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A highly stable Yb:KYW based dual crystal regenerative amplifier is demonstrated, which generates at 1 kHz 6.5-mJ pulses before and up to 4.7-mJ sub-ps pulses after compression with multilayer-dielectric gratings, respectively. The stretcher is compact and based on chirped-fiber Bragg gratings. In continuous-wave operation, 20 W are extracted with a slope efficiency of 40%. The experimental data are in agreement with detailed simulations of the laser dynamics.
© 2014 Optical Society of America
1. Introduction
High-energy ultrashort pulse lasers are enabling tools for strong field physics. Optical parametric (chirped pulse) amplifiers (OP(CP)A) provide broadband amplification of ultrashort pulses to high energies while limiting thermal issues. In several architectures, regenerative amplifiers are used in the pump line for OPCPAs. Many systems based on Ti:Sapphire technology suffer from limited scalability towards higher average powers and from stability issues. The limitation of the average power can be overcome with an Ytterbium based pump line, while the stability can be increased by a careful cavity design. In our pump lines, the last, power amplification stages are based on a composite thin-disk multipass amplifier working at cryogenic temperature [1], requiring a few mJ input energy delivered by the regenerative amplifier. A reliable operation of the power amplifiers is possible if the output of the regenerative amplifier is itself stable, in power, pointing and beam parameters, which we achieve by dispatching the thermal load onto several crystals.
The constraints set by the thin-disc multipass amplifier on the regenerative amplifier concern firstly the central wavelength: the gain medium being cryogenically cooled Yb:YAG, the central wavelength is fixed to 1029.5 nm. Secondly, in order to generate the broadband spectrum to be amplified in the OPAs, white-light supercontinuum generation can be used, requiring pulses with a few hundreds of femtosecond duration [2]. Materials with emission cross-section broad enough for amplifying sub-picosecond pulses at this wavelength are typically, but not limited to, Yb:YAG [3], Yb:KYW [4], Yb:CALGO [5] and Yb:CaF2 [6]. Some of the characteristics of these crystals are summarized in Tab. 1: the lifetime τL, the emission and absorption cross-sections for laser and pump wavelength σe,L and σa,P, respectively, the emission bandwidth Δλ and the thermal conductivity κ. As the bandwidth of Yb:YAG at room temperature is 10-11 nm, gain narrowing limits the pulse duration close to a picosecond after amplification. Yb:CaF2 is quite brittle and has a thermal conductivity of 9.7 W/m/K falling to half for 2.59% doping concentration [6]. Yb:CALGO is promising for its thermal conductivity and its broad spectrum, but the gain maximum is at 1042 nm, preventing broadband amplification around 1030 nm, as demonstrated in [7]. Yb:KYW, with a thermal conductivity of 3.3 W/m/K [8], 18 nm bandwidth and 3x10−20 cm2 emission cross-section, is hence a good candidate [8]. In order to reduce thermal effects in the crystal in our regenerative amplifier, the thermal load has been divided onto two crystals and the cavity designed to remain insensitive to variations of thermal lens strength. This way, the output beam parameters are independent of the pumping conditions and the switch on time is kept extremely short. The use of two crystals has been already demonstrated in [10] for increasing the gain and in [7] for the repartition of the thermal load.
Table 1. Characteristics of different laser crystals.
In previous works, the highest energy reported from a Yb:KYW regenerative amplifier was 5.5 mJ at cryogenic temperature, for a central wavelength of 1028 nm [9]. In 2007, Delaigue et al. have demonstrated a regenerative amplifier delivering 1.8 mJ at 2 kHz repetition rate [10]. 27 mJ at 100 Hz, with 1030 nm central wavelength, have been demonstrated in 2011 [11], but this system consisted of a multi-pass amplifier seeded by a commercial regenerative amplifier delivering 2 mJ. The highest reported energy from an Yb:KYW regenerative amplifier was 10 mJ by C. P. João et al. in 2011 [12], however with a central wavelength of 1040 nm, corresponding to an extraction along the other axis, np, which presents a higher emission cross-section, and seeded with µJ level pulses.
We report here on a bulk, dual-crystal regenerative amplifier delivering 6.5 mJ before compression, and 4.2 mJ, sub-ps pulses after compression at 1 kHz repetition rate. To the best of our knowledge, this is the highest pulse energy generated in a bulk Yb:KYW regenerative amplifier operating at 1030 nm.
2. Experimental setup
The experimental setup, as shown in Fig. 1, consists of 3 main parts: the oscillator with stretcher, the regenerative amplifier and the compressor. The oscillator is a commercially available 42.5 MHz Yb:KYW laser, delivering 690 mW, 210-fs long pulses centered at 1029.5 nm. Since the later amplification stages are based on an Yb:YAG amplifying medium at cryogenic temperature, a stretching ratio of 0.65 ns/nm is implemented to account for strong gain narrowing. A compact solution for this highly dispersive stretcher is a chirped fiber Bragg gratings (CFBG). To ensure equal dispersion in stretcher and compressor for an optimal recompression to its Fourier limit after amplification, the opposite phase of the compressor is designed into the CFBG fabricated by Teraxion in PM fiber. For manufacturing reasons, the high amount of dispersion (GDD = −378.5 ps2, TOD = 10.7 ps3 and FOD = −4.9 ps4) required the additional distribution of the dispersion in four CFBGs, each 15 cm long and with 5 nm super-Gaussian filter bandwidth. The dispersion of the gain material in the regenerative amplifier is negligible according to calculations. The losses due to each CFBG including circulator amount to 6 dB, and have to be compensated for by fiber amplifiers 1 and 2 with 25 dB gain. At the output of the stretcher, the 3.2 ns long pulses have 0.6 nJ energy. This setup could be straightforwardly simplified by using longer CFBGs, which are now commercially available, removing at the same time the losses originating from the circulators: the fiber amplifiers would then not be further necessary.
Fig. 1 Layout of the regenerative amplifier with stretcher and compressor. Osc stands for oscillator, C1-C3 circulators, CFBG1-4 chirped fiber Bragg gratings, FA1-2 fiber amplifiers, TFP thin-film polarizer, PC Pockels Cell, λ/4 quarter waveplate, λ/2 half-waveplates, M1-M8 high reflectors, DC dichroic mirrors, L lenses, PBS polarization beam splitter, XTAL crystals, LD laser diode, FI Faraday isolator, RM high reflector roof mirror, FM1-2 high reflector folding mirrors, G1-2 multi-dielectric layer gratings. OC, standing for output coupler, was an output coupler used for the characterization of the cavity in continuous-wave operation without the extension for the switching elements. S represents the symmetry point of the short cavity extending from M1 to OC; the extension from M4 to M7 is a 0-q transformation imaging the beam parameters from OC to M7.
A dual-crystal cavity, similar to the one described in [7], is designed to be insensitive to variations of the thermal lenses in the crystals from 280 mm to more than 800 mm focal length. This is ensured with the positioning of the crystal one Rayleigh length away of the focus, as described in [13]. The beam parameters (size and divergence) vary freely with the variations of the thermal lens between the crystal and the focus, but remain stable in the rest of the cavity. The crystals are first characterized in a short cavity comprising M1-3, both dichroic mirrors and the output coupler OC. The high reflector M1 can also be replaced by an output coupler. Each half of this short-cavity, symmetric around S, mid-point between both crystals, is stable in itself; the single-crystal short-cavities are used to test the crystals independently of each other and to align the beam overlap in both crystals. The extended cavity with high-reflectors M4-M7 includes a 4-f telescope for relay imaging the beam from the OC onto M7; the switching elements, consisting of a Pockels cell (PC), a quarter-waveplate (λ/4) and a thin-film polarizer (TFP), are inserted into the expanded beam to minimize the non-linearities accumulated during amplification.
The 3 mm long 2%-doped Yb:KYW crystals, cut along the ng-axis, are pumped and emit polarized along the nm axis. The water cooling of the slab is performed along the np-axis; the linear thermal expansion coefficients of Yb:KYW are 1.9x10−6 K−1 on np axis and 10.3x10−6 K−1 on the nm axis [14]. The laser diode, model P2-120-0982-2-TKS-C from N-Light, delivers a maximum power of 120 W through a multi-mode fiber with NA 0.22 and 200 µm mode-field diameter. Its wavelength is tuned to the peak absorption of Yb:KYW at 981 nm by temperature control. The laser diode can be operated either in continuous-wave (CW) or quasi-continuous wave (QCW) modes. A demagnification of 3:1 ensures mode-matching between pump and laser modes. The output of the laser diode is split into two equal parts with a polarizing beam splitter for pumping both crystals equally.
The cavity is designed to minimize non-linearities during amplification: the laser mode radius is 350 µm at 1/e2 in the crystals, and 600 µm in the Pockels cell. To achieve these beam radii, the radii of curvature are selected to be 500 mm and 1000 mm for the mirrors M2, M3 and M5, M6, respectively, and the distances adjusted accordingly. The relatively large spot size in the crystals however limits the available gain.
Finally, the design of the multi-layer dielectric compressor is a Treacy compressor [15] folded in two steps for a reduced footprint. Conventionally, each grating supports two passes: after the first pass on each, the pulses are compressed to half of its initial duration and the beam is spatially chirped. After the second pass, the pulses are temporally and also spatially fully compressed. In this work, four passages are made in the compressor, at the expense of some efficiency. The folding in vertical direction is carried out using roof mirrors RM. As the 1760 l/mm gratings are separated by 1.109 m perpendicular distance, the compressor is additionally folded horizontally with high-reflectors FM1&2. In total, the footprint is reduced to a quarter of the one of the unfolded compressor.
3. Numerical simulations
The evolution of the population inversion ni(z,t) and laser fluence ΦL(z,t) over time, as well as the evolution of the pump and laser fluences ΦL(z,t) and ΦP(z,t) over the propagation length z in the crystals are defined by the following differential equations for a quasi-three level system:
Here, represents the inversion in the crystals, defined as in [16], Eq. (7).2.23, with which is the ratio between emission and absorption cross sections. The index i refers to both crystals, while the indices L, P, a and e indicate laser, pump, absorption and emission, respectively. σ symbolizes the cross section and τf the upper-state lifetime. TR, cavity photon lifetime, is defined as with d cavity length, α total cavity losses, c speed of light. The first equation describes the evolution of the population inversion in each crystal, depending on the pump and laser fluences. The pump fluence is described in each crystal with Eq. (1.2) ; the pump fluence is assumed to be flat-top in time and space. The progression of the laser fluence over the crystal length, given in Eq. (1.3), depends on the population inversion; the intra-cavity losses are taken care of by Eq. (1.4).These differential equations were solved via Matlab routines and a self-written ODE (Ordinary Differential Equation) solver using Euler and Runge-Kutta algorithms. The choice between both algorithms is a trade off between computing time and precision, using the Euler solver for Eqs. (1.2)-(1.4) and the Runge-Kutta 4th order solver for Eq. (1.1). In the simulation, the propagation of pump and laser beam through the crystal is computed in one step, according to the assumption of crystals short compared to the time resolution. The pump and laser fluences are initialized at t = 0 over the first crystal in the propagation direction z, whereas the population inversion is kept to 0. The pump is initialized for all t at the entrance of the crystal with a flat-top long pulse, according to the QCW pumping. The actual algorithm solved first Eq. (1) for both crystals at time t, using ΦP,i and ΦL calculated at , then the pump and laser fluences are propagated at time t over the crystal length. During the propagation over z, ODE Eq. (3) and Eq. (4) were solved for each slice, the fluences at the end of one slice being the initial condition of the next one.
The parameters used in the simulation are summarized in Table 2 and Fig. 2 illustrates the laser fluence and inversion in one crystal over time during one amplification cycle and zoomed into the pulse build up.
Table 2. Laser parameters used in the simulation.
Fig. 2 Laser fluence and average inversion in the first crystal vs. time: (a) over 10 periods and (b) zoomed into one amplification cycle. The plain curves are the simulations with 17.2 cm−1 absorption coefficient and the dashed ones with 12.0 cm.1 absorption coefficient.
The pump and laser beam parameters are chosen according to the experimental setup. The losses are estimated from the intra-cavity elements, and fine-tuned to match the experimental results. Two cases are simulated: first assuming an absorption coefficient of 17.2 cm−1 and then an effective absorption coefficient of 12.0 cm−1, to account for the spectral mismatch between pump diode and absorption line of Yb:KYW. The pump light is not fully absorbed due to its FWHM bandwidth of 4.2 nm, compared to the 3.6 nm absorption bandwidth (FWHM) of Yb:KYW.
Figure 2(a), shows the evolution of the inversion and amplification over 10 regenerative amplifier cycles, and Fig. 2(b) zooms into one amplification cycle. The energy obtained in each cycle is constant and no sign of bistable behavior is observed. In the simulation, 32 cavity round trips are used for one regenerative amplifier cycle to show saturation and reabsorption. 8 mJ, respectively 6.5 mJ, output energy are expected for a repetition rate of 1 kHz, taking 17.2 cm−1, respectively 12.0 cm−1 pump absorption coefficient into account.
4. Experimental results
The system was first characterized in continuous-wave and cavity-dumped operation and then as regenerative amplifier.
4.1 Continuous-wave operation
The cavity is optimized in the continuous-wave regime for extracting maximum power with a diffraction limited beam, while keeping the spot-radius in the crystals bigger than 300 µm. In both crystals, the small signal absorption is 65%. Figure 3(a) shows the slope efficiency obtained with different output couplers: 10%, 15% and 20%. For this measurement, an attenuator composed of a half-waveplate and a polarization beam splitter is inserted in the pump path to vary the pump power while keeping the pump wavelength constant. The maximum output power is obtained with 15% output coupling and a slope efficiency of 40.3%. The free-running wavelength is 1031 nm. The high threshold at 55 W incident pump power is due to the increased spot size inside the crystals. The output powers and the slope efficiency measured with the other two output couplers are close to the results obtained with the 15% output coupler, meaning that the laser head is relatively insensitive to losses. Figure 3(b) displays the tuning curve, measured for 112 W pump power and a 15% output coupler. The laser head is tuned from 1021 nm to 1033 nm with a Lyot Filter and a maximum output power of 19.4 W is achieved at 1031 nm. Then the center wavelength of the stretched seed pulses is aligned with the wavelength for maximum gain.
Fig. 3 Characterization of the dual-crystal laser head in continuous-wave operation. (a): slope efficiency for different output couplers. (b): tuning curve obtained for 112 W pump power and 15% output coupling.
After insertion of the switching elements, thereby introducing some additional losses, the maximal output power dropped to 19 W for optimum output coupling obtained by adjusting the quarter-waveplate and the Pockels cell. Figure 4(a) shows the beam profile measurement taken with the beam analyzer M2-200s from Spiricon at the TFP output of the laser, while Fig. 4(b) shows the far field of the beam. The beam parameter M2 is better than 1.1, however the beam size is slightly wider than expected. By measuring the beam waists for different pump power, i.e. various thermal lenses, the strength of the thermal lens was estimated to be stronger than expected. From [17], the thermal lens during lasing can be estimated by the formula:
where A is a material specific coefficient, depending on the thermo-optic coefficient and pump diameter, Pabs the absorbed pump power, ηP, ηr, ηl the quantum defect, the radiative quantum efficiency of the upper manifold, and the laser extraction efficiency, respectively, λP, λL, λF the pump, laser and fluorescence wavelengths, respectively. For the pumping conditions of this laser head, the thermal lens is calculated to be 250 mm. The cavity is designed so that the spot size in the crystal is insensitive, i.e. constant within 10% variations around the nominal beam diameter, to focal lengths of the thermal lens longer than 280 mm. Below this value, the spot size increases rapidly with a decrease in focal length; for a value below 210 mm, the cavity becomes unstable. Re-calculating the spot sizes in the cavity taking the 250 mm thermal focal strength in both crystals into account results in an output beam diameter of 1.7 mm in agreement with the measurement. In this configuration, the spot sizes in the crystals are 350 to 400 µm wide, minimizing non-linearities. This new operation point results of the experimental optimization of the laserhead toward higher output energies.Fig. 4 (a) Measurement of beam profile: the caustic corresponded to close to diffraction-limited beam with M2 < 1.1. (b) Beam profile in the focus.
4.2 Cavity-dumped and seeded operation
After continuous-wave characterization, the cavity is operated first in cavity-dumped (CD) regime and then as regenerative amplifier. The Pockels-cell driver is triggered with the pulse delay generator from SRS model DG645. The laser diode is operated in QCW and CW regimes. In QCW operation, the pump duration is set to 500 µs, corresponding to 1.5 times the lifetime of Yb:KYW, which reduced the thermal load in the crystals. The maximum energy extracted from the cavity-dumped laser head is 5.5 mJ at 1 kHz repetition rate at full pump power. As shown in Fig. 5(a), the output energy is only limited by the available pump power, as there is no noticeable roll-over behavior visible. The extraction time is set to 804 ns corresponding to 38 round trips for 125 W pump power.
Fig. 5 Energy extracted in (a) cavity-dumped operation and (b) as regenerative amplifier versus incident pump power. The extraction time is set to 804 ns and 640 ns, respectively. (b) shows both simulation and experimental results.
In seeded operation the repetition rate is varied between 100 Hz and 1750 Hz, the highest repetition rate achievable with our driver. The maximum energy of 6.5 mJ is extracted at a repetition rate of 1 kHz using 0.6 nJ seed pulses. At this seed energy, the extractable energy is near constant for repetition rates below 1400 Hz; above this value, the extractable energy begins to decrease, as expected considering the lifetime of Yb:KYW. To achieve a gain of 60 dB, 31 round trips corresponding to 640 ns are required. Most of the discrepancies between simulations with the absorption coefficient of 17.2 cm−1 and experimental results originate from the difficulty in modeling the absorption of pump light in the experiment due to the uncertainty in the exact effective pump absorption coefficient. The simulation with the lower, effective absorption coefficient of 12.0 cm−1, predicting 6.5 mJ output energy, is consistent with the experimental results.
Figure 5(b) shows the variation of the output energy with the incident pump power, experimentally and simulated, for a fixed amplification time. The errors bars on the experiment are caused by the in situ pump power measurement. By increasing the pump power in the simulations, without considering the limitations due to thermal effects, the output energy would roll-over for high pump powers to reach nearly 10 mJ.
The narrowing of the amplified output spectrum is illustrated on Fig. 6(a). The 4.9 nm wide seed spectrum is centered at 1030 nm. Filtering by the CFBGs and the spectral reshaping in the fiber amplifiers significantly narrows the output spectrum compared to the seed spectrum. We believe that self-phase modulation at the entrance of the fiber stretcher causes the shoulders in the seed spectrum. The output spectrum of the cavity-dumped laser is 5.7 nm wide centered at 1028 nm wavelength. As expected, the output spectrum of the seeded regenerative amplifier is the overlap of both spectra.
Fig. 6 (a) Spectra and (b) autocorrelation of regenerative amplifier output. The amplified spectrum, red plain curve, corresponds to the overlap of the seed spectrum (blue, dashed curve) and the output under cavity dumping operation (green, dashed dotted line). The autocorrelation is fitted to a Gaussian and the energy in the pedestals is calculated to be 15%. The inset shows the calculated autocorrelation of the transform-limited pulse profile corresponding to the measured spectrum.
After compression, the pulses are measured to be as short as 650 fs, assuming a Gaussian fit, as shown in Fig. 6(b). The transform-limited pulse duration is calculated to be 612 fs (see Fig. 6(b) inset). Nevertheless, 16% of the energy is in the pedestals originating from both the spectral shape of the pulses and the dispersion mismatch between compressor and CFBGs. The transmission of the double-deck compressor is as high as 81%, due to high quality multi-layer diffraction gratings with an efficiency close to 97.5% in the first order. A frequency doubling measurement in BBO with more than 50% conversion efficiency confirms that there was no sign of uncompressed background, which could have been caused by the CFBGs. The beam quality after compression remains excellent, while the beam becomes slightly elliptical in the diffraction direction, even after removal of all spatial chirp.
The B-Integral during amplification is estimated by the nonlinear index, cross-sections of the laser beam in the amplifier material and pulse peak intensity. Considering the non-linear index values of 15x10−16 cm2/W for KYW [18], 5x10−16 cm2/W for BBO [19] and 3x10−16 cm2/W for fused silica [20], and beam radii of 400 µm in the crystal and 1.5 mm in the Pockels cell. The accumulated non-linear phase shift in the regenerative amplifier amounts to 0.4 rad, using the highest non-linear index values reported in the literature for each of the components. No signs of non-linear spectral or spatial distortions are observed.
As the regenerative amplifier is the base of the front-end of a parametric amplifier chain, energy and pointing stability are critical. RMS fluctuations in energy and pointing have been measured at 1 kHz repetition rate in two different ways, first with an energy meter and second with a fast photodiode (EOT4000) monitoring the pulses before their compression coupled to a fast oscilloscope (Lecroy WaveRunner 640Zi). With the fast photodiode, the RMS fluctuations amount to 1.7% over 1000 consecutive pulses, while the energy meter reports 0.5% over 100,000 consecutive shots and 0.83% over more than 50 h and every thousandth shot recorded, as shown in Fig. 7(a). The detection bandwidth of the measurement with photodiode is 3.8 GHz, and the photodiode can resolve the spectral shape of the stretched pulses. This allows monitoring fine fluctuations in the spectral distribution, due to, for example, mode beating in the fiber stretcher, which would lead to a noise increase, even if the integrated energy per pulse remains constant. The low fluctuations of the output energy are due to the saturation of the gain of the amplifier, compensating for the variations of the seed energy.
Fig. 7 Study of the stability of the regenerative amplifier. (a) Long term measurement of the energy with a Coherent energy meter. (b) Pointing measurement with a CCD camera in the focus of a 750 mm lens. The centroid is shown.
Figure 7(b) illustrates the pointing stability of the regenerative amplifier, measured with a CCD camera on the focus of a 750 mm focal length lens. Both the centroid and the peak intensity locations of the beam are analyzed, the centroid being displayed on Fig. 7(b). From the peak intensity location, the pointing is better than 10 µrad in both beam axes over half a day.
5. Conclusion
We demonstrate a regenerative amplifier delivering 6.5 mJ at 1 kHz repetition rate before compression with a beam quality parameter better than 1.1. To the best of our knowledge, this is the highest reported pulse energy generated in a bulk Yb:KYW regenerative amplifier. The pulses, stretched to 2.35 ns, can be compressed to 650 fs with a multi-layer dielectric grating compressor with 81% efficiency. When operated in continuous-wave, a maximum output power of 19.4 W is achieved with 40.3% slope efficiency and M2<1.1 with 15% output coupling; the laser is tunable from 1021 nm to 1033 nm. The experimental results are in good agreement with numerical simulations of the laser dynamics within the uncertainty in pump light absorption. This laser is used as a pump laser for a CEP stable front-end and seeding of a high energy pump line for driving of an OPCPA [2]. In this application, the demonstrated stability of the sub-components of the front-end, whether white-light generation or parametric amplification, directly depends on the stability of the driving laser.
The achievement of the high energy has been made possible by splitting the thermal load onto two crystals: the energy stored in the laser media is twice the one possible with one crystal. The cavity design, demonstrated here with 2 crystals, can straightforward be extended to more crystals, without influence on the beam parameters, by symmetrizing the cavity. The stability domains of the cavity would however then be narrowed; this means that the insensitivity of the cavity toward thermal lens variations would be reduced to a narrower range than in the case of 1 or 2 crystals inside the cavity. The range of thermal lensing where the cavity is insensitive depends on the beam sizes and thermal lens strength at the operation point of the cavity, too.
Acknowledgments
This work has been funded by the DFG excellence cluster The Hamburg Centre for Ultrafast Imaging - Structure, Dynamics. The authors thank Dr. Max J. Lederer and Dr. Joachim Meier for helpful discussions.
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