Spatially dispersive scheme for transmission and synthesis of femtosecond pulses through a multicore fiber

A new scheme is presented for fiber transmission of ultrashort laser pulses. A dispersive device divides the input pulses into spatially separated spectral components which are individually launched in the different channels of a multicore fiber before being recombined at the output by a second dispersive device. The parallel transmission of narrow spectral bands avoids self-phase modulation and could be appropriate to deliver high peak power pulses. Phase management of the spectral bands by an active element offers recovery of the seed pulse duration at the fiber output as well as pulse shaping capabilities. Both are reported in a proof of concept experiment using 190 fs input pulses and a 5 cores polarization maintaining fiber. Extension of the concept to femtosecond pulses amplification is suggested. ©2012 Optical Society of America OCIS codes: (060.2360) Fiber optics links and subsystems; (060.4005) Microstructured fibers; (320.7140) Ultrafast processes in fibers; (320.5540) Pulse shaping. References and links 1. A. M. Larson and A. T. Yeh, “Delivery of sub-10-fs pulses for nonlinear optical microscopy by polarizationmaintaining single mode optical fiber,” Opt. Express 16(19), 14723–14730 (2008). 2. D. G. Ouzounov, K. D. Moll, M. A. Foster, W. R. Zipfel, W. W. Webb, and A. L. Gaeta, “Delivery of nanojoule femtosecond pulses through large-core microstructured fibers,” Opt. Lett. 27(17), 1513–1515 (2002). 3. T. Le, G. Tempea, Z. Cheng, M. Hofer, and A. Stingl, “Routes to fiber delivery of ultra-short laser pulses in the 25 fs regime,” Opt. Express 17(3), 1240–1247 (2009). 4. S. Ramachandran, M. F. Yan, J. Jasapara, P. Wisk, S. Ghalmi, E. Monberg, and F. V. Dimarcello, “High energy (nJ) femtosecond pulse delivery with record dispersion high order mode fiber,” Opt. Lett. 30(23), 3225–3227 (2005). 5. W. Göbel, A. Nimmerjahn, and F. Helmchen, “Distortion-free delivery of nanoJoule femtosecond pulses from a Ti:sapphire laser through a hollow-core photonic crystal fiber,” Opt. Lett. 29(11), 1285–1287 (2004). 6. S. W. Clark, F. O. Ilday, and F. W. Wise, “Fiber delivery of femtosecond pulses from a Ti:sapphire laser,” Opt. Lett. 26(17), 1320–1322 (2001). 7. M. Lelek, E. Suran, F. Louradour, A. Barthelemy, B. Viellerobe, and F. Lacombe, “Coherent femtosecond pulse shaping for the optimization of a non-linear micro-endoscope,” Opt. Express 15(16), 10154–10162 (2007). 8. F. Luan, J. C. Knight, P. Russell, S. Campbell, D. Xiao, D. T. Reid, B. J. Mangan, D. P. Williams, and P. J. Roberts, “Femtosecond soliton pulse delivery at 800nm wavelength in hollow-core photonic bandgap fibers,” Opt. Express 12(5), 835–840 (2004). 9. P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. S. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107(20), 203901 (2011). 10. F. Weise, G. Achazi, and A. Lindinger, “Parametrically polarization shaped pulses via hollow core photonic crystal fiber,” Phys. Rev. A 82(5), 053827 (2010). 11. B. J. Mangan, A. C. Muir, and J. C. Knight, “Photonic bandgap fiber with multiple hollow cores,” J. Lightwave Technol. 28(9), 1287–1290 (2010). #175641 $15.00 USD Received 6 Sep 2012; revised 5 Oct 2012; accepted 9 Oct 2012; published 15 Oct 2012 (C) 2012 OSA 22 October 2012 / Vol. 20, No. 22 / OPTICS EXPRESS 24769 12. I. Hartl, A. Marcinkevicius, H. A. McKay, L. Dong, and M. E. Fermann, “Coherent beam combination using multicore leakage channel fibers,” in Advanced Solid-State Photonics, Technical Digest Series (Optical Society of America, 2009), paper TuA6. 13. J. Lhermite, E. Suran, V. Kermène, F. Louradour, A. Desfarges-Berthelemot, and A. Barthélémy, “Coherent combining of 49 laser beams from a multiple core optical fiber by a spatial light modulator,” Opt. Express 18(5), 4783–4789 (2010). 14. I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008). 15. T. Eidam, S. Hanf, E. Seise, T. V. Andersen, Th. Gabler, Ch. Wirth, Th. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35(2), 94–96 (2010). 16. S. Zhou, F. W. Wise, and D. G. Ouzounov, “Divided-pulse amplification of ultrashort pulses,” Opt. Lett. 32(7), 871–873 (2007). 17. Patent pending # WO 2012042141 (A1) FR 2964503 (A1) Procédé et dispositif d’amplification d’un signal optique. 18. I. P. Christov, “Amplification of femtosecond pulses in a spatially dispersive scheme,” Opt. Lett. 17(10), 742– 744 (1992). 19. W.-Z. Chang, T. Zhou, L. A. Siiman, and A. Galvanauskas, “Femtosecond pulse coherent combining and spectral synthesis using four parallel chirped pulse fiber amplifiers”, in Advanced Solid-State Photonics, Technical Digest Series (Optical Society of America, 2011), paper AM4a.25.


Introduction
It is often required for powerful ultrashort laser pulses in the near infrared to be delivered through a flexible optical waveguide.Different kinds of optical fibers and various set-ups have been successfully implemented for that purpose [1][2][3][4][5][6][7][8].All systems work by means of a proper management of both large chromatic dispersion and nonlinearity of the waveguide which distort the guided pulses.Femtosecond pulse propagation through single mode optical waveguide is well known and governed by a generalized nonlinear Schrodinger equation accounting for chromatic dispersion and nonlinear effects.Among the solutions for fiber delivery of near infrared femtosecond pulses, the more complete ones achieve compensation of both dispersion and self phase modulation (Kerr effect) through time and spectral compression [6,7] or through soliton propagation [8].The most encountered schemes however preserve a linear propagation regime.In that cases the effect of nonlinearity are minimized by stretching the initial pulse like in chirp pulse amplification [1], or by the use of specific waveguide such as large mode area fiber [2,3], high dispersion fiber [4], hollow core photonic crystal fiber (HC-PCF) [5], etc.For broadband pulses, limitations come from the compensation of the high orders of the dispersion and from self-phase modulation still occurring at very high peak powers even in air filled HC-PCF.Ultimately, Raman selffrequency shift [8], gas ionization losses [9] or self-focusing may fix the maximum power that can be transmitted.The delivery systems are usually set to provide a short laser pulse as close as possible (sometimes shorter) to that delivered by the laser.For the transmission of pulses with a tailored and reconfigurable shape an additional modulator is needed [10], based for example on a liquid crystal spatial light modulator in 4-f dispersive arrangement with a grating pair.
We propose here a new configuration which combines fiber transmission and shaping capabilities for short pulses.The initial pulse spectrum is split in few spectral bands which are subsequently transmitted in separate channels of a multicore fiber (MF) before being coherently recombined at the output.Owing to the active phase control, the synthesized pulse at the exit can be almost similar to the input pulse or can be shaped.The approach may enhance the delivered power by approximately the square of the fiber channels number and it can be adapted to various spectral ranges.The scheme is likewise appropriate for fiber amplification of ultrashort laser pulse at high average power.
In a proof-of-principle experiment we demonstrated spatially dispersed transmission of a 190 fs pulse at 1030 nm through a five cores microstructured fiber and recovery of the seed pulse after optimization of the spectral phase by a deformable mirror.Simple pulse shaping was also demonstrated.

Spatially dispersive concept for transmission of femtosecond pulses through a multicore fiber
The principle of the pulse delivery system is schematically depicted on Fig. 1.As mentioned above, the design starts by a spatial dispersion of the laser spectrum.It can be performed by various means, for example by a chain of dichroic mirrors or simply by a grating spectroscope.The spectral resolution must be of the order of R = N.ν 0 /Δν, N denoting the number of fiber cores to be used for waveguiding, Δν being the laser full spectral bandwidth, and ν 0 the central frequency.The spatially dispersed spectrum is imaged on the fiber input face so that different frequency bands are then coupled to different channels of the multicore fiber.Depending on the channel, the input signal corresponds to a pulse with a different carrier wavelength, possibly with a different amplitude and phase.Neighboring guides carry fields whose carrier frequency differs by +/− (Δν/N).The duration δτ' of the fields split in the MF's cores depends on the initial pulse duration, on the number of spectral channels as well as on the dispersive device resolution.Considering a Fourier Transform laser pulse with a secant hyperbolic profile, characterized by its full width at half maximum in intensity (FWHM) duration δτ and spectral width δυ (δυ.δτ = 0.32), δτ' would be of the order of N.δτ (it was assumed that the spectrum full width is about twice the FWHM and that the resolution was fixed so that the split spectra did not overlap).A phase modulator inserted between the dispersive device and the fiber can modify the phase of the different fields before they are launched into the fiber waveguides.The MF cores must be uncoupled to preserve the fields in their spatial transverse distribution until the fiber exit.Regarding the MF it can be made of standard solid core waveguides or hollow core waveguides like the fiber reported in [11].The individual waveguides must be single mode and polarization maintaining in the best situation.On the output side, a second dispersive device is needed to recombine the different wavelengths in a single beam.A symmetric version of the input dispersive device is the simplest example of an appropriate set-up.A spectroscope, with the fiber core array placed in the spectral plane and where light coming from the MF travels back through the device, would merge the different spectral components in a single beam.The temporal structure of the synthesized pulse then results from the coherent sum of the individual fields and depends on their respective delay and phase.Differences of delay between components are unlikely to vary according to environmental perturbation on the contrary to their phase.Assuming that differential delays are weak or can be compensated, the control of the phase by the modulator should permit to restore the initial laser pulse or to synthesize a shaped pulse.This is the task devoted to a servo loop which commands the modulator from the signal delivered by an autocorrelator.The advantage of a MF is that since the different cores are close to each other and share the same environment, differential perturbations of the optical path length should be weak and slow.That was demonstrated by Hartl et al. [12] with more than one day of phase stability on a 4.5 m long piece of MF without control.Requirement on active phasing for coherent combining and pulse synthesis are therefore strongly relaxed.Finally it can be expected that the group velocity among the core of the array only weakly differs so that, because they all have a common physical length, the time delay can be rather close for each channel.
In fiber delivery of short pulses the characteristic parameters of the guided propagation are usually the dispersive length L D and the nonlinear length L NL .They are defined by the well known relationships L D = −2πc δτ 2 /(λ 2 .D) and L NL = A eff .λ/(2πn 2 P) where λ denotes the central wavelength, D the dispersion, δτ the pulse width, A eff the guided mode effective area, n 2 the Kerr nonlinear refractive index and P the peak power.By comparison with single core fibers, the use of a MF with N cores together with spatial dispersion gives a scaling of L D by approximately a N 2 coefficient (the pulse duration being multiplied by ~N as explained above).Therefore, in most cases, the length L MF of the delivery MF will be shorter than L D so that it is the ratio between L MF and L NL which matters here.Since the total effective area and the pulse duration in each core are both multiplied by ~N in the case of the MF, the peak power of light coupled in the individual waveguides is at the same time a small fraction (~1/ N 2 ) of that of the input laser pulse, so that the impact of nonlinearity is significantly reduced on a propagation distance L MF .
We have carried out a proof of concept experiment which is reported below.

Proof of concept experiment
The MF used in our experiment (Fig. 2) was a microstructured fiber, fabricated by stack and draw technology at IRCICA.The fiber has 19 cores, five of which were actually used here, but fibers with up to 49 cores have been fabricated [13].The fiber cores surrounded by air holes (black holes on Fig. 2) are single mode at the operating wavelength of 1032 nm.The fiber includes Boron-doped rods (dark grey holes on Fig. 2) on opposite side of the cores which through internal stresses make the silica core polarization preserving.The measured birefringence was 1.3 10 −4 .The guided mode diameter was 14.7 microns and the pitch between cores was 47 microns.The outer diameter of the MF was 350 microns.The dispersion was measured to be −34 ps/km.nm.The source was a Mikan Yb:KGW laser from Amplitude Systèmes delivering pulses with a 7 nm bandwidth (FWHM) at a central wavelength of 1032 nm.For spatial dispersion of the laser spectrum we used here a standard grating which displayed the frequency components on a deformable mirror (DM, phase modulator on Fig. 1) located in the focal plane of a positive lens.The DM is one of the possible ways to modify the optical phase by electronic control of the actuators.It gave a 13 π modulation range at 1032 nm and the actuation speed was as fast as 100µs.The spectrum reflected by the DM was imaged by a couple of lenses on the entrance face of the multicore fiber (MF).A microlens array optimized the coupling efficiency in the MF cores.Resolution of the dispersive set-up was adjusted to fit the geometrical characteristics of the fiber so that the laser spectrum was broken down in five spectral bands.Each band had a width of about 2.65 nm (FWHM) with some overlap with its neighbors.Polarization of the laser field was linear and was oriented so as to coincide with one birefringence axis of the fiber cores.The MF was about one meter long and was laid hanging almost straight between the two opposite fiber holders.Figure 3(a) compares the initial laser spectrum 7 nm wide with the five spectra measured at the different outputs of the core array.The superposition of spectra collected and guided by the 5 cores was as wide as the seed pulse spectrum with their peak amplitude fitting its envelope.The modulated output spectrum slightly departs from the initial hyperbolic secant squared shape.The modulation is due to the spectrum sampling and to coupling with the Gaussian mode of each fiber cores.This was in agreement with the expectations of the design, indicating that the spatial dispersion and coupling worked properly on the input side.Autocorrelation traces of signal delivered by the individual guides were nearly similar in shape and duration (~930 fs).One example is given in Fig. 3(b) for comparison with the trace of the laser pulse.The broadening of the pulse autocorrelation peak from 290 fs to 930 fs was mainly due to the filtering of a ~2.6 nm spectral band in the laser spectrum (780 fs) and the complementary contribution came from group velocity dispersion (150 fs).On the output side, a second dispersive device built around a second grating recombined the five spectral bands in a single beam.The transmitted radiation was then characterized with a spectrum analyzer and with a background free second harmonic generation autocorrelator.
Initially, the DM was set flat.It was therefore unlikely that the optical phases accumulated by the different frequencies after transmission through the fiber were identical.Indeed the autocorrelation trace of the field synthesized by the spectral recombination was smooth but broader (490 fs) than the one of the laser pulse.By adjustment of the DM surface, piston phase-shift were introduced on the different wavelength bands to maximize the pulse peak intensity detected with a two photon photodiode (TPA-PD).For optimization, we followed the approach of Vellekoop and Mosk used for focusing beam through scattering media [14].Starting from one side band we tuned the phase of the neighboring band to get the maximum signal from the TPA photodiode.Then we proceed in the same way with the next band, and the followings until the fifth band.Additional round of phase adjustments using the same process improved further the reference parameter.With the servo loop switch on, the synthesized pulse was short and close to the laser pulse.The corresponding autocorrelation trace, shown on Fig. 3(c), was close to that of the seed pulse, except very low side lobes, with a width of 390 fs FWHM.Assuming a secant hyperbolic shape for the pulses, the recovered pulse duration (251 fs) was only increased by ~60 fs with respect to the laser pulse.The experimental data are in perfect agreement with computations based on simulations of the laser pulse spectral splitting, followed by linear propagation through the fiber with five identical cores and then spectral recombination.An optimization routine based on the Vellekoop approach has been included in the model for identification of the theoretical phase lags which lead to the synthesized pulse with the highest intensity.The recorded spectrum associated with the shortest recombined pulse was found in perfect agreement with the expectations derived from modeling of the set-up (see Fig. 3(d)).The theoretical residual spectral phase after optimization is also plot on the same graph.
After optimization, the settings can be kept fixed (open feedback loop) and, without any special precautions to get rid of environmental perturbations, the pulse quality deduced from autocorrelation trace remained extremely stable.Touching the MF and even holding it with the hands did not alter the system operation and did not require modification of the DM command to keep the reconstructed pulse short.This was a clear demonstration of the benefit due to the multicore waveguide.Change in the recovered pulse was only significant when MF experienced high mechanical stress like the one introduced by bending.
Despite the time delay difference between the cores due to different central wavelengths and despite the second order dispersion inside each of these spectral bands, coherent spectral combining permitted to restore a pulse nearly as short as the seed pulse.The slight remaining difference was mainly due to group velocity deviations between cores of slightly different opto-geometric parameters and also to laser spectrum reshaping.The chromatic differential delays can be roughly compensated by simply bending a part of the fiber which introduces a stretching of the outer waveguide of the MF and a compression of the inner waveguide.An additional fine tuning can be performed through a twist in the bent part.This is what we demonstrated by using a longer piece of fiber of 1.5 m.In the initial state, with the DM disconnected, we recorded the long autocorrelation trace (nearly 2 ps) shown in Fig. 4. Then the servo loop was activated.While looking to the autocorrelation trace we played with the twist to get the shortest pulses.A typical result is reported on Fig. 4 where the autocorrelation width is 327 fs, a value closer to the laser pulse autocorrelation than the previous measurement with a straight fiber of shorter length.The corresponding pulse should be of 210 fs duration, only 10% far from the initial laser pulse.Simulation led to the trace shown in blue on Fig. 4 with a good agreement with the experimental data except for the side bands of lower intensity.Residual differential time delays between the five components amounting to 1/3 of the value for a straight fiber has been accounted for in the computations.A full compensation gave only few femtosecond supplementary reduction in autocorrelation width.With the current set-up, the delivered pulses were limited by the laser available power to 3.8 kW peak power.The system made up with off-the-shelves components (apart from the MF) had a weak overall transmission of 11.3%.Most of the laser power was lost before entering the fiber because of relay imaging lenses, lens array and folding mirrors which were not optimized.Light coupling in the multicore structure was the main source of additional losses, with an efficiency limited to 35%.Improved performance may be reached simply by the use of components with adapted coatings.

Synthesis of shaped pulses
An additional capability of the scheme is pulse shaping.By an appropriate choice of phases introduced by the DM, we demonstrated first the synthesis of twin pulses.We followed the same procedure as for getting the shortest recombined pulse except that phase adjustments are chosen in order to maximize the intensity of one of the autocorrelation secondary peaks (side lobes).The resulting experimental autocorrelation trace is shown on Fig. 5(a) and corresponds to a couple of almost identical pulses of 245 fs duration separated by 880 fs.The corresponding spectrum was obviously modified with respect to the previous situation and a typical recording is given in Fig. 5(b).Again the measurements are in perfect agreement with the theoretical predictions derived from the model.Taking the DM settings for the shortest pulse case as a reference, it was possible to derive the phase profile experimentally introduced to get the double pulse.The values agree with the one provided by the simulation as indicated in Fig. 5(b).As another example, we adjusted phase distribution to profile a nearly square shaped pulse by looking for a triangular autocorrelation trace.The result is given in Fig. 5(c) where the experimental trace is actually triangular and very close to the one obtained by theoretical optimization.Similarly to the previous case, the data on the spectral band phase settings, as well as the pulse spectrum shape, are in very good agreement with the simulations.

Conclusion
To conclude, we have proposed a spatially dispersive stretcher-free scheme for fiber delivery of ultrashort laser pulses by means of a multicore fiber.In view of a proof of concept demonstration, a 190 fs laser pulse at 1032 nm has been split in five spectral components which were separately transmitted in different cores of a passive MF before being recombined coherently.The synthesized pulse at the system output had duration very close to the laser input, once the phase of the different spectral bands has been adjusted by a servo-controlled deformable mirror.Experimental data were in good agreement with results derived from a numerical study.It was demonstrated that, for a given layout of the multicore fiber, the system is extremely robust with respect to environmental perturbations so that stable operation was maintained for several hours with the servo disconnected.The difference in group velocity between the fields of different carrier wavelengths has been compensated by opto-geometric effects through proper bending of the MF.The performances reported are directly related to the experimental configuration.The capability of the set-up to restore, without additional device, a pulse similar in duration to the input pulse is directly connected to the fiber characteristics (length, group velocity dispersion (GVD), uniformity), to the laser bandwidth and to the number of spectral bands.However, as a general rule, to preserve a good quality and a short duration for the transmitted pulse, the phase variation due to GVD within each spectral band must be kept well below 2π.That constraint comes from the fact that the reconstructed spectral phase must be as much as possible flat to get the shortest pulse.Phase adjustment being managed only by differential effects between the different spectral channels, phase distortions inside the elementary spectral channel cannot be rectified and must be kept weak.Simulations indicate that by using the whole array of 19 cores of our MF, the reconstructed pulse would be of ~270 fs duration after 3 meters propagation, without compensation of chromatic dispersion in group delay.In such a case the power threshold for the onset of nonlinear effects would be comparable to that of a single core delivery fiber with pre-chirping and post compression with a stretching ratio of ~360.In order to fully exploit the 2D array of cores of most multicore fibers, a 2D display of the laser spectrum must be performed.That can be achieved with a device including two gratings with tilted orientation and appropriate dispersive properties.The approach investigated for pulse transmission is also well suited to femtosecond amplification in fibers.In that case the MF must be doped with rare earth ion and diode pumped.In order to make a source of ultrashort broadband pulses at high average power with fiber technology, the most studied design is based on chirped pulse amplification (CPA) with a chain of fiber amplifiers of optimized features [15].Several alternative approaches have been investigated, that aim at performance scaling of ultrafast lasers in particular pulse energy.One of them consisted in pulse division (time multiplexing) keeping a standard amplifier [16] before recombination.It was recently proposed to split the spectrum of pulses from a master oscillator in few spectral bands for their power amplification in separate fibers followed by their coherent recombination at the output [17].The advantage of the scheme is that spectral gain narrowing can be mitigated by an adapted amplification of the isolated frequency bands.It is the discrete version of the concept of spatially dispersed amplification initially studied by Christov for dye amplifiers [18] and further exploited with solid-state regenerative amplifiers.A demonstration with four Yb fiber amplifiers was recently reported by Galvanauskas with 480 fs pulses at 1050 nm [19].We suggest here a new version of the concept based on the use of a multicore fiber amplifier for a more compact and more robust implementation.Fabrication of an ytterbium doped MF is envisaged in the future to demonstrate the potential of the set-up in amplifying conditions.

Fig. 2 .
Fig. 2. Polarization preserving microstructured multicore fiber.Only the 5 cores encircled were used in the experiment.Black parts represent air, grey parts are in silica, dark grey parts represent Boron doped rods as detailed in inset.

Fig. 3 .
Fig. 3. Experimental spectra (left part) and autocorrelation traces (right part).Top right (a), the spectrum split in five bands fills in the envelope of the initial laser spectrum.In (b) the autocorrelation of the initial laser pulse (290 fs width) is compared to that of pulses in an isolated frequency band (width 930 fs).Figure (c), bottom right, reports the autocorrelation trace of the pulse recovered after transmission through the multicore fiber and coherent superposition of the five spectral components (width 390 fs).The associated spectrum is shown in Figure (d), bottom left.Experimental data in (c) and (d) (empty circles) are in good agreement with simulations (blue traces in continuous and dashed lines).
Fig. 3. Experimental spectra (left part) and autocorrelation traces (right part).Top right (a), the spectrum split in five bands fills in the envelope of the initial laser spectrum.In (b) the autocorrelation of the initial laser pulse (290 fs width) is compared to that of pulses in an isolated frequency band (width 930 fs).Figure (c), bottom right, reports the autocorrelation trace of the pulse recovered after transmission through the multicore fiber and coherent superposition of the five spectral components (width 390 fs).The associated spectrum is shown in Figure (d), bottom left.Experimental data in (c) and (d) (empty circles) are in good agreement with simulations (blue traces in continuous and dashed lines).

Fig. 4 .
Fig. 4. (a) Autocorrelation trace of the output pulse without servo (filled red circle).Trace recorded with phase control (empty red circle) after partial compensation of the differential time delay between the five carrier wavelengths through fiber bending.The width decreased from nearly 2 ps to 327 fs with a 90 fs reduction due to differential time delay compensation.Simulation of the recovered pulse autocorrelation (blue line), assuming compensation of 2/3 of group delay differences, agrees with the observation.(b) Experimental spectrum (empty red circle) corresponding to the autocorrelation trace shown in Fig. 4-a.Theoretical spectral intensity (blue line) and phase (blue dotted line) derived from simulation are given for comparison

Fig. 5 .
Fig. 5. Autocorrelation traces (left (a) and (c)) of synthesized pulses shaped in a pulse doublet (a) or with a nearly top hat profile (c).The corresponding spectra ((b) connected with case (a) and (d) with case (c)) together with the phase adjustments in the five spectral bands are shown on the right part.Experimental data (empty circles) are in good agreement with simulations (blue traces in continuous and dashed lines).