We propose and investigate experimentally an interferometrically stable, polarization-selective pulse multiplexing scheme for direct laser amplification of picosecond pulses. The basic building block of this scheme is a Sagnac loop which allows for a straightforward scaling of the pulse-multiplexing scheme. Switching the amplifier from single-pulse amplification to burst mode increases extraction efficiency, reduces parasitic non-linearities in the gain medium and allows for higher output energies. Time-frequency analysis of the amplified output pulses demonstrates the viability of this approach.
© 2012 OSA
Intense pump pulses with durations in the range of 10 – 50 ps are of particular interest for the rapidly evolving field of chirped parametric pulse amplification (OPCPA) [1–5]. Such ps pump pulses provide sufficiently high broadband parametric gain with good efficiency; they are easy to synchronize with OPCPA seed pulses  and are relatively insensitive to the temporal jitter caused by environmental influences on the OPCPA setup. Pulse stretchers and compressors required to stretch a broadband seed pulse to the duration of such picosecond pump pulses and to recompress it after parametric amplification are very compact. Direct picosecond pulse amplification obviates the complexity and compressor losses of the CPA amplification scheme and can be performed in high-gain Nd-doped crystals that do not exhibit sufficient bandwidth to support the CPA scheme. The main difficulty with direct picosecond pulse amplification to high energies is the onset of parasitic non-linearities that limits energy scaling. Accumulation of non-linearities is avoided by increasing the amplifier mode cross-section and achieving robust gain in a single-pass. Picosecond pulses in excess of 1 J can be produced by this method with Nd:YAG and Nd:YLF amplifiers at repetition rates of 5–10 Hz. For cw pumped kHz repetition rate amplifiers, the strategy of expanding the beam cross-section does not work, because the pump powers required to maintain high single-pass gain would result in thermal fracture of the crystal and/or parasitic effects such as thermally induced birefringence as well as mode volume reduction and beam focusing due to thermal lensing.
Two techniques to circumvent energy scaling in picosecond amplification have been recently proposed: Tilted Pulse Amplification (TPA) , requiring pulse tilting with diffraction gratings, which is rather inexpedient; and Divided Pulse Amplification (DPA) , based on temporal pulse-multiplexing in a stack of birefringent crystals. Unfortunately, it is practically impossible to apply the DPA technique in the case of long picosecond pulses because temporal separation of two replicas of a 50 ps pulse in a birefringent crystal (for example YVO4) requires a crystal that is over 7 cm long, and the length of the crystal doubles with each successive pulse division. Here, a variant of DPA, a Sagnac-Interferometer MultiPass-Loop (SIMPL) , is demonstrated that provides sufficient pulse separation for 10–50 ps pulses without introducing excessive nonlinear phase in the amplifier chain.
2. Sagnac loop as basic building block
The main building block of the SIMPL scheme is an interferometrically stable common-path counter-propagating Sagnac interferometer with polarization beam-splitting. A schematic implementation is shown in Fig. 1(a). The polarization of an incoming, linearly polarized laser pulse is rotated by a half-wave plate such that the pulse energy is equally split by a thin film polarizer (TFP) into a transmitted, horizontally (p)-polarized and a reflected, vertically (s)-polarized beam. After individual amplification of the pulse replicas in a laser crystal they are recombined on the same TFP. The Sagnac-Loop is intrinsically interferometrically stable, since any phase distortion along the optical path is acquired by both replicas in equal measure.
To avoid excessive non-linear distortions, the B-integral,10], has to be minimized. Here, λ is the wavelength, I(x) is the optical intensity along the beam axis and n2 is the nonlinear refractive index. In the case of SIMPL, the main prerequisite for lowering the B-integral of the amplifier is the temporal separation of pulse replicas inside the amplifying crystal of the Sagnac loop. This can be achieved by adjusting the clockwise and anti-clockwise distances from the TFP to the crystal such that one optical path is longer than the other. Thus, the intensity inside the crystal is reduced by a factor of n, where n is the number of pulse replicas being amplified. After one round trip, the temporal overlap of the two pulse replicas is restored as they recombine on the polarizing beam splitter. The TFP, which initially splits the incoming pulse, also acts as an output coupler for the recombined, amplified pulse. In general, the output from the Sagnac loop should be decoupled from the input by using appropriate polarization optics. In the configuration shown in Fig. 1(a) the polarization state of the pulse replicas is not changed during one round trip. Therefore, the output is automatically separated from the input. More elaborate schemes of the Sagnac-Loop are shown in Fig. 1(b) and 1(c), where each pulse replica passes the amplifier crystal twice. The temporal separation of the pulse replicas is preserved during both passages and is then compensated for on the return path to the polarizing beam splitter.
Although the configurations depicted in Fig. 1(a) and 1(b) are the most straightforward ones, they are virtually not applicable because of thermally induced birefringence. Figure 1(c) shows a realistic modification of the Sagnac loop that addresses the problem of intrinsic or thermally induced birefringence. Before passing the laser crystal, a half-wave plate turns the polarization state of the reflected, s-polarized beam into horizontal polarization. Since the polarization states of the pulse replicas are interchanged inside the loop, the input and output ports become identical. Therefore, special care has to be taken to separate the incoming seed pulse from the amplified output pulse. The out-coupling unit in this case comprises of an additional TFP at the entrance and a Faraday rotator. The incoming, p-polarized beam is transmitted through the first TFP and is then rotated by +45° by the Faraday rotator. A subsequent TFP splits the pulse into its horizontal and vertical polarization components. After one round trip inside the Sagnac loop amplifier, the pulse replicas recombine at the TFP. Again, the Faraday rotator turns the polarization by +45°, resulting in a vertically polarized pulse, which is reflected off from the entrance TFP. By this means, the input port is decoupled from the output port.
3. Scalability of SIMPL
SIMPL is not limited to only two pulse replicas. By folding secondary Sagnac loops inside a parent loop the number of pulse replicas can be doubled. For isotropic crystals such as Nd:YAG, a configuration as in Fig. 2(a) can be used. This arrangement is closely related to the pulse splitting scheme from Zhou et al. . Here, the basic building block, highlighted by the dashed rectangle, doubles the number of incoming pulses. This basic unit resembles one of the stacked birefringent crystals used by Zhou et al. After passing the crystal, the polarization state of the pulse replicas is rotated by 90° by using a quarter-wave plate or faraday rotator in double-pass, the latter having the advantage of compensating induced depolarization . On the way back, those pulses that were initially transmitted through the TFPs are now reflected off. Step-by-step, the temporal separation of the replicas is brought to zero until a single, amplified output pulse is restored.
This scheme, however, may suffer from thermally induced birefringence. Using gain media with sufficiently strong natural birefringence eliminates thermally induced depolarization losses. Figure 2(b) demonstrates a modification of the SIMPL scheme, which can be used in combination with non-isotropic, birefringent crystals. To minimize reflection losses at Brewster-cut amplifier crystals, the half-wave plate within the very last building block, just before the first focusing mirror, turns the vertical into horizontal polarization state. As in the previous set-up, an additional basic building block doubles the number of incoming pulses. In front of the TFP a Faraday rotator turns incoming horizontal and vertical polarization states by 45°. In this manner, the number of pulses is doubled since the TFP separates horizontal and vertical polarization components. Here, the laser pulse is split into a total of eight replicas of equal power before amplification. The temporal delay between pulse replicas can be adjusted via translation stages, shown as blue rectangles. Since the amplifier crystal is a Brewster-cut crystal, the half-wave plate within the very last building block, just before the first focusing mirror, turns the vertical into horizontal polarization state. Via a horizontal rooftop the pulses pass the crystal twice and travel in opposite direction with respect to the incoming path. Step-by-step, the amplified pulse replicas are recombined at the TFPs until a single pulse is restored and ejected at the last polarizing beam splitter from the Sagnac loop.
4. General concept of pulse division
The SIMPL configuration is particularly suited for longitudinally pumped solid state amplifiers. The main idea behind the scheme is to reduce the beam cross-section while keeping the pump at the maximum level just below the damage threshold of the crystal. By dividing the seed pulse into n replicas the accumulated non-linear phase will be reduced by a factor of n, cf. Eq. (1). This in turn allows to reduce the amplifier mode area of the seed beam by the same factor of n, which would preserve the initial input intensity. In return, the gain seen by the pulse replicas increases, because of a higher degree of inversion in the amplifier crystal. Also the extraction efficiency of the amplifier is increased, which is related to the fluence of the seed beam . Furthermore, the advantage of SIMPL for an unsaturated or weakly saturated amplifier thus becomes obvious if the area of the pump mode is correspondingly reduced. Since the logarithmic gain coefficient g is proportional to the population inversion density Δn inside the amplifier crystal,
Nd-based systems, especially Nd:YAG, may profit from using SIMPL since the efficiency of picosecond amplification of those systems is strongly limited by the fact that only one of two 4F3/2 Stark-sublevels participates in the amplification. The laser transitions with the highest cross sections, emitting at 1064 nm and 1061 nm, start from the higher lying sublevel which comprises only 40% of the total 4F3/2 population at room temperature. Only some low-gain transitions, for example at 946 nm, start from the lower level. Via thermalization the upper 4F3/2 sublevel is replenished by the energetically lower lying sublevel . This thermalization time is approximately 3–5 ns . Thus, for nanosecond pulses the remaining part of the population from the second Stark sub-level thermalizes to the working level early enough. However, for direct picosecond amplification this additional inversion is typically lost because the thermalization time is comparable or longer than the pulse duration. Splitting the seed pulse into replicas will automatically help to utilize this untapped inversion.
5. Amplification and coherent pulse recombination
5.1. SIMPL with 2 pulse replicas
The viability of SIMPL was tested in a proof-of-principle experiment that amplified ∼20 ps chirped seed-pulses from a Ti:Sapphire CPA system. The proof of a successful amplification in counter-propagating arms, followed by an efficient coherent pulse recombination is illustrated in Fig. 3. For this demonstration a broadband amplifier was chosen deliberately because a simple spectral measurement of the broadband recombined pulse would immediately confirm whether all frequencies, corresponding to different time instances, are added in phase. The setup was built according to the schematic drawing in Fig. 1(c) as a post-amplifier to a 1 kHz amplifier. The seed pulse was evenly split into 150 μJ pulses per arm. Both replicas were amplified to 700 μJ per arm, resulting in 1.35 mJ of the recombined output. The single-pass gain was kept rather low in order to avoid unequal amplification of the two seed pulse replicas due to gain saturation. Directing the whole seed energy into one single arm results in optical damage of the Ti:Sapphire crystal, whereas the split-pulse amplification remains below the damage threshold. As is evident from Fig. 3, the dominating part of the losses (about 10%) in the recombined pulse can be attributed to the uneven spectral transmission of the thin-film polarizer used in this experiment. Nevertheless, the spectral recombination is remarkably good.
5.2. SIMPL with 4 pulse replicas
The scalability of the output power by increasing the number of pulse replicas was demonstrated with a four-replica SIMPL amplifier, cf. Fig. 4. Here, the recombination is achieved exclusively with half-wave plates without the need for expensive Faraday rotators. In this configuration a vertical rooftop after the second beam splitter changes the beam height two of the pulse replicas. The vertical position of the pulse replicas is interchanged after the first pass through the crystal by a second vertical rooftop.
Figure 5(a) shows the output energy as a function of total seed energy in this configuration. In order to minimize uneven splitting of the seed pulse on the TFPs, a narrower bandwidth of the seed pulse was used, cf. Fig. 5(b). Because of the smaller bandwidth, approximately 20 nm at the -level of the power spectrum, the maximum available seed energy was significantly lower than in the aforementioned two-replica set-up. Again, the overall gain was deliberately kept low in order to minimize recombination losses due to gain saturation. The seed pulse duration was adjusted by tuning the prism compressor to ∼450 fs in order to show the ability of SIMPL to attain high output pulse peak intensity while preserving the pulse quality on the one hand, and its ability to prevent crystal damages on the other hand. In the four-copy, double-pass SIMPL amplifier the extracted power can be up to four times higher than in a conventional amplifier where seed pulses are not split into several replicas, while keeping the pulse quality the same. As in the case of the two-replica SIMPL amplifier discussed above, the recombined spectrum of the four-replica SIMPL amplifier is smooth without signs of any spectral interferences, demonstrating the intrinsic interferometric stability of the SIMPL amplifier.
6. Temporal characterization of recombined output pulses
To further characterize the performance of the SIMPL scheme we analyze amplified pulses at the output of the Sagnac-loop using second harmonic Frequency-Resolved Optical Gating (SH-FROG) . In order to compare single pulse amplification with multi-replica amplification, the setup sketched in Fig. 4 is used. For the single-pulse case the wave-plates are rotated such that the incoming pulse is not divided into replicas. The results are summarized in Table 1. In the first case, which serves as a reference case, the seed energy is kept rather low in order to avoid any non-linear phase effects inside the amplifier crystal. The output energy for the reference case is 54 μJ. As the seed energy is increased, the amplifier crystal experiences higher intensities. As a result, the cumulative non-linear phase shift, described by the B-integral, increases and distorts the spatial and temporal pulse profile. Any further increase of the seed energy results in optical damage of the amplifier crystal. The split-pulse amplification, on the other hand, not only remains below the damage threshold of the crystal but shows a temporal phase that is almost indistinguishable from the phase of the reference case.
The measured and reconstructed SH-FROG traces for the first, second and fourth case (reference, moderate single-pulse amplification and SIMPL amplification, respectively) are shown in Fig. 6. Measured and reconstructed SH-FROG traces agree very well. The similarity of the SH-FROG traces of the recombined pulse from the SIMPL scheme with an output energy of 220 μJ [Fig. 6(c)] and the reference case [Fig. 6(a)] is quite obvious. In contrast, the SH-FROG trace of the pulse that is obtained without pulse division and recombination with an output energy of 185 μJ [Fig. 6(b)] clearly deviates from the reference case. Figure 7 emphasizes the quality of the recombined pulse of the SIMPL amplifier. Figure 7(a) shows the measured and retrieved spectra (blue and green, respectively) of the reference pulse. In comparison, the shape of the spectrum of the amplified pulse for case 2 in Fig. 7(b) clearly differs and is subject to substantial spectral broadening due to self phase modulation. The spectrum of the SIMPL output pulse in Fig. 7(c) does not show any noticeable difference from the reference case. Spectral shape and width are conserved remarkably well. The right hand side panels in Fig. 7 are even more convincing. In the case of moderate amplification without pulse division, see the middle row of Fig. 7, the differential phase, which is proportional to the temporal intensity profile, is about 2.5 rad at the peak of the envelope, clearly indicating substantial non-linear phase shift of the pulse.
The accumulated B-integral can be estimated using the Frantz-Nodvik equation :Equation (1) can be rewritten as: Table 1.
The seed energy in case 2 is 20.5 μJ, whereas in case 4 the seed energy per replica is 6.1 μJ. Therefore, the calculation for the B-integral in the second case gives a value of 2.48 rad, whereas for the recombined SIMPL pulse the non-linear phase shift is as small as 0.75 rad. The nonlinear phase shift in the reference case 1 is about 0.7 rad. The cumulative B-integral must be kept below ≤3–5 to avoid damages to the crystal and distortions to the laser pulse . This simple estimate is supported by the data presented in Fig. 7, where the differential phase of the amplified single-pulse of the second case significantly exceeds that of the recombined SIMPL pulse, which is almost flat across the temporal intensity profile. Thus, the accumulated non-linear phase of a single seed pulse at the output energy level of 185 μJ is substantially higher than the accumulated non-linear phase for the case where the seed power is distributed over four replicas, with a recombined output energy of 220 μJ.
In this paper we have demonstrated a new approach to divided pulse amplification which is based on polarization-selective pulse multiplexing using TFPs which is best suited for narrowband picosecond pulses. By exploiting the intrinsic interferometric stability of the Sagnac loop coherent recombination of the pulse replicas can be achieved. Moreover, due to the possibility of interleaving several Sagnac-loops our approach offers a straightforward scalability of the amplification scheme. The main advantage of the SIMPL technique is the reduction or avoidance of parasitic non-linearities in the amplifier medium which allows for higher output energies. Spectral and temporal analyses of amplified output pulses have shown the viability of this new approach. SIMPL can also be applied in combination with (OP)CPA, either to avoid scaling stretchers and compressors to extremely large sizes, for example in carrier-envelope-phase-stable amplifiers, or to avoid spectral shifts and gain narrowing in CPA, avoiding elaborate arrangements, such as amplification comprising both positively and negatively chirped stages .
This work has been supported by the Austrian Science Fund (FWF), grants U33-N16 and F1619-N08, and by the Austrian Research Promotion Agency (FFG), Eurostars grant 834415.
References and links
1. A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992). [CrossRef]
2. R. T. Zinkstok, S. Witte, W. Hogervorst, and K. S. E. Eikema, “High-power parametric amplification of 11.8-fs laser pulses with carrier-envelope phase control,” Opt. Lett. 30, 78–80 (2005). [CrossRef] [PubMed]
3. N. Ishii, L. Turi, V. S. Yakovlev, T. Fuji, F. Krausz, A. Baltuska, R. Butkus, G. Veitas, V. Smilgevicius, R. Danielius, and A. Piskarskas, “Multimillijoule chirped parametric amplification of few-cycle pulses,” Opt. Lett. 30, 567–569 (2005). [CrossRef] [PubMed]
4. S. Witte, R. Zinkstok, W. Hogervorst, and K. Eikema, “Generation of few-cycle terawatt light pulses using optical parametric chirped pulse amplification,” Opt. Express 13, 4903–4908 (2005). [CrossRef] [PubMed]
5. K. Yamakawa, M. Aoyama, Y. Akahane, K. Ogawa, K. Tsuji, A. Sugiyama, T. Harimoto, J. Kawanaka, H. Nishioka, and M. Fujita, “Ultra-broadband optical parametric chirped-pulse amplification using an Yb : LiYF4 chirped-pulse amplification pump laser,” Opt. Express 15, 5018–5023 (2007). [CrossRef] [PubMed]
6. N. Ishii, C. Teisset, T. Fuji, S. Kohler, K. Schmid, L. Veisz, A. Baltuska, and F. Krausz, “Seeding of an eleven femtosecond optical parametric chirped pulse amplifier and its Nd3+ picosecond pump laser from a single broadband Ti:Sapphire oscillator,” IEEE J. Sel. Top. Quantum Electron. 12, 173–180 (2006). [CrossRef]
9. S. Roither, A. Verhoef, O. D. Mücke, G. Reider, A. Pugzlys, and A. Baltuska, “Sagnac-interferometer multipass-loop amplifier,” in “Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies,” (Optical Society of America, 2008). CTuK4.
10. A. E. Siegman, Lasers (University Science Books, 1986).
11. W. Koechner, “Properties of solid-state laser materials,” in Solid-State Laser Engineering, vol. 1 of Springer Series in Optical Sciences (SpringerBerlin / Heidelberg, 2006), pp. 38–101.
12. J. Degnan, D. Coyle, and R. Kay, “Effects of thermalization on Q-switched laser properties,” IEEE J. Quantum Electron. 34, 887–899 (1998). [CrossRef]
13. D. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993). [CrossRef]
14. W. Koechner and M. Bass, Solid State Lasers: A Graduate Text (Springer, New York Berlin Heidelberg, 2003).
15. M. Kalashnikov, K. Osvay, I. Lachko, H. Schnnagel, and W. Sandner, “Suppression of gain narrowing in multi-TW lasers with negatively and positively chirped pulse amplification,” Appl. Phys. B 81, 1059–1062 (2005). [CrossRef]