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Abstract
We report the demonstration of a pulse synthesizer based on spatial beam splitting and pulse stacking for the generation of picosecond laser pulses of Joule-level energy with arbitrary shape. An array of liquid crystals is used to control the amplitude of ten individual sub-pulses, and sliding retroreflectors are used to adjust their temporal separations. The synthesizer was used in combination with a λ=1.03 µm diode-pumped cryogenically-cooled Yb: YAG chirped pulse amplification laser to synthesize 1.3 J pulses or pulse trains of arbitrary shapes up to 9 ns duration with a temporal resolution as short as 8 ps. This pulse synthesizer offers the opportunity to incorporate a self-learning system to search for the optimal laser pulse shapes for various applications including optimized plasma conditions in laser-plasma based soft x-ray lasers and plasma sources for extreme ultraviolet lithography.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Laser pulse shaping and sequencing have been useful in a wide variety of applications, such as providing the optimal drive for inertial confinement fusion [1,2], increasing the gain and energy of plasma-based soft x-ray lasers [3–5], pre-compensation of pulse shape distortion in fiber amplifier systems [6], efficient optical parametric amplification [7], and optical manipulation of molecular motion [8]. Pulse-shaping also has application in increasing the conversion efficiency in laser-driven plasma sources for EUV lithography [9].
Several methods have been used to generate tailored pulse shapes and pulse sequences. One is based on amplitude modulation, either direct modulation of the drive current of a CW master oscillator [10,11] or external modulation of its CW output [6,12–14]. In the direct modulation method, an arbitrary waveform generator (AWG) generates an electrical waveform which is converted and amplified by a current driver. The output of the current driver is then used to drive a CW master oscillator to generate laser pulses with arbitrary shapes. In the external modulation method, a single electro-optical modulator (EOM) or multiple EOMs controlled by an AWG are used to modulate the output of a CW master oscillator to obtain arbitrary laser pulse shapes, which are seeded into amplifiers to generate shaped pulses with higher energy. Shaped pulses with energies up to 437 mJ and durations down to 0.43 ns have been demonstrated with a chain of amplifiers [15]. The EOM-based pulse shaping scheme can also be used to compensate the pulse shape distortion due to the gain saturation of amplifiers in fiber-based MOPA systems. However, since the master oscillators operate in the CW mode, pulses generated using this method are not compressible.
Besides amplitude modulation, phase modulation can also be used to temporally shape laser pulses [16]. Phase modulation can be achieved by introducing an array of liquid crystals between a nondispersive pair of gratings. The gratings are positioned at the object plane, and the image plane of a $4f$ lens system and the array of liquid crystals is placed at the Fourier plane of the $4f$ lens system. The array of liquid crystals works as a phase mask. Since the signal $f({t - \tau} )$ in the time domain and the signal $F(\omega )\textrm{exp}({ - i\omega \tau } )$ in the spectral domain are a Fourier transform pair, the phase retardation that is introduced into a certain spectral component in the spectral domain results in a temporal delay of the corresponding spectral component in the time domain. Consequently, the temporal delay is limited to a few picoseconds [17]. Additionally, the amplitude of the temporally delayed pulses must be selected beforehand by using an amplitude mask. Another recently developed technique generated narrowband, low energy, temporally-shaped seed pulses with 4 ps resolution and several hundred picoseconds lengths through spectral shaping of a seed pulse combined with difference frequency generation [18]. This technique is advantageous because it allows direct temporal patterning as the mapping from the spectral shaping to time is linear and one-to-one. However, the maximum record length is limited to the achievable stretch length of the chirped pulse amplification system involved in the creation of these pulses.
Pulse stacking is a promising technique to temporally shape laser pulses. This technique usually involves pulse splitting and recombination. The pulse splitting can be implemented using amplitude division. An input laser pulse is split into ordinary and extraordinary sub-pulses using birefringent prisms. The sub-pulses are retroreflected by end mirrors and recombine at a polarizer. The shaping and amplification of picosecond pulses up to 100 mJ level energy was realized using pulse stacking [7]. However, the number of sub-pulses is limited by the complexity of the mechanical design. To the best of our knowledge, none of these systems simultaneously generate synthesized pulses of Joule-level energy, and a record length greater than a few hundred picoseconds with a resolution of a few picoseconds.
We report a pulse shaping technique with programmability for the generation of Joule-level pulses and pulse trains of arbitrary shapes up to 9 ns in duration. The resolution can be chosen to be 300 ps FWHM or 8 ps FWHM for the uncompressed or compressed pulses respectively, depending on the specific application. In order to implement this pulse shaping technique which is also based on pulse stacking, a pulse synthesizer was built and inserted into a cryogenically cooled diode-pumped Yb: YAG laser system [19,20]. The generated sub-pulses can be compressed to sub-5 ps FWHM. Trains of ten sub-pulses can be generated with peak powers of > 10 GW for the case in which all the sub-pulses are of equal amplitude.
2. Experimental setup
The pulse synthesizer, illustrated in Fig. 1(a), consists of three functional modules: a two-stage cylindrical telescope, an array of liquid crystals, and a set of sliding retro-reflectors inserted into a cryogenically cooled diode-pumped Yb: YAG laser system. The laser system, described latter, is composed of two room temperature regenerative amplifiers and a sequence of two cryogenically cooled Yb: YAG high power amplifiers. The input pulse from the first regenerative amplifier is horizontally expanded 100 times by the two-stage cylindrical telescope. The first telescope consists of an f = −5 cm cylindrical lens followed by an f = 10 cm cylindrical lens, having an expansion factor of 2. The second stage consists of an f = 1 cm acylindrical lens and a 100 cm radius of curvature concave cylindrical mirror, having an expansion factor of 50. The use of the acylindrical lens and the concave cylindrical mirror significantly reduce the spherical aberration. The horizontally expanded pulse is subsequently split into ten sub-pulses. Each sub-pulse passes through a liquid crystal retarder and is reflected back by a retro-reflector. In the prototype described here, the retro-reflectors are mobilized on rails manually and the pulse trains are monitored with an autocorrelator. The resolution and the reproducibility of the time delays between the sub-pulses ultimately depends on the duration of the sub-pulses. The retro-reflectors can be motorized to increase the resolution and reproducibility of time delays. The retroreflected sub-pulses pass through the liquid crystals and the telescope again, where they are recombined. Finally, the sub-pulses are extracted by a polarizing cube. The pulse entering the pulse synthesizer is linearly polarized, and the direction of polarization can be tuned using a λ/2 wave plate. The polarization state of each sub-pulse changes after it passes through a liquid crystal twice and can be controlled by selecting the voltage applied to the corresponding liquid crystal. The measured transmission dependence of one single channel on the voltage applied is shown in Fig. 1(b). There are two peaks of transmission corresponding to double-pass phase retardations of π and 3 π. The voltage range from 1 V to 1.8 V was chosen for controlling the transmission.
Fig. 1. (a) A 3-D schematic diagram and side view of the pulse synthesizer. 1. Polarizing cube, 2. half-wave plate, 3. negative cylindrical lens, 4. positive cylindrical lens, 5. positive acylindrical lens, 6. flat mirror, 7. concave cylindrical mirror, 8. liquid crystals, 9. mobilized retroreflectors. (b) The dependence of the transmission of a pulse synthesizer channel on the voltage applied to the corresponding liquid crystal. The transmission is normalized to its peak value. The two peaks represent phase retardation of π and 3π, respectively. The shadowed region identifies the voltage range of adjustment used.
A photograph of the pulse synthesizer illustrating the individual components is shown in Fig. 2. A block diagram of the system that controls the voltage applied to the liquid crystals is illustrated in Fig. 3. A photodiode detects the output of the laser system in real-time. The signal is digitized by an oscilloscope and is relayed to a laptop computer running the control algorithm. A control program compares the shape of the detected signal with the designed pulse shape and adjusts the voltages on the liquid crystals through a voltage control circuit in order to match the pulse shape of the output of the laser system to the designed pulse shape. The control circuit of the liquid crystals has a voltage resolution of 0.3 mV, which corresponds to a transmission change of ∼0.04 percent.
Fig. 2. Photograph showing the layout and components of the pulse synthesizer. The solid and dashed red arrows indicate the optical path of the beams entering and exiting the pulse synthesizer, respectively.
Fig. 3. Synthesizer control system block diagram. The oscilloscope relays the waveform of the laser pulse detected by the photodiode to a computer. The control program obtains the difference between the detected waveform and a designed pulse shape and converts it into the voltages that need to be applied to the liquid crystals. The laser system will output a pulse shape that is closer to the designed pulse shape. The control system forms a closed loop designed to generate output pulses that closely matches the design pulse.
The control program algorithm consists of three functional steps: initialization, comparison, and adjustment. 1) Initialization. An amplitude array of ten elements mn, with n = 1 - 10 is introduced to describe the designed pulse shape. The element mn represents the amplitude of the nth sub-pulse and has a range from 0 to 1. For example, a synthesized square pulse is represented by an array Ms = [1,1,1,1,1,1,1,1,1,1] and a synthesized up-ramp pulse is represented by an array Mr = [1,2,3,4,5,6,7,8,9,10]/10, as shown in Fig. 4(a) and Fig. 4(b). When the program starts, it uses an initialization amplitude array M0 = [1, 0, 0, 0, 0, 0, 0, 0, 0, 1] to maximize the amplitudes of the first sub-pulse and the tenth sub-pulse found at times t = p1 and t = p10, respectively, and minimize the amplitudes of the other sub-pulses, as shown in Fig. 4(c). The amplitude of each sub-pulse is changed according to the measured transmission as a function of voltage shown in Fig. 1(b). Since in this example, the sub-pulses are evenly separated, the temporal separation between every two adjacent sub-pulses is calculated as s= (p10 - p1)/9. Therefore, the time corresponding to the peaks of all ten sub-pulses is determined as an array of times: P = [ p1, p1+s, p1+2s, p1+3s, p1+4s, p1+5s, p1+6s, p1+7s, p1+8s, p1+9s], where p1 + 9s = p10. 2) Comparison. The program reads an acquired waveform from the oscilloscope. Given an array of times P, the amplitudes of the sub-pulse peaks in the acquired waveform can be found as an array Aacq = [a1, a2, a3, a4, a5, a6, a7, a8, a9, a10]. The amplitude array Aacq is normalized to its maximum element and is subsequently subtracted from the designed amplitude array Mdes, resulting in an amplitude difference array D = [d1, d2, d3, d4, d5, d6, d7, d8, d9, d10], where dn = mn - an. 3) Adjustment. Using the amplitude difference array D and the measured transmission as a function of voltage, an array of voltage control signals V = [v1, v2, v3, v4, v5, v6, v7, v8, v9, v10] is generated and relayed to the voltage control circuit. The voltage control circuit then adjusts the voltages on the liquid crystals according to V, changing the shape of the synthesized pulse. Steps 2 and 3 are repeated until the measured pulse converges to the desired pulse.
Fig. 4. (a) Programmed synthesized square pulse, (b) programmed synthesized up-ramp pulse, (c) initialization of the control program.
The pulse synthesizer was implemented in a cryogenically cooled diode-pumped high power Yb: YAG laser system, as illustrated in Fig. 5. Laser seed pulses are generated by a mode-locked Yb: KYW oscillator. The oscillator produces pulses at a repetition rate of 56 MHz with an average power of 1 W. The oscillator pulses have a ∼5 nm FWHM spectral bandwidth centered at 1032 nm and a pulse duration of ∼ 300 fs. In order to be amplified, these pulses are stretched into 300ps FWHM pulses in a folded Martinez stretcher [21]. The stretched pulses are selected at 20 Hz repetition rate using a Pockels cell and are injected into a regenerative amplifier [22]. This first regenerative amplifier produces 0.8 mJ laser pulses which are injected into the pulse synthesizer. After the pulse synthesizer, the total energy of the synthesized pulse is about 10 µJ and may vary with the pulse shape. The throughput of the synthesizer is limited to ∼30%. Moreover, the sub-pulses are not co-linear after the pulse synthesizer. To facilitate efficient amplification in the high energy cryogenically-cooled Yb: YAG power amplifiers, the synthesized pulses are injected into a second regenerative amplifier which not only increases their pulse energy to compensate for loses in the pulse synthesizer but also improves their beam quality. The sub-pulses from the pulse synthesizer are overlapped with the pump spot in the second regenerative amplifier gain medium by adjusting the retro-reflectors. The small seeding aperture of the second regenerative amplifier only allowed about 4% of the synthesizer output to be effectively coupled. After being amplified by the second regenerative amplifier, the total pulse energy of the train of ten sub-pulses is brought back to ∼ 0.8 mJ. The beam quality of the sub-pulses is significantly improved by the second regenerative amplifier, and additionally the sub-pulses are made co-linear after being amplified, as required for efficient further amplification and use. The difference in path lengths among the sub-pulses can a few meters, with diffraction leading to differences in beam profiles. However, the sub-pulses are re-shaped by the second regenerative amplifier, resulting in identical beam profiles.
The synthesized pulse train is first amplified to ∼100 mJ by the first of two cryogenically-cooled Yb: YAG amplifiers and is subsequently further amplified to 1.3 J by the second amplifier. This two stages of high power cryogenically-cooled Yb: YAG amplifiers are similar to those described in [23] and [19] respectively. They are based on liquid nitrogen-cooled active mirror slabs and make use of multi-pass configurations. A sequence of two Pockels cells and three polarizers is inserted between the second regenerative amplifier and the first cryogenically-cooled power Yb: YAG amplifier to suppress on-axis amplified spontaneous emission and leakage from the second regenerative amplifier.
Another advantage of this pulse shaping technique is that the synthesized high energy pulses are chirped and can be compressed into sub-pulses of picosecond duration by a grating pulse compressor [20]. The cryogenically cooled Yb: YAG amplifiers have a bandwidth of ∼ 0.3 nm, which is sufficient to allow compression into pulses of sub-5 ps duration [23]. This bandwidth leads to a coherence length of ∼ 2.3 mm, meaning that interference between two sub-pulses is not substantial for temporal separations longer than ∼8 ps. Interferometric precision is not required for sub-pulse separations longer than the coherence time. The peak power of a sub-pulse in a compressed pulse shape can be as high as 10 GW for the case in which all ten sub-pulses have equal amplitude.
3. Results and discussion
The pulse synthesizer enables us to generate high energy synthesized pulses and pulse sequences with arbitrary shapes. Figure 6 shows examples of synthesized pulse shapes and pulse sequences in the nanosecond pulse regime with a total pulse energy of 1.3 J. A sequence of 300 ps FWHM pulses, a rectangular pulse and a down-ramp pulse are shown. From the output of the pulse synthesizer (10 µJ) to the output of the second cryogenically-cooled Yb: YAG amplifier (1.3 J), the amplification factor is as high as 1.3 × 105. The programmable nature of the device allows us to compensate for gain saturation to obtain high energy pulses of arbitrary shapes. Hence, we have demonstrated a pulse synthesizer with the capacity to form any pulse shapes under high amplification factors.
Fig. 6. Examples of 1.3 J synthesized pulses. (a) Synthesized train of five pulses. (b) synthesized square pulse, (c) synthesized down-ramp pulse.
The use of the pulse synthesizer in a chirped pulse amplification laser system also allows us to also generate pulses and pulse sequences of arbitrary shape in the picosecond regime. These pulses were generated adding a grating compressor to the same setup which is used to generate the pulses shown in Fig. 6. The gratings are dielectric gratings with 1720 lines/mm for 1.03 µm wavelength. The efficiency of the compressor is ∼ 70%. After the compressor, the sub-pulses were compressed to ∼ 8 ps FWHM. Figure 7 shows four examples of the picosecond pulse sequences. As mentioned above, the sub-pulses are re-shaped and made collinear by the second regenerative amplifier, resulting in identical beam profiles of the sub-pulses. Consequently, a synthesized pulse shows a uniform beam profile. Additionally, a single pulse and a synthesized pulse has identical focal spots, as illustrated in Fig. 8.
Fig. 7. Autocorrelation results of compressed synthesized trains of picosecond pulses. (a) Synthesized train of nine pre-pulses of nearly equal intensity and a main pulse. The temporal separation between two adjacent pre-pulses is 30 ps, and the main pulse is delayed by 670 ps from the last pre-pulse. (b) A zoomed-in figure of the nine pre-pulses in (a). (c) Synthesized train of nine pre-pulses and a main pulse. The pre-pulses form a down-ramp shape. (d) A zoomed-in figure of the nine pre-pulses in (c). (e) Synthesized up-ramp pulse train of nine pulses. (f) Synthesized plateau pulse train. The temporal separation between two adjacent pre-pulses is 30 ps. The total energy of the pulse train is 0.9 J and the duration of each pulse is ∼ 8 ps FWHM.
Fig. 8. a) Beam profile corresponding to a 1.3 J synthesized pulse at the output of the amplifier chain. The 1.3 J synthesized pulse is similar to the pulse shown in Fig. 7(a) before being compressed. (b) and (c) show the foci of a single pulse and a synthesized pulse, respectively. The single pulse has a pulse energy of ∼ 1 J and a compressed pulse duration of ∼ 8 ps FWHM. The synthesized pulse is the pulse (a) in Fig. 7.
The capabilities of this pulse shaper can be further extended. The position of the retroflectors can be altered by motors controlled by a computer, which will allow adjusting the temporal separation between any two sub-pulses in real-time. The real-time programmability of this pulse synthesizer offers the opportunity to develop a self-learning system to search for the optimal pulse shapes for given applications. These include, for example, the excitation of laser plasma-based soft x-ray lasers which are very sensitive to the amplitude, the shape and the time of pre-pulses [3–5]. Another example is the optimization of the EUV emission of laser-created plasmas for advanced lithography [9], where a high level of control of pre-pulses could result in an improvement in conversion efficiency into the EUV. The control system could be upgraded to measure the output of the EUV lithography light source or soft x-ray laser source, and a genetic algorithm could be used to scan the parameter space of pulse shapes and intensity for optimal output.
4. Conclusion
In summary, we have demonstrated a novel pulse shaping technique for Joule-level laser pulses based on spatial beam division and recombination. With this technique, we were able to synthesize 1.3 J pulses and pulse trains of arbitrary shapes up to 9 ns duration. The resolution can be chosen to be 300 ps FWHM or 8 ps FWHM for the uncompressed or compressed pulses respectively, depending on the specific application. The demonstrated pulse shaping technique is expected to be a powerful tool in several applications in light-matter interactions for radiation sources in which the time history of the main pulse and pre-pulses is important
Funding
National Science Foundation (1509925, 1701238); U.S. Department of Energy (DE-FG02-04ER15592).
Acknowledgment
The instrument was developed with the support of the National Science Foundation Awards ID 1509925 and PFI: AIR Award ID 1701238, and the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under award DE-FG02-04ER15592 for the development of sub-10nm wavelength soft x-ray lasers. We acknowledge support from ASML for a graduate student fellowship.
Disclosures
The authors declare no conflicts of interest.
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