1. Introduction

In order to make a source of ultrashort broadband pulses at high average power with fiber technology, the most encountered design is based on chirped pulse amplification (CPA) with cascaded fiber amplifiers of optimized parameters. Limpert et al. obtained up to 830 W of average power with pulses of 680 fs duration after compression [1]. Performance scaling of ultrafast lasers, in terms of pulse energy or peak power, has been widely investigated based on various approaches. For example, pulse time division keeping a single amplifier [2], has been shown to offer a 2^N enhancement in nonlinear power threshold, where N stands for the number of pulse splitters. A 1 MW peak power was demonstrated with 2.2 ps pulses in a stretcher free Yb doped fiber amplifier with 5 pulse splitters [3]. In another technique, pulse coherent combining was implemented through spatial division with a parallel set of amplifiers associated to an active phase control [4]. With two large mode area fiber CPA, pulses of 3 mJ and ~500 fs duration were obtained after compression leading to a 6 MW peak power [5]. Recently, spatial division in a passive co-phasing scheme was combined with time division to get ultrashort pulses of 50 fs duration and up to 52 MW peak power in a stretcher free fiber amplifier [6]. It was also suggested to combine spatial and spectral division in such a way that the pulse is split in spectral bands, which are subsequently amplified in separate fiber amplifiers, before being coherently recombined at the output [7]. It is the discrete version of the initial concept proposed by I. P. Christov [8] of spatially dispersed amplification which was exploited with dye and solid-state amplifiers. A demonstration with three Yb-doped fiber amplifiers was recently reported by W-Z Chang et al. where the concept is combined with CPA to get 400 fs pulses at 1059 nm [9]. The advantage of the design is that spectral narrowing from the gain can be avoided, so that amplification of ultra-broadband pulses can be readily achieved on the complete bandwidth of the rare-earth ions. It is even possible to imagine the use of different fiber amplifiers to cover a wider band. It must be noticed that, even without prior pulse stretching, spatially dispersed concept with N amplification arms leads to decrease by roughly ~N² the peak power of the pulse seeding each channel. Linear amplification is thus preserved for higher delivered powers.

This paper proposes a new version of the technique which is based on the use of a multicore fiber amplifier instead of separate fiber amplifiers. This amplifying scheme is thought to be more compact and less demanding in terms of servo control because of its intrinsic robustness. It was previously implemented with a passive five-core fiber in view of fiber delivery of high peak power pulses [10]. For amplification, a specialty multicore fiber was designed and fabricated with an array of 12 ytterbium doped cores. Despite the compactness of the amplifying scheme, we preserved independently tunable gains. We used gain tunability, associated with phase control of the 12 channels of spectrally dispersed amplification, to achieve spectral coherent combination and amplified pulse synthesis in a proof-of-principle experiment.

2. Multicore fiber with a linear array of ytterbium doped waveguides

The motivation for combining spatially dispersive amplification and multicore fiber (MF) are three-fold. First of all, a MF is extremely compact while providing a possibly large amplifying section. The fiber used in the present experiments has 15 cores (see Fig. 1), of which twelve were actually used. Secondly, since the different cores are close to each other and undergo the same thermal, acoustical and mechanical perturbations, deviation in the optical path length difference because of the environment is weak and slow by comparison with separate individual fibers. Hartl et al. [11] reported more than one day of phase stability on a 4.5 m long piece of MF without servo control. Therefore it seems possible to achieve phase control for coherent combining and pulse synthesis from time to time only, once or twice per day in some cases, without a permanent feedback loop. Thirdly, the different waveguides of the MF have a common physical length so that it is reasonable to expect that time delays are close for each channel in a short fiber piece. A seven core fiber has been already applied to amplification of 110 fs pulses but, in that case, the structure exhibited coupled cores so that it was used as a specific large mode area waveguide fed by a standard Gaussian laser beam [12].

 

Fig. 1 Ytterbium doped multicore fiber. Cores appear as white spots and silica cladding in grey. The fiber was fabricated by stack and draw technique.

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On the contrary, in the experiments below, the waveguides were not coupled so that each spectral band could be separately amplified. The MF (Fig. 1) was a microstructured fiber, fabricated by stack and draw technology at IRCICA. The fiber cores (white spots on Fig. 1) were single mode at the average wavelength of 1028 nm. The guided mode diameter was 5 µm and the pitch between cores was 24 µm. The outer diameter of the MF was 500 µm. Ytterbium doping was estimated to be 0.75% wt leading to ~5 dB absorption per centimeter at 976 nm. The fiber was specifically designed and fabricated for a proof of concept experiment with core pumping. It was not suited to high power amplification but fiber design and fabrication can be adapted for actual high level amplification. In the following experiments, only twelve cores were exploited because of the availability of pump diodes.

3. Spatially dispersive amplification of femtosecond pulses with a multicore fiber: experimental set-up

The experimental arrangement is schematically depicted on Fig. 2. The source was a Mikan Yb:KGW laser from Amplitude Systemes delivering pulses with a 5 nm bandwidth (full width at half maximum in intensity – FWHMI) at a central wavelength of 1028 nm and a 54 MHz repetition rate. The set-up consisted first in a spatial dispersion of the laser spectrum. In [9] it was based on dichroic mirrors. Here we used a standard blazed grating (G, 600 g/mm) spectroscope which displayed the frequency components on a deformable mirror (DM), located in the focal plane of a positive lens. The DM tailored the spectral phase profile through position dependent piston phase-shifts, by electronic control of the mirror surface. It gave access to phase modulation higher than 5π at 1028 nm. The spectrum reflected by the DM was imaged with a telescope on a micro-lens array (MLA). Microlenses served to help light coupling into the cores of the amplifying fiber. The MLA component we used was not perfectly suited to the fiber parameters and we measured a global coupling efficiency of 20%. Resolution of the dispersive set-up was adjusted to fit the geometrical characteristics of the fiber (design rules for a proper use of the MF can be found in [10]) and the laser spectrum was divided in twelve spectral bands. Each band had a width of about 0.85 nm (FWHMI) with some significant overlap with its neighbors. Indeed the separation in central wavelength between the different lines was ~0.92 nm. The pump system consisted in twelve fiber coupled laser diodes, spliced to a fiber bundle, which formed a linear array of pump beams. At the exit of the fiber bundle, the pump beamlets were collimated by a microlens array of 250 µm pitch. A telescope adapted the period of the pump pattern to that of the fiber core array. The pump and signal fields were combined by a dichroic mirror and both were launched into the fiber through the same lens array. The MF was about one meter long and was laid hanging almost straight between the two opposite fiber holders. In each core it was possible to get a ~30 dB small signal gain. On the output side, a second grating spectroscope recombined in a single beam the amplified fields of different color exiting from the twelve fiber cores. The amplified output beam was then characterized with a spectrum analyzer and with a background free second harmonic generation autocorrelator.

 

Fig. 2 Schematic drawing depicting the setup. The pulse from the laser oscillator (O_Sc) is dispersed by a grating (G). The pulse spectrum is displayed on the deformable mirror (DM) for phase profiling and then imaged on the microlens array (MLA) for coupling in the multicore fiber amplifier (MF). On the fiber opposite side, the exit fields are collimated by a microlens array (MLA) and then combined in a common direction by a spectroscope (lens L + grating G) to form the output beam. Pump radiations are combined with the laser field through the dichroic mirror D_C.

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Figure 3(a) compares the 5 nm wide (FWHMI) initial laser spectrum with the twelve spectra measured one by one at the amplifier output. The pump power settings were chosen here to provide a good transmission and a uniform amplification of the whole components.

 

Fig. 3 Experimental spectra (a) and autocorrelation traces (b). (a) The spectrum split in twelve bands fills in the envelope of the initial laser spectrum. (b) The autocorrelation of the initial laser pulse (228 fs duration FWHMI) is compared to that of pulses in an isolated frequency band (~1.8 ps duration FWHMI).

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Autocorrelation traces of the signal delivered by the individual guides were nearly similar in shape and duration (~2.6 ps autocorrelation width, 1.8 ps pulse duration FWHMI). One example is given in Fig. 3(b) for comparison with the trace of the laser pulse of 350 fs width (228 fs pulse duration FWHMI with a sech² profile). The broadening of the pulse autocorrelation peak is roughly consistent with the filtering of a spectral line of 0.85 nm bandwidth.

4. Coherent spectral synthesis of the amplified pulse

In the initial stage, the DM was set flat and the optical phase after transmission through the fiber was randomly distributed among the different frequencies. This was due partly to imperfections in the set-up and also to the fiber. Indeed despite the length of the waveguides can be considered as identical in the array, this is not the case of the propagation constants. Deviations significantly smaller than 10⁻⁶ m⁻¹ in absolute value would have been required, which is not achievable in practice. Chromatic dispersion introduced additional alterations of the phase distribution in the array. The autocorrelation trace of the field synthesized by the spectral recombination in this initial stage was modulated and broad (~4 ps) (see Fig. 4).

 

Fig. 4 Autocorrelation trace of the synthesized pulse at the 12 channel amplifier output before (red line) and after (green line) adjustments of gains and pre-compensation of the spectral phase to get the shortest pulse.

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Our first goal was to synthesize a short intense pulse. At the beginning we played on the pump power. Adjustment of the amplifier pump levels was made to maximize the signal delivered by a two-photon photodiode which probed the synthesized pulse peak intensity. Optimization of the gain of the different spectral components was made one by one, beginning with central lines. Tuning the individual pump power of each core had two impacts. One was the standard change of the gain and consequently of the output pulse intensity. The second one was a change of the amplified field phase. Pump induced phase-shifts in fiber amplifiers were already exploited for active coherent combining of laser in MOPA configuration [13]. One can think that, with proper design, spectral coherent combining could also be achievable with phase modulation solely controlled by the pump lasers. Because in our experiments we had an extra degree of freedom on the phase disconnected from the amplitude settings, the above mentioned procedure was then repeated to adjust the DM surface. The input spectral phase profile was tailored to pre-compensate for phase deviations between the different wavelength bands due to propagation in the MF. One round of adjustment was performed, according to the approach of Vellekoop and Mosk [14], with some improvements after one or two additional rounds using the same process. After optimization of the phase compensation we measured a synthesized pulse almost as short as the laser pulse. The corresponding autocorrelation trace, shown on Fig. 4, was close (width 384 fs) to that of the seed pulse (width 350 fs), except very low side lobes (~6% of the normalized peak) separated by 3.5 ps. The latter are signature of weak satellite pulses connected with the modulation and sampling period of the spectrum. Satellite pulses came from second order interferences in the individual pulse superimposition, which happened in the pedestal of the recombined signal. Separation in time from the main peak is given by the inverse of the frequency separation between the individual pulses. Assuming a secant hyperbolic shape for the pulses, the recovered pulse duration (250 fs FWHMI) was only increased by 10% with respect to the laser pulse. Our second goal was to push the stretcher-free amplifier to its maximum performances in linear regime. On each amplifying channel, we raised the pump power up to the point where self phase modulation (SPM) started to broaden the spectra, separately observed at the output.

In that case, the recombined signal output power reached 370 mW. The corresponding gain amounted to 12 dB for a total coupled pump power of 460 mW. Thereafter, pump settings were kept fixed. The phases were adjusted by only playing with the DM in view of synthesizing the shortest pulse. The recorded autocorrelation trace and the spectrum of the combined field are shown on Fig. 5. The synthesized pulse had 280 fs duration FWHMI (430 fs autocorrelation width x 0.65), only broadened by 50 fs with respect to the oscillator pulse. Based on the recorded spectrum and assuming that the synthesized pulse was Fourier transform, we computed the expected pulse profile and its autocorrelation which is plot on Fig. 5(b). The simulated trace is very close to the measured trace except for the weak side lobes. In order to quantify the advantage provided by the fibered dispersive amplification and for reference, we measured the output signal that can be obtained from a single channel amplifier whilst preserving a linear amplification regime. The seed pulse with its complete spectrum (228 fs duration FWHMI) was launched into one core of the MF. We increased the pump power while looking at the output spectrum. Spectral broadening due to Kerr nonlinearity started to be noticeable at the fiber amplifier exit for a delivered signal power of only 4 mW. The pulse duration was lengthened by chromatic dispersion to about 280 fs FWHMI. It means that, for the fixed experimental parameters of our experiments, i.e. the laser pulse duration, the doped fiber length and mode area, it would be difficult to get more than 4 mW average power without the onset of SPM. Under the same requirement, spectrally divided amplification scheme provided up to 370 mW, delivering 92 times more available power. The value is not much far from the rough estimate of a 12² gain, as previously indicated in the introduction. The spatial division in 12 channels, offering a guided mode area 12 times bigger than a single core, only partly explained the benefit of the technique.

 

Fig. 5 (a) Spectrum of the 12 recombined channels when the fiber amplifier was operated just below the threshold for nonlinear spectral broadening. (b) autocorrelation (blue) of the corresponding synthesized pulse after pre-compensation of the spectral phase to get the shortest output pulse. Autocorrelation trace of the oscillator is given for reference (black). Autocorrelation trace of the pulse computed by Fourier transform of the recorded spectrum assuming a constant spectral phase is plot for comparison (open red circle).

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Once adjusted for a short pulse synthesis, the amplifier was run for hours in an unprotected environment without feedback servo. The two-photon signal from the photodiode which served for settings was recorded during 5 hours. The data show (see Fig. 6) that there were no abrupt changes on that period, and that a smooth decrease of the delivered peak power was observed on the diode voltage. Since the measurement is proportional to the square of the pulse peak power, the nearly 10% drop should indicate a decrease of the pulse peak power of just 5%. On a 120 s time scale, fluctuations were reduced to within 1%. This was a clear demonstration of the benefit due to the multicore waveguide.

 

Fig. 6 Recording of the signal from a two-photon photodiode which is proportional to the square of the synthesized pulse peak power. The multicore fiber amplifier was run without servo in an unprotected environment.

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5. Pulse amplification and shaping

An additional capability of the scheme is pulse shaping, with two degrees of freedom on the intensity and phase distributions of the amplified spectral components. We demonstrated the synthesis of twin pulses by playing on the spectral gain, by varying the pump power of the different channels, and by an appropriate choice of phases introduced by the DM. At the beginning, the coherent combining and the gain settings were chosen to recover a short pulse at the amplifier output. Then we switched off one power supply out of two, in the set of pump diodes (row numbers 2, 4, 6, 8, 10 and 12). Consequently the output combined spectrum was periodically modulated according to wavelength (period ~2 nm) because six spectral components were missing. Regarding the phase, we followed the same procedure as previously and then added a π offset in one spectral channel out of two. That modulation was made in order to alternate positive and negative amplitudes in the wavelength comb which was required for the synthesis of a couple of pulses. The resulting experimental autocorrelation trace is shown on Fig. 7(a) and corresponds to the expected twin pulses, each of 290 fs duration FWHMI separated by 1.75 ps. Parasitic satellite pulses gave extra peaks in the autocorrelation indicating that the shaping was not perfect. However the measured trace was pretty close to the simulated trace derived from the recorded spectrum given in Fig. 7(b). The recovered pulse train is shown in the inset of Fig. 7(a). The peak power of the unwanted side pulses corresponded to 15% of the main pulses.

 

Fig. 7 (a) Autocorrelation trace after spectral shaping and optimization of phases to synthesize twin pulses at the amplifier output. A theoretical trace computed from the recorded spectrum is given for comparison. The corresponding pulse sequence is shown in inset. (b) Combined beam spectrum recorded at the amplifier output when half of the pump diodes of the multicore amplifier were switched off.

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6. Conclusion and discussion

To conclude, we have investigated experimentally the use of a multicore fiber for the implementation of spatially dispersive stretcher-free amplification of ultrashort laser pulses. In view of a preliminary demonstration, a 228 fs laser pulse at 1028 nm was split in twelve spectral components, which were separately amplified in twelve cores of an Yb-doped MF, before being coherently recombined. The synthesized pulse at the system output had duration very close to the laser input (within 10 to 25%), once the amplitude and phase of the different spectral bands were optimized. It is the first time, to our best knowledge, that spectrally divided amplification has been implemented with multicore fiber and also with so many spectral elements. Spectral synthesis of an amplified pulse almost as short as the seed pulse has been reported as well as amplified pulse shaping. The experiments clearly demonstrated that the amplified power before the onset of nonlinear effects was raised by almost two orders of magnitude (actual coefficient x 92), thanks to the 12-tone amplification scheme. It was checked that the multicore fiber is extremely robust with respect to environmental perturbations so that stable coherent combining was maintained for several hours without servo. It was shown also that the scheme offers the capability of shaping the amplified pulse, by tailoring the spectral gain and spectral phase profiles. Knowing that the ultimate theoretical peak power limit, set by self-focusing in short pulse fiber amplifier, is about 4 MW [15], if we assume that a fiber amplifier with 12-large area cores can be operated close to this power level in the studied scheme, then coherent spectral combining could lead theoretically to a pulse with more than 0.5 GW peak power. That performance would be a breakthrough in stretcher free fiber amplification of femtosecond pulses.

Grating based beam combiners, as we have used, are sometimes considered as non ideal for spectral combining because of residual chirp in the delivered beam. A spatial chirp was not expected in the combined beam near field in the reported configuration. The spectrum envelope was measured and checked to be identical in the whole cross-section of the combined beam. A chirp could appear in the beam wave-vector spectrum, due here to the spectral width of the individual output fields from the different cores of the fiber. In the present situation, the spectrum in each waveguide was limited to less than 1 nm bandwidth. After the diffraction grating combiner, the divergence (angular spreading) of the output beam coming from the finite beam size and the one due to the channel spectral width were calculated to be of close value. It can be reduced further by changing the resolution of the input grating splitter so that the different spectra shrink and no longer overlap at the exit. Spatially dispersive amplification with a multicore doped fiber can be implemented also with a set of dichroic mirrors for spatial splitting of the spectral components. The stretcher free spectral division scheme represents an alternative to CPA fiber system with the advantage of avoiding spectral narrowing, but the proposed architecture can be improved and combined with CPA. Indeed, the simplified version of the scheme investigated here can be combined with stretchers at the input of the channels and compressor on the exit side for a better extraction of energy, as it was discussed by W-Z. Chang et al [9]. It is often difficult with rare earth doped fiber amplifiers to optimize the gain on a very broad bandwidth with the choice of parameters available for a standard fiber. The spatially dispersive principle opens the opportunity to adapt the amplifier features separately to the different spectral bands, in view of the amplification of an ultrawide bandwidth for the generation of intense ultrashort fields. This can be implemented with multiple separate fiber amplifiers, as well as with multicore fibers, by using different kinds of rare earth ion doping or with different doping levels or co-dopants.