A 2.051-µm laser source delivering picosecond pulses with energies as high as 34 mJ at a 1 kHz repetition rate is reported. The main amplifier system is based on Ho:YLF and consists of a regenerative amplifier (RA) and a single-pass booster amplifier running at room temperature. The continuous-wave pumped, high-gain RA produces pulse trains with up to 10-mJ energy when operating in a stable periodic doubling regime. The recorded complete RA bifurcation diagram agrees well with our numerical simulations. At the highest pulse energy after the booster amplifier the pulse-to-pulse fluctuations are as low as 0.9% rms. Pulse compression is performed up to the 10-mJ level resulting in a duration of 37 ps.
© 2015 Optical Society of America
High-repetition rate, high-energy ultrafast sources in the mid-infrared (mid-IR) are of critical importance for applications in nonlinear optics such as strong field physics [1,2], high-harmonic generation [3,4], the development of novel x-ray sources [5,6], and THz generation [7,8]. Optical parametric chirped-pulse amplification (OPCPA) represents an established technique for the generation of high-energy ultrashort mid-IR pulses [9,10]. In this amplification scheme, picosecond near-infrared pulses of high energy drive the parametric process by which the mid-IR pulses are amplified. The application of high energy pump sources working at 2 µm instead of 1-µm sources widens the range of applicable nonlinear materials in the spectral range beyond 4 µm. In particular, highly efficient non-oxide crystals such as ZnGeP2 (ZGP) can be applied for OPCPA .
Holmium-doped amplifiers seeded by femto- or picosecond pulses appear well suited to pump ZGP-based OPCPA schemes. Among the Ho-doped hosts, Ho:YLF and Ho:YAG are most widely used as 2-µm gain media and have proven their suitability for high energy operation above 100 mJ in the nanosecond regime [12–14]. The age of 2-µm picosecond regenerative amplifiers (RA) with millijoule pulse energy started in 2013 with the demonstration of a Ho:YAG RA yielding 3 mJ at a 5 kHz repetition rate . In the same year, Dergachev reported 1.7 mJ at 1 kHz using Ho:YLF as gain medium and additional single-pass power amplification up to 11 mJ in a double-rod arrangement . Recently, 5.5 mJ pulse energy from a Ho:YLF RA have been reported . However, this RA operates at a fairly low repetition rate of 100 Hz, corresponding to an average power of 0.5 W. In addition, Hemmer et al. demonstrated single-pass amplification at 100 Hz using a cryogenically cooled Ho:YLF rod yielding up to 39 mJ pulse energy .
Very recently, we have demonstrated a high repetition rate Ho:YLF RA, delivering up to 1.1 mJ pulses at a 10 kHz repetition rate with a clean single output energy signature . In the few-kilohertz regime, the pulse repetition rate frep approaches the reciprocal upper-state lifetime τ of the respective Ho-transition, i.e., frep ≈τ−1, which may result in dramatic in- and/or multistabilities of the output energy . We have carefully analyzed this nonlinear behavior and were able to demonstrate a Ho:YLF RA operating in a double pulsing regime delivering stable 8 mJ pulses at a 1 kHz repetition rate . In parallel to this work, a Ho:YLF RA delivering 6.9 mJ at 1 kHz repetition rate in a linear cavity arrangement has been presented . The authors investigated bifurcation instabilities by varying the round trip number only. The single-energy regime at 1 kHz was achieved for more than 33 round trips at the applied pump power of 108 W, with, however, a beam profile of limited quality and very limited long time stability.
Here we report new results and progress towards a compact 1-kHz Ho:YLF picosecond amplifier system operating at room temperature. Our system features a high-gain RA that enables the generation of stable pulses with energies >10 mJ. The RA is designed for operation in the double pulsing regime and act as seed source for a booster amplifier. Stable pulse trains up to 34 mJ pulse energy are achieved by single passing the Ho:YLF amplifier rod, corresponding to an average output of 34 W.
2. Experimental setup
The experimental setup of the chirped pulse amplification (CPA) system at 2 µm wavelength is shown in Fig. 1. The seed source and the regenerative amplifier (RA) are similar to our system reported in . The supercontinuum (SC) is generated in a highly nonlinear fiber by launching 75 fs pulses at 1.55 μm from an Er:fiber laser operating at 40 MHz repetition rate (Fig. 1). Since the Tm:fiber preamplifier is designed to amplify the spectral range from 2030 to 2110 nm only a small part of the SC spectrum in the anomalous dispersion range is used. This fraction of the SC spectrum is centered at 2075 nm and the soliton fission process is managed for minimum noise amplification as well as resulting output fluctuations . After pre-amplification the seed pulses are negatively chirped with energy of 18 nJ and 9 ps duration. The subsequent pulse picker reduces the repetition rate to the few-kilohertz range. A chirped volume Bragg grating CVBG (OptiGrate) based on photo-thermo-refractive (PTR) glass serves as stretcher . Its 13.5-nm wide reflection band is centered at 2053 nm and the measured reflectivity amounts to 90%. The antireflection(AR)-coated, rectangular shaped CVBG (aperture: 5 x 5 mm2) with a length of 50 mm exposes a stretching factor of −27 ps/nm. The seed pulses are stretched to a duration of ~950 ps by double-passing the CVBG (FWHM bandwidth of stretched pulse: 6 nm). Since the CVBG reflection band is much narrower than the ~70 nm broad spectrum (zero level) of the seed pulses, the energy of the stretched pulses is reduced to 0.5 nJ.
The birefringent Ho:YLF material is selected as the gain medium for the RA and the booster amplifier, mainly because of its ~5-times lower nonlinearity compared to the isotropic Ho:YAG . The polarization orientation in the Ho:YLF crystals is chosen parallel to the c-axis (E║c, π-polarization) because of the two times higher emission cross section compared to the E⊥c orientation (σ-polarization) .
The RA is designed as a ring cavity with an AR-coated, 50 mm long, 0.5% Ho-doped YLF rod as active medium positioned in one resonator waist. The direct water-cooled Ho:YLF crystal is end-pumped by a randomly-polarized cw Tm:fiber laser emitting at 1940 nm (IPG Photonics). The pump beam diameter in the active medium is chosen close to the ~900 µm diameter of the laser mode. A Galilean type telescope is implemented to adapt the seed beam to the RA resonator mode. An RTP Pockels cell (Leysop), operating in the λ/2 regime, is placed in the second waist of the RA cavity for injecting the seed pulse and extracting the amplified pulse.
The single-rod booster amplifier is utilized in single-pass geometry with longitudinal pumping (Fig. 1). The pump power for this amplifier is provided by a cw Tm:fiber laser (IPG Photonics), identical to the pump laser for the RA. It delivers up to 105 W randomly-polarized output at 1939 nm wavelength. Due to the nearly diffraction-limited beam quality of the pump laser an excellent overlap between pump and amplified beam is provided. The collimated pump beam is focused into the 50-mm long, 0.75% Ho-doped YLF booster amplifier rod to a spot size of ~1.6 mm. The latter is chosen comparably large to avoid any damage to the Ho:YLF crystal. To minimize adverse effects of water vapor absorption on the pump beam and the generated 2-µm pulses, both amplifiers are purged with nitrogen.
In CPA systems where stretching is provided by a CVBG, the same device can also be used for compression . We opt for a second CVBG as compressor to prevent any risk of back coupling in the high gain RA. The reflection band of the compressor CVBG (OptiGrate) is centered at 2051 nm and exposes a width of 11 nm. It also differs in dispersion with a stretching factor of −43 ps/nm whereas the physical dimensions and reflectivity are the same as the stretcher CVBG.
3. Regenerative amplifier – modeling and experimental results
The amplified pulse train in cw-pumped RAs is influenced by gain depletion caused by the previous pulse, in particular when operating at repetition rates close to or higher than the inverse of the upper state lifetime . Rather complex behavior may appear here, including period doubling and multi-stabilities. In the literature [20,26–28], such nonlinear dynamics are associated with a total gain in the order of 106 and energy extractions of ~50% with respect to the absorbed pump power. Except of  these reports are dedicated to Nd- and Yb-doped gain media in the 1 µm spectral range, where the targeted few-kHz repetition rates are of less concern due to the roughly ten times shorter upper state lifetime compared to Ho-doped materials. For the investigated gain medium Ho:YLF with an upper-state lifetime of 14 ms, the lower limit of the RA repetition rate at which bifurcations can start to occur is around 0.1 kHz.
We performed numerical simulations of the bifurcation diagrams for few-kHz repetition rate Ho:YLF regenerative amplifiers. A modified Frantz-Nodvik equation  is used for calculation of the pulse amplification, which takes into account the spectral features of Ho:YLF and its quasi-three-level behavior [30,31]. The absorption cross sections of Ho:YLF at 1940 nm are 0.35 x 10−20 cm2 and 1.02 x 10−20 cm2 for σ- and π-polarization, respectively. The emission cross section at 2050 nm is 1.50 x 10−20 cm2 for π-polarization . Given the targeted repetition rate of 1 kHz for the booster amplifier, the parameters for high-energy, stable double-pulsing of the RA at 2 kHz are simulated.
With respect to our previous work  an optical-to-optical efficiency >20% of our RA is supposed. In view of the 50 W maximum pump power, extraction of 10 W average power is expected. Two effects caused by the high average power of the pump laser, have to be taken into account for stable operation. First, a negative thermal lens develops in the pumped YLF crystal, resulting in an increased laser mode. Second, the pump mode decreases due to thermal effects in our current pump lens configuration. The overlap of both modes determines the active volume, and, therefore, the saturation energy. The pump optics is designed such that stable double pulsing operation is reached for about 50 W pump power in the saturated regime.
Calculated bifurcation diagrams for a 2 kHz repetition rate are shown in Fig. 2 for three selected numbers of round trips. The simulations were based on the experimental parameters described in section 2. The analysis displays the typical multistabilities of Ho:YLF RA's when operating at few-kHz repetition rate [18,20]. For a seed energy of 0.5 nJ the amplification threshold occurs at ~10 W of pump power followed by a linear increase in a single-pulse energy regime. At the first bifurcation point which typically occurs at a pump power between 20 and 30 W, periodic doubling sets in. This is followed by a region of irregular behavior and therein the saturation level is reached. Further increase of pump power leads to the double pulsing regime with a branch of high and a branch of very low output power. Finally, the system turns in a second single-pulse energy regime, however, at higher pump power than available in our experiments.
Next, we consider the influence of the number of round trips in the RA cavity for a fixed energy of the seed pulse of 0.5 nJ. At a lower round trip number, a higher pulse energy can be extracted because of the higher saturation level, i.e., 13 mJ vs 9 mJ for 20 and 30 roundtrips, respectively (Figs. 2(a) and 2(c)). In contrast, at higher round trip numbers the saturated single-energy regime is reached at lower pump power, 60 W in the case of 30 round trips (Fig. 2(c)). Owing to the pump mode size decrease, the saturated pulse energy drops slightly with increasing pump power. The stable double pulsing regime is established at 55, 47 and 42 W pump power for 20, 25, and 30 round trips, respectively. As a consequence, we operate our RA at about 25 round trips to benefit from the maximum pulse energy in the stable double pulsing regime with respect to the maximum available pump power (Fig. 2(b)).
To check the validity of the calculations, we examine the bifurcation diagram of the RA at 2 kHz repetition rate by evaluating the pulse energy distributions for pump power values between 5 and 51 W. In this range, 100 emitted pulses are recorded by an energy-calibrated 12 GHz photodiode in pump power steps of 1 W. The experimental results are presented in Fig. 3(a) where the distribution of RA pulse energies is plotted as function of pump power. The amplification threshold is at a pump power of ~8 W, followed by a range with a linear increase of single-pulse energy with pump power. This interval ends at a first bifurcation located at a pump power of 18 W (output pulse energy 0.5 mJ). After the first bifurcation point a short region of period-doubling starts before the onset of chaotic behavior at ~25 W pump power. Saturation of the amplifier is reached at ~40 W with a pulse energy of 10.5 mJ. Above 45 W pump power the chaotic region turns into a stable periodic-doubling regime.
The measured bifurcation diagram is consistent with our simulations for 25 round trips (Fig. 2(b)). The slight deviations below 30 W pump power are attributed to reduced overlap of pump and laser mode in this range which is not implemented in the model yet.
The stable emission in the upper bifurcation branch delivers up to 10 mJ pulse energy whereas the pulse energy in the lower bifurcation arm is 50 µJ only and remains nearly unchanged with increasing pump power. Next, we study the stability of our RA on a longer time scale and the pulse-to-pulse fluctuations of the resulting 1 kHz pulse train of the upper bifurcation branch at ~9.5 mJ. The long term stability measured with an energy meter for more than two hours is shown in Fig. 3(b) for 47 W pump power. The short time pulse-to-pulse stability is analyzed by recording 1000 consecutive pulses within a time window of 0.5 s using the fast photodiode. The energy values of the 500 pulses display peak-to-peak fluctuations <5%. We observe an excellent stability for both, the long and short-term measurement with pulse-to-pulse rms-values <0.9%. The saturation of the gain medium in every second amplification cycle ensures the remarkably good stability. The very high pulse energy of 10 mJ corresponds to a net gain of ~107 and yields the maximum average power of 10 W. For the applied pump power of 47 W, this corresponds to a high optical-to-optical efficiency of 21%.
The emission spectrum of the Ho:YLF RA output is centered at 2051 nm and displays a spectral bandwidth of 2.9 nm (FWHM), mostly limited by gain narrowing. As a further consequence of the latter, the chirped pulse duration is reduced to 210 ps. The pulse duration was measured using a commercial autocorrelator (APE). The generated spatial beam profile exhibits TEM00 characteristics with M2 <1.1.
4. Booster amplifier
Figure 4(a) shows the pulse energy vs. pump power for single-pass amplification at 1 kHz repetition rate measured with seed pulses of 9.5 mJ energy from the regenerative amplifier. For reasons of time exposure, the slope was recorded without attaining full thermal equilibrium of the amplifier at each data point. The single-pass amplifier output was 34 mJ in thermal equilibrium and for optimized mode overlap at the maximum cw pump power of ~105 W. At this pump level it takes about 1 h to attain steady state 34 mJ. This pulse energy corresponds to an average power of 34 W and a sizeable extraction efficiency of 23%. The Ho:YLF booster amplifier single-pass gain is 3.6. Although the peak intensity has a very high value of about 7 GW/cm2, no signs of damage are observed neither at the crystal nor the AR-coating. No thermal roll-over is observed for the direct water-cooled amplifier as evident from the nearly linear pulse energy vs. pump power behavior (Fig. 4(a)). This slope also reflects operation of the booster amplifier below the saturation level. Gain saturation is expected for a pump power >500 W and longer nanosecond seed pulses. To ensure 1 kHz operation of the booster amplifier, the intermediate low energy pulses can be easily suppressed by implementing a synchronized chopper between the RA and the booster amplifier. Even without suppression, however, the energy of the amplified intermediate RA pulses amounts to only 260 µJ. This pulse energy is only 0.7% of that of the high energy pulse and, thus, negligible for the planned OPA pumping, owing to the exponential scaling of the non-saturated OPA gain with pump intensity .
The long and short time pulse stability was characterized with the same techniques as for the RA. These results, presented in Fig. 4(b), reveal an excellent performance. The long-term stability as well as the short term peak-to-peak fluctuations of the RA is preserved in the single pass amplification. The measured pulse-to-pulse stability amounts to <0.9% rms in the 34 mJ kilohertz pulse train. Similar to the pulse stability, the beam quality after the booster is nearly unaffected by the amplification process and measured to be better than an M2 of 1.2 (inset Fig. 4(a)).
The optical spectrum of the booster output retains the same shape as the RA with the center at 2051 nm and a FWHM of 2.9 nm (Fig. 5(a)). In principle, this spectrum supports bandwidth-limited pulse durations of ~2 ps. In the case of optimal compression the peak power would exceed 1012 W/cm2 because the aperture of the compressor CVBG is 5 x 5 mm2. This value is on the order of the onset of SPM in PTR glass . Even though we are not expecting optimal compression because of the non-matched stretcher and compressor GDD, we limited the pulse energy for compression to 11 mJ.
After a single path through the CVBG, the pulse duration is 37 ps, as derived from the measured autocorrelation trace under assumption of a Gaussian-pulse shape (Fig. 5(b)). This number is close to the value of 30 ps calculated from the pure GDD of both CVBGs. The generated pulse duration of several tens of picoseconds is well suited for high-energy pumping of OPCPAs. For shorter pulses the peak power would imply the risk of damaging the nonlinear crystals such as ZGP . The autocorrelation function exhibits a slight modulation which corresponds to the small ~1 nm modulation of the envelope of the spectrum. The origin of this modulation is not fully clear at this time. It may reflect some accumulated spectral phase during the amplification process. As long as we operated our setup with reflection gratings as stretcher no signs of such etalon effects were detected [18,20].
In conclusion, we have demonstrated the combination of a Ho:YLF RA and a single pass booster amplifier delivering 34 mJ picosecond pulses at 1 kHz repetition rate, which is to the best of our knowledge the highest pulse energy reported for kHz CPA systems at 2 µm. The system is distinguished by an exceptional high stability with a pulse-to-pulse rms as low as 0.9%. This low noise level relies on the high-gain Ho:YLF RA, which is optimized for stable operation in the double pulsing regime. Based on numerical simulations the operation points were identified and confirmed by the measured RA bifurcation diagram at 2 kHz. Utilizing the 1 kHz pulse train in the high-gain bifurcation branch, 10 mJ pulses were generated, the highest energy to date of any picosecond RA emitting in the 2 µm spectral range. Seeding the booster amplifier with 9.5 mJ pulses the single pass gain was measured to 3.6. The demonstrated average power of 34 W corresponds to a high extraction efficiency beyond 20% with respect to the optical pump power. The latter value holds for the RA as well. Initial compression experiments up to 11 mJ pulse energy were performed resulting in a pulse duration of 37 ps. Compression at maximum pulse energy is intended by using CVBGs with larger aperture . The system appears scalable with respect to pulse energy but at the cost of operation at cryogenic temperatures  or by adding further booster amplifier stages.
This work has been funded through the SAW grant No. SAW-2014-MBI-1 of the Leibniz Gemeinschaft.
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