1. Introduction

Ultrafast laser amplifier systems have found widespread application in areas of science and technology, such as high-harmonic generation [1], studies of protein dynamics [2] and chemical reactions [3], laser machining [4] and laser particle acceleration [5]. Most high-power ultrafast laser amplifiers make use of the chirped-pulse amplification (CPA) technique [6] in which a femtosecond pulse is positively chirped to increase its duration to 0.1–1 ns, amplified and then recompressed back to femtosecond duration. The most-successful architecture uses a ti:sapphire crystal, pumped by a green laser, as a gain medium. Ti:sapphire laser systems have been implemented in two basic configurations: very high repetition rate systems (>100 kHz) with low pulse energy (<10 uJ), pumped by CW lasers [7] and low to medium repetition rate systems (10 Hz - 10 kHz) with high pulse energy (1 mJ - a few Joules) pumped by pulsed lasers [8,9].

A very large fraction of ultrafast laser applications require pulses with moderate energy, in the tens of microjoules to a millijoule range, and with peak powers of gigawatts- for example, as an energy source for broadly-tunable optical parametric amplifiers (OPA’s), or simply to generate peak focused intensity of ~10¹⁴–10¹⁵ W cm^-2 for material ablation or VUV/EUV harmonic generation. Although these applications often require pulse energies in excess of that available from CW-pumped amplifier systems, they benefit from higher repetition rates than those pumped by pulsed lasers. As ultrafast science progresses, many experiments require extensive signal averaging to obtain the signal-to-noise ratio necessary for observing subtle effects. Average powers available from ultrafast laser systems have been increased from ~1 watt in the 1990’s, to ~10 W today through the use of cryogenic cooling of the ti:sapphire crystal [9–11]. This has allowed millijoule-level ultrafast laser systems to be implemented at repetitions rates as high as 10 kHz.

Nevertheless, a gap has remained in ultrafast technology at pulse repetition-rates of 20–100 kHz and pulse energies of ~0.1 millijoule. CW laser-pumped systems have output pulse energies of ~5 µJ, which is marginal or insufficient for many applications, such as pumping multiple OPA’s, or for efficient high-order harmonic generation. On the other hand, systems using pulsed pump lasers are generally engineered to generate millijoule pulses. Many experiments are compelled to use these kilohertz systems but only use a small fraction of the total energy output. Recently, a 100 kHz regenerative amplifier based on DPA was demonstrated, producing 28µJ, 39 fs pulses with horizontal and vertical M2 values of 3.6 and 5.3, respectively [12]. In addition, Yb-fiber laser amplifiers have been demonstrated that operate at > 10 kHz and have a pulse energy of ~140 uJ [13]. In other work, fiber amplifiers have produced very short (~43 fs) pulses [14], but fiber systems have not been demonstrated that encompasses all three properties: >10 kHz repetition rate, sub-40 fs pulses, and >100 µJ pulse energy.

A few papers report fractional millijoule CPA systems running at ~10 kHz repetitions rates [15,16]. However, use of these systems has been limited, despite the fact that high-power frequency-doubled Nd:YAG lasers operating at 20–50 kHz and with average powers of ~100W are readily available. The reason is that thermal lensing is a serious limitation on performance. When the pump laser is focused onto a ti:sapphire crystal, local heating causes a lensing effect. This lensing gets progressively worse at higher repetition rates as the heat load per unit area increases. The thermal lens focal length inside the amplifier crystal [17] is given by

where k is the thermal conductivity of the crystal, r is the pump radius, dn/dT is the change in the index of refraction with temperature, E is the pump pulse energy that is converted to heat, ν is the repetition frequency, and F=E/(πr ²) is the pump fluence. For Ti:sapphire at 77 K, k=9.8 W/(cm K) [18] and dn/dT=1.8×10^-6/K [19] and at 50 K, k≈30 W/(cm K) [18] and dn/dT=1.8×10^-6/K [19]. Figure 1 shows the thermal lens focal length, at 50 and 77 K, as a function of repetition-rate, when the peak focused fluence is kept constant at 3 J cm^-2 for a gain of ~5 per pass. A number of laser amplifier systems have made use of cryogenic cooling for higher performance [9–11,20], but this is, to our knowledge, the first presentation of a system using ti:sapphire cooled to 50 K. For example, a 100 kHz system running at 50 K would have a thermal lens of ~110 cm, while the same system at 77 K would have a thermal lens of ~36 cm, or at room temperature, ~2 mm.

 

Fig. 1. Focal length of the thermal lens induced in a Ti:sapphire crystal at 77 K (solid) and 50 K (dashed). The fluence is kept constant at 3 J cm^-2.

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In this work, we implement a cryogenically-cooled laser amplifier designed to be scaleable to very high repetition rates. We use a modified multipass amplifier design that can use pump pulse energies significantly less than the 8–10 mJ required in past designs. Since commercial green pump lasers are limited to ~100W average power, the large pump pulse energy has limited the repetition rate of such a single stage, single pump laser amplifier to 10–15 kHz. To overcome this limitation, the new design makes use of tighter focusing in the amplifier ring, and incorporates a new optical design that greatly reduces accumulated astigmatism. Finally, we combine these new optical designs with downchirped pulse amplification (DPA), rather than conventional CPA, to reduce compressor losses [11]. The result is a compact, single stage amplifier design that is scalable to tens of kHz and produces moderate pulse energy with excellent beam quality. The use of a cavity-dumped seed laser eliminates the need for a pockels cell pulse selection, which has been another significant limitation on repetition rate.

2. Experimental setup

In DPA, the seed pulse is stretched using negative dispersion and then compressed using positive dispersion by passing the beam through a block of glass. Figure 2 shows a schematic of the amplifier system setup. The front end of the amplifier system is a cavity-dumped oscillator with a repetition rate that is variable up to 2 MHz. At repetition rates of 10–15 kHz, the cavity-dumped energy is ~15 nJ per pulse with a spectrum that can support a 12 fs pulse. Two different stretcher designs were used in this project. For the comparison between old and new ring designs, the stretcher consisted of a grating pair followed by a prism pair. The grating pair provided the majority of the pulse stretching, while the prism pair pre-compensated for the large amount of third-order dispersion (TOD) in the material compressor. Subsequently, we obtained a pair of grisms [20]. A grism is a single optical element containing both a prism and a grating, and which is designed for an optimum ratio of second to third-order dispersion, allowing for efficient recompression. All subsequent measurements were made using the grisms as the stretcher (Fig. 2). The pulse from the grism stretcher is adjustable from 5–30 ps, has a pulse energy of ~1 nJ. The beam is near Brewster’s angle on all of the entrance and exit faces. These grisms were fabricated using off-the-shelf aluminum coated gratings, which limited the double pass stretcher efficiency to ~10%; however, the use of optimized gold coated gratings will increase this to >75%. Nevertheless, the high input energy of the cavity-dumped seed laser allowed us to demonstrate saturated gain of the amplifier.

 

Fig. 2. Schematic diagram of the DPA amplifier system.

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After the stretcher, the beam is then sent into an amplifier consisting of a seven-mirror, ten pass multipass ring and a cryogenically cooled Ti:sapphire amplifier crystal. To obtain a smaller focal spot (~150 µm diameter) in the amplifier crystal, mirrors with a smaller (75 cm) radius of curvature (ROC) are used in this ring, compared with the standard 1.0 m ROC mirrors used previously[21]. However, use of shorter ROC mirrors in this multipass design [22] causes a degradation of the output mode (Fig. 3(a)) due to increased astigmatism. A new amplifier ring design was therefore implemented to minimize the incident angle of the beam on the curved mirrors (Fig. 4) and resulted in virtually no astigmatism in the output beam (Fig. 3(b)).

 

Fig. 3. M² measurement of the amplified beam with (a) old ring design and (b) new ring design. The output of the new design has an M² of 1.18 and 1.26 in the x- and y-directions, respectively.

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Fig. 4. Schematic diagram of astigmatism-minimized amplifier ring. Only three passes are shown, but up to 10 passes can be employed with minimal astigmatism.

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The 6 mm amplifier crystal is housed in a ultra-high vacuum cell and cooled to ~50 K using a closed loop helium cryo-cooler. The system was pumped by a commercially available, doubled Nd:YAG laser (532 nm) capable of running at 5–20 kHz with up to 50 W average power. The pump pulse energy was limited to 2.3 mJ to allow the repetition rate to be increased to >40 kHz. The uncompressed, amplified output power was measured as a function of seed pulse duration by adjusting the grism separation (Fig. 5). The output power varies greatly with input seed pulse duration, reaching a maximum around 22±3 ps. At shorter pulse lengths, the finite lower state lifetime reduces the amplifier output. A simulation based on the Frantz-Nodvik equations [23] was developed to extract the lower state lifetime; the result is shown in Fig. 5(a). The simulation and the data are in very good agreement when a lower state lifetime in the range of 0.25–5 ps is assumed. The variation in the lifetime is due to the unknown ratio of the upper to lower level degeneracy in ti:sapphire. The product of this degeneracy ratio with the lower state lifetime is 25 for a best fit with the data. The simulation (Fig. 5(a) inset) shows that the output energy starts to saturate at a seed pulse width of ~75 ps. The drop in efficiency at longer pulse lengths is a result of the experimental setup. The gratings of the grisms are only 1” square, which limited the amount of stretch that could be applied before serious spectral clipping occurred. The amplified power dropped when the spectral clipping became too large-a pair of grisms with dimension 50–75 mm will allow for sufficient stretch to obtain near-ideal energy extraction, while still maintaining a very compact geometry. The maximum output pulse energy of the amplifier is 290 µJ at 10 kHz and 270 µJ at 15 kHz, with a pulse-to-pulse intensity stability of 1.7% and 3.0% rms at 10 and 15 kHz, respectively. At 15 kHz, the grism separation was adjusted and the relative timing of the pump and seed pulses was reoptimized (Fig. 5(b), circles). This resulted in slightly higher energies at the shorter seed pulse lengths.

 

Fig. 5. Power before compression as a function of seed pulse length for (a) 10 kHz repetition rate and (b) 15 kHz repetition rate. Data was taken while only adjusting grism separation (squares) and while adjusting both grism separation and timing between pump and seed pulses (circles). Simulation results are shown as solid line in (a) and in (a) inset, which extrapolates the model to estimate the pulse duration required for efficient energy extraction from ti:sapphire.

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After the amplifier, the beam is sent into a telescope to provide a beam that slowly diverges from ~1 cm to ~2 cm diameter as the beam passes through the compressor material. This divergence minimizes the B-integral in the compressor while also allowing for a smaller block of glass for the compressor. Calculations and measurements indicate that the variation of the pulse width across the beam profile is negligible. This telescope also serves as a spatial filter, which ensures a spatial mode close to TEM₀₀ with a throughput of 90%. The compressor consists of 120 cm of uncoated SF18 glass. An AR coated slab, that is on order, should provide 95% throughput for the compressor.

The pulse duration from the amplifier was measured using second-harmonic generation frequency resolved optical gating (SHG FROG). Figure 6 shows the reconstructed pulse and phase, with a FWHM of 35.5±1 fs. The transform limit of the amplified spectrum is ~28 fs. FROG measurements taken at different radial positions of the beam profile reconstruct to the same value. This shows that the center and edges of the divergent beam do not traverse significantly different amounts of material. The output beam quality is good, as can be seen by the M² of the beam (Fig. 3(b)), which were measured to be 1.18 and 1.26 in the x- and y-directions, respectively. Nonlinear effects, such as B-integral, would distort the beam profile, leading to a large M² value. Since the M² is close to one in both directions, we conclude that nonlinear effects in the compressor are negligible. This is consistent with our calculations that the B-integral should be less than 0.5 in this configuration.

 

Fig. 6. Temporal profile and phase of amplified pulse as measured with frequency-resolved optical gating (FROG).

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3. Conclusion

In conclusion, we have demonstrated a laser amplifier system based on downchirped pulse amplification that can be operated at medium energies and very high repetition rates. The modified design makes use of a tighter focus amplifier ring capable of achieving saturated gain at lower pump pulse energies. This modified amplifier design greatly reduces accumulated astigmatism in the multipass ring. The result is a compact single stage amplifier that is scaleable to 40 kHz or greater repetition rate with excellent beam quality and no degradation in amplifier performance. Such a system will provide a pulse energy and peak power sufficient for many applications, at higher pulse repetition frequencies than are currently available.