A compact multicore ytterbium doped fiber amplifier has been implemented according to the spectral division scheme. It was shown that it allows amplification of pulses with about 40 nm wide spectrum. Compensation of the different spectral bands delay through bending and twist of the multicore ribbon fiber followed by appropriate setting of their phase permitted the synthesis of pulses close to 100 fs duration.
© 2015 Optical Society of America
Femtosecond pulses are now utilized for a great variety of applications spanning from the industry to the scientific research and covering the biomedical fields as well. For a cost-effective use, the most part of these applications needs pulses of high energy at high repetition rate. These features are covered by solid-sate technology with ytterbium doped slab and thin-disc approaches and by fiber technology with specialty microstructured fibers in the last amplification stages. Concerning fiber laser chains, various designs of large mode area fibers and various methods were proposed to circumvent the limitations introduced by nonlinear effects which distort the amplified fields and may damage the fiber itself through beam self-focusing. For instance, pulse stretching permitted to realize a chirped pulse amplifier system (CPA) which delivered 12 MW pulses of 640 femtoseconds duration at hundreds watts average power . The concept of divided pulse amplification (DPA) is another example which was proposed to scale the pulse energy of a single amplifier (or a linear amplification chain) . Splitting of the input pulse in delayed replicas mitigate self-phase modulation whilst preserving good energy extraction. This temporal multiplexing technique combined with CPA has led to 1 GW pulses in a double-pass scheme for passive coherent recombination . Up to 2.9 GW of peak power and 1.25 mJ pulses at 1030 nm have been obtained at 30 kHz with larger delays by use of an active loop for pulses coherent summation . In addition to nonlinear effects, fiber laser chains are also impaired by thermal effects and transverse mode instability on one hand and by spectral gain narrowing on another hand. For all the above reasons and because there exists a few applications related to particle generation or acceleration with even more demanding performances than what is currently available, coherent beam combining of femtosecond pulses started to be investigated in the past years, following the trends of continuous wave lasers. Spatially separated amplification brings new flexibility regarding management of nonlinearity, management of heat removal as well management of gain saturation and bandwidth. Schemes for beam coherent combining are mostly based on a master oscillator power amplifier (MOPA) system with a set of parallel amplifiers seeded by the division of the oscillator output. Recovery of a single beam at the amplifier outputs was achieved by coherent summation on polarizing beam splitters  or on standard beam splitters in so called filed aperture arrangement [6,7] or just after far field diffraction in the tiled aperture configuration . The servo used for a stable and efficient combining were based on standard techniques such as Hänsch-Couillaud or LOCSET (Locking of Optical Coherence by Single-detector Electronic-frequency Tagging) or SPGD (Stochastic Parallel Gradient Descent) methods. A record breaking performance of 22 GW peak power (5.7 mJ) was demonstrated with the coherent combination of pulses from four parallel CPA fiber amplifiers . Finally, passive coherent combining was also reported which was based on the chaining of fiber amplifiers in Sagnac interferometer loop . 3.1 GW pulses of 300 fs duration at 50 kHz where obtained in a fully passive system thanks to the association of the DPA concept and of the Sagnac arrangement .
It must be emphasized at that point that powerful femtosecond laser chains based on Yb doped fibers were limited in bandwidth and hence in pulse brevity by gain spectral narrowing (GSN). GSN results from the non-uniform gain across the bandwidth to amplify. It leads to a reshaping and a compression of the pulse spectrum each time a strong amplification is required. Because usually the laser pulse is strongly chirped for power amplification in fibers, self-phase modulation due to the silica nonlinearity does not mitigate the spectral narrowing. In the published data, the spectral bandwidth of the amplified radiations was measured to be approximately of 10 nm for a 10-20 dB gain . To overcome that limitation which impacts the affordable peak power, one has adapted to fibers the concept of spatially dispersed amplification exploited for femtosecond solid state amplifiers [12,13]. The proposed scheme consists in splitting the femtosecond oscillator output spectrum into different spectral bands which are then routed to separate amplification arms. At the exit, the different channels are recombined in a single beam and their relative phases adjusted by a servo for coherent synthesis of an amplified ultrashort pulse and for recovery of the initial pulse profile and duration. Validation of the technique has been made with separate parallel fiber amplifiers (up to 4 bands) [14,15] as well as with multicore fiber amplifier (up to 12 bands)  and at high average power with two separate channels only . The total amplified fields had a bandwidth of 7nm, 9 nm and 19 nm respectively for the synthesis of pulses of 356 fs, 280 fs and 130 fs. In the present paper, we report a new advance in the field where we achieved amplification over a ~40 nm bandwidth in a 12 channels multicore ytterbium doped fiber together with delay compensation in the active fiber itself. Management of the differential group delay and phase lead to the synthesis of an ultrashort pulse close to 100 fs duration.
2. Experimental set-up
The experimental set-up started with a femtosecond Yb:KGW oscillator delivering 250 fs pulses at 54 MHz repetition rate. The spectrum of the laser centered at 1028 nm is first broadened by launching the pulse train into a short piece (10 cm) of polarization maintaining single mode fiber (PM-980XP). Self-phase modulation occurring during propagation in the optical fiber gave rise to an almost tenfold spectral broadening so that 50 nm wide pulses were available to seed the amplification stage [Fig. 1]. According to the amplifier architecture under investigation, the pulses must then be split in different spectral parts. One option would be to use a cascade of dichroic mirrors with sliding long pass wavelengths. That could be made compact with the fabrication of just two specialty dichroic mirrors with non-uniform coatings . For a more flexible arrangement, we chose to use a spectroscopic device well suited to the use of a multicore ribbon fiber amplifier [Fig. 2]. The laser beam was here spatially dispersed by a diffraction grating (G1) with 300 grooves/mm and 90% diffraction efficiency. The signal spectrum was displayed by the lens (L1) on a MEMS deformable mirror (DM, Boston Micromachines Multi-DM) for further control of the spectral phase. The spectrum was then re-imaged with demagnification by the telescope L2-L3 on an array of microlenses for coupling into the twelve active waveguides of an ytterbium doped multicore fiber. So the input pulses were split in twelve spectral channels regularly separated by 3.8 nm and of ~3 nm bandwidth (FWHM) each, for separate amplification in the fiber. The heart of our amplifier was a specially designed optical fiber which was fabricated at IRCICA (Lille, France). It consisted in a linear array of 15 single mode ytterbium doped cores, only twelve of them were used in practice. The distance of 30 microns between neighboring cores was sufficient to get rid of coupling whilst ensuring a high compactness. In addition, it fitted the pitch of the microlens array. The amplifying waveguides were designed for core pumping (absorption of ~500 dB/m at 976 nm) in order to allow for individual adjustment of the gain of each spectral component through tailoring of the different pump powers. Coupling of the twelve pump laser diode radiations into the fiber cores was performed through a dichroic mirror (DiM) using the same microlens array as the signal fields. A linear array of pumpbeams was prepared upstream thanks to another microlens array combined with a fiber bundle whose inputs were spliced to fibered laser diodes. The amplifying fiber was 1.2 m long and it was possible to obtain up to 30 dB gain in each of the twelve channels.
In view of making pulse synthesis at the exit by recombining the spectral parts in a single beam, one had to manage both phase and group delay of the different channels. Chromatic group velocity dispersion is the main contribution to differential time delays. Slight inhomogeneity in effective refractive index among the guides of the array introduced additional delay differences. The latter were measured by spectral interferometry giving an almost linear distribution of the differential time delay across the linear core array. Although this was not intentional it can be explained by the fabrication process. Indeed the 12 Yb doped cores were drawn from the same MCVD preform and the conventional solution doping was used to incorporate the Yb ions (as well as Al). This was done vertically leading to a gradient in Yb and Al concentration and so to a small refractive index gradient along the preform. Stacking the twelve Yb rods in the order of drawing has led then to a quasi linear distribution of differential time delays between the cores. The measured values were summed up with the theoretical values of the GVD (−37 ps/km.nm) connected with the distribution of wavelengths among the cores. The resulting delays decreased almost linearly from core #1 (1009 nm) to core #12 (1052 nm) in steps of ~360 fs from one core to the next. It was therefore mandatoryto compensate for the differential group velocities in order to synthesize a pulse as short as possible with good efficiency. That was achieved in the fiber itself by bending and twist. We coiled the multicore fiber so as to make a loop in a plane perpendicular to the linear array of cores [Fig. 3]. The two opposite ends of the fiber were kept tightly fixed by their holders. It is straightforward to show that if the guide array stays perpendicular to the bending plan all along the fiber then the geometry of the arrangement does not change the time delay between the guides. On the contrary if the fiber loop is now tilted, whilst the fiber ends remains fixed, a twist is added. By consequence a time delay deviation appears which scales linearly with the distance from the fiber center. The optical path length change follows to first order a simple law:Figure 4 shows the experimental data with time shifts of up to +/− 5 ps. The measurements confirmed the expected linear variation of delay across the array whatever the tilt angle.
After considering the tuning of delays we can describe the exit side of the spectral division amplifier. The multicore fiber output was collimated by a microlens array before being sent for spectral combining in a second grating spectroscope. This second device was almost identical to the first one but used in opposite direction. So the 12 carrier wavelengths, exiting from the 12 cores of the array, shined the grating with the proper angles of incidence so as to be diffracted in a common direction thus forming a single amplified beam. A background free SHG autocorrelator and a two photon photodiode served for adjustment of the spectral bands delay and phase.
3. Results and discussion
The experiments started by adjustment of the coupling of the broadened laser spectrum in the core array as well as simultaneously the coupling of the pump beam array. The matching between the pitch of the core array with that of the microlenses as well as with that of the pump array was not perfect and an optimized coupling in all the cores was not achievable for the same setting. That obliged to balance the coupling in the 12 cores at the expense of a decrease of the overall coupling efficiency (~50% for the pump waves, ~20% for the signal). On the output side, we measured separately the spectra exiting from the different waveguides of the amplifier. The superposition of these normalized spectra is given in Fig. 5. The choice of the parameter of the input dispersive device (resolution of the spectroscope compared with spacing between spectral channels) gave an overlap of the individual spectral components. That situation was preferred in order to reduce the spectral modulation in the recombined spectrum so that the synthesized signal exhibits weak satellite pulses.
As a starting point, we measured the autocorrelation trace of the combined output to serve as a reference. The trace was about 2.6 ps wide (FWHM). Then, we play with the orientation of the multicore fiber loop looking for a shrinkage of the autocorrelation trace related to the matching of the time delays. Once an optimum was found, we tuned the phase of the spectral components to shorten the synthesized pulse. As a metric of the pulse duration, and of the corresponding peak power, we used the photo-current ITPP delivered by a two photon photodiode. We proceeded manually by changing the phase of one spectral band at a time through the command of the DM surface. Following the iterative continuous process of Vellekoop and Mosk for phase optimization  we changed the phase of the channel under concern until a maximum was reached for ITPP. Then, we successively adjusted the phase of another channel in the same way. We started from a central spectral component and continued with components of both sides. Several (2 to 4) rounds of phase setting on the 12 bands were necessary to reach what we estimated to be the shortest synthesized pulse. In parallel to the measurement of the photodiode current, the evolution of the autocorrelation trace permitted to follow also the change in pulse profile. There was no need for a real time servo control optimization of the phase values because the single fiber structure made thermal and mechanical perturbations very uniform on all the cores. Consequently, the phase relationships between the fields were extremely stable (over hours) even in a non-protected environment. To give a picture of the setting process, we made numerical modeling of the complete set-up including the measured parameters of the multicore fiber. The SHG-FROG traces of the computed synthesized pulses at the amplifier output are given in Fig. 6 below.
They correspond to the different steps followed in practice to get the highest peak power pulses. Figure 6(a) represents the initial situation with strong group delay mismatch between the spectral components. Through a progressive tilt of the fiber loop the mismatch was reduced and the time-frequency distribution of energy got more compact [Figs. 6(b) and 6(c)]. Then, the following traces [Figs. 6(d)-6(g)] depict the impact of the progressive setting of the phase (zero order) of the elementary bands for synthesis of the shortest pulses. As expected the profile got compressed along the time axis and got bell shaped and smoothed along the spectral dimension. In practice, after the optimization process, we recorded the power spectrum given in Fig. 7(a) and we measured the autocorrelation trace shown on Fig. 7(b) (blue line) which is plot together with the trace recorded in the initial situation (purple line) for comparison. There was a reduction in the width by a coefficient 15 of the autocorrelationthat shrank down to 168 fs (FWHM). Assuming that the main pulse of the synthesized field be of Gaussian shape, we derived a pulse duration of 119 fs (FWHMI). That value is very close to the one (102 fs) deduced from the modeling of the whole set-up. We computed the Fourier Transform (FT) pulse one could expect from the spectrum of Fig. 7(a) in case the spectral phase be perfectly flat. Its autocorrelation is plot in red dotted line on Fig. 7(b) for reference. The FT pulse duration of 70 fs is shorter than the one derived from the synthesized pulse measurement. The reason could be the non-uniform phase in the broad input spectrum, or the residual uncompensated delays. But the stronger impact comes from the residual uncompensated high orders of the spectral phase (second order and above - ~2 rad in the present case) within each channel. In these experiments the average output power was only of ~100 mW limited by the onset of nonlinear effects and not by the available pump power. It was connected with the stretcher free configuration leading to pulses of about 500 fs in duration at the input of each fiber core together with the small area of the guided mode (5.1 µm Mean Field Diameter). Although the multicore Yb-doped fiber was not polarization maintaining, its birefringence had a weak impact on the system performance. The linear state of polarization of the input signals was almost preserved for all the channels after propagation on the short fiber (1.2 m). It did not change when the fiber loop, about 22 cm in diameter, was tilted for delay compensation. In our laboratory environment without temperature regulation, the amplifier being installed on an optical table without damping system, the stability of the output pulses was good. The autocorrelation trace and average power did not evolve when letting the amplifier in operation for more than an hour. Because the different amplifying channels shared the same mechanical and thermal environment in the multicore fiber, the differential time delays and even the differential phase-shifts were extremely robust with respect to external perturbations. This property has been already highlighted  and for watt class multicore amplifiers the relative phase noise density at low frequency was measured to be three orders of magnitude below the one of separate amplifiers. A similar multicore fiber amplifier based on spatially dispersion concept has shown to give a 5% drop in the synthesized pulse peak power after 5 hours operation .
We have performed experiments supported by simulations proving that pulses of nearly 40 nm bandwidth can be amplified in Ytterbium doped fibers thanks to the spectral division architecture. The input pulse spectrum was split in twelve bands which were separately amplified in the cores of a multicore ribbon Yb-doped fiber. The twelve components were recombined in a single beam for the synthesis of an amplified pulse. Compensation of the differential group delay between the amplifying channels was achieved and tuned by tilting a loop of the multicore gain fiber itself. A deformable mirror was used for zero order phase adjustment. With the implemented spectral division set up, we demonstrated the synthesis of pulses close to 100 fs duration in a ‘conventional compressor’ free configuration. The use of a multicore fiber relaxes the requirements related to an active control of the phase relationships. The reported experiments were even carried out without a servo. A 40 nm bandwidth is not a real limit since the gain of Yb-doped silica fiber is larger. The limits in synthesized pulse brevity seem to be rather connected with the compensation of group delay that could be achieved in practice and to the un-compensated second-order spectral phase in the individual spectral bands. One solution could come from a division of the spectrum in a larger number of channels. Another option could be the association of a spectral combiner with a compressor. In that case, synthesis of pulses as short as 70 fs (based on our modeling) should be reachable with the current set-up. The Yb-doped ribbon multicore fiber used here in the experiments offered limited performances because of the cores’ small area and because of the lack of a double cladding. Large mode area multicore Yb-doped microstructured fibers have been already fabricated and used to mitigate mode instability . They could be appropriate for scaling of the concept to high performances in terms of power and energy. In double clad structures where the pump power is shared by all the amplifying cores, tailoring of the spatial gain profile to fight against GSN could be achieved through a non-uniform rare-earth doping among the gain array.
The authors acknowledge the financial support of Agence Nationale de la Recherche through the MultiFemto project (ANR 2011 BS09 028 01). The authors thank A. Lerouge and K. Delplace for their contributions to the multicore fiber fabrication as well as D. Labat for his help on the fiber characterization. G. Bouwmans and L. Bigot acknowledge the financial support of Labex CEMPI (ANR-11-LABX-0007)and Equipex FLUX (ANR-11-EQPX-0017).
References and links
1. T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35(2), 94–96 (2010). [CrossRef] [PubMed]
3. Y. Zaouter, F. Guichard, L. Daniault, M. Hanna, F. Morin, C. Hönninger, E. Mottay, F. Druon, and P. Georges, “Femtosecond fiber chirped- and divided-pulse amplification system,” Opt. Lett. 38(2), 106–108 (2013). [CrossRef] [PubMed]
4. M. Kienel, A. Klenke, T. Eidam, S. Hädrich, J. Limpert, and A. Tünnermann, “Energy scaling of femtosecond amplifiers using actively controlled divided-pulse amplification,” Opt. Lett. 39(4), 1049–1052 (2014). [CrossRef] [PubMed]
5. A. Klenke, S. Hädrich, T. Eidam, J. Rothhardt, M. Kienel, S. Demmler, T. Gottschall, J. Limpert, and A. Tünnermann, “22 GW peak-power fiber chirped-pulse-amplification system,” Opt. Lett. 39(24), 6875–6878 (2014). [CrossRef] [PubMed]
6. L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers,” Opt. Lett. 36(5), 621–623 (2011). [CrossRef] [PubMed]
7. L. A. Siiman, W.-Z. Chang, T. Zhou, and A. Galvanauskas, “Coherent femtosecond pulse combining of multiple parallel chirped pulse fiber amplifiers,” Opt. Express 20(16), 18097–18116 (2012). [CrossRef] [PubMed]
8. L. P. Ramirez, M. Hanna, G. Bouwmans, H. El Hamzaoui, M. Bouazaoui, D. Labat, K. Delplace, J. Pouysegur, F. Guichard, P. Rigaud, V. Kermène, A. Desfarges-Berthelemot, A. Barthélémy, F. Prévost, L. Lombard, Y. Zaouter, F. Druon, and P. Georges, “Coherent beam combining with an ultrafast multicore Yb-doped fiber amplifier,” Opt. Express 23(5), 5406–5416 (2015). [CrossRef] [PubMed]
9. Y. Zaouter, L. Daniault, M. Hanna, D. N. Papadopoulos, F. Morin, C. Hönninger, F. Druon, E. Mottay, and P. Georges, “Passive coherent combination of two ultrafast rod type fiber chirped pulse amplifiers,” Opt. Lett. 37(9), 1460–1462 (2012). [CrossRef] [PubMed]
10. F. Guichard, Y. Zaouter, M. Hanna, K. L. Mai, F. Morin, C. Hönninger, E. Mottay, and P. Georges, “High-energy chirped- and divided-pulse Sagnac femtosecond fiber amplifier,” Opt. Lett. 40(1), 89–92 (2015). [CrossRef] [PubMed]
11. D. Mortag, T. Theeg, K. Hausmann, L. Grüner-Nielsen, K. G. Jespersen, U. Morgner, D. Wandt, D. Kracht, and J. Neumann, “Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system,” Opt. Commun. 285(5), 706–709 (2012). [CrossRef]
13. Method and device for amplifying an optical signal, patent FR20100057107 20100907; WO2011FR52027 20110905.
14. 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-States Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2012), paper AM4A.25. [CrossRef]
15. W.-Z. Chang, T. Zhou, L. A. Siiman, and A. Galvanauskas, “Femtosecond pulse spectral synthesis in coherently-spectrally combined multi-channel fiber chirped pulse amplifiers,” Opt. Express 21(3), 3897–3910 (2013). [CrossRef] [PubMed]
16. P. Rigaud, V. Kermene, G. Bouwmans, L. Bigot, A. Desfarges-Berthelemot, D. Labat, A. Le Rouge, T. Mansuryan, and A. Barthélémy, “Spatially dispersive amplification in a 12-core fiber and femtosecond pulse synthesis by coherent spectral combining,” Opt. Express 21(11), 13555–13563 (2013). [CrossRef] [PubMed]
17. F. Guichard, M. Hanna, L. Lombard, Y. Zaouter, C. Hönninger, F. Morin, F. Druon, E. Mottay, and P. Georges, “Two-channel pulse synthesis to overcome gain narrowing in femtosecond fiber amplifiers,” Opt. Lett. 38(24), 5430–5433 (2013). [CrossRef] [PubMed]
18. A. Klenke, M. Wojdyr, M. Müller, M. Kienel, T. Eidam, H. J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Large pitch Multicore Fiber for Coherent Combination of Ultrashort Pulses,” in 2015 European Conference on Lasers and Electro-Optics - European Quantum Electronics Conference, (Optical Society of America, 2015), paper CJ 1.2.
19. I. M. Vellekoop and A. P. Mosk, “Phase control algorithms for focusing light through turbid media,” Opt. Commun. 281(11), 3071–3080 (2008). [CrossRef]
20. H.-J. Otto, A. Klenke, C. Jauregui, F. Stutzki, J. Limpert, and A. Tünnermann, “Scaling the mode instability threshold with multicore fibers,” Opt. Lett. 39(9), 2680–2683 (2014). [CrossRef] [PubMed]