December 15, 2014 / Vol. 39, No. 24 / OPTICS LETTERS
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22 GW peak-power fiber chirped-pulseamplification system Arno Klenke,1,2,* Steffen Hädrich,1,2 Tino Eidam,1,2 Jan Rothhardt,1,2 Marco Kienel,1,2 Stefan Demmler,1 Thomas Gottschall,1 Jens Limpert,1,2,3 and Andreas Tünnermann1,2,3 1
Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Albert-Einstein-Str. 15, 07745 Jena, Germany 2
3
Helmholtz-Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
Fraunhofer Institute for Applied Optics and Precision Engineering, Albert-Einstein-Str. 7, 07745 Jena, Germany *Corresponding author: arno.klenke@uni‑jena.de Received October 1, 2014; accepted October 24, 2014; posted November 10, 2014 (Doc. ID 224195); published December 10, 2014
In this Letter, we report on a femtosecond fiber chirped-pulse-amplification system based on the coherent combination of the output of four ytterbium-doped large-pitch fibers. Each single channel delivers a peak power of about 6.2 GW after compression. The combined system emits 200 fs long pulses with a pulse energy of 5.7 mJ at 230 W of average power together with an excellent beam quality. The resulting peak power is 22 GW, which to the best of our knowledge is the highest value directly emitted from any fiber-based laser system. © 2014 Optical Society of America OCIS codes: (140.7090) Ultrafast lasers; (060.2320) Fiber optics amplifiers and oscillators; (140.3298) Laser beam combining. http://dx.doi.org/10.1364/OL.39.006875
Laser systems able to emit high-peak-power femtosecond pulses at high repetition rates are demanded from a variety of applications. One example is the generation of high-harmonics in the XUV wavelength range [1]. In this case, sufficient peak powers are required to initiate the highly nonlinear effect. Additionally, large average powers are beneficial for numerous applications of the harmonic radiation [1]. Furthermore, even more ambitious applications such as laser-wakefield acceleration [2] require a combination of even higher peak powers and average powers that are not available with today’s technology. There are different approaches to extend the achievable parameter field of current laser sources toward this goal. On one hand, a lot of work is devoted to increasing the repetition rate (and, therefore, the average power) of state-of-the-art bulk-laser technology already emitting extreme peak powers [3]. However, this proves to be difficult because of the occurrence of thermal effects in the large-scale active medium, limiting the average power to the multi-10 W range. Another approach is to use laser architectures that have already proven to handle high average powers and to improve their peak-power capability. This includes slabs [4], thin-discs [5], and fibers [6]. Ytterbium-based femtosecond fiber amplifiers are an especially promising approach because their simple and efficient single-pass setups, the broad spectral bandwidth of ytterbium-silica, and their capability to deliver high average powers [6] with an excellent beam quality. However, their peak power is limited because of the confinement of the propagating light in the small fiber core. With advanced fiber designs, the mode-field diameter of ytterbiumdoped fibers has been scaled up to the 100 μm range at the 1 μm wavelength range, while preserving a high beam quality [7]. So far, pulse energies of 2.2 mJ and peak powers of 3.8 GW have been achieved with a single amplifier [8]. Theoretically, a limit in the range of 10 GW for pulse and fiber parameters similar to those used in the 0146-9592/14/246875-04$15.00/0
experiments presented herein has been estimated [9]. However, a further increase of the mode-field diameter allowing for even higher pulse energies will be challenging at 1 μm wavelength because of the increasing sensitivity to production tolerances of the fibers [10]. Additionally, at higher average powers, thermal guiding of the mode becomes more important [10], thus decreasing the effective diameter. Therefore, a scaling concept independent on the amplifier technology has been demonstrated using parallelization of multiple amplifiers and a subsequent coherent combination of the beams, first for continuous-wave operation [11] and then for ultrashort pulses [12,13]. In this approach, the output of a laser front-end is divided into multiple spatially separated channels. In each channel, the amplifier can now be pushed to its specific limitations. Finally, the output beams and pulses from the amplifiers are coherently combined into a single beam and pulse. Consequently, such a setup can be thought of as an amplifying interferometer. In the case of perfect recombination, the total pulse energy and average power results from the sum of each of the individual channels. However, because of dispersion, nonlinearity differences in the amplifiers, mismatches of the spatial beam profiles, or the beam overlap, the efficiency of the combination will be smaller than 100%, which is described in detail in [14,15]. Because of their simple single-pass setup and reproducible beam profile, fiber lasers are ideal candidates for this spatial multiplexing concept. So far, this approach has been demonstrated for up to four femtosecond amplifiers [16,17] in the chirped-pulse-amplification (CPA) regime with combined peak powers of up to 6 GW. In this contribution, we present a laser further pushing the pulse energy of such systems. Additionally, we are able to significantly reduce the pulse duration of the compressed pulses. Consequently, to the best of our knowledge, the resulting peak power of 22 GW represents the highest value so far for ultrafast fiber-based systems. © 2014 Optical Society of America
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Fig. 2. Spectrum with compensated (blue) and residual (red) spectral phase of the combined pulse.
Fig. 1. Schematic overview of the experimental setup. AOM, acousto-optic modulator; HC, Hänsch–Couillaud detector.
The experimental setup (Fig. 1) consists of a modelocked oscillator running at a repetition rate of 64 MHz with an average power of 1 W, whose pulses are stretched from 60 fs to 2 ns in an Offner-type grating stretcher with a spectral transmission bandwidth of 22 nm and an efficiency of 40%. In the stretcher (and the compressor), dielectric gratings with 1740 lines/ mm are employed. After stretching, a fraction of the power (about 30 mW) is inserted into a fiber-coupled acousto-optic modulator (AOM) that reduces the repetition rate to 2.1 MHz followed by the first preamplifier. Afterward, the pulses pass a spectral phase-shaping system based on a spatial light modulator (SLM). The multiphoton-intrapulse-interference-phase-scan (MIIPS) technique [18] is employed to measure the residual phase at the system output and to optimize the pulse quality. A second preamplifier increases the average power to about 1 W before the repetition rate is reduced again in a second AOM to the final value of 40 kHz. The last element of the front-end is a third amplifier that provides a pulse energy of 50 μJ total for the main amplification stage. In this stage, the output beam is split into four channels using a cascaded setup of three polarization dependent beam splitter cubes followed by appropriate delay lines to ensure temporal overlapping after recombination. Each of the delay lines contains a piezo-driven mirror (bandwidth of about 1 kHz) for fine adjustment of the path length and stabilization of the path length differences. The spatially separated beams are then coupled into four parallel-operated ytterbium-doped large-pitch fiber amplifiers [7] with a mode-field diameter of about 80 μm and lengths between 85 and 95 cm. Circular polarization is used in the main-amplifier fibers to reduce the impact of self-phase modulation [19] and, therewith, to reduce the amount of phase that has to be applied to the SLM. Afterward, the output beams of the amplifiers are coherently recombined into a single beam using a similar setup consisting of three thin-film polarizers (TFPs). These elements provide superior thermooptical properties at high average powers compared to
beam splitter cubes. After every combination step of two beams, a small fraction of the combined beam is directed toward a Hänsch-Couillaud detector [20] to measure the polarization state. This information is processed with a PID regulator that controls the corresponding delay line to optimize the beam for linear polarization. Thus, this recombined beam can be combined again with another linear polarized beam at the next combination step after its polarization has been rotated with a half-wave plate. After the last combination step, the resulting pulse is finally recompressed to the femtosecond regime with a dielectric-grating compressor with an efficiency of 80%. Figure 2 shows the measured spectrum of the combined pulse. As can be seen, the impact of nonlinearities can be observed as spectral modulations [21]. Despite the huge overall amplification of ∼75 dB (including ∼20 dB losses because of components, fiber coupling, characterization, etc.), an FWHM bandwidth of close to 10 nm could be preserved starting from a nearly rectangular 22 nm FHWM bandwidth behind the stretcher. With the help of the MIIPS algorithm, in addition to the spectral amplitude measurement, the uncompensated spectral phase could be determined (red line in Fig. 2, multiplied by 10 for better visibility). Both measurements allow for the full reconstruction of the temporal pulse profile as shown in Fig. 3. An autocorrelation measurement performed in parallel results in a similar pulse
Fig. 3. Temporal intensity profile of the compressed and combined pulse (black), together with the Fourier limited pulse (blue).
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Fig. 5. Beam profiles behind the compressor of (a) and (d): channels 1-4 and (e) the combined beam.
Fig. 4.
Measured and retrieved autocorrelation traces.
duration (see Fig. 4). Although the residual phase could not be reduced to zero because of phase-amplitude coupling in the shaper (which causes a change in the spectral phase of the pulse because of nonlinearities), the pulse quality is still excellent for a fiber-based system at these energy levels. The coupling is caused by refraction when phase-jumps between adjacent pixels of the spatial-light modulator happen. (The peak-to-peak value of the compensated phase is ∼180 rad while the shaper has a dynamic range of 15 rad.) In total, the combined pulse has an energy of 5.7 mJ and a pulse duration of 200 fs with a peak power of 22 GW. This is more than a factor of three beyond the highest previously reported peak power of a fiber-based system [17]. As can be seen from Fig. 3, some power (about 16%) is contained in pre- and post-pulses. The peak power available with a transformlimited pulse would be 30 GW if a perfectly flat phase could be achieved. Therefore, an improved phase compensation and additional implementation of amplitude shaping to achieve even shorter pulses is the subject of ongoing activities. At the given repetition rate, the corresponding average power is 230 W. Each amplifier on its own delivered a compressed pulse energy of 1.6 mJ. Assuming a lossless compression, the maximum peak power per amplifier could be estimated to be around 7.8 GW, which is close to the theoretical limit for the parameters used in this experiment [9]. The B-Integral in the main amplifiers is estimated to be ∼5 rad by numerically simulating the pulse evolution inside the fibers with the help of the one-dimensional rate equations [22]. However, it should be noted that there is additional nonlinear polarization rotation occurring during the propagation through the fibers that is mostly pre-compensated by slightly changing the wave plate positions which makes the exact determination of the B-integral value difficult. The combination process of the four amplifiers achieved a high combining efficiency of 88%, despite the higher sensitivity of this value to mismatches of the amplifiers when working at high nonlinearities [14]. The combining efficiency is defined as the average power of the combined beam divided by the sum of the average powers of the individual channels at the system output. The beam profiles of the four single-channel beams, in addition to the combined beams that were recorded behind the compressor, are shown in Fig. 5. As can be seen,
there are some small differences between the profiles because of slightly different collimation. However, the combination results in a very good beam profile. Still, the intensity profile is not sufficient to estimate the quality of a laser beam as the spatial phase also plays a major role. Therefore, a measurement of the M2 value behind the compressor was carried out (Fig. 6). This results in a nearly diffraction-limited value of 1.3 × 1.2 for the combined beam and comparable values (within the margins of error) for the single amplifiers. In summary, the combined beam and combined pulses show the same properties like those emitted by a single amplifier, except for the scaled performance values. Therefore, the presented experiment proves the capability of ultrafast fiber-laser systems using coherent combination to, on one hand, exploit new parameter regimes inaccessible with today’s laser technology and, on the other hand, maintain the advantages (beam quality, stability, and efficiency) of a state-of-the-art single-emitter system. In conclusion, we have demonstrated a coherently combined femtosecond fiber CPA system delivering a record peak power of 22 GW at an average power of 230 W. This was achieved at a high combining efficiency of 88% preserving an excellent beam quality. Additionally, the individual channels have been pushed close to the theoretically predicted limit [9]. It is expected that with new approaches like multi-core fibers [23], the number of channels of such systems can be easily increased. In combination with temporal multiplexing (dividedpulse amplification) [24], this will allow building high repetition-rate TW-class table-top fiber laser systems in the near future. Finally, these systems could replace state-of-the-art Ti:Sa lasers and deliver repetition rates and average power orders of magnitude above today’s state of the art. This will open novel possibilities for many applications and allow for the first time, to the best of our knowledge, the possibility to make the important step
Fig. 6. Caustic of the combined beam for the M2 measurement.
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from single-shot proof-of-principle experiments toward real-world applications. This work has been partly supported by the German Federal Ministry of Education and Research (BMBF) under contract 13N12082 “NEXUS” and the European Research Council under grant agreement no. [617173] “ACOPS”. A. Klenke and M. Kienel acknowledge financial support by the Helmholtz-Institute, Jena. T. Eidam acknowledges financial support by the Carl-Zeiss-Stiftung. References 1. U. Keller, IEEE Photon. J. 2, 225 (2010). 2. V. Malka, J. Faure, Y. Gauduel, and E. Lefebvre, Nat. Phys. 4, 447 (2008). 3. S. Banerjee, K. Ertel, P. Mason, P. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. Collier, Opt. Lett. 37, 2175 (2012). 4. P. Russbueldt, T. Mans, J. Weitenberg, H. Hoffmann, and R. Poprawe, Opt. Lett. 35, 4169 (2010). 5. H. Fattahi, H. Barros, M. Gorjan, T. Nubbemeyer, B. Alsaif, C. Teisset, M. Schultze, S. Prinz, M. Haefner, M. Ueffing, A. Alismail, L. Vámos, A. Schwarz, O. Pronin, J. Brons, X. Geng, G. Arisholm, M. Ciappina, V. Yakovlev, D. Kim, A. Azzeer, N. Karpowicz, D. Sutter, Z. Major, T. Metzger, and F. Krausz, Optica 1, 45 (2014). 6. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, Opt. Express 19, 13218 (2011). 7. J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, Light Sci. Appl. 1, e8 (2012). 8. T. Eidam, J. Rothhardt, F. Stutzki, F. Jansen, S. Hädrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, Opt. Express 19, 255 (2011).
9. D. Schimpf, J. Limpert, and A. Tünnermann, J. Opt. Soc. Am. B 27, 2051 (2010). 10. F. Stutzki, F. Jansen, H. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, Optica 1, 1233 (2014). 11. T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005). 12. E. Seise, A. Klenke, J. Limpert, and A. Tünnermann, Opt. Express 18, 27827 (2010). 13. J. Limpert, A. Klenke, M. Kienel, S. Breitkopf, T. Eidam, S. Hädrich, C. Jauregui, and A. Tunnermann, IEEE J. Sel. Top. Quantum Electron. 20, 268 (2014). 14. A. Klenke, E. Seise, J. Limpert, and A. Tünnermann, Opt. Express 19, 25379 (2011). 15. G. Goodno, C. Shih, and J. Rothenberg, Opt. Express 18, 25403 (2010). 16. L. Siiman, W. Chang, T. Zhou, and A. Galvanauskas, Opt. Express 20, 18097 (2012). 17. A. Klenke, A. Hoffmann, S. Hädrich, T. Eidam, T. Gottschall, J. Limpert, and A. Tünnermann, Proc. SPIE 8961, 89611D (2014). 18. V. V. Lozovoy, I. Pastirk, and M. Dantus, Opt. Lett. 29, 775 (2004). 19. D. Schimpf, T. Eidam, E. Seise, S. Hädrich, J. Limpert, and A. Tünnermann, Opt. Express 17, 18774 (2009). 20. T. W. Hänsch and B. Couillaud, Opt. Commun. 35, 441 (1980). 21. D. Schimpf, E. Seise, J. Limpert, and A. Tünnermann, Opt. Express 16, 10664 (2008). 22. Y. Wang, C.-Q. Xu, and H. Po, Opt. Commun. 242, 487 (2004). 23. H. Otto, A. Klenke, C. Jauregui, F. Stutzki, J. Limpert, and A. Tünnermann, Opt. Lett. 39, 2680 (2014). 24. M. Kienel, A. Klenke, T. Eidam, S. Hädrich, J. Limpert, and A. Tünnermann, Opt. Lett. 39, 1049 (2014).
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22 GW peak-power fiber chirped-pulseamplification system Arno Klenke,1,2,* Steffen Hädrich,1,2 Tino Eidam,1,2 Jan Rothhardt,1,2 Marco Kienel,1,2 Stefan Demmler,1 Thomas Gottschall,1 Jens Limpert,1,2,3 and Andreas Tünnermann1,2,3 1
Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Albert-Einstein-Str. 15, 07745 Jena, Germany 2
3
Helmholtz-Institute Jena, Fröbelstieg 3, 07743 Jena, Germany
Fraunhofer Institute for Applied Optics and Precision Engineering, Albert-Einstein-Str. 7, 07745 Jena, Germany *Corresponding author: arno.klenke@uni‑jena.de Received October 1, 2014; accepted October 24, 2014; posted November 10, 2014 (Doc. ID 224195); published December 10, 2014
In this Letter, we report on a femtosecond fiber chirped-pulse-amplification system based on the coherent combination of the output of four ytterbium-doped large-pitch fibers. Each single channel delivers a peak power of about 6.2 GW after compression. The combined system emits 200 fs long pulses with a pulse energy of 5.7 mJ at 230 W of average power together with an excellent beam quality. The resulting peak power is 22 GW, which to the best of our knowledge is the highest value directly emitted from any fiber-based laser system. © 2014 Optical Society of America OCIS codes: (140.7090) Ultrafast lasers; (060.2320) Fiber optics amplifiers and oscillators; (140.3298) Laser beam combining. http://dx.doi.org/10.1364/OL.39.006875
Laser systems able to emit high-peak-power femtosecond pulses at high repetition rates are demanded from a variety of applications. One example is the generation of high-harmonics in the XUV wavelength range [1]. In this case, sufficient peak powers are required to initiate the highly nonlinear effect. Additionally, large average powers are beneficial for numerous applications of the harmonic radiation [1]. Furthermore, even more ambitious applications such as laser-wakefield acceleration [2] require a combination of even higher peak powers and average powers that are not available with today’s technology. There are different approaches to extend the achievable parameter field of current laser sources toward this goal. On one hand, a lot of work is devoted to increasing the repetition rate (and, therefore, the average power) of state-of-the-art bulk-laser technology already emitting extreme peak powers [3]. However, this proves to be difficult because of the occurrence of thermal effects in the large-scale active medium, limiting the average power to the multi-10 W range. Another approach is to use laser architectures that have already proven to handle high average powers and to improve their peak-power capability. This includes slabs [4], thin-discs [5], and fibers [6]. Ytterbium-based femtosecond fiber amplifiers are an especially promising approach because their simple and efficient single-pass setups, the broad spectral bandwidth of ytterbium-silica, and their capability to deliver high average powers [6] with an excellent beam quality. However, their peak power is limited because of the confinement of the propagating light in the small fiber core. With advanced fiber designs, the mode-field diameter of ytterbiumdoped fibers has been scaled up to the 100 μm range at the 1 μm wavelength range, while preserving a high beam quality [7]. So far, pulse energies of 2.2 mJ and peak powers of 3.8 GW have been achieved with a single amplifier [8]. Theoretically, a limit in the range of 10 GW for pulse and fiber parameters similar to those used in the 0146-9592/14/246875-04$15.00/0
experiments presented herein has been estimated [9]. However, a further increase of the mode-field diameter allowing for even higher pulse energies will be challenging at 1 μm wavelength because of the increasing sensitivity to production tolerances of the fibers [10]. Additionally, at higher average powers, thermal guiding of the mode becomes more important [10], thus decreasing the effective diameter. Therefore, a scaling concept independent on the amplifier technology has been demonstrated using parallelization of multiple amplifiers and a subsequent coherent combination of the beams, first for continuous-wave operation [11] and then for ultrashort pulses [12,13]. In this approach, the output of a laser front-end is divided into multiple spatially separated channels. In each channel, the amplifier can now be pushed to its specific limitations. Finally, the output beams and pulses from the amplifiers are coherently combined into a single beam and pulse. Consequently, such a setup can be thought of as an amplifying interferometer. In the case of perfect recombination, the total pulse energy and average power results from the sum of each of the individual channels. However, because of dispersion, nonlinearity differences in the amplifiers, mismatches of the spatial beam profiles, or the beam overlap, the efficiency of the combination will be smaller than 100%, which is described in detail in [14,15]. Because of their simple single-pass setup and reproducible beam profile, fiber lasers are ideal candidates for this spatial multiplexing concept. So far, this approach has been demonstrated for up to four femtosecond amplifiers [16,17] in the chirped-pulse-amplification (CPA) regime with combined peak powers of up to 6 GW. In this contribution, we present a laser further pushing the pulse energy of such systems. Additionally, we are able to significantly reduce the pulse duration of the compressed pulses. Consequently, to the best of our knowledge, the resulting peak power of 22 GW represents the highest value so far for ultrafast fiber-based systems. © 2014 Optical Society of America
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Fig. 2. Spectrum with compensated (blue) and residual (red) spectral phase of the combined pulse.
Fig. 1. Schematic overview of the experimental setup. AOM, acousto-optic modulator; HC, Hänsch–Couillaud detector.
The experimental setup (Fig. 1) consists of a modelocked oscillator running at a repetition rate of 64 MHz with an average power of 1 W, whose pulses are stretched from 60 fs to 2 ns in an Offner-type grating stretcher with a spectral transmission bandwidth of 22 nm and an efficiency of 40%. In the stretcher (and the compressor), dielectric gratings with 1740 lines/ mm are employed. After stretching, a fraction of the power (about 30 mW) is inserted into a fiber-coupled acousto-optic modulator (AOM) that reduces the repetition rate to 2.1 MHz followed by the first preamplifier. Afterward, the pulses pass a spectral phase-shaping system based on a spatial light modulator (SLM). The multiphoton-intrapulse-interference-phase-scan (MIIPS) technique [18] is employed to measure the residual phase at the system output and to optimize the pulse quality. A second preamplifier increases the average power to about 1 W before the repetition rate is reduced again in a second AOM to the final value of 40 kHz. The last element of the front-end is a third amplifier that provides a pulse energy of 50 μJ total for the main amplification stage. In this stage, the output beam is split into four channels using a cascaded setup of three polarization dependent beam splitter cubes followed by appropriate delay lines to ensure temporal overlapping after recombination. Each of the delay lines contains a piezo-driven mirror (bandwidth of about 1 kHz) for fine adjustment of the path length and stabilization of the path length differences. The spatially separated beams are then coupled into four parallel-operated ytterbium-doped large-pitch fiber amplifiers [7] with a mode-field diameter of about 80 μm and lengths between 85 and 95 cm. Circular polarization is used in the main-amplifier fibers to reduce the impact of self-phase modulation [19] and, therewith, to reduce the amount of phase that has to be applied to the SLM. Afterward, the output beams of the amplifiers are coherently recombined into a single beam using a similar setup consisting of three thin-film polarizers (TFPs). These elements provide superior thermooptical properties at high average powers compared to
beam splitter cubes. After every combination step of two beams, a small fraction of the combined beam is directed toward a Hänsch-Couillaud detector [20] to measure the polarization state. This information is processed with a PID regulator that controls the corresponding delay line to optimize the beam for linear polarization. Thus, this recombined beam can be combined again with another linear polarized beam at the next combination step after its polarization has been rotated with a half-wave plate. After the last combination step, the resulting pulse is finally recompressed to the femtosecond regime with a dielectric-grating compressor with an efficiency of 80%. Figure 2 shows the measured spectrum of the combined pulse. As can be seen, the impact of nonlinearities can be observed as spectral modulations [21]. Despite the huge overall amplification of ∼75 dB (including ∼20 dB losses because of components, fiber coupling, characterization, etc.), an FWHM bandwidth of close to 10 nm could be preserved starting from a nearly rectangular 22 nm FHWM bandwidth behind the stretcher. With the help of the MIIPS algorithm, in addition to the spectral amplitude measurement, the uncompensated spectral phase could be determined (red line in Fig. 2, multiplied by 10 for better visibility). Both measurements allow for the full reconstruction of the temporal pulse profile as shown in Fig. 3. An autocorrelation measurement performed in parallel results in a similar pulse
Fig. 3. Temporal intensity profile of the compressed and combined pulse (black), together with the Fourier limited pulse (blue).
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Fig. 5. Beam profiles behind the compressor of (a) and (d): channels 1-4 and (e) the combined beam.
Fig. 4.
Measured and retrieved autocorrelation traces.
duration (see Fig. 4). Although the residual phase could not be reduced to zero because of phase-amplitude coupling in the shaper (which causes a change in the spectral phase of the pulse because of nonlinearities), the pulse quality is still excellent for a fiber-based system at these energy levels. The coupling is caused by refraction when phase-jumps between adjacent pixels of the spatial-light modulator happen. (The peak-to-peak value of the compensated phase is ∼180 rad while the shaper has a dynamic range of 15 rad.) In total, the combined pulse has an energy of 5.7 mJ and a pulse duration of 200 fs with a peak power of 22 GW. This is more than a factor of three beyond the highest previously reported peak power of a fiber-based system [17]. As can be seen from Fig. 3, some power (about 16%) is contained in pre- and post-pulses. The peak power available with a transformlimited pulse would be 30 GW if a perfectly flat phase could be achieved. Therefore, an improved phase compensation and additional implementation of amplitude shaping to achieve even shorter pulses is the subject of ongoing activities. At the given repetition rate, the corresponding average power is 230 W. Each amplifier on its own delivered a compressed pulse energy of 1.6 mJ. Assuming a lossless compression, the maximum peak power per amplifier could be estimated to be around 7.8 GW, which is close to the theoretical limit for the parameters used in this experiment [9]. The B-Integral in the main amplifiers is estimated to be ∼5 rad by numerically simulating the pulse evolution inside the fibers with the help of the one-dimensional rate equations [22]. However, it should be noted that there is additional nonlinear polarization rotation occurring during the propagation through the fibers that is mostly pre-compensated by slightly changing the wave plate positions which makes the exact determination of the B-integral value difficult. The combination process of the four amplifiers achieved a high combining efficiency of 88%, despite the higher sensitivity of this value to mismatches of the amplifiers when working at high nonlinearities [14]. The combining efficiency is defined as the average power of the combined beam divided by the sum of the average powers of the individual channels at the system output. The beam profiles of the four single-channel beams, in addition to the combined beams that were recorded behind the compressor, are shown in Fig. 5. As can be seen,
there are some small differences between the profiles because of slightly different collimation. However, the combination results in a very good beam profile. Still, the intensity profile is not sufficient to estimate the quality of a laser beam as the spatial phase also plays a major role. Therefore, a measurement of the M2 value behind the compressor was carried out (Fig. 6). This results in a nearly diffraction-limited value of 1.3 × 1.2 for the combined beam and comparable values (within the margins of error) for the single amplifiers. In summary, the combined beam and combined pulses show the same properties like those emitted by a single amplifier, except for the scaled performance values. Therefore, the presented experiment proves the capability of ultrafast fiber-laser systems using coherent combination to, on one hand, exploit new parameter regimes inaccessible with today’s laser technology and, on the other hand, maintain the advantages (beam quality, stability, and efficiency) of a state-of-the-art single-emitter system. In conclusion, we have demonstrated a coherently combined femtosecond fiber CPA system delivering a record peak power of 22 GW at an average power of 230 W. This was achieved at a high combining efficiency of 88% preserving an excellent beam quality. Additionally, the individual channels have been pushed close to the theoretically predicted limit [9]. It is expected that with new approaches like multi-core fibers [23], the number of channels of such systems can be easily increased. In combination with temporal multiplexing (dividedpulse amplification) [24], this will allow building high repetition-rate TW-class table-top fiber laser systems in the near future. Finally, these systems could replace state-of-the-art Ti:Sa lasers and deliver repetition rates and average power orders of magnitude above today’s state of the art. This will open novel possibilities for many applications and allow for the first time, to the best of our knowledge, the possibility to make the important step
Fig. 6. Caustic of the combined beam for the M2 measurement.
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from single-shot proof-of-principle experiments toward real-world applications. This work has been partly supported by the German Federal Ministry of Education and Research (BMBF) under contract 13N12082 “NEXUS” and the European Research Council under grant agreement no. [617173] “ACOPS”. A. Klenke and M. Kienel acknowledge financial support by the Helmholtz-Institute, Jena. T. Eidam acknowledges financial support by the Carl-Zeiss-Stiftung. References 1. U. Keller, IEEE Photon. J. 2, 225 (2010). 2. V. Malka, J. Faure, Y. Gauduel, and E. Lefebvre, Nat. Phys. 4, 447 (2008). 3. S. Banerjee, K. Ertel, P. Mason, P. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. Collier, Opt. Lett. 37, 2175 (2012). 4. P. Russbueldt, T. Mans, J. Weitenberg, H. Hoffmann, and R. Poprawe, Opt. Lett. 35, 4169 (2010). 5. H. Fattahi, H. Barros, M. Gorjan, T. Nubbemeyer, B. Alsaif, C. Teisset, M. Schultze, S. Prinz, M. Haefner, M. Ueffing, A. Alismail, L. Vámos, A. Schwarz, O. Pronin, J. Brons, X. Geng, G. Arisholm, M. Ciappina, V. Yakovlev, D. Kim, A. Azzeer, N. Karpowicz, D. Sutter, Z. Major, T. Metzger, and F. Krausz, Optica 1, 45 (2014). 6. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, Opt. Express 19, 13218 (2011). 7. J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, Light Sci. Appl. 1, e8 (2012). 8. T. Eidam, J. Rothhardt, F. Stutzki, F. Jansen, S. Hädrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, Opt. Express 19, 255 (2011).
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