF and SMF for the ‘optimized’ MZI-synthesized pulse shape – (Media 1) (Fig. 4a).

For completeness, similar data for pulse compression aiming at a source for 640 Gbit/s systems (pulses with duration of ~400 fs), are shown in Fig. 5. Here, an MZI with a relative delay of 1.2xFWHM was considered. In this case, an ER of 17.5 dB was achieved using an HNLF input power of 80 mW.

Fig. 5. Pulses compressed to 400 fs FWHM using LPFG-MZI with 1.2xFWHM delay: (a) temporal and (b) spectral intensity characteristics.

We mentioned that our method is energetically efficient and requires relatively low peak input pulse power. The linear pulse shaping stage has an energetic efficiency (defined as the ratio of the filter output and input pulse powers) of about -1.5 dB [3

, 15

], which compares favorably with the alternative technique based on SSFBG [6

], in which the pulse shaping stage had an energetic efficiency of about -10.5 dB (considering 100% peak reflectivity in the SSFBG and neglecting loss in the circulator). Further, the pulses synthesized here are relatively short (~3 ps), which requires launching considerably lower input pulse energies into the HNLF fiber. In our analysis, 8 pJ pulses were sufficient, while 100 pJ pulses would be needed to trigger similar level of nonlinearities considering ideal 10-ps (FWHM) parabolic pulses (e.g., such as those generated in [6

]). This translates into a total energetic budget improvement of 21 dB with 11-dB lower peak power required at the HNLF input. This may be particularly important when considering operation at high repetition rates. For example, considering a 33 dBm amplifier, which is commercially available today, the pulse energy of 8-pJ that is required in our design, would allow to use signals at repetition rates up to 240 GHz (a 2-W average power at the amplifier output for a signal with a repetition rate of 240 GHz corresponds to an energy of 8 pJ per pulse). However, in the previously published approach [6

], which required at least 100-pJ pulses, it would be possible to reach speeds only up to 20 GHz (2-W average power with a repetition rate of 20 GHz corresponds to energy of 100 pJ per pulse). Additionally, this scheme may also require an additional pre-amplifier to compensate for the high insertion loss of the linear pulse re-shaping stage. This energetic comparison is based on our results compared with those published in [6

] – using different HNLF may influence significantly the obtained results. Our main message here is that our approach avoids the midstep of 10 ps parabolic pulse generation (that cannot be avoided when using currently-fabricable SSFBG) resulting in a better energetic budget.

Each of the generated ultrashort pulses exhibits a broad spectral bandwidth without any deep intensity variation along its spectrum and with a frequency phase profile that has also very low ripples. In fact, the presented results clearly reveal that each of the generated pulses forms a high-quality supercontinuum spectrum that is extremely compact (i.e., it does not exhibit any significant energy ‘leaking’ outside its well-defined broad spectral bandwidth). As follows from Fig. 4b, the generated supercontinuum can be as broad as 2.3 THz (19 nm) FWHM with an intensity ripple <2.2 dB.

4. Experiment

The experimental setup, Fig. 6, consisted of an actively mode-locked laser with a repetition rate of 10 GHz (UOC, Pritel Inc. U.S.A.), an LPFG-based MZI filter, a high-power Erbium doped fiber amplifier (EDFA) with maximum output power of 2 W, a 500-m section of HNLF (OFS Inc., Denmark), an attenuator (attenuation 11 dB) and standard SMF-28 fiber. The laser emitted transform-limited sech²-like pulses of 1.35 ps and 1.5 ps, depending on the intracavity filter used. The attenuator was necessary in order to avoid nonlinearities in the SMF-28 that was used for linear dispersion compensation. The output spectra were acquired with an optical spectrum analyzer (OSA); the output pulse temporal profiles were measured with an autocorrelator. According to the theoretical analysis presented above, an MZI providing a relative delay equivalent to 1.2xFWHM (we recall that FWHM here refers to the FWHM time-width of the input optical pulse) is needed for the experiment for lower level of temporal compression (results in Fig. 5), whereas an MZI delay of 1.3xFWHM is required for the higher level compression experiment (results in Fig. 4). This can be achieved using two MZI filters that provide slightly different delays; alternatively, a single MZI filter excited by two input pulses with slightly different FWHM time-widths can be also used. In our experiment, we used a single MZI filter and two input pulses with slightly different FWHM time-widths (1.35 ps and 1.5 ps). The fabricated LPFG-MZI filter provided a relative delay of 1.2xFWHM for the 1.5-ps input pulse and of 1.3xFWHM for the 1.35-ps input pulse, respectively; this filter consisted of a pair of 8-mm long LPFGs spaced apart by 53 mm inscribed into the SM980 (4.5/125) optical fiber from Fibercore Ltd., U.K. (N.A.=0.16). For the LPFG inscription, we used the point-by-point technique with a CO₂ laser. The LPFG period was 391 μm. The transmission of the fabricated LPFG-based MZI filter is shown in Fig. 7.

Fig. 6. Experimental set-up: the design parameters were LPFG-MZI delay, pulse energy at the HNLF input and the length of the dispersion-compensating SMF-28 fiber.

Fig. 7. Spectral transmission function of the used LPFG-MZI filter (solid, black) and spectral power density of the 1.5-ps input pulse after being filtered by the shown LPFG-MZI (blue, dashed).

The laser wavelength was set to 1547.4 nm, which coincides with one of the transmission maxima of the LPFG-MZI, Fig. 7 (in the middle of the indicated bandwidth). The results of pulse compression using the two given optimized values of the MZI delay (1.2xFWHM and 1.3xFWHM for >400-fs and 260-fs pulse compression, respectively) are shown in Fig. 8. We used average input powers of 100 mW and 160 mW, respectively. The reported temporal widths were calculated from the autocorrelation traces considering sech² temporal shapes. In the first experiment, Fig. 8(a), pulses of 330 fs FWHM, slightly shorter than the theoretical target of ~400 fs, were obtained. In the other experiment, Fig. 8(b), pulses down to 257 fs were obtained. The inset of Fig. 8(b) illustrates how fine tuning in the experiment was performed. Once the length of the dispersion compensating fiber was set (e.g., 24 m), we slightly varied the input power into the HNLF and observed the autocorrelation. For certain level of the input power, the shortest autocorrelation trace was observed. Similar ‘fine tuning’ was observed in the simulations. The level of pulse pedestals and satellite pulses was too low to be evaluated from the autocorrelation trace, which confirms the good quality of the pulse compression process. To further evaluate the pulse quality, we evaluated its time-bandwidth product that was usually close to 0.5 in simulations and close to 0.7–0.8 in experiments. We believe that the poorer results obtained experimentally are mainly due to the absence of the dispersion slope compensation – its precise compensation was considered in the simulations (leading to almost transform-limited pulse waveforms), but no attempt to compensate it was made in the conducted experiments.

Fig. 8. Measured autocorrelation traces of the pulses at the HNLF output (dashed) and after subsequent compression in a 24-m long SMF-28 fiber (solid), considering a 1.5-ps input pulse (a) and a 1.35-ps input pulse (b). Inset: FWHM time-width of the compressed pulses for different HNLF input powers.

Finally, Fig. 9 shows the spectral characteristics of the pulses obtained at the HNLF output when ‘optimized 1.3xFWHM’ and sech² pulses of 160 mW average power are launched at the HNLF input. Comparing these measured results with the theoretical predictions, Fig. 4b, we observe that there is a very good agreement in terms of both the shape and the spectral width. For higher input pulse powers, a sudden break of the supercontinuum occurred indicating that there is an optimum level of the input power which provides the broadest possible flat supercontinuum energy spectrum without any ‘breaks’. The same phenomenon was also observed in the simulations. The measured LPFG-MZI-generated supercontinuum energy spectrum, Fig. 9, has ~1.5 dB amplitude ripple across its flat part and has a FWHM of over 20 nm with 86% of its energy concentrated within the FWHM bandwidth. As expected from the theoretical analysis, a high energy confinement in the flat supercontinuum bandwidth without any wave-breaking sidelobes was experimentally observed. This compares favorably to sech²-generated supercontinuum, Fig. 9, which has only 61% of its energy within the FWHM spectral bandwidth and exhibits ample sidelobes that are generally responsible for the wave breaking phenomenon.

The generated supercontinuum was very stable. We measured its spectral characteristics repeatably during 10 minutes and there was no observable change in the spectral characteristics within the measurement accuracy of the OSA – the observed maximum deviation was always below 0.05 dB.

Fig. 9. Measured spectral characteristics of the signal at the HNLF output considering 1.5-ps FWHM sech² input pulses (blue, dashed) and considering ‘optimized’ shaped input pulses (solid, black). Average power level at the HNLF input is 160 mW.

5. Conclusion

We performed a detailed theoretical and experimental analysis of a novel highly energetically efficient pulse compression technique. It is based on a low-loss linear pre-shaping of picosecond-scale pulses generated from a high repetition rate laser and their subsequent propagation through a HNLF. The used pre-shaping device is based on an LPFG filter that has inherently large bandwidth. Consequently, the synthesized pre-shaped pulses can be relatively short (e.g. 3.2 ps FWHM in the experiments reported here), requiring only a moderate average power at the HNLF input (e.g. <160 mW for a 10-GHz signal) to trigger the desired nonlinear interactions.

Detailed numerical simulations of the pulse propagation in a nonlinear dispersive optical fiber were performed with the aim of optimizing the system parameters and the ‘initial pulse shape to be synthesized, targeting the generation of a broad flat supercontinuum at the HNLF output. We have demonstrated that the use of our LPFG-based pulse re-shaping device translates into a significant improvement in the pedestal and satellite pulse suppression in the output compressed pulses, i.e. from -11 dB for sech² input pulses to -17 dB for parabolic-like input optical pulses obtained by re-shaping the sech² original pulses with our LPFG filtering device. Using ideal parabolic-shaped pulses, this number would be further improved to -20 dB. Starting from 1.3-ps FWHM sech² input pulses, we experimentally generated 3.2-ps FWHM parabolic-like pulses that were subsequently compressed using HNLF propagation and linear dispersion compensation in a SMF-28 fiber down to 257 fs (FWHM) with negligible pedestals and satellite pulses. These high-quality ultrashort pulses may be of interest for a wide range of applications, including ultrafast linear pulse shaping. We also investigated the possibility of generating pulses better suited for 640-GHz clock rate systems. To obtain 330-fs pulses, we needed only 100 mW at the HNLF input. Due to the relatively low required input power, this technique may be used for high repetition rate sources; to give an example, for pulse compression at a repetition rate of 160 GHz, the required average power at the HNLF input would be about 1.6 W, which is readily achievable with available EDFAs. The generated pulses are not only interesting for their temporal features (high-repetition-rate ultrashort pulses) but they should also prove useful for a wide range of applications requiring a wide-band supercontinuum energy spectrum, such as optical coherence tomography, spectral-slicing WDM sources etc. In our experiment, we obtained a 20-nm wide supercontinuum that has almost a square-like spectral profile with power ripple <1.5 dB and 86% of its energy concentrated within the FWHM spectral bandwidth.

Acknowledgment

We would like to acknowledge Prof. Martin Rochette from McGill University in Montreal for lending us the amplifier booster. We also thank Dr. Francesca Parmigiani from University of Southampton for her help with the theoretical analysis. This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Czech Science Foundation (contract no. GA102/07/0999).

References and links

1.	L. K. Oxenlowe, R. Slavík, M. Galili, H. C. H. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gb/s timing jitter-tolerant data processing using a long-period fiber-grating-based flat-top pulse shaper,” IEEE J. Sel. Top. in Quantum Electron. 14, 566–572 (2008).
2.	F. Parmigiani, M. Ibsen, T. T. Ng, L. Provost, P. Petropoulos, and D. J. Richardson, “An efficient wavelength converter exploiting a grating based saw-tooth pulse shaper,” Photon. Technol. Lett. 20, 1461–1463 (2008).
3.	R. Slavík, Y. Park, and J. Azaña, “Long period fiber grating-based filter for generation of picosecond and sub-picosecond transform-limited flat-top pulses,” Photon. Technol. Lett. 20, 806–808 (2008).
4.	A. M. Wiener, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable femtosecond pulse shaping by use of amultielement liquid-crystal phase modulator,” Opt. Lett. 15, 326–328 (1990).
5.	K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, “Flexible pulse waveform generation using silica-waveguide-based spectrum synthesis circuit,” Electron. Lett. 40, 537–538 (2004).
6.	F. Parmigiani, C. Finot, K. Mukasa, M. Ibsen, M. A. F. Roelens, P. Petropoulos, and D. J. Richardson, “Ultra-flat SPM-broadened spectra in a highly nonlinear fiber using parabolic pulses formed in a fiber Bragg grating,” Opt. Express 14, 7617–7622 (2006). [PubMed]
7.	F. Parmigiani, T. T. Ng, M. Ibsen, P. Petropoulos, and D. J. Richardson, “Timing jitter tolerant OTDM demultiplexing using a saw-tooth pulse shaper,” presented at ECOC, Brussels, Belgium, 2008.
8.	A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Optical frequency conversion, pulse compression and signal copying using triangular pulses,” presented at ECOC, Brussels, Belgium, 2008, Paper Mo.3.F.4.
9.	D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, “Wave-breaking-free pulses in nonlinear-optical fibers,” J. Opt. Soc. Am. B 10, 1185–1190 (1993).
10.	M. Nakazawa, E. Yoshida, H. Kubota, and Y. Kimura, “Generation of a 170 fs, 10 GHz transform-limited pulse train at 1.55 μm using a dispersion-decreasing, erbium-doped active soliton compressor,” Electron. Lett. 30, 2038–2039 (1994).
11.	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. Lett. 15, 15824–15835 (2007).
12.	L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. 8, 289–291 (1983). [PubMed]
13.	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. 85, 6010–6013 (2003).
14.	Y. Park, M. H. Asghari, T.-J. Ahn, and J. Azaña, “Transform-limited picosecond pulse shaping based on coherence synthesization,” Opt. Express 15, 9584–9599 (2007). [PubMed]
15.	R. Slavík, Y. Park, T. -J. Ahn, and J. Azaña, “Synthesis of picosecond parabolic pulses formed by a long period fiber grating structure and its application for flat-top supercontinuum generation,” presented at OFC/NFOEC, San Diego, CA, 2008, Paper OTuB4.
16.	A. I. Latkin, S. Boscolo, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber,” presented at OFC/NFOEC, San Diego, CA, 2008, Paper OTuB7.
17.	Y. Takushima and K. Kikuchi, “10-GHz, over 20-Channel Multiwavelength Pulse Source by Slicing Super-Continuum Spectrum Generated in Normal-Dispersion Fiber,” Photon. Technol. Lett. . 11, 322 (1999).
18.	I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001).
19.	D. D. David, T. K. Gaylord, E. N. Glytsis, and S. C. Mettler, “CO2 laser-induced long-period fibre gratings: spectral characteristics, cladding modes and polarization independence,” Electron. Lett. 34, 1416–1417 (1998).
20.	C. Finot, G. Millot, C. Billet, and J. M. Dudley, “Experimental generation of parabolic pulses via Raman amplification in optical fiber,” Opt. Express 11, 1547–1552 (2003). [PubMed]
21.	K.J. Blow and D. Wood, “Theoretical description of Transient Stimulated Raman Scattering in Optical Fibers,” IEEE J. Quantum. Electron. 25, 2665–2673 (1989).
22.	N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-order optical differentiators,” Opt. Commun. 230, 115–129 (2004).

OCIS Codes
(320.5520) Ultrafast optics : Pulse compression
(320.5540) Ultrafast optics : Pulse shaping
(350.2770) Other areas of optics : Gratings
(320.6629) Ultrafast optics : Supercontinuum generation

ToC Category:
Ultrafast Fiber Lasers

History
Original Manuscript: February 19, 2009
Revised Manuscript: April 2, 2009
Manuscript Accepted: April 4, 2009
Published: April 14, 2009

Citation
David Krcmarík, Radan Slavík, Yongwoo Park, and José Azaña, "Nonlinear pulse compression of picosecond parabolic-like pulses synthesized with a long period fiber grating filter," Opt. Express 17, 7074-7087 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7074

Sort: Author | Year | Journal | Reset

References

L. K. Oxenlowe, R. Slavík, M. Galili, H. C. H. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, "640 Gb/s timing jitter-tolerant data processing using a long-period fiber-grating-based flat-top pulse shaper," IEEE J. Sel. Top. in Quantum Electron. 14, 566-572 (2008).
F. Parmigiani, M. Ibsen, T. T. Ng, L. Provost, P. Petropoulos, and D. J. Richardson, "An efficient wavelength converter exploiting a grating based saw-tooth pulse shaper," Photon. Technol. Lett. 20, 1461-1463 (2008).
R. Slavík, Y. Park, and J. Azaña, "Long period fiber grating-based filter for generation of picosecond and sub-picosecond transform-limited flat-top pulses," Photon. Technol. Lett. 20, 806-808 (2008).
A. M. Wiener, D. E. Leaird, J. S. Patel, and J. R. Wullert, "Programmable femtosecond pulse shaping by use of amultielement liquid-crystal phase modulator," Opt. Lett. 15, 326-328 (1990).
K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, "Flexible pulse waveform generation using silica-waveguide-based spectrum synthesis circuit," Electron. Lett. 40, 537-538 (2004).
F. Parmigiani, C. Finot, K. Mukasa, M. Ibsen, M. A. F. Roelens, P. Petropoulos, and D. J. Richardson, "Ultra-flat SPM-broadened spectra in a highly nonlinear fiber using parabolic pulses formed in a fiber Bragg grating," Opt. Express 14, 7617-7622 (2006). [PubMed]
F. Parmigiani, T. T. Ng, M. Ibsen, P. Petropoulos, and D. J. Richardson, "Timing jitter tolerant OTDM demultiplexing using a saw-tooth pulse shaper," presented at ECOC, Brussels, Belgium, 2008.
A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, "Optical frequency conversion, pulse compression and signal copying using triangular pulses," presented at ECOC, Brussels, Belgium, 2008, Paper Mo.3.F.4.
D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, "Wave-breaking-free pulses in nonlinear-optical fibers," J. Opt. Soc. Am. B 10, 1185-1190 (1993).
M. Nakazawa, E. Yoshida, H. Kubota, and Y. Kimura, "Generation of a 170 fs, 10 GHz transform-limited pulse train at 1.55 ?m using a dispersion-decreasing, erbium-doped active soliton compressor," Electron. Lett. 30, 2038-2039 (1994).
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. Lett. 15, 15824-15835 (2007).
L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, "Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers," Opt. Lett. 8, 289-291 (1983). [PubMed]
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. 85, 6010-6013 (2003).
Y. Park, M. H. Asghari, T. -J. Ahn, and J. Azaña, "Transform-limited picosecond pulse shaping based on coherence synthesization," Opt. Express 15, 9584-9599 (2007). [PubMed]
R. Slavík, Y. Park, T. -J. Ahn, and J. Azaña, "Synthesis of picosecond parabolic pulses formed by a long period fiber grating structure and its application for flat-top supercontinuum generation," presented at OFC/NFOEC, San Diego, CA, 2008, Paper OTuB4.
A. I. Latkin, S. Boscolo, and S. K. Turitsyn, "Passive nonlinear pulse shaping in normally dispersive fiber," presented at OFC/NFOEC, San Diego, CA, 2008, Paper OTuB7.
Y. Takushima, and K. Kikuchi, "10-GHz, over 20-Channel Multiwavelength Pulse Source by Slicing Super-Continuum Spectrum Generated in Normal-Dispersion Fiber," Photon. Technol. Lett. 11, 322 (1999).
I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, "Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber," Opt. Lett. 26, 608-610 (2001).
D. D. David, T. K. Gaylord, E. N. Glytsis, and S. C. Mettler, "CO2 laser-induced long-period fibre gratings: spectral characteristics, cladding modes and polarization independence," Electron. Lett. 34, 1416-1417 (1998).
C. Finot, G. Millot, C. Billet, and J. M. Dudley, "Experimental generation of parabolic pulses via Raman amplification in optical fiber," Opt. Express 11, 1547-1552 (2003). [PubMed]
K. J. Blow and D. Wood, "Theoretical description of Transient Stimulated Raman Scattering in Optical Fibers," IEEE J. Quantum. Electron. 25, 2665-2673 (1989).
N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, "A new theoretical basis of higher-order optical differentiators," Opt. Commun. 230, 115-129 (2004).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Click here to see a list of articles that cite this paper