We report a high-gain, cw-pumped regenerative amplifier which is based on Ho-doped crystals and seeded by a versatile broadband source emitting between 2050 and 2100 nm. The regenerative amplifier is implemented in a chirped-pulse amplification system operating at room temperature. Using Ho:YLF as gain medium, 1.1 mJ pulses with a 50 ps pulse duration and a 10 kHz repetition rate are generated at 2050 and 2060 nm, corresponding to an average power of 11 W. Using the same seed source, a 10 kHz Ho:YAG regenerative amplifier at 2090 nm is studied in the same configuration. In all cases the regenerative amplifier parameters are chosen to operate in a tunable single-energy regime without instabilities.
© 2015 Optical Society of America
Broadband power-scalable ultrafast laser systems in the mid-infrared (mid-IR) are desirable for shorter cut-off wavelengths in high-harmonic generation [1,2] and for driving hard x-ray plasma sources . Applications of such sources, e.g., for ionization in the strong field regime  or ultrafast x-ray diffraction in the condensed phase , require operation at multi-kilohertz repetition rates for achieving sufficient detection sensitivity and/or signal-to-noise ratio. Optical parametric chirped-pulse amplification (OPCPA) has emerged as a powerful technique for the generation of high-energy ultrashort mid-IR pulses [6,7], limited, however, to wavelengths below 4 µm when using ~1 µm pump sources .
Suitable OPCPA sources at longer mid-IR wavelengths require signal seed sources with a bandwidth supporting sub-100 fs pulses and adequate pump laser systems which work at wavelengths above 2 µm with kilohertz repetition rates and provide pulse durations of up to several tens of picoseconds. Ho-based amplifiers seeded by picosecond pulses appear well suited to pump OPCPA schemes operating in the few-cycle regime beyond 4 µm wavelength . Among the 2-µm laser gain media, Ho-doped materials offer long upper-state lifetimes as well as high stimulated-emission cross sections, which render them favorable for obtaining high-repetition rate, high-energy pulses. Using Tm-doped pump lasers, direct excitation of the upper emitting level of Ho (5I7) at ~1.9 µm enables a high efficiency on the ~2.1 µm laser transition together with a minimum thermal load . The extremely low quantum defect promotes average power scaling. In principle, co-doped Tm,Ho media pumped at ~0.8 µm are also feasible but suffer from excess heat related to up-conversion processes . Moreover, the finite efficiency of energy transfer would severely limit power scaling .
Among the numerous singly Ho-doped host materials, the fluorides (YLF, LuLF) [12,13], and garnets (YAG, LuAG)  are most widely used and have proven their suitability for high energy operation (>100 mJ) in the nanosecond regime [13–15]. Millijoule Ho:YAG  and Ho:YLF  regenerative amplifiers (RA) with kilohertz pulse repetition rate have been demonstrated. The former involve a rather complex seed source, including cascaded OPA stages, and operate at comparably low net amplification. The Ho:YLF RA  was a master oscillator/power amplifier setup with a narrow-band Ho:YLF oscillator as a seed. Very recently, Hemmer et al. reported 5.5 mJ pulse energy of a Ho:YLF RA . This RA was operated at a low repetition rate of 100 Hz, corresponding to an average power of 0.5 W. The seed source incorporates a multi-stage pre-amplifier and is designed for narrowband operation.
At kilohertz repetition rates close to the inverse upper state lifetime of Ho, one enters an operation regime in which continuously pumped RAs can display energy instability and/or a multistable output energy . This issue, a key problem for any application of RAs in experiments, has not been addressed in a systematic and quantitative way for the wavelength range around 2 µm.
In this article, we present a Ho-based picosecond RA generating millijoule pulse energies at multi-kHz repetition rates. Our system features a versatile broadband seed source that enables operation at Ho emission wavelengths between 2050 and 2100 nm. The RA is designed for operation in a continuously scalable and stable single-pulse energy regime. Best performance is achieved using Ho:YLF as the active material, delivering few-10 ps pulses with 1.1 mJ at 10 kHz repetition rate, corresponding to an average output of 11 W .
2. Modeling of regenerative amplifier stability
In continuous-wave (cw) pumped regenerative amplifiers operating at repetition rates close to or higher than the inverse of the gain relaxation time, the amplification of a pulse is influenced by the gain depletion caused by the previous pulse. This can lead to violation of the single-energy regime, including both stable operation such as periodic doubling (bifurcation) as well as chaotic patterns, where subsequent pulses exhibit variations in energy (“deterministic chaos”). 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 such instabilities can start to occur is around 80 Hz.
Temporal dynamics of kilohertz repetition rate regenerative amplifiers were first analyzed in  using Yb:glass as active medium. A more detailed theoretical description of the chaotic behavior and bifurcations in RAs was presented in . Experimental studies of the RA stability problem were only reported for systems emitting in the spectral range around 1 µm [21,22]. Here we present simulations of the “deterministic chaos” diagrams for the high repetition rate Ho:YLF regenerative amplifiers targeted in this work. A modified Frantz-Nodvik equation  is used for calculation of the pulse amplification, which takes into account the spectral features of Ho-doped amplifiers and its quasi-three-level behavior. The populations in the ground and excited state manifold are calculated based on the rate equations for cw-pumped Ho:YLF .
Results are shown in Fig. 1 for two repetition rates. In the simulation, we consider a seed source which delivers broadband pulses with seed energies <1 nJ, similar to the experiments reported in section 4. For a seed energy of 0.15 nJ and 24 round trips a linear increase of the single-pulse energy with pump power up to ~1 mJ is expected. After this first bifurcation point the periodic doubling sets in followed by a region of chaos. Further increase of pump power leads to an intermediate stable regime with three distinct pulse energy levels before it turns to the next chaotic area. The region of single-pulse energy performance displays only a low dependence on seed pulse energy (0.1 - 20 nJ). However, changing the pulse repetition rate expose a noticeable influence. Operating at 10 kHz the onset of instabilities is expected at around 50 W pump power (Fig. 1(a)) whereas at 5 kHz this point is shifted to lower pump power at around 30 W (Fig. 1(b)). The above-threshold pump power, necessary to reach the first bifurcation point, is about two times lower in the latter case. Since the time between two amplification cycles is doubled and the losses due to stimulated emission are low, one can expect a very similar inversion and, therefore, gain in both cases.
3. Experimental set-up
The layout of the laser system shown in Fig. 2 consists of four main parts, (i) a supercontinuum seed source (Toptica), (ii) a Tm:fiber pre-amplifier (AdValue), (iii) a pulse stretcher and (iv) the RA. The supercontinuum is generated in a highly nonlinear fiber (HNLF) by launching 75 fs pulses at 1.55 µm from an Er:fiber oscillator/power amplifier operating at a 40 MHz repetition rate. The HNLF output encompasses the spectral range 1.8 – 2.4 µm at an average power of 48 mW. A single-stage Tm:fiber amplifier suffices to pre-amplify the supercontinuum pulses. This pre-amplifier is designed to support the spectral range from 2050 to 2100 nm in which the peak gain wavelengths of the most favorable Ho-transitions are located . The input pulses are negatively chirped, permitting amplification in fiber-based systems in the anomalous regime without risk of nonlinear phase distortion and avoiding collapse or self-compression. They experience temporal stretching during amplification from the negative group delay dispersion (GDD) of the Tm-doped fiber. The pre-amplified pulses reach 18 nJ in energy at a 9 ps duration with a GDD of −0.85 ps2. Figure 3(a) (black solid line) shows their spectrum extending from 2030 to 2110 nm (zero level).
After pre-amplification, the pulse train passes a pulse picker (RTP) and an optical isolator. The former reduces the 40 MHz repetition rate to 10 kHz. Subsequently, pulses are stretched to ~400 ps using a double-pass in a 600 line/mm reflective Treacy-type grating arrangement  with a total GDD of –35 ps2. Because of reflection losses, the stretched pulses have a reduced total energy of 2 nJ. Although this setup does not permit shaping at high spectral resolution, blocking of undesired spectral segments apparently suffices for suppressing spectral sidebands and for avoiding pre- or post-pulses.
The RA design is based on a ring cavity  because of its proven stability against changes of pump power and resulting changes of the thermal lens (Fig. 1). This approach which was also applied in [16, 18] allows the implementation of two thin-film polarizers for separating input and output ports. A Faraday rotator as it is typically used in a linear cavity, is not necessary here and was omitted. The ring resonator is formed by 6 highly reflecting mirrors and requires operation of an RTP Pockels cell (Leysop) in the λ/2 regime, in combination with a half-wave plate. As active media, we employ 50 mm long antireflection-coated Ho-doped rods, which are end-pumped by an unpolarized cw Tm:fiber laser at 1940 nm (IPG Photonics) and directly water-cooled to room temperature.
Our study focuses on the birefringent Ho:YLF as a gain medium, given its ~5-times lower nonlinearity as well as its lower and negative thermal change of refractive index dn/dT in comparison to the isotropic Ho:YAG . In contrast, Ho:YAG emits at longer wavelengths and may therefore appear preferable over Ho:YLF for pumping OPCPA, granted the weaker residual absorption in ZnGeP2, which has been favorably employed for mid-IR OPAs . The emission cross sections for E║c and E⊥c in Ho:YLF are given as inset in Fig. 3(a) . The measured single pass gain spectra of Ho:YLF (E║c) and Ho:YAG when seeded with our supercontinuum source are included in Fig. 3(b).
4. Experimental results and discussion
Given the targeted high repetition rate and single-energy performance, the RA is operated at 10 kHz (Fig. 1(a)). Initially we inserted a 0.5% Ho-doped YLF crystal in E║c orientation (π-polarization) in the RA, in order to benefit from the maximum gain cross section at 2050 nm . The seed spectrum was spectrally shaped to suppress the gain peak at 2060 nm (Fig. 3(a), red horizontal bar), resulting in a seed energy of ~0.15 nJ.
Figure 4(a) shows the pulse energy versus pump power for the RA's investigated. At 2050 nm, the highest pulse energy of 1.1 mJ is achieved for the Ho:YLF RA operating with 24 round trips (Fig. 4(a), red squares). The pulse energy corresponds to a net gain of ~107 and yields the maximum average power of 11 W. Taking into account the applied pump power of 48 W this corresponds to a sizeable optical-to-optical efficiency of 23%. The linear dependence in Fig. 4(a) verifies the calculated continuous tunable energy scaling (Fig. 1(a)). Since no saturation occurred during amplification at this energy level, output energies appear further scalable. However, the analysis of the pulse-to-pulse stability at 1.1 mJ as compared to <1.0 mJ (Fig. 5(a)) indicate a slight but significant increase of pulse energy fluctuations. Thus, the 1.1 mJ pulse energy value marks the limit of the tunable single-energy regime and corresponds to the first bifurcation point of our system (Fig. 1(a)). As a consequence, only further average power scaling in the tunable single-pulse regime is possible for which the repetition rate has to be increased. The generated spatial beam profile exhibits TEM00 characteristics with M2 <1.2 (Fig. 4(a), inset). The resonator arrangement ensures spatial mode stability over the whole pump power range without need for compensation of thermal effects. Reducing the pulse repetition rate the onset of periodic double pulsing and chaotic behavior starts at a substantially lower power level (Fig. 1(b)). In the case of 5 kHz this level is reached in our RA at about 32 W pump power.
Spectra of the amplified pulses are measured with an imaging spectrometer (iHR320, Horiba Scientific) and summarized in Fig. 3(b). For the present Ho:YLF (E║c) case with a 2050 nm seed (red bar in Fig. 3(a)), the spectrum of the amplifier output has its maximum at 2051 nm with a spectral width (FWHM) of 3.2 nm (red contour in Fig. 3(b)). Ho:YLF exhibits a second gain maximum at 2060 nm with lower gain for the same polarization orientation parallel to the c-axis (E║c) (Fig. 3(a), inset). Tailoring the spectrum of the input pulses fed into the RA allows for changing the spectral position of the amplified pulses. Amplified pulses centered at 2062 nm are readily generated with input pulses of 0.7 nJ energy taking into account the gain spectrum (Fig. 3(b)) and the seed spectral range between 2055 and 2110 nm (green horizontal bar in Fig. 3(a)). Compensating the lower gain around 2060 nm by increasing the number of round-trips from 24 to 33, we generated similar pulse energies up to 0.95 mJ at a 10 kHz repetition rate with nearly the same slope efficiency (Fig. 4(a)). The recorded emission spectrum for the E║c orientation displays a spectral bandwidth of 1.7 nm (FWHM, green profile in Fig. 3(b)), mostly limited by gain narrowing in the Ho:YLF RAs.
So far, all demonstrated Ho:YLF power amplifiers operated in single-pass arrangements at 2050 nm (E║c) [13,17] because of the very low gain at this wavelength for E⊥c orientation (inset, Fig. 3(a)). At 2060 nm, in contrast, the spectral position and the peak emission cross section are nearly identical for both orientations (Fig. 3(a), inset). As shown in Fig. 4(a), amplification for the σ-polarization (E⊥c) at 2060 nm is only slightly reduced compared to E║c, resulting in maximum pulse energies of 0.91 mJ. The emission spectrum exhibits a bandwidth of 2.1 nm (orange profile in Fig. 3(b)). Single-rod Ho:YLF double-pass power amplifiers at 2060 nm are, thus, an option, and a reduced gain narrowing is expected because of the slightly displaced peak wavelengths of ~1.5 nm (Fig. 3(b)).
The pulse duration for the Ho:YLF RAs was measured at maximum pulse energy with a commercial autocorrelator (APE). We find a value of ~50 ps (Fig. 4(b)) which appears well suited for pumping OPCPAs. In principle, the spectra support minimum pulse duration of ~2 ps, requiring a recompression of the RA output which is not studied here.
Finally, a 1% Ho-doped YAG rod was tested in our RA operating at 2090 nm. The simulated bifurcation diagram for the Ho:YAG RA differs from that of Ho:YLF (Fig. 1) only marginally. Applying the same procedure as described above, the seed spectrum was shaped to suppress the 2097 nm line (Fig. 3(a), blue horizontal bar). The energy of the seed pulse was 0.7 nJ. From the output characteristics at a 10 kHz repetition rate (blue symbols in Fig. 4(a)), one expects a performance similar to the Ho:YLF RA. We, however, limited the maximum pulse energy to 0.5 mJ to prevent any damage, given the much stronger gain narrowing compared to Ho:YLF. This precaution is confirmed by the narrower emission bandwidth of 1.2 nm (FWHM, blue profile in Fig. 3(b)) and the concomitant shorter pulse duration of 25 ps. For scaling of the Ho:YAG RA to the mJ-level, further pulse stretching to >100 ps is required .
To get insight into the pulse-to-pulse stability the Ho:YLF RA pulse train was analyzed with high temporal resolution for pulse energies between 0.5 and 1.1 mJ (Fig. 5). For that reason, a 12 GHz photo diode (calibrated by a power meter) and a 4 GHz oscilloscope were used to measure the pulse-to pulse energy characteristics, i.e., 1000 consecutive pulses were recorded within a time window of 100 ms. Each 4 ns long single pulse trace contained 1032 data points. As shown in Fig. 5(a), a nearly unchanged pulse-to-pulse energy fluctuation of ~2.3% (standard deviation) is obtained for pulse energies from 0.5 to 0.9 mJ. When scaling the pulse energy to 1.1 mJ a slight but continuous increase of the standard deviation to 3.0% is observed (Fig. 5(a)). To visualize our measuring procedure the energy values of 1000 consecutive pulses in the 10 kHz pulse train are plotted in Fig. 5(b) at maximum pump power (48 W). The slightly increased pulse energy fluctuations above 1.0 mJ are the first sign for the onset of periodic doubling (Fig. 1(a)). The long term power stability of the Ho:YLF RA at 0.9 mJ pulse energy was measured for 45 min using a power meter. As indicated in Fig. 5(c), we observe an excellent stability of our source, with an average power rms <1% and peak-to-peak fluctuations <7%.
The low seed energy of <1 nJ in our experiments makes a larger number of cavity round trips necessary to achieve the targeted pulse energy level. As a noticeable Q-switch background has been reported for the Ho:YAG RA in , we measured the background of our RAs. This spurious background appears in both propagation directions at the same intensity level and the temporal pulse evolution was monitored for the main pulse train as well as the counter-propagating direction (Fig. 6). In the counter-propagating direction, an extremely weak pulse is detected at about 10−6 of the main pulse, which is attributed to imperfections of AR coatings. On the main pulse train there are virtually no indications for self Q-switching or any other background. In the counter-propagating direction a vanishing small background is apparent at an energy level of 10−7 of the main pulse. No significant differences with respect to the contrast and background are measured for the Ho:YLF and Ho:YAG RAs. Due to limitations of the Pockels cell, a trailing satellite pulse is observed at 11 ns delay and a contrast of 1:300 in the main pulse train.
In conclusion, we have demonstrated continuously tunable, single-energy, 10 kHz picosecond RAs operating at 2 µm. Pulse energies as high as 1.1 mJ were generated at 2050 nm by designing a high-gain, broadband seeded, cw-pumped Ho:YLF RA which incorporates CPA. The demonstrated average power exceeds 10 W, corresponding to a remarkable optical-to-optical efficiency beyond 20%. The novel broadband seed source enables operation of RAs in the spectral range between 2050 – 2100 nm, encompassing most of the 2 µm Ho-transition. Despite an exceptional high net gain ~107 of the RA, no indication for a background was detected down to an energy level of 10−7. The operation in the single-energy regime of the RA was confirmed by monitoring the excellent pulse-to-pulse energy stability. Suitability for high-gain, high-energy RAs at 2 µm is demonstrated for Ho:YLF and Ho:YAG. The achieved output parameters of the RAs are consistent with our simulations, indicating the onset of instabilities for pulse energies >1.1 mJ. The system appears scalable with respect to pulse energy but at the cost of operation in the “deterministic chaos” region. Implementing temporal stretching to well beyond 100 ps, we expect power scalability to hold for subsequent multi-pass power amplification stages and for accessing applications like medical surgery, femtosecond mid-IR parametric amplification and eye-safe filamentation in the atmosphere.
We acknowledge the expert technical support by Dennis Ueberschär. This work has been funded through the SAW grant no. SAW-2014-MBI-1 of the Leibniz Gemeinschaft.
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