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OPTICS LETTERS / Vol. 40, No. 4 / February 15, 2015
Multidimensional coherent pulse addition of ultrashort laser pulses Marco Kienel,1,2,* Michael Müller,1 Arno Klenke,1,2 Tino Eidam,1,2 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 Helmholtz-Institute Jena, Fröbelstieg 3, 07743 Jena, Germany 3
Fraunhofer Institute for Applied Optics and Precision Engineering, Albert-Einstein-Str. 7, 07745 Jena, Germany *Corresponding author: marco.kienel@uni‑jena.de Received September 17, 2014; revised January 7, 2015; accepted January 13, 2015; posted January 14, 2015 (Doc. ID 223366); published February 6, 2015
Spatially and temporally separated amplification and subsequent coherent addition of femtosecond pulses is a promising performance-scaling approach for ultrafast laser systems. Herein we demonstrate for the first time the application of this multidimensional scheme in a scalable architecture. Applying actively controlled divided-pulse amplification producing up to four pulse replicas that are amplified in two ytterbium-doped step-index fibers (6 μm core), pulse energies far beyond the damage threshold of the single fiber have been achieved. In this proof-of-principle experiment, high system efficiencies are demonstrated at both high pulse energies (i.e., in case of strong saturation) and high accumulated nonlinear phases. © 2015 Optical Society of America OCIS codes: (140.7090) Ultrafast lasers; (140.3280) Laser amplifiers; (140.3298) Laser beam combining; (140.3615) Lasers, ytterbium. http://dx.doi.org/10.1364/OL.40.000522
Today, high-performance ultrafast laser systems have opened up new possibilities for a variety of applications in industry, medicine, or fundamental science [1]. For the most demanding applications such as high-harmonic generation [2] or laser-based particle acceleration [3], ultrashort pulses with extremely high peak powers are required. Hereby, the achievable pulse energies and, therewith, the peak powers and intensities that can be generated are typically limited by nonlinear effects or optically induced damage. A way to overcome these limitations is to reduce the peak intensity during amplification by increasing either the beam cross-section or the pulse duration. Thus, today all state-of-the-art laser systems emitting highest peak powers are bulk lasers with large beam diameters. Additionally, they employ the wellknown technique of chirped-pulse amplification (CPA) [4], i.e., the pulse duration is increased during amplification by some orders of magnitude and compressed afterward. A novel approach for generating high peak powers is, instead of using only one single amplifier, to use many medium- or even small-energy amplifiers and to coherently combine their outputs afterward. This brings the advantage that more sophisticated laser geometries such as fibers, slabs, or thin disks can be employed. It allows, for the first time, to simultaneously produce high peak and average powers with an excellent beam quality and efficiency. Until now, the techniques for separated amplification and coherent combination can be divided into two approaches. The first one is spatially separated amplification, also referred to as coherent beam combination [5]. In this, the beam is split into a number of N beams and amplified in N spatially separated amplifiers. This can be seen as an artificial scaling of the mode-field diameter. Subsequently, these beams are coherently recombined improving ideally the average output power and pulse peak power by a factor of N. Especially fiber amplifiers benefit from this approach due to their 0146-9592/15/040522-04$15.00/0
single-pass architecture and, hence, their possibility for a straightforward spatial multiplexing. Recently, femtosecond pulses with 22 GW of pulse peak power and 230 W of average power have been achieved applying four large-mode area fibers in a fiber-CPA system [6]. The second approach to improve the pulse peak power is temporally separated amplification, also referred to as divided-pulse amplification (DPA) [7–10]. In this case, the pulses are split temporally into a number of M pulse replicas, which can be seen as an artificial increase of the CPA stretching ratio. This pulse train is generated prior to amplification and recombined afterward to one intense pulse, ideally improving the peak power by a factor of M. Recently, DPA has been applied in a fiber-CPA system achieving 1-GW femtosecond pulses within a single fiber employing a passive double-pass implementation [11]. Further scaling has been restricted, since saturation of the amplifier deforms the pulse train accompanied by nonlinear phase (B-integral) differences among them leading to a collapse of the combining efficiency. Applying separated pulse division and combination using an active DPA (ADPA) approach [12] provides a solution for this problem. Here, the input pulse train can be shaped to a growing amplitude resulting in a saturated output pulse train with (nearly) constant amplitude and, which is more important, the same amount of nonlinear phase acquired for each replica. Thus, with ADPA the achieved peak power could be improved to nearly 3 GW [12]. In this contribution, we report on the first (to the best of our knowledge) combination of both the spatial and the temporal multiplexing approach providing a scalable N · M multidimensional amplification scheme. In particular, the amplification and efficient recombination of eight pulses, i.e., four pulse replicas amplified in a two-channel combining setup, are demonstrated in a proof-ofprinciple experiment applying an active stabilization for both multiplexing dimensions. Figure 1 depicts the experimental setup. As front end, two different sources have been applied for investigating © 2015 Optical Society of America
February 15, 2015 / Vol. 40, No. 4 / OPTICS LETTERS
Fig. 1. Schematic representation of the multidimensional architecture applying two fiber main amplifiers and a pulse division up to four pulse replicas using the ADPA approach (PBS—polarizing beam splitter, HWP/QWP—half-/quarter-wave plate).
both the saturated and the unsaturated amplification regime at low and high B-integral values. For the first front end, femtosecond pulses from a mode-locked solid-state oscillator are stretched in a 170-m-long 6-μm corediameter fiber to approximately 50 ps duration. In the second case, pulses from a front end of a state-of-theart fiber-CPA system [6] are employed. These are already stretched to approximately 1.5 ns duration using a reflection-grating stretcher. The front-end pulses are pre-amplified in two 1-m-long core-pumped Yb-doped single-mode fibers with core diameters of 6 μm enclosing a fiber-coupled acousto-optic modulator. This provides seed pulses in the mW-average power range with adjustable repetition rate. Optical isolators are used to separate the amplification stages. For pulse division, two folded interferometric delay lines are employed consisting of combinations of polarizing beam splitters (PBSs) and half-/quarter-wave plates (HWPs/QWPs) producing up to four pulse replicas with alternating orthogonal p- and s-polarization [12]. A delay of 4.3 ns (the temporal hardcut for the stretcher of the fiber-CPA front end) between each replica is produced ensuring complete temporal separation. For efficient recombination in a separate combination stage, piezo-driven mirrors are employed in each delay line in order to match the corresponding path lengths. To provide sufficient degrees of freedom for shaping the pulse train and to compensate for saturation a small nondelaying Mach–Zehnder interferometer-type stage is additionally introduced [12]. Afterward, the generated pulse train is divided into two channels of a Mach–Zehnder-type amplifying interferometer by another division using a further combination of HWP and PBS. Due to this division, pulse trains of four pulses each with equal polarization but different phase patterns enter each channel, while one of them double-passes a piezodriven mirror delay-line for active phase control. These pulse trains are amplified in 1.2-m-long polarizationmaintaining (PM) core-pumped Yb-doped single-mode fibers with core diameters of 6 μm (the estimated saturation energy is 13 μJ). Polarization-dependent isolators
523
in front of each main amplifier prevented feedback from the division interferometers. HWPs are applied to propagate the trains through the correct axes of the fibers and, ultimately, overlap them at the right output port of the subsequent PBS. Due to the imposed phase patterns, the initial alternating polarizations are recovered. A further HWP flips the polarization orientation of the pulse train by 90° to remove the temporal delays with the help of similar delay lines as for pulse division. Ring-delay lines have been applied instead of double-pass lines [12] to prevent back reflections and, hence, lasing of the high-gain main amplifiers due to possible leakage from the second pass through the PBSs of the interferometers. Finally, a combination of HWP and PBS separates all fractions from the combined output that are in the wrong polarization state. A few percent of the output beam is ejected onto a photo-diode required for active stabilization. For the experiments described herein, the LOCSET technique [13] is employed, which uses distinct RFmodulations, in this case 4.5, 6.0, and 7.3 kHz, imprinted on each delayed branch by the three phase actuators. Requiring just a single detector, the control electronics generates error signals caused by phase fluctuations for the respective path by demodulating at the corresponding frequency. To minimize the error signals, the corrected phases are fed back to the piezos, therefore, maximizing the combined output. The most important parameter for every combining architecture is the system efficiency ηsys [14]. It is defined as the ratio between the power contained within the main combined output pulse and the sum of the output powers for each amplifier. This value includes both the losses of the combining process itself and the losses due to the additional components required for combining. Of course, in the multidimensional case, ηsys > 1∕N · M has to be fulfilled in order to achieve a power increase in comparison to a single emitter. However, in order to achieve high wall-plug efficiencies, typically ηsys values as close as possible to 100% are desirable. Therefore, it is interesting to investigate the evolution of ηsys both for an increasing channel/replica count and for increasing pulse energies (and therewith B-integral and saturation) per channel. Since the proposed architecture depicted in Fig. 1 employs spatial and temporal multiplexing independent from each other, scaling considerations for an increasing channel [15] and replica count [12] are in good approximation also valid in this multidimensional case. The same holds for the energy-scaling considerations. In general, spatial multiplexing is typically more efficient at high energies due to the symmetric combination process. Unfortunately, as discussed above, this is not the case for temporal multiplexing due to saturation and the deformation of the pulse-train. ADPA can, contrary to passive DPA, compensate for this deformation. However, typically, there is still some efficiency drop at highest energies due to residual amplitude differences in the pulse train that is optimized for vanishing B-integral differences and the shaping of each individual replica due to saturation. Thus, in the following, two operation points have been investigated, one with high B-integral but negligible saturation and one with both strong nonlinear phases and strong saturation.
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Fig. 2. System efficiencies as a function of the output pulse energy within the main combined pulse for the combination of two channels applying no pulse division (one rep.), and a division into two and four pulse replicas for (a) 50-ps pulses and (b) 1.5-ns pulses.
First, the amplifiers are operated with the 50-ps pulses to investigate the unsaturated regime at high B-integrals. Therefore, the seed power in front of each main amplifier is kept constant at 1 mW, which is amplified with a maximum gain of approximately 280 each, while the repetition rate is reduced iteratively from 20.0 MHz to a minimum of 124.9 kHz. In Fig. 2(a) the determined system efficiencies as a function of the pulse energy within the main pulse at the system output are depicted for the combination of both channels applying no pulse division (one replica), and a division into two- and four-pulse replicas. It can be seen that high system efficiencies have been achieved even for extremely high B-integrals (estimated for the maximum energy to 18, 22, and 28 rad for four, two, and one replica, respectively). The offset from 100% combining efficiency is due to the losses from the optical components behind the main amplifiers. Considering only the p-polarization transmission properties of the PBSs employed after the main amplifiers, a theoretical maximum of about 94% could be expected, which is also marked in Fig. 2. The propagation loss through each delay line for temporal combination is about 1%–2%. Further impacts are wavefront mismatches resulting from the different path lengths of the beams to be combined. For this reason the beam diameter is increased to 4.5 mm to keep the combination losses for the temporal recombination between the first and the fourth pulse replica below 2%. Any additional efficiency degradation can be attributed to dispersion and B-integral differences between both channels [15] and differences in both pulse-train shapes after the amplifiers. The latter is due to, on the one hand, slightly different fiber inputcouplings, and, on the other hand, residual differences in the amplification characteristics of the channels. Next, to operate the amplifiers in saturation, the 1.5-ns input pulses are employed, which also raises the damage threshold. The seed power of each amplifier again is kept constant at 1 mW, while the repetition rate is reduced from 2.0 MHz to a minimum of 5.9 kHz. Figure 2(b) shows the determined system efficiencies in dependence on the output pulse energy within the main pulse again for the application of one-, two-, and four-pulse replicas. At low pulse energies, a similar behavior as for the picosecond pulses is obtained, since saturation is not as pronounced. The similar drop in efficiency for both pulse divisions at increasing pulse energies demonstrates that this is owed
Fig. 3. (a) Photo-diode measurements of the input pulse train (orange) and outputs of both amplifiers (red and blue) and (b) for the combined pulse at a pulse energy of 37 μJ.
by deviations between both channels, as described above. For the case applying four pulse replicas, a maximum combined pulse energy of 37 μJ has been achieved (verified by energy meter measurements). This value is approximately five times above the single-pulse damage threshold of the fiber. The estimated B-integrals within the main amplifiers are 7 rad at the maximum energy for each case. At repetition rates going down to the kHzrange, amplified spontaneous emission has to be considered, which is 75% even for the highest energies prove the power-scaling ability of this multidimensional technique. For comparison, the calculated efficiency for a similar passive DPA approach employing the model presented in [10] is also depicted in Fig. 2(b). Here, a small-signal gain of 30 dB for each amplifier and PBS with Rs ≥ 99%, T p ≥ 97% are used. The rapid efficiency drop due to saturation can be clearly seen preventing the passive setup from reaching these energies at all. Figure 3(a) shows the pulse trains at the output of the pulse division stage and at the outputs of both fiber amplifiers at an energy of 37 μJ, which are measured with an 18-ps rise-time photo-diode and a 30-GHz sampling scope. Saturation is clearly visible at these energy values. Additionally, please note the slight amplitude decrease of the output pulse train resulting from the B-integral adaption of each replica. In Fig. 3(b) the combined output pulse is depicted for a pulse energy of 37 μJ. At this energy level, pre- and postpulses become more severe due to temporal combination losses regarding the effects discussed above. The pulse contrast is in the order of 20 dB, which slightly decreases toward higher energies. Although this value is already sufficient for a variety of applications, further contrast improvements are feasible, e.g., via temporal gating, and are subject of ongoing research. In conclusion, the multidimensional amplification approach, i.e., the combination of both spatially and temporally separated amplification, has been demonstrated in a scalable architecture for the first time. Applying four-pulse replicas using the ADPA method and two fiber amplifier channels in a completely phase-locked
February 15, 2015 / Vol. 40, No. 4 / OPTICS LETTERS
implementation, high system efficiencies have been demonstrated at both high pulse energies and high B-integrals. In a next step, this concept will be applied to a state-of-the-art fiber-CPA system scaling the achievable pulse energy per channel to the multi-mJ range. We are confident that increasing the channel and replica count to an 8 × 4 scheme will make TW-class fiber lasers feasible in the near future. This work has been partly supported by the German Federal Ministry of Education and Research (BMBF) under contract 13N12082 “NEXUS,” contract 13N13167 “MEDUSA” and by the European Research Council under the ERC grant agreement no. [617173]. A. K. and M. K. acknowledge financial support by the HelmholtzInstitute Jena. T. E. acknowledges financial support by the Carl-Zeiss Stiftung. References 1. H. Fattahi, H. G. Barros, M. Gorjan, T. Nubbemeyer, B. Alsaif, C. Y. Teisset, M. Schultze, S. Prinz, M. Haefner, M. Ueffing, A. Alismail, L. Vámos, A. Schwarz, O. Pronin, J. Brons, X. T. Geng, G. Arisholm, M. Ciappina, V. S. Yakovlev, D.-E. Kim, A. M. Azzeer, N. Karpowicz, D. Sutter, Z. Major, T. Metzger, and F. Krausz, Optica 1, 45 (2014). 2. M. Krebs, S. Hädrich, S. Demmler, J. Rothhardt, A. Zair, L. Chipperfield, J. Limpert, and A. Tünnermann, Nat. Photonics 7, 555 (2013). 3. W. P. Leemans, B. Nagler, A. J. Gonsalves, Cs. Tóth, K. Nakamura, C. G. R. Geddes, E. Esarey, C. B. Schroeder, and S. M. Hooker, Nat. Phys. 2, 696 (2006).
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4. D. Strickland and G. Mourou, Opt. Commun 56, 219 (1985). 5. T. Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11, 567 (2005). 6. A. Klenke, S. Hädrich, T. Eidam, J. Rothhardt, M. Kienel, S. Demmler, T. Gottschall, J. Limpert, and A. Tünnermann, Opt. Lett. 39, 6875 (2014). 7. S. Szatmari and P. Simon, Opt. Commun 98, 181 (1993). 8. S. Podleska, “Method for stretching and recompressing optical impulses, involves dividing impulses in two perpendicular polarized impulse parts in stretching loop with different deceleration arms,” German Patent DE102006060703 (December 19, 2006). 9. S. Zhou, F. W. Wise, and D. G. Ouzounov, Opt. Lett. 32, 871 (2007). 10. M. Kienel, A. Klenke, T. Eidam, M. Baumgartl, C. Jauregui, J. Limpert, and A. Tünnermann, Opt. Express 21, 29031 (2013). 11. Y. Zaouter, F. Guichard, L. Daniault, M. Hanna, F. Morin, C. Hönninger, E. Mottay, F. Druon, and P. Georges, Opt. Lett. 38, 106 (2013). 12. M. Kienel, A. Klenke, T. Eidam, S. Hädrich, J. Limpert, and A. Tünnermann, Opt. Lett. 39, 1049 (2014). 13. T. M. Shay, Opt. Express 14, 12188 (2006). 14. J. Limpert, A. Klenke, M. Kienel, S. Breitkopf, T. Eidam, S. Hädrich, C. Jauregui, and A. Tünnermann, IEEE J. Sel. Top. Quantum Electron. 20, 268 (2014). 15. A. Klenke, E. Seise, J. Limpert, and A. Tünnermann, Opt. Express 19, 25379 (2011).
OPTICS LETTERS / Vol. 40, No. 4 / February 15, 2015
Multidimensional coherent pulse addition of ultrashort laser pulses Marco Kienel,1,2,* Michael Müller,1 Arno Klenke,1,2 Tino Eidam,1,2 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 Helmholtz-Institute Jena, Fröbelstieg 3, 07743 Jena, Germany 3
Fraunhofer Institute for Applied Optics and Precision Engineering, Albert-Einstein-Str. 7, 07745 Jena, Germany *Corresponding author: marco.kienel@uni‑jena.de Received September 17, 2014; revised January 7, 2015; accepted January 13, 2015; posted January 14, 2015 (Doc. ID 223366); published February 6, 2015
Spatially and temporally separated amplification and subsequent coherent addition of femtosecond pulses is a promising performance-scaling approach for ultrafast laser systems. Herein we demonstrate for the first time the application of this multidimensional scheme in a scalable architecture. Applying actively controlled divided-pulse amplification producing up to four pulse replicas that are amplified in two ytterbium-doped step-index fibers (6 μm core), pulse energies far beyond the damage threshold of the single fiber have been achieved. In this proof-of-principle experiment, high system efficiencies are demonstrated at both high pulse energies (i.e., in case of strong saturation) and high accumulated nonlinear phases. © 2015 Optical Society of America OCIS codes: (140.7090) Ultrafast lasers; (140.3280) Laser amplifiers; (140.3298) Laser beam combining; (140.3615) Lasers, ytterbium. http://dx.doi.org/10.1364/OL.40.000522
Today, high-performance ultrafast laser systems have opened up new possibilities for a variety of applications in industry, medicine, or fundamental science [1]. For the most demanding applications such as high-harmonic generation [2] or laser-based particle acceleration [3], ultrashort pulses with extremely high peak powers are required. Hereby, the achievable pulse energies and, therewith, the peak powers and intensities that can be generated are typically limited by nonlinear effects or optically induced damage. A way to overcome these limitations is to reduce the peak intensity during amplification by increasing either the beam cross-section or the pulse duration. Thus, today all state-of-the-art laser systems emitting highest peak powers are bulk lasers with large beam diameters. Additionally, they employ the wellknown technique of chirped-pulse amplification (CPA) [4], i.e., the pulse duration is increased during amplification by some orders of magnitude and compressed afterward. A novel approach for generating high peak powers is, instead of using only one single amplifier, to use many medium- or even small-energy amplifiers and to coherently combine their outputs afterward. This brings the advantage that more sophisticated laser geometries such as fibers, slabs, or thin disks can be employed. It allows, for the first time, to simultaneously produce high peak and average powers with an excellent beam quality and efficiency. Until now, the techniques for separated amplification and coherent combination can be divided into two approaches. The first one is spatially separated amplification, also referred to as coherent beam combination [5]. In this, the beam is split into a number of N beams and amplified in N spatially separated amplifiers. This can be seen as an artificial scaling of the mode-field diameter. Subsequently, these beams are coherently recombined improving ideally the average output power and pulse peak power by a factor of N. Especially fiber amplifiers benefit from this approach due to their 0146-9592/15/040522-04$15.00/0
single-pass architecture and, hence, their possibility for a straightforward spatial multiplexing. Recently, femtosecond pulses with 22 GW of pulse peak power and 230 W of average power have been achieved applying four large-mode area fibers in a fiber-CPA system [6]. The second approach to improve the pulse peak power is temporally separated amplification, also referred to as divided-pulse amplification (DPA) [7–10]. In this case, the pulses are split temporally into a number of M pulse replicas, which can be seen as an artificial increase of the CPA stretching ratio. This pulse train is generated prior to amplification and recombined afterward to one intense pulse, ideally improving the peak power by a factor of M. Recently, DPA has been applied in a fiber-CPA system achieving 1-GW femtosecond pulses within a single fiber employing a passive double-pass implementation [11]. Further scaling has been restricted, since saturation of the amplifier deforms the pulse train accompanied by nonlinear phase (B-integral) differences among them leading to a collapse of the combining efficiency. Applying separated pulse division and combination using an active DPA (ADPA) approach [12] provides a solution for this problem. Here, the input pulse train can be shaped to a growing amplitude resulting in a saturated output pulse train with (nearly) constant amplitude and, which is more important, the same amount of nonlinear phase acquired for each replica. Thus, with ADPA the achieved peak power could be improved to nearly 3 GW [12]. In this contribution, we report on the first (to the best of our knowledge) combination of both the spatial and the temporal multiplexing approach providing a scalable N · M multidimensional amplification scheme. In particular, the amplification and efficient recombination of eight pulses, i.e., four pulse replicas amplified in a two-channel combining setup, are demonstrated in a proof-ofprinciple experiment applying an active stabilization for both multiplexing dimensions. Figure 1 depicts the experimental setup. As front end, two different sources have been applied for investigating © 2015 Optical Society of America
February 15, 2015 / Vol. 40, No. 4 / OPTICS LETTERS
Fig. 1. Schematic representation of the multidimensional architecture applying two fiber main amplifiers and a pulse division up to four pulse replicas using the ADPA approach (PBS—polarizing beam splitter, HWP/QWP—half-/quarter-wave plate).
both the saturated and the unsaturated amplification regime at low and high B-integral values. For the first front end, femtosecond pulses from a mode-locked solid-state oscillator are stretched in a 170-m-long 6-μm corediameter fiber to approximately 50 ps duration. In the second case, pulses from a front end of a state-of-theart fiber-CPA system [6] are employed. These are already stretched to approximately 1.5 ns duration using a reflection-grating stretcher. The front-end pulses are pre-amplified in two 1-m-long core-pumped Yb-doped single-mode fibers with core diameters of 6 μm enclosing a fiber-coupled acousto-optic modulator. This provides seed pulses in the mW-average power range with adjustable repetition rate. Optical isolators are used to separate the amplification stages. For pulse division, two folded interferometric delay lines are employed consisting of combinations of polarizing beam splitters (PBSs) and half-/quarter-wave plates (HWPs/QWPs) producing up to four pulse replicas with alternating orthogonal p- and s-polarization [12]. A delay of 4.3 ns (the temporal hardcut for the stretcher of the fiber-CPA front end) between each replica is produced ensuring complete temporal separation. For efficient recombination in a separate combination stage, piezo-driven mirrors are employed in each delay line in order to match the corresponding path lengths. To provide sufficient degrees of freedom for shaping the pulse train and to compensate for saturation a small nondelaying Mach–Zehnder interferometer-type stage is additionally introduced [12]. Afterward, the generated pulse train is divided into two channels of a Mach–Zehnder-type amplifying interferometer by another division using a further combination of HWP and PBS. Due to this division, pulse trains of four pulses each with equal polarization but different phase patterns enter each channel, while one of them double-passes a piezodriven mirror delay-line for active phase control. These pulse trains are amplified in 1.2-m-long polarizationmaintaining (PM) core-pumped Yb-doped single-mode fibers with core diameters of 6 μm (the estimated saturation energy is 13 μJ). Polarization-dependent isolators
523
in front of each main amplifier prevented feedback from the division interferometers. HWPs are applied to propagate the trains through the correct axes of the fibers and, ultimately, overlap them at the right output port of the subsequent PBS. Due to the imposed phase patterns, the initial alternating polarizations are recovered. A further HWP flips the polarization orientation of the pulse train by 90° to remove the temporal delays with the help of similar delay lines as for pulse division. Ring-delay lines have been applied instead of double-pass lines [12] to prevent back reflections and, hence, lasing of the high-gain main amplifiers due to possible leakage from the second pass through the PBSs of the interferometers. Finally, a combination of HWP and PBS separates all fractions from the combined output that are in the wrong polarization state. A few percent of the output beam is ejected onto a photo-diode required for active stabilization. For the experiments described herein, the LOCSET technique [13] is employed, which uses distinct RFmodulations, in this case 4.5, 6.0, and 7.3 kHz, imprinted on each delayed branch by the three phase actuators. Requiring just a single detector, the control electronics generates error signals caused by phase fluctuations for the respective path by demodulating at the corresponding frequency. To minimize the error signals, the corrected phases are fed back to the piezos, therefore, maximizing the combined output. The most important parameter for every combining architecture is the system efficiency ηsys [14]. It is defined as the ratio between the power contained within the main combined output pulse and the sum of the output powers for each amplifier. This value includes both the losses of the combining process itself and the losses due to the additional components required for combining. Of course, in the multidimensional case, ηsys > 1∕N · M has to be fulfilled in order to achieve a power increase in comparison to a single emitter. However, in order to achieve high wall-plug efficiencies, typically ηsys values as close as possible to 100% are desirable. Therefore, it is interesting to investigate the evolution of ηsys both for an increasing channel/replica count and for increasing pulse energies (and therewith B-integral and saturation) per channel. Since the proposed architecture depicted in Fig. 1 employs spatial and temporal multiplexing independent from each other, scaling considerations for an increasing channel [15] and replica count [12] are in good approximation also valid in this multidimensional case. The same holds for the energy-scaling considerations. In general, spatial multiplexing is typically more efficient at high energies due to the symmetric combination process. Unfortunately, as discussed above, this is not the case for temporal multiplexing due to saturation and the deformation of the pulse-train. ADPA can, contrary to passive DPA, compensate for this deformation. However, typically, there is still some efficiency drop at highest energies due to residual amplitude differences in the pulse train that is optimized for vanishing B-integral differences and the shaping of each individual replica due to saturation. Thus, in the following, two operation points have been investigated, one with high B-integral but negligible saturation and one with both strong nonlinear phases and strong saturation.
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Fig. 2. System efficiencies as a function of the output pulse energy within the main combined pulse for the combination of two channels applying no pulse division (one rep.), and a division into two and four pulse replicas for (a) 50-ps pulses and (b) 1.5-ns pulses.
First, the amplifiers are operated with the 50-ps pulses to investigate the unsaturated regime at high B-integrals. Therefore, the seed power in front of each main amplifier is kept constant at 1 mW, which is amplified with a maximum gain of approximately 280 each, while the repetition rate is reduced iteratively from 20.0 MHz to a minimum of 124.9 kHz. In Fig. 2(a) the determined system efficiencies as a function of the pulse energy within the main pulse at the system output are depicted for the combination of both channels applying no pulse division (one replica), and a division into two- and four-pulse replicas. It can be seen that high system efficiencies have been achieved even for extremely high B-integrals (estimated for the maximum energy to 18, 22, and 28 rad for four, two, and one replica, respectively). The offset from 100% combining efficiency is due to the losses from the optical components behind the main amplifiers. Considering only the p-polarization transmission properties of the PBSs employed after the main amplifiers, a theoretical maximum of about 94% could be expected, which is also marked in Fig. 2. The propagation loss through each delay line for temporal combination is about 1%–2%. Further impacts are wavefront mismatches resulting from the different path lengths of the beams to be combined. For this reason the beam diameter is increased to 4.5 mm to keep the combination losses for the temporal recombination between the first and the fourth pulse replica below 2%. Any additional efficiency degradation can be attributed to dispersion and B-integral differences between both channels [15] and differences in both pulse-train shapes after the amplifiers. The latter is due to, on the one hand, slightly different fiber inputcouplings, and, on the other hand, residual differences in the amplification characteristics of the channels. Next, to operate the amplifiers in saturation, the 1.5-ns input pulses are employed, which also raises the damage threshold. The seed power of each amplifier again is kept constant at 1 mW, while the repetition rate is reduced from 2.0 MHz to a minimum of 5.9 kHz. Figure 2(b) shows the determined system efficiencies in dependence on the output pulse energy within the main pulse again for the application of one-, two-, and four-pulse replicas. At low pulse energies, a similar behavior as for the picosecond pulses is obtained, since saturation is not as pronounced. The similar drop in efficiency for both pulse divisions at increasing pulse energies demonstrates that this is owed
Fig. 3. (a) Photo-diode measurements of the input pulse train (orange) and outputs of both amplifiers (red and blue) and (b) for the combined pulse at a pulse energy of 37 μJ.
by deviations between both channels, as described above. For the case applying four pulse replicas, a maximum combined pulse energy of 37 μJ has been achieved (verified by energy meter measurements). This value is approximately five times above the single-pulse damage threshold of the fiber. The estimated B-integrals within the main amplifiers are 7 rad at the maximum energy for each case. At repetition rates going down to the kHzrange, amplified spontaneous emission has to be considered, which is 75% even for the highest energies prove the power-scaling ability of this multidimensional technique. For comparison, the calculated efficiency for a similar passive DPA approach employing the model presented in [10] is also depicted in Fig. 2(b). Here, a small-signal gain of 30 dB for each amplifier and PBS with Rs ≥ 99%, T p ≥ 97% are used. The rapid efficiency drop due to saturation can be clearly seen preventing the passive setup from reaching these energies at all. Figure 3(a) shows the pulse trains at the output of the pulse division stage and at the outputs of both fiber amplifiers at an energy of 37 μJ, which are measured with an 18-ps rise-time photo-diode and a 30-GHz sampling scope. Saturation is clearly visible at these energy values. Additionally, please note the slight amplitude decrease of the output pulse train resulting from the B-integral adaption of each replica. In Fig. 3(b) the combined output pulse is depicted for a pulse energy of 37 μJ. At this energy level, pre- and postpulses become more severe due to temporal combination losses regarding the effects discussed above. The pulse contrast is in the order of 20 dB, which slightly decreases toward higher energies. Although this value is already sufficient for a variety of applications, further contrast improvements are feasible, e.g., via temporal gating, and are subject of ongoing research. In conclusion, the multidimensional amplification approach, i.e., the combination of both spatially and temporally separated amplification, has been demonstrated in a scalable architecture for the first time. Applying four-pulse replicas using the ADPA method and two fiber amplifier channels in a completely phase-locked
February 15, 2015 / Vol. 40, No. 4 / OPTICS LETTERS
implementation, high system efficiencies have been demonstrated at both high pulse energies and high B-integrals. In a next step, this concept will be applied to a state-of-the-art fiber-CPA system scaling the achievable pulse energy per channel to the multi-mJ range. We are confident that increasing the channel and replica count to an 8 × 4 scheme will make TW-class fiber lasers feasible in the near future. This work has been partly supported by the German Federal Ministry of Education and Research (BMBF) under contract 13N12082 “NEXUS,” contract 13N13167 “MEDUSA” and by the European Research Council under the ERC grant agreement no. [617173]. A. K. and M. K. acknowledge financial support by the HelmholtzInstitute Jena. T. E. acknowledges financial support by the Carl-Zeiss Stiftung. References 1. H. Fattahi, H. G. Barros, M. Gorjan, T. Nubbemeyer, B. Alsaif, C. Y. Teisset, M. Schultze, S. Prinz, M. Haefner, M. Ueffing, A. Alismail, L. Vámos, A. Schwarz, O. Pronin, J. Brons, X. T. Geng, G. Arisholm, M. Ciappina, V. S. Yakovlev, D.-E. Kim, A. M. Azzeer, N. Karpowicz, D. Sutter, Z. Major, T. Metzger, and F. Krausz, Optica 1, 45 (2014). 2. M. Krebs, S. Hädrich, S. Demmler, J. Rothhardt, A. Zair, L. Chipperfield, J. Limpert, and A. Tünnermann, Nat. Photonics 7, 555 (2013). 3. W. P. Leemans, B. Nagler, A. J. Gonsalves, Cs. Tóth, K. Nakamura, C. G. R. Geddes, E. Esarey, C. B. Schroeder, and S. M. Hooker, Nat. Phys. 2, 696 (2006).
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