1. Introduction

Remarkable progress of ultra-intense short-pulse lasers, especially of Ti:sapphire lasers, has opened a variety of new interesting scientific and technical fields [1, 2]. The pulse-to-pulse energy stability of the laser pulse energy is of essential importance for any applications. As an example, terawatt-class lasers have been applied to the generation of extreme-ultraviolet (XUV), x-ray, or high-energy particle radiation. The intensity fluctuation of the generated radiation pulses is originated from that of the driving laser pulses, and in many cases the fluctuation is enhanced through the conversion process. Therefore, it is necessary that the fluctuation of the laser pulse energy is as small as possible.

Terawatt-class Ti:sapphire laser systems consist of a master oscillator and power amplifiers (MOPA). Short seed pulses are generated by a mode-locked Ti:sapphire oscillator or a short pulse fiber laser, and amplified to several millijoule by a regenerative or an eight-pass pre-amplifier, and furthermore, amplified to several tens to several hundreds of millijoules by one stage or two stages of multipass power amplifiers. To pump the power amplifiers with output-pulse energy more than several tens of millijoules, a green pulse of a hundred millijoule or more is necessary. Under the present technical progress of high energy pulse lasers, though the stable LD-pumped solid state lasers are recently on great progress, we have no choice still but depend on conventional flush-lamp pumped solid state lasers (typically second harmonics of Nd:YAG lasers). The short-term pulse energy fluctuations of the pump lasers are typically 1% rms at least. (The fundamental light can be less fluctuated, but the second harmonic light is in enhancement.) This leads to limitation of pulse-to-pulse output energy stability of the laser system. For instance, a 10-TW Ti:sapphire laser system running under a saturation condition exhibits 1.3% energy fluctuation with 1.1% pump-energy fluctuation [3].

Pulse-to-pulse energy stabilization for low-energy (less than a few millijoules) laser pulses has been performed by several different ways. Active optical filters for adaptive attenuation of the output pulse energies in short-pulse laser systems have been assembled with a Pockels cells driven by photosensitive high-speed high-voltage circuits [4, 5]. The device can detect an input laser pulse and apply an appropriate transmission correction to the same laser pulse to produce a quasi-constant output energy. This method can be applied in principle to high-energy ultrashort-pulse laser systems when a large-aperture Pockels cell is available. Up to now, however, there is no report for high energy lasers to our knowledge. In regenerative amplifiers, the output pulse energy has been stabilized by controlling the cavity loss either actively or passively. An actively stabilized regenerative amplifier equipped with a feedback-controlled Pockels cell in the regenerative cavity has been demonstrated [6, 7]. From the viewpoint of stabilization performance, the feedback control method has a benefit to ensure the pulse-to-pulse energy stability during long-term operation. However, since the pulse build-up time in the feedback-controlled regenerative amplifier must be extended to a few microseconds for an action of the feedback circuit, the net dispersion in optical components in the amplifier is considerably enlarged. It is not preferable in ultrashort-pulse chirped-pulse amplification (CPA) systems which should be designed so that the dispersion is as small as possible to obtain high temporal quality of the output laser pulses. Moreover, this method cannot be applied to high-energy laser systems equipped with multipass amplifiers of only several optical passes. On the other hand, a passive method has been also demonstrated for stable operation of the Ti:sapphire regenerative amplifier [8]. By optimizing both the cavity round-trip times and the optical loss in the amplifier, the output fluctuation caused by the gain fluctuation can be effectively suppressed. In the plot of output energy of the amplifier (J _out) versus stored energy in the laser medium (J _sto), as calculated by the Frantz-Nodvik model [9–11], there appears less output fluctuation operation (here is called stationary plateau) by simply selecting the cavity round-trip times depending on the optical loss. If the single-pass loss of an amplifier is negligible small, the stationary plateau does not appear. But conveniently, the cavity of a Ti:sapphire regenerative amplifier has some inherent loss typically about 5 to 15% per round-trip, which is almost sufficient to operate on the stationary plateau. Therefore the energy stabilization of regenerative amplifiers can be realized with no additional components. In principle, this method can be extended to high-energy multipass amplifiers by optimizing a number of amplifier passes and inserting appropriate artificial losses between amplifier passes.

In this paper, we present a new concept for the Ti:sapphire chirped-pulse amplifier system with high energy, high pulse-to-pulse stability, low group-delay dispersion, and simple construction. The passive stabilization method has been extended to the high-energy two-stage multipass amplifier. In consequence, a root-mean-square (rms) fluctuation in pulse energy of 0.3% with an average energy of 94 mJ was achieved in only eight amplification passes. This is the lowest pulse-to-pulse fluctuation, to the best of our knowledge, obtained by Ti:sapphire chirped-pulse amplifiers with pulse energies of the 100 millijoule class.

2. Design of amplifiers

In the plot of J _out versus J _sto for a multipass amplifier, as mentioned above, a stationary plateau can be seen under the appropriate losses. To find the stationary plateau for multipass amplifiers, we have performed numerical analysis based on the Frantz and Nodvik model [9–11]. Assuming uniform transverse beam profiles, we can get the output fluence J _out ^(p) for the number of optical passes through the gain medium p:

where J _in and J _sat are the input and saturation fluences, respectively. G ₀ ^(p) is the small-signal gain given by

Here J _sto ^(p) is the stored energy per unit cross-section in the gain medium. The initial fluence J _sto ⁽⁰⁾ is proportional to the pump fluence when nonlinear losses for pumping (i.e., the absorption saturation, the amplified spontaneous emission, etc.) are negligible. Therefore, fluctuation of the pump source can be considered as fluctuation of the J _sto ⁽⁰⁾. Losses for an amplified beam are incorporated in this model by the equation of

where R is the single-pass loss in the amplifier. The reduction of the stored fluence is given by

Here, we consider a typical 100-mJ class Ti:sapphire CPA system with which consists of a seed source generating sub-nanosecond chirped pulses with nanojoule energy, the first-stage multipass amplifier as a high-gain pre-amplifier, and the second-stage multipass amplifier as a low-gain power amplifier. First, we discuss the pre-amplifier. As an example of the stationary plateau, Fig. 1(a) shows the output fluence J _out ^(p) as functions of stored energy J _sto ⁽⁰⁾ for a 16-pass amplifier. The initial fluence J _in ⁽⁰⁾ is 10^-7 J/cm². The saturation fluence J _sat is assumed to be 0.9 J/cm² for all our calculations. A clear stationary plateau can be seen for the loss R of 0.09 per pass in the stored energy range of about 1.3 to 1.6 J/cm². Figure 1(b) shows pass-by-pass build-up of the amplified pulse fluence in the condition of the plateau appearance. Note that a pulse is amplified to the maximum at several passes before the final pass, and the maximum fluence in the amplifier is several tens of percent higher than the output fluence. The pulse fluence should not exceed the damage threshold of a Ti:sapphire crystal during the amplification. Figure 1(b) shows that the maximum fluence is about 1.3 J/cm². Because this fluence is lower than the damage threshold of Ti:sapphire crystal for a sub-nanosecond chirped pulse, this plateau range is practically realized to use for stabilization. Figure 2(a) shows stationary plateaus for 4-, 6-, 8-, and 16-pass amplifiers with the appropriate R values. Even when the amplifier has a smaller number of passes, the stationary plateau appears if the single-pass loss R is large enough. However, the reduction of the number of passes leads to increase of the amplified pulse fluence. For example, in the eight-pass amplifier, the maximum fluence in the amplification and the output fluence in the final pass at J _sto ⁽⁰⁾ = 3.3 are 2.8 and 2.1 J/cm², respectively. Such high-fluence pulse might cause damages on optical elements in the amplifier. It is concluded that the stabilization in high-gain multipass amplifiers with a little number of passes is essentially difficult. Then we consider a low-gain multipass amplifier used as the second-stage amplifier. Such power amplifiers generally have a gain from 10 to 100. Figure 2(b) shows stationary plateaus for 3-, 4-, 5-, and 6-pass amplifiers with J _in ⁽⁰⁾ = 10^-2 J/cm². In the six-pass amplifier, the maximum fluence in the amplifier and the output fluence in the final pass at J _sto ⁽⁰⁾ = 2.5 are 1.6 and 0.7 J/cm², respectively. This fluence is acceptable for chirped pulse amplification, although the extraction efficiency expressed by J _out ⁽⁶⁾/J _sto ⁽⁰⁾ is relatively low (30 to 40%). From the above-mentioned results, we can design an independently stabilized two-stage multipass amplifier. To avoid damages of laser crystals and optical elements, the pre-amplifier and the power amplifier require the numbers of passes more than about 16 and 6, respectively. This design is possible in principle. However it has serious disadvantages that the number of passes of pre-amplifier is large, and the efficiency of the power amplifier is low.

 

Fig. 1. (a). The output fluence J _out ^(p) as a function of stored energy J _sto ⁽⁰⁾ in 16-pass amplifier for different single-pass losses R. (b). The build-up traces of the amplified pulse fluence in the plateau range.

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Fig. 2. The stationary plateaus for 3- to 16-pass amplifiers with an input fluence J _in ⁽⁰⁾ of (a) 10^-7 and (b) 10^-2 J/cm².

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Here we propose the new concept of a two-stage multipass amplifier without the disadvantages of the both large number of passes and low efficiency. The two amplifier stages are pumped by pump pulses separated from one pump source. Therefore, the gain fluctuations of the two amplifiers can be synchronized, namely, the system has a fixed ratio A of the stored energy in the pre-amplifier to that in the power amplifier,

In the calculation the product of the pre-amplifier output fluence and the coupling factor K is substituted into the power amplifier input fluence,

where P _pre is the number of passes of pre-amplifier. The coupling factor K relates to a coupling loss between the pre-amplifier and the power amplifier, and a magnification of a beam expander. In this proposed scheme, we can find the stationary plateau even without loss in the pre-amplifier and with a little number of passes. Figure 3(a) shows the stationary plateaus of power amplifier output for the stored energy ratio A of 1 to 2.5 with K = 20. We choose the both numbers of passes of the pre and power amplifiers to be four, and the loss for pre-amplifier R _pre is zero. The output pulse fluence at the stationary plateau strongly depends on the stored energy ratio A. Smaller ratio A gives less single-pass loss of the power amplifier R _pow and higher extraction efficiency, but considerably larger amplified pulse fluence. For the case with A = 2 and R = 0.28, the maximum fluence in the amplifier and the output fluence after the final pass in the plateau range are 1.4 and 1.1 J/cm², respectively. This fluence is low enough to be accepted for chirped pulse amplification. Moreover, relatively high extraction efficiency more than 50% is achievable. The ratio A is coupled with the optimal value of the loss R _pow to obtain a stationary plateau. It means that the plateau curve can be controlled and optimized only by adjusting the ratio A even for a fixed loss R _pow. This could be very useful for practical optimization and operation of a laser system for any experiments. Next, we estimate the coupling factor K for the stationary plateau. Figure 3(b) shows stationary plateaus of the power amplifier output for the coupling factor K of 10 to 40 with A = 2. The plateau curve does not strongly depend on the factor K. Therefore, to design an amplifier system we can have relatively large flexibility for the beam diameters for the pre-amplifier and the power amplifier. That is to say, this stabilization scheme can be applied to amplifiers of a wide range of the output energy.

 

Fig. 3. The stationary plateaus for a two-stage multipass amplifier (a four-pass pre-amplifier and a four-pass power amplifier) pumped by a single pump source with the parameters of (a) the stored energy ratio A and (b) the coupling factor K.

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3. Experiment

We have experimentally demonstrated highly stable operation of a two-stage multipass Ti:sapphire amplifier. The schematic diagram of the experimental setup is shown in Fig. 4. It consisted of a mode-locked oscillator, a pulse stretcher, a four-pass pre-amplifier, a four-pass power amplifier, and a frequency-doubled Nd:YAG laser with 7-ns pulse duration as a pump source. The mode-locked oscillator (Coherent, Mira) generated a pulse train of 100-fs pulses with 80 MHz repetition rate. The central wavelength was 790 nm. The femtosecond pulses were stretched to 400 ps by the 2000 lines/mm grating stretcher. The pulses then passed through a Faraday isolator and a pair of lens, and then entered the pre-amplifier as a seed pulse with 1.5-nJ pulse energy and about 1-mm beam diameter. The pre-amplifier consisted of a 18-mm-long Brewster-cut Ti:sapphire crystal, three focusing mirrors (f = 1 m), and flat mirrors. After the first two passes the amplified pulse train was passed through a half-wave plate and an electro-optic pulse gating system (Fastpulse Technology, 5046SC) that synchronized with the mode-locked oscillator and the Nd:YAG pump laser. The pulse gating system generated a 10-ns high-transmission gate, selected a single pulse at the front of the amplified pulse train, and suppressed the amplified spontaneous emission. The selected pulse was amplified to about 10 mJ in another following two passes. The output pulse of the pre-amplifier was then expanded to about 4 mm by a pair of a convex and a concave mirror, and passed through the second pulse gating system, and then entered the power amplifier. The four-pass power amplifier consisted of a 10-mm-long normal-cut Ti:sapphire crystal with anti-refractive coating, four 6-mm-thickness non-coated fused silica plates, and flat mirrors arranged in a bow-tie configuration. The fused silica plates were placed in the beam passes after the first, second, and third amplification, and gave losses of about 30% per pass for s-polarized light at an incident angle of about 45 degrees. The frequency-doubled Nd:YAG laser (Spectra Physics, GCR 250) was flash-lamp pumped, and generated about 600-mJ green pump pulses with 10 Hz repetition rate. The pump pulses were divided into 1:4 by a beam splitter, and were provided to two amplifiers after passed through image relay optics. Pump beam diameters at the pre-amplifier and the power amplifier crystals were 1.2 and 4 mm, respectively. The average pump energies of each amplifier were fine-tuned by attenuators using a rotating polarizer.

 

Fig. 4. Experimental setup.

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Using a pyroelectric energy meter (Ophir, Laserstar with PE50BB-DIF), we recorded 500 pulses at one time and determined the average pulse energy as well as the rms of the pulse-to-pulse energy fluctuation, the maximum and the minimum pulse energies. The rms and the peak-to-peak of the pump energy fluctuation were typically 1.7 and 10%, respectively. We carefully adjusted the average pump energies for the pre-amplifier and the power amplifier to minimize the fluctuation of the output energy from the power amplifier. In an optimized condition, the average output energy of the pre-amplifier was 11 mJ when the average absorbed pump energy was 88 mJ. The rms and the peak-to-peak of the pulse energy fluctuation of the pre-amplifier output were 18 and 105%, respectively. For the output from the power amplifier, the average energy, the rms energy fluctuation, the maximum energy, and the minimum energy as a function of average absorbed pump energy in the power amplifier are shown in Fig. 5. The rms energy fluctuation remarkably decreased with increasing average pump energy. At the maximum average pump energy of 405 mJ, the rms and the peak-to-peak energy fluctuation were 0.3 and 2 %, respectively, and the average output energy of 94 mJ was obtained. The rms fluctuation was suppressed by a factor of 5 compared to the pump fluctuation. In this experiment the ratio A of pump fluence for the pre-amplifier to that for the power amplifier was about 2.4. The stored energy J _sto in the power amplifier was estimated to be 2.1 J/cm² with assuming that the 65% (≈ λ _l/λ _p, λ _l and λ _p are the wavelength of the lasing and the pump respectively) of absorbed pump energy was converted to the stored energy. And besides, the average output fluence over the pump area and the extraction efficiency of the power amplifier were estimated to be 0.75 J/cm² and 36%, respectively. Those values were reasonably consistent with the result of the numerical calculation shown in Fig. 3.

 

Fig. 5. (a). The average energy, the rms energy fluctuation, (b) the maximum energy, and the minimum energy of the power amplifier output as a function of average absorbed pump energy.

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4. Conclusion

We presented a new concept of Ti:sapphire chirped-pulse amplifier systems with high energy, high pulse-to-pulse stability, and simple construction. By applying the passive stabilization to the two-stage multipass amplifier, an rms fluctuation in pulse energy of 0.3% with an average energy of 94 mJ was successfully achieved in only eight amplification passes. The presented scheme is very simple and easy to be realized only by inserting the losses into only the second multipass amplifier. An advantage of the passive method is that its applicability is not restricted by the properties of such an additional device used in active method. The present scheme can be easily extended to high repetition rates, high average powers, large aperture sizes, or other laser wavelengths, and as an additional advantage, the total number of passes through the gain media can be reduced down to only eight, which reduces the dispersion of the amplifier system efficiently.