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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 17 — Aug. 17, 2009
  • pp: 15264–15273
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Multi-terawatt chirped pulse optical parametric amplifier with a time-shear power amplification stage

Paweł Wnuk, Yuriy Stepanenko, and Czesław Radzewicz  »View Author Affiliations


Optics Express, Vol. 17, Issue 17, pp. 15264-15273 (2009)
http://dx.doi.org/10.1364/OE.17.015264


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Abstract

We report on a compact and simple, broadband optical parametric chirped pulse amplifier system that amplifies femtosecond pulses directly from a titanium sapphire oscillator up to 2 TW power. Our system relies on a new technique - time shear - that improves the time overlap between the seed and pump pulses and, thus, improves the efficiency of the power amplification stage pumped with a ns laser. Parametric amplification was achieved in two stages: a multipass, noncollinear geometry preamplifier with a single β-barium borate crystal, and a power booster stage incorporating three β-barium borate crystals in the new time-shear design. Both stages were pumped with pulses from a commercial 10 Hz frequency doubled ns Nd:YAG laser. The system delivers 49 mJ pulses with a temporal width of 23 fs and its overall conversion efficiency after pulse compression is 10%.

© 2009 OSA

1. Introduction

Since, in contrast to the standard laser amplifier, the parametrical amplifier cannot store energy, it is crucial to ensure a proper time overlap between pump and amplified pulses in order to achieve reasonable conversion efficiency. One attractive possibility to achieve high extraction efficiency is to use ps pump lasers which can also deliver high instantaneous pump power leading to high parametric gain. This comes at the price of high setup complexity since the requirement for the precise time overlap of seed and pump pulses on ps time scale which results in sophisticated synchronization schemes. Moreover no commercial ps Nd:YAG sources with high energies are available, thus only custom designs can be considered. For example, using precise time synchronization with phase locking to high harmonics of the seed laser repetition frequency, authors of [6

6. S. Witte, R. Th. Zinkstok, A. L. Wolf, W. Hogervorst, W. Ubachs, and K. S. E. Eikema, “A source of 2 terawatt, 2.7 cycle laser pulses based on noncollinear optical parametric chirped pulse amplification,” Opt. Express 14(18), 8168–8177 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-18-8168. [CrossRef] [PubMed]

] were able to reach 2 TW power level. All optical synchronization was used in [7

7. F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14(26), 12822–12827 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-26-12822. [CrossRef] [PubMed]

]. Seed pulses were broadened in a photonic fiber and the infrared part of the resulting spectrum was then amplified in a regenerative amplifier and a power booster stage consisting of three Nd:YAG rods. The amplified ps pulses were then used to pump optical parametric amplifier delivering 110mJ of the pulse energy with 4.5% RMS fluctuations. However, more then 18% of the amplifier output was in the form of uncompressible parametric fluorescence.

Possibly, a more tempting approach to pump a terawatt OPCPA amplifier is to use the well established commercial ns Nd:YAG pump lasers (up to 10 J, 5-10 ns @532 nm). This approach offers relative simplicity and low cost [8

8. X. Yang, Z. Xu, Z. Zhang, Y. Leng, J. Peng, J. Wang, S. Jin, W. Zhang, and R. Li, “Dependence of spectrum on pump-signal angle in BBO-I noncollinear optical-parametric chirped-pulse amplification,” Appl. Phys. B 73, 219–222 (2001).

]. The ns Nd:YAG pump lasers are very reliable and convenient to use, still such pumping schemes encounter a problem of a rather poor time overlap between the pump pulse (5-10 ns typical) and the stretched femtosecond pulse which is typically about 1-2 ns long [9

9. I. Jovanovic, C. A. Ebbers, and C. P. J. Barty, “Hybrid chirped-pulse amplification,” Opt. Lett. 27(18), 1622–1624 (2002), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-27-18-1622. [CrossRef]

]. This time duration disparity leads to the poor temporal overlap of the seed and pump laser, resulting in a low efficiency of the parametric amplifier.

An approach that gives a better time overlap and, thus, better efficiency uses femtosecond seed pulses that are stretched to a few ns. However, setups with such a high stretching factor result in either a limited spectral bandwidth of amplifier [10

10. I. Jovanovic, B. J. Comaskey, C. A. Ebbers, R. A. Bonner, D. M. Pennington, and E. C. Morse, “Optical parametric chirped-pulse amplifier as an alternative to Ti:sapphire regenerative amplifiers,” Appl. Opt. 41(15), 2923–2929 (2002), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-15-2923. [CrossRef] [PubMed]

,11

11. H. Yoshida, E. Ishii, R. Kodama, H. Fujita, Y. Kitagawa, Y. Izawa, and T. Yamanaka, “High-power and high-contrast optical parametric chirped pulse amplification in β-BaB2O4 crystal,” Opt. Lett. 28(4), 257–259 (2003), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-4-257. [CrossRef] [PubMed]

] (16nm and 7nm respectively, with efficiencies of about 25%) or a design of the stretcher/compressor pair with impractically large mirrors and diffraction gratings, which leads to a complex and expensive system with large footprints. The authors of [12

12. H. Okada, H. Kiriyama, M. Mori, Y. Nakai, T. Shimomura, M. Tanoue, S. Kondo, S. Kanazawa, H. Daido, T. Kimura, and T. Tajima, “Demonstration of highly efficient broadband amplification in an optical parametric chirped-pulse amplifier system,” Opt. Rev. 16(1), 1–3 (2009). [CrossRef]

,13

13. H. Kiriyama, M. Mori, Y. Nakai, Y. Yamamoto, M. Tanoue, A. Akutsu, T. Shimomura, S. Kondo, S. Kanazawa, H. Daido, T. Kimura, and N. Miyanaga, “High-energy, high-contrast, multiterawatt laser pulses by optical parametric chirped-pulse amplification,” Opt. Lett. 32(16), 2315–2317 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-16-2315. [CrossRef] [PubMed]

] used a sophisticated stretcher design with two diffraction gratings and two cylindrical mirrors in a double pass configuration. The pulses were stretched to 1 ns FWHM (temporal window of the stretcher was about 3 ns), which resulted in a high conversion efficiency of 26% (with 5.5 ns FWHM pump laser). Still, in order to compress such pulses a large aperture grating in the compressor is required.

Yet another approach for high conversion efficiency is to use a hybrid chirped pulse amplifiers. Those systems incorporate an optical parametric preamplifier as well as a laser amplifier based on, e.g. titanium sapphire crystal [9

9. I. Jovanovic, C. A. Ebbers, and C. P. J. Barty, “Hybrid chirped-pulse amplification,” Opt. Lett. 27(18), 1622–1624 (2002), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-27-18-1622. [CrossRef]

,14

14. H. Kiriyama, N. Inoue, Y. Akahane, and K. Yamakawa, “Prepulse-free, multi-terawatt, sub-30-fs laser system,” Opt. Express 14(1), 438–445 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-438. [CrossRef] [PubMed]

16

16. X. Zhou, H. Lee, T. Kanai, S. Adachi, and S. Watanabe, “An 11-fs, 5-kHz optical parametric/Ti:sapphire hybrid chirped pulse amplification system,” Appl. Phys. B 89(4), 559–563 (2007). [CrossRef]

]. For such hybrid setups, OPCPA amplifier acts as high gain amplifier with a great contrast (up to 10−11) [14

14. H. Kiriyama, N. Inoue, Y. Akahane, and K. Yamakawa, “Prepulse-free, multi-terawatt, sub-30-fs laser system,” Opt. Express 14(1), 438–445 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-438. [CrossRef] [PubMed]

]. The pulses are then amplified in a power booster stage which is composed of standard titanium sapphire laser amplifiers. It has been shown that in the titanium sapphire power amplification stage the extraction efficiency could be as high as 40%s [17

17. J. Zhang, M. Suzuki, M. Baba, Z. Wei, Z. Wang, P. Wang, J. Zhang, J. Zheng, and H. Kuroda, “Development of a compact efficient 10 Hz 20 TW Ti:sapphire laser system with a 1 kHz regenerative amplifier,” Appl. Opt. 46(13), 2498–2502 (2007). [CrossRef] [PubMed]

]. The most recent review on the progress in OPCPA development can be found in [18

18. A. Dubietis, R. Butkus, and A. P. Piskarskas, “Trends in chirped pulse optical parametric amplification,” IEEE J. Sel. Top. Quantum Electron. 12(2), 163–172 (2006), http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1632161&isnumber=34227. [CrossRef]

].

It has been shown that one possible solution to the time overlap problem in OPCPA amplifier is application of a multi-pass configuration [19

19. Y. Stepanenko and C. Radzewicz, “High-gain multipass noncollinear optical parametric chirped pulse amplifier,” Appl. Phys. Lett. 86(21), 211120 (2005). [CrossRef]

,20

20. Y. Stepanenko and C. Radzewicz, “Multipass non-collinear optical parametric amplifier for femtosecond pulses,” Opt. Express 14(2), 779–785 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-2-779. [CrossRef] [PubMed]

]. In this approach the amplified beam is passed several times through a single nonlinear crystal interacting, on each pass, with a different part of a longer pump pulse. This scheme works well with low energy pulses where the saturation applies to the last pass only. However, it cannot be used in the power amplifier stage for two reasons: (1) a large diameter of the amplified beam makes it difficult to align consecutive passes on a cone as required for a broadband operation [19

19. Y. Stepanenko and C. Radzewicz, “High-gain multipass noncollinear optical parametric chirped pulse amplifier,” Appl. Phys. Lett. 86(21), 211120 (2005). [CrossRef]

], and (2) one cannot assure proper saturation conditions for each pass because of different intensities of the amplified beam.

In this work we describe a new method which is suitable for the power amplifier stage and, in our setup, improves the time overlap by a factor of 3. Together with the previously described multi-pass preamplifier, it allows the development of a broadband, simple and efficient terawatt level OPCPA system which amplifies short pulses directly from a titanium sapphire oscillator using commercially available ns pump laser. One of the design goals was to make the system compact and simple. Because of that our design does not include components that are standard in classical broadband terawatt level titanium sapphire amplifier systems such as a pulse picker system, a pulse slicer setup, Faraday rotators, gain shaping filters or mirrors with custom reflectivity curves [21

21. A. Amani Eilanlou, Y. Nabekawa, K. L. Ishikawa, H. Takahashi, and K. Midorikawa, “Direct amplification of terawatt sub-10-fs pulses in a CPA system of Ti:sapphire laser,” Opt. Express 16(17), 13431–13438 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-13431. [CrossRef] [PubMed]

].

The main goal of the present investigation is to show experimentally the feasibility of a new time-shear method to increase the efficiency of the TW OPCPA pumped with a ns laser. The idea of time-shear was proposed and numerically investigated in [22

22. T. Harimoto and K. Yamakawa, “Numerical analysis of optical parametric chirped pulse amplification with time delay,” Opt. Express 11(8), 939–943 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-8-939. [CrossRef] [PubMed]

]. Briefly, in order to achieve high energy conversion efficiency, each pass of a relatively short seed pulse through the nonlinear crystal is delayed with respect to a long pump pulse as shown in Fig. 1
Fig. 1 Time-shearing technique scheme, green color – pump laser, red color – seed laser; 0-4 – illustration of the temporal profiles and time overlap of pump and seed pulses, 0 – before amplifier, 1-3 – in 1-3 crystal of the amplifier, 4 – pump pulse after amplifier.
. Because of the delay, the seed pulse can interact several times with the pump laser pulse, each time with its undepleted part. Assuming proper design of such a multi-crystal power stage one can achieve almost complete saturation at each of the crystals and thus significant power conversion even with the seed pulse shorter by a factor of few than the pump pulse as is the case of this study.

2. Experiment and results

The scheme of our multi-terawatt OPCPA system is presented in Fig. 2
Fig. 2 Schematic of the OPCPA setup. OSC – titanium sapphire oscillator, PS – liquid crystal spatial light modulator, STR – pulse stretcher, COMP – pulse compressor, HWP – half waveplate, P – polarizer, T – relay imaging telescope, VT – vacuum relay imaging telescope, BBO1-4 – BBO crystals 11mm, 10mm, 5mm, 3.8mm respectively, PreAmp – multipass preamplifier, Amp – booster amplifier with time shear.
. It consists of a femtosecond oscillator, a pulse shaper based on Liquid Crystal Spatial Light Modulator (LC-SLM), a pulse stretcher, a high gain multipass parametric pre-amplifier and an energy booster stage built according to the time-shearing scheme.

We used a home-built titanium sapphire oscillator delivering 80 MHz, 800 mW train of pulses at the central wavelength of 810 nm and 200 nm bandwidth. The stretcher, designed to achieve a large bandwidth and a moderate stretching factor, was built in Martinez configuration [23

23. O. E. Martinez, “3000 Times grating compressor with positive group velocity dispersion: Application to fiber compensation in 1.3–1.6 μm region,” IEEE J. Quantum Electron. QE-23(1), 59–64 (1987). [CrossRef]

] with F/3 spherical mirror (d = 203.2 mm, f = 609.6 mm) and 1500 l/mm 140 mm-wide diffraction grating. It is well known that stretchers of Martinez design introduce significant spherical aberrations resulting in a large fourth-order spectral phase which cannot be compensated with a standard diffraction grating pulse compressor. The pulse shaper setup, based on LC-SLM (Jena Optic SLM-640d, 640 pixels), was used to pre-compensate this effect.

A ray tracing code was written and used to calculate the residual phase introduced by the stretcher/compressor pair. Figure 3
Fig. 3 Spectrum of the seed pulse (black solid line), measured relative spectral phase introduced by the stretcher/compressor pair (blue dashed line), theoretical spectral phase introduced by a stretcher-compressor pair (green solid line), spectral phase after applying compensation phase with the LCD shaper (red solid line)
shows the calculated residual spectral phase introduced by the stretcher/compressor pair (green curve). With a 100 nm spectral window and pulses stretched to 1 ns (time difference between spectral components at the edges of the spectral window of the stretcher) the residual phase after the compressor was over 100 radian at the wings, and was increasing rapidly with the width of the spectral window. This effect sets the upper limit on the spectral width that can be compensated using pixelated devices such as a LCD pulse shaper - the Niquist limit states that the phase difference on adjacent pixels must not be higher than π. The results of our calculations show that the shortest pulse width, which can be obtained without compensation of those aberrations is approximately 70 fs which is about 3.5 times longer than that for the Fourier transform limited pulse. In order to find a precise compensation phase which should be applied to the SLM we used a spectral interference technique. Briefly, we split the femtosecond beam just in front of the LCD pulse shaper, propagated one of the beams through the whole amplifier and combined the beams interferometrically at the input slit of a spectrometer (Ocean Optics USB2000). The spectral phase difference between the pulses in the two beams was extracted from the spectral interference signal using the Fourier method [24

24. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995), http://www.opticsinfobase.org/abstract.cfm?URI=josab-12-12-2467. [CrossRef]

]. The residual phase before and after applying the compensation phase on the SLM is shown in the Fig. 3 as blue and red lines respectively.

We have developed a computer code that models the operation of the OPCPA. The code solves nonlinear, coupled wave equations, to numerically simulate parametric amplification process. It takes into account beams’ spatial distribution, seed and pump temporal pulse profiles and allows for the pump depletion. We assume cylindrical symmetry of the amplification process i.e. neglect pump beam walk-off, which is justified given the beam sizes and crystal lengths. The code was used to optimize the amplifier parameters i.e. crystal lengths, beams diameters and pump beam energy division between preamplifier and power amplifier.

The seed beam exiting the stretcher was sent to the high gain multipass preamplifier similar to the one described in [19

19. Y. Stepanenko and C. Radzewicz, “High-gain multipass noncollinear optical parametric chirped pulse amplifier,” Appl. Phys. Lett. 86(21), 211120 (2005). [CrossRef]

,20

20. Y. Stepanenko and C. Radzewicz, “Multipass non-collinear optical parametric amplifier for femtosecond pulses,” Opt. Express 14(2), 779–785 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-2-779. [CrossRef] [PubMed]

]. The beam was first down collimated to match the size of the pump beam (1 mm, 1/e2 diameter) generated by a single longitudinal mode, 8 ns FWHM pulse duration Nd:YAG laser (Continuum Powerlite 8010) delivering 530 mJ at 532 nm. The pump laser beam spatial profile was characterized as a fourth order super-Gaussian mode. The green pump laser pulse was split by means of a set of high damage threshold thin film polarizers and halfwave plates into two beams. This allowed for smooth tuning of the pump pulse energy from 0 to 100 mJ and from 0 to 430 mJ in the weaker and stronger arms respectively. The weaker beam was used to pump the preamplifier stage and the stronger one was directed to the power booster stage. In order to avoid hotspots and beam distortions both beams were relay imaged onto nonlinear crystals.

Since parametric amplification is an instantaneous process there is no energy storage in the amplifier medium. This allows one to avoid a pulse picker in the seed beam path - the pump pulse itself acts as a gate to select pulses at the 10 Hz repetition rate from the 80 MHz pulse train. The calculations show that pre- and post-pulses have a negligible time overlap with the pump pulse wings. We have determined experimentally that the energy of those pulses at the output of the whole system is only three times their input energy - an insignificant value when compared with the overall amplifier gain (3.8 108 in our case). Still, proper timing between the pump and the seed pulses is required; in our amplifier, an electronic system ensured synchronization with a time jitter of approximately ± 0.5 ns.

The preamplifier stage used three passes of the seed beam through 6x6x11 mm3, 22.3 degrees cut angle BBO crystal with protective coatings. Although the phase matching condition requires the angle of about 23.2 degrees, a smaller value was chosen in order to avoid parametric fluorescence amplification resonantly enhanced by multiple reflections from the crystal faces. The size of the pump beam on the nonlinear crystal surface was chosen to keep the pump beam intensity below 600 MW/cm2, assuring safe operation far enough from the damage threshold. Non-collinear geometry with the angle of 2.3 degree between the pump and the seed beam ensured wide bandwidth parametric amplification. Special care was taken to orient the optic axis of the nonlinear crystal to partially compensate the pump beam (extraordinary) walk-off effect. We rotated the polarization of the pump beam with a removable half-wave plate to observe the displacement direction of the extraordinary beam and, thus, unambiguously determine the correct crystal orientation.

At the input to the preamplifier the seed beam power was 14 mW which corresponds to 180 pJ per pulse. Each pass through the crystal was optimized separately for the highest amplification, using a signal from a fast photodiode observed on an oscilloscope as a feedback. The single round trip time in the preamplifier was 1.1 ns in order to assure an effective overlap of the seed pulse with the pump pulse. After the preamplifier the energy of the seed was 1.5 mJ with 10% RMS fluctuations. This corresponds to 1.6% efficiency and the average amplification of 200 per pass. Figure 4
Fig. 4 Spectra of the unamplified pulse (black curve), pulse after the preamplifier (red curve, light grey shaded) and after power booster stage (blue curve, dark grey shaded).
shows the spectrum of the pulse before amplification (black curve) and after the preamplifier stage (red curve). Relatively higher amplification of the wings indicates slight saturation in the amplification process during the last pass through the BBO crystal.

The beam from the preamplifier was upcollimated to match the pump beam diameter of 4.5 mm (1/e2 diameter) in the power amplifier stage consisting of three BBO crystals set in time-shear configuration. The lengths of the crystals were optimized using our numerical code to achieve the highest energy extraction efficiency after each crystal, while keeping the pump intensity well below the crystal damage threshold (in the power amplifier stage the pump intensity was set at 460MW/cm2). The optimal lengths of crystals were calculated to be 10 mm, 5 mm and 3.8 mm. The optic axis angle of each crystal was set initially at 24 degrees with respect to the pump beam and the angle between the pump and seed beams was set at 2.3 degree. Consecutive passes of the amplified pulse were delayed by 1.1 ns to assure an overlap with the undepleted part of the pump beam in each BBO crystal (Fig. 1). The same procedure for pump-seed angle optimization as for the preamplifier stage was used in the energy booster: the pulse energy was optimized behind each crystal independently to reach the maximum extraction of the energy available in the pump. Both the gain and the bandwidth of this stage critically depend on the proper alignment of the phase matching angle and the noncollinear angle. For the proper energy extraction efficiency and stability the pump and the seed beam spatial overlap, their relative intensities and lengths of nonlinear crystal in each pass must be carefully selected. By choosing optimal relative intensities and crystal lengths one can achieve deep saturation with energy flow between the seed and the pump pulses slightly reversed. This regime reduces the sensitivity of the amplifier to the pump laser pulse time jitter and energy fluctuations and leads to self-stabilization of the whole system [20

20. Y. Stepanenko and C. Radzewicz, “Multipass non-collinear optical parametric amplifier for femtosecond pulses,” Opt. Express 14(2), 779–785 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-2-779. [CrossRef] [PubMed]

,25

25. S. K. Zhang, M. Fujita, M. Yamanaka, M. Nakatsuka, Y. Izawa, and C. Yamanaka, “Study of the stability of optical parametric amplification,” Opt. Commun. 184(5-6), 451–455 (2000). [CrossRef]

]. We measured the pulse energy after consecutive crystals to be: 24 mJ, 46 mJ and 66 mJ resulting in an optical efficiency of the power amplifier stage of 15%. The advantage of the time shearing technique should be emphasized: without it the system would deliver just 24 mJ (the pulse energy after the first crystal) and the extraction efficiency would be only 5.5% which is almost 3 times smaller than our result.

The spectrum of the pulse after the final amplification stage is shown in Fig. 4 (blue curve). Its shape is almost a rectangle, which confirms significant saturation of the power amplifier stage. The precise optimization of the spatial and time overlap resulted in 2% RMS fluctuations which are determined entirely by the pump laser energy fluctuations (1.5% RMS) and its time jitter ( ± 0.5 ns). The measured beam profile of the amplified pulse after recompression is shown in Fig. 5
Fig. 5 Beam spatial profile together with vertical and horizontal sum-profiles taken with 12-bit CCD camera. The color scale shown in the picture is linear.
. The profile is smooth and its shape is close to fourth-order super-Gaussian characteristic of the pump beam. Indeed, for the deep saturation one should expect the amplified beam to resemble the shape of the pump beam. A careful inspection of Fig. 5 shows a slight dip in the center of the beam which might be attributed to slight signal back-conversion which is the strongest in the center of the beam.

The amplified beam was recompressed in a standard diffraction grating compressor. The compressor efficiency was 75% which resulted in 49 mJ energy of the recompressed pulse. The pulse time duration (see Fig. 6
Fig. 6 Time profile of the pulse measured with a single-shot FROG (black curve) together with the calculated Fourier transform limited pulse (red curve) of FWHM = 19.8 fs.
) measured with a single shot FROG was τ = 23 ± 1 fs FWHM, yielding the calculated peak power of slightly more than 2 TW. In order to evaluate the compressibility of the amplified pulse, we have calculated the temporal intensity of the Fourier transform limited pulse corresponding to the measured output pulse spectrum. Our calculations show that the Fourier transform limited pulse duration is 19.8 fs (see Fig. 6) which is just 15% shorter than that of the actual compressed pulse. The good compressibility is not very surprising if one bears in mind the pulse shaping system incorporated in our amplifier.

We have also measured the amplified parametric fluorescence energy after the compressor and found it to be approximately 200 μJ which is just 0.4% of the energy of the recompressed pulse. The level of the parametric fluorescence in our system is much lower then that reported in [7

7. F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14(26), 12822–12827 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-26-12822. [CrossRef] [PubMed]

] (18%) for picosecond pulse pumped OPCPA and 11% for titanium sapphire based broadband terawatt system reported in [21

21. A. Amani Eilanlou, Y. Nabekawa, K. L. Ishikawa, H. Takahashi, and K. Midorikawa, “Direct amplification of terawatt sub-10-fs pulses in a CPA system of Ti:sapphire laser,” Opt. Express 16(17), 13431–13438 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-13431. [CrossRef] [PubMed]

]. Assuming that the amplified parametric fluorescence time duration is comparable to that of the pump pulse one can calculate the nanosecond scale contrast of ~10−8. As discussed before the pre-pulse contrast was 8·10−9, i.e. slightly less than the contrast due to the parametric fluorescence.

3. Discussion

Let us consider the theoretical limitations on the energy extraction efficiency of the power amplifier stage in our OPCPA. The 3 ns long time window in which the amplified pulse interacts with the pump pulse contains 34% of the pump pulse energy. Assuming a perfect parametric amplification with the efficiency limited by the Stokes shift only – every pump photon converted into a photon in the amplified beam - (66% for λpump = 532 nm and λseed = 810 nm) one can expect the amplified pulse energy to be 96 mJ (before the compressor). Thus, the energy measured in our power amplifier (66 mJ) corresponds to approximately 70% of the ideal conversion efficiency and 45% absolute power extraction efficiency. The missing 30% can be attributed to reflections from crystal surfaces and the pump pulse spatial intensity distribution - the pump beam is super-Gaussian and the saturation is achieved at different lengths of the crystal for different positions in the beam, which means that some parts of the beam are not saturated while other are over-saturated. If the pump pulse were of an ideal square spatial profile then a perfectly even saturation across the beam could be achieved together with very good conversion efficiency. Our modeling shows that the spatial distribution of the pump beam can account for as much as 20% loss of the conversion efficiency.

The implementation of time-shearing technique should be especially attractive with Nd:YAG lasers delivering pulses with square temporal profile. With such lasers becoming commercially available one can hope for the energy extraction efficiency in the power amplifier stage approaching the theoretical limit (66% in that case) simply because there will be almost no unconverted tails left in the pump pulse (see Fig. 1). The time-shear approach combined with square time profile pump laser will yield a very compact and inexpensive design for multi-TW OPCPA. Still, our results show that the spatial profile of the pump laser might limit the efficiency by as much as 20%. It is worth noting that the technique described in this paper can be very easily implemented in many of the existing OPCPA systems pumped with ns pulses, allowing for significant efficiency improvement with just a minor rearrangement of the power amplifier stage.

The time-shear technique described in this paper, while suitable for ns pump lasers (operating typically 10 Hz repetition rate), fails completely with kHz systems characterized by significantly longer pulses (typically 100 ns or more) simply because, in this case, the number of crystals required in the power amplifier stage is not practical.

4. Conclusions

We have demonstrated a new compact and efficient OPCPA design capable of generating 2 TW peak power. The 10 Hz repetition rate system utilizes a novel power amplifier stage based on the time-shear technique and uses a commercially available nanosecond Nd:YAG laser as a pump source. With a moderate seed pulse stretching (1 ns) and relatively long pump pulses (8 ns) we have achieved 15% conversion efficiency in the power amplifier stage, which is almost a factor of 3 higher than the efficiency of a fully saturated single crystal power amplifier. At the same time the efficiency calculated for the 3 ns time window in which the amplified pulse overlaps the pump pulse is approx. 45%, i.e. approx. 70% of the maximum for the given wavelengths of the pump and seed. The output pulse energy is stable to within 2% RMS and almost insensitive to the time jitter of the pump pulse. The footprint of the whole system including the oscillator, the pump laser and the OPCPA itself is 1.2x2.5 m2. The efficiency and the size of the system could be improved by using the Öffner geometry stretcher [26

26. G. Cheriaux, P. Rousseau, F. Salin, J. P. Chambaret, B. Walker, and L. F. Dimauro, “Aberration-free stretcher design for ultrashort-pulse amplification,” Opt. Lett. 21(6), 414–416 (1996), http://www.opticsinfobase.org/abstract.cfm?URI=ol-21-6-414. [CrossRef] [PubMed]

], which should allow one to eliminate the LCD-based pulse shaper.

Further power upgrades are feasible by adding subsequent energy amplifier stages incorporating large aperture LBO crystals and Nd:YAG lasers with higher pulse energy. Our calculations show that by using an additional energy amplification stage consisting of 3 LBO crystals and a commercial 5 ns 2 J Nd:YAG pump laser with a Gaussian time profile, it should be possible to achieve 420 mJ in the compressed femtosecond pulse.

An entirely new level of the energy conversion efficiency can be expected with application of new, commercially available square temporal profile Nd:YAG pump lasers. By combining these lasers with the time-shear technique one could expect to reach the efficiency close to the theoretical limit value of 66% for this type of an amplifier, without resorting to large aperture optics in the stretcher and compressor.

Acknowledgments

This work was supported by MNiSW grant No N202 019 32/0698.

References and links

1.

A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88(4-6), 437–440 (1992). [CrossRef]

2.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, I. V. Yakovlev, S. G. Garanin, S. A. Sukharev, N. N. Rukavishnikov, A. V. Charukhchev, R. R. Gerke, and V. E. Yashin, “200 TW 45 fs laser based on optical parametric chirped pulse amplification,” Opt. Express 14(1), 446–454 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-446. [CrossRef] [PubMed]

3.

C. N. Danson, P. A. Brummitt, R. J. Clarke, J. L. Collier, B. Fell, A. J. Frackiewicz, S. Hancock, S. Hawkes, C. Hernandez-Gomez, P. Holligan, M. H. R. Hutchinson, A. Kidd, W. J. Lester, I. O. Musgrave, D. Neely, D. R. Neville, P. A. Norreys, D. A. Pepler, C. J. Reason, W. Shaikh, T. B. Winstone, R. W. W. Wyatt, and B. E. Wyborn, “Vulcan Petawatt—an ultra-high-intensity interaction facility,” Nucl. Fusion 44(12), S239–S246 (2004). [CrossRef]

4.

O. V. Chekhlov, J. L. Collier, I. N. Ross, P. K. Bates, M. Notley, C. Hernandez-Gomez, W. Shaikh, C. N. Danson, D. Neely, P. Matousek, S. Hancock, and L. Cardoso, “35 J broadband femtosecond optical parametric chirped pulse amplification system,” Opt. Lett. 31(24), 3665–3667 (2006), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-24-3665. [CrossRef] [PubMed]

5.

E. Hugonnot, G. Deschaseaux, O. Hartmann, and H. Coïc, “Design of PETAL multipetawatt high-energy laser front end based on optical parametric chirped pulse amplification,” Appl. Opt. 46(33), 8181–8187 (2007), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-33-8181. [CrossRef] [PubMed]

6.

S. Witte, R. Th. Zinkstok, A. L. Wolf, W. Hogervorst, W. Ubachs, and K. S. E. Eikema, “A source of 2 terawatt, 2.7 cycle laser pulses based on noncollinear optical parametric chirped pulse amplification,” Opt. Express 14(18), 8168–8177 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-18-8168. [CrossRef] [PubMed]

7.

F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14(26), 12822–12827 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-26-12822. [CrossRef] [PubMed]

8.

X. Yang, Z. Xu, Z. Zhang, Y. Leng, J. Peng, J. Wang, S. Jin, W. Zhang, and R. Li, “Dependence of spectrum on pump-signal angle in BBO-I noncollinear optical-parametric chirped-pulse amplification,” Appl. Phys. B 73, 219–222 (2001).

9.

I. Jovanovic, C. A. Ebbers, and C. P. J. Barty, “Hybrid chirped-pulse amplification,” Opt. Lett. 27(18), 1622–1624 (2002), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-27-18-1622. [CrossRef]

10.

I. Jovanovic, B. J. Comaskey, C. A. Ebbers, R. A. Bonner, D. M. Pennington, and E. C. Morse, “Optical parametric chirped-pulse amplifier as an alternative to Ti:sapphire regenerative amplifiers,” Appl. Opt. 41(15), 2923–2929 (2002), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-15-2923. [CrossRef] [PubMed]

11.

H. Yoshida, E. Ishii, R. Kodama, H. Fujita, Y. Kitagawa, Y. Izawa, and T. Yamanaka, “High-power and high-contrast optical parametric chirped pulse amplification in β-BaB2O4 crystal,” Opt. Lett. 28(4), 257–259 (2003), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-4-257. [CrossRef] [PubMed]

12.

H. Okada, H. Kiriyama, M. Mori, Y. Nakai, T. Shimomura, M. Tanoue, S. Kondo, S. Kanazawa, H. Daido, T. Kimura, and T. Tajima, “Demonstration of highly efficient broadband amplification in an optical parametric chirped-pulse amplifier system,” Opt. Rev. 16(1), 1–3 (2009). [CrossRef]

13.

H. Kiriyama, M. Mori, Y. Nakai, Y. Yamamoto, M. Tanoue, A. Akutsu, T. Shimomura, S. Kondo, S. Kanazawa, H. Daido, T. Kimura, and N. Miyanaga, “High-energy, high-contrast, multiterawatt laser pulses by optical parametric chirped-pulse amplification,” Opt. Lett. 32(16), 2315–2317 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-16-2315. [CrossRef] [PubMed]

14.

H. Kiriyama, N. Inoue, Y. Akahane, and K. Yamakawa, “Prepulse-free, multi-terawatt, sub-30-fs laser system,” Opt. Express 14(1), 438–445 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-438. [CrossRef] [PubMed]

15.

H. Kiriyama, M. Mori, Y. Nakai, T. Shimomura, M. Tanoue, A. Akutsu, H. Okada, T. Motomura, S. Kondo, S. Kanazawa, A. Sagisaka, J.-L. Ma, I. Daito, H. Kotaki, H. Daido, S. V. Bulanov, T. Kimura, and T. Tajima, “Generation of high-contrast and high-intensity laser pulses using an OPCPA preamplifier in a double CPA, Ti:sapphire laser system,” Opt. Commun. 282(4), 625–628 (2009). [CrossRef]

16.

X. Zhou, H. Lee, T. Kanai, S. Adachi, and S. Watanabe, “An 11-fs, 5-kHz optical parametric/Ti:sapphire hybrid chirped pulse amplification system,” Appl. Phys. B 89(4), 559–563 (2007). [CrossRef]

17.

J. Zhang, M. Suzuki, M. Baba, Z. Wei, Z. Wang, P. Wang, J. Zhang, J. Zheng, and H. Kuroda, “Development of a compact efficient 10 Hz 20 TW Ti:sapphire laser system with a 1 kHz regenerative amplifier,” Appl. Opt. 46(13), 2498–2502 (2007). [CrossRef] [PubMed]

18.

A. Dubietis, R. Butkus, and A. P. Piskarskas, “Trends in chirped pulse optical parametric amplification,” IEEE J. Sel. Top. Quantum Electron. 12(2), 163–172 (2006), http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1632161&isnumber=34227. [CrossRef]

19.

Y. Stepanenko and C. Radzewicz, “High-gain multipass noncollinear optical parametric chirped pulse amplifier,” Appl. Phys. Lett. 86(21), 211120 (2005). [CrossRef]

20.

Y. Stepanenko and C. Radzewicz, “Multipass non-collinear optical parametric amplifier for femtosecond pulses,” Opt. Express 14(2), 779–785 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-2-779. [CrossRef] [PubMed]

21.

A. Amani Eilanlou, Y. Nabekawa, K. L. Ishikawa, H. Takahashi, and K. Midorikawa, “Direct amplification of terawatt sub-10-fs pulses in a CPA system of Ti:sapphire laser,” Opt. Express 16(17), 13431–13438 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-13431. [CrossRef] [PubMed]

22.

T. Harimoto and K. Yamakawa, “Numerical analysis of optical parametric chirped pulse amplification with time delay,” Opt. Express 11(8), 939–943 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-8-939. [CrossRef] [PubMed]

23.

O. E. Martinez, “3000 Times grating compressor with positive group velocity dispersion: Application to fiber compensation in 1.3–1.6 μm region,” IEEE J. Quantum Electron. QE-23(1), 59–64 (1987). [CrossRef]

24.

L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995), http://www.opticsinfobase.org/abstract.cfm?URI=josab-12-12-2467. [CrossRef]

25.

S. K. Zhang, M. Fujita, M. Yamanaka, M. Nakatsuka, Y. Izawa, and C. Yamanaka, “Study of the stability of optical parametric amplification,” Opt. Commun. 184(5-6), 451–455 (2000). [CrossRef]

26.

G. Cheriaux, P. Rousseau, F. Salin, J. P. Chambaret, B. Walker, and L. F. Dimauro, “Aberration-free stretcher design for ultrashort-pulse amplification,” Opt. Lett. 21(6), 414–416 (1996), http://www.opticsinfobase.org/abstract.cfm?URI=ol-21-6-414. [CrossRef] [PubMed]

OCIS Codes
(140.4480) Lasers and laser optics : Optical amplifiers
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(320.7090) Ultrafast optics : Ultrafast lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: April 28, 2009
Revised Manuscript: June 10, 2009
Manuscript Accepted: July 4, 2009
Published: August 14, 2009

Citation
Paweł Wnuk, Yuriy Stepanenko, and Czesław Radzewicz, "Multi-terawatt chirped pulse optical parametric amplifier with a time-shear power amplification stage," Opt. Express 17, 15264-15273 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-15264


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References

  1. A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88(4-6), 437–440 (1992). [CrossRef]
  2. V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, I. V. Yakovlev, S. G. Garanin, S. A. Sukharev, N. N. Rukavishnikov, A. V. Charukhchev, R. R. Gerke, and V. E. Yashin, “200 TW 45 fs laser based on optical parametric chirped pulse amplification,” Opt. Express 14(1), 446–454 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-446 . [CrossRef] [PubMed]
  3. C. N. Danson, P. A. Brummitt, R. J. Clarke, J. L. Collier, B. Fell, A. J. Frackiewicz, S. Hancock, S. Hawkes, C. Hernandez-Gomez, P. Holligan, M. H. R. Hutchinson, A. Kidd, W. J. Lester, I. O. Musgrave, D. Neely, D. R. Neville, P. A. Norreys, D. A. Pepler, C. J. Reason, W. Shaikh, T. B. Winstone, R. W. W. Wyatt, and B. E. Wyborn, “Vulcan Petawatt—an ultra-high-intensity interaction facility,” Nucl. Fusion 44(12), S239–S246 (2004). [CrossRef]
  4. O. V. Chekhlov, J. L. Collier, I. N. Ross, P. K. Bates, M. Notley, C. Hernandez-Gomez, W. Shaikh, C. N. Danson, D. Neely, P. Matousek, S. Hancock, and L. Cardoso, “35 J broadband femtosecond optical parametric chirped pulse amplification system,” Opt. Lett. 31(24), 3665–3667 (2006), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-24-3665 . [CrossRef] [PubMed]
  5. E. Hugonnot, G. Deschaseaux, O. Hartmann, and H. Coïc, “Design of PETAL multipetawatt high-energy laser front end based on optical parametric chirped pulse amplification,” Appl. Opt. 46(33), 8181–8187 (2007), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-33-8181 . [CrossRef] [PubMed]
  6. S. Witte, R. Th. Zinkstok, A. L. Wolf, W. Hogervorst, W. Ubachs, and K. S. E. Eikema, “A source of 2 terawatt, 2.7 cycle laser pulses based on noncollinear optical parametric chirped pulse amplification,” Opt. Express 14(18), 8168–8177 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-18-8168 . [CrossRef] [PubMed]
  7. F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14(26), 12822–12827 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-26-12822 . [CrossRef] [PubMed]
  8. X. Yang, Z. Xu, Z. Zhang, Y. Leng, J. Peng, J. Wang, S. Jin, W. Zhang, and R. Li, “Dependence of spectrum on pump-signal angle in BBO-I noncollinear optical-parametric chirped-pulse amplification,” Appl. Phys. B 73, 219–222 (2001).
  9. I. Jovanovic, C. A. Ebbers, and C. P. J. Barty, “Hybrid chirped-pulse amplification,” Opt. Lett. 27(18), 1622–1624 (2002), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-27-18-1622 . [CrossRef]
  10. I. Jovanovic, B. J. Comaskey, C. A. Ebbers, R. A. Bonner, D. M. Pennington, and E. C. Morse, “Optical parametric chirped-pulse amplifier as an alternative to Ti:sapphire regenerative amplifiers,” Appl. Opt. 41(15), 2923–2929 (2002), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-15-2923 . [CrossRef] [PubMed]
  11. H. Yoshida, E. Ishii, R. Kodama, H. Fujita, Y. Kitagawa, Y. Izawa, and T. Yamanaka, “High-power and high-contrast optical parametric chirped pulse amplification in β-BaB2O4 crystal,” Opt. Lett. 28(4), 257–259 (2003), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-4-257 . [CrossRef] [PubMed]
  12. H. Okada, H. Kiriyama, M. Mori, Y. Nakai, T. Shimomura, M. Tanoue, S. Kondo, S. Kanazawa, H. Daido, T. Kimura, and T. Tajima, “Demonstration of highly efficient broadband amplification in an optical parametric chirped-pulse amplifier system,” Opt. Rev. 16(1), 1–3 (2009). [CrossRef]
  13. H. Kiriyama, M. Mori, Y. Nakai, Y. Yamamoto, M. Tanoue, A. Akutsu, T. Shimomura, S. Kondo, S. Kanazawa, H. Daido, T. Kimura, and N. Miyanaga, “High-energy, high-contrast, multiterawatt laser pulses by optical parametric chirped-pulse amplification,” Opt. Lett. 32(16), 2315–2317 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-16-2315 . [CrossRef] [PubMed]
  14. H. Kiriyama, N. Inoue, Y. Akahane, and K. Yamakawa, “Prepulse-free, multi-terawatt, sub-30-fs laser system,” Opt. Express 14(1), 438–445 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-438 . [CrossRef] [PubMed]
  15. H. Kiriyama, M. Mori, Y. Nakai, T. Shimomura, M. Tanoue, A. Akutsu, H. Okada, T. Motomura, S. Kondo, S. Kanazawa, A. Sagisaka, J.-L. Ma, I. Daito, H. Kotaki, H. Daido, S. V. Bulanov, T. Kimura, and T. Tajima, “Generation of high-contrast and high-intensity laser pulses using an OPCPA preamplifier in a double CPA, Ti:sapphire laser system,” Opt. Commun. 282(4), 625–628 (2009). [CrossRef]
  16. X. Zhou, H. Lee, T. Kanai, S. Adachi, and S. Watanabe, “An 11-fs, 5-kHz optical parametric/Ti:sapphire hybrid chirped pulse amplification system,” Appl. Phys. B 89(4), 559–563 (2007). [CrossRef]
  17. J. Zhang, M. Suzuki, M. Baba, Z. Wei, Z. Wang, P. Wang, J. Zhang, J. Zheng, and H. Kuroda, “Development of a compact efficient 10 Hz 20 TW Ti:sapphire laser system with a 1 kHz regenerative amplifier,” Appl. Opt. 46(13), 2498–2502 (2007). [CrossRef] [PubMed]
  18. A. Dubietis, R. Butkus, and A. P. Piskarskas, “Trends in chirped pulse optical parametric amplification,” IEEE J. Sel. Top. Quantum Electron. 12(2), 163–172 (2006), http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1632161&isnumber=34227 . [CrossRef]
  19. Y. Stepanenko and C. Radzewicz, “High-gain multipass noncollinear optical parametric chirped pulse amplifier,” Appl. Phys. Lett. 86(21), 211120 (2005). [CrossRef]
  20. Y. Stepanenko and C. Radzewicz, “Multipass non-collinear optical parametric amplifier for femtosecond pulses,” Opt. Express 14(2), 779–785 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-2-779 . [CrossRef] [PubMed]
  21. A. Amani Eilanlou, Y. Nabekawa, K. L. Ishikawa, H. Takahashi, and K. Midorikawa, “Direct amplification of terawatt sub-10-fs pulses in a CPA system of Ti:sapphire laser,” Opt. Express 16(17), 13431–13438 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-13431 . [CrossRef] [PubMed]
  22. T. Harimoto and K. Yamakawa, “Numerical analysis of optical parametric chirped pulse amplification with time delay,” Opt. Express 11(8), 939–943 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-8-939 . [CrossRef] [PubMed]
  23. O. E. Martinez, “3000 Times grating compressor with positive group velocity dispersion: Application to fiber compensation in 1.3–1.6 μm region,” IEEE J. Quantum Electron. QE-23(1), 59–64 (1987). [CrossRef]
  24. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12(12), 2467–2474 (1995), http://www.opticsinfobase.org/abstract.cfm?URI=josab-12-12-2467 . [CrossRef]
  25. S. K. Zhang, M. Fujita, M. Yamanaka, M. Nakatsuka, Y. Izawa, and C. Yamanaka, “Study of the stability of optical parametric amplification,” Opt. Commun. 184(5-6), 451–455 (2000). [CrossRef]
  26. G. Cheriaux, P. Rousseau, F. Salin, J. P. Chambaret, B. Walker, and L. F. Dimauro, “Aberration-free stretcher design for ultrashort-pulse amplification,” Opt. Lett. 21(6), 414–416 (1996), http://www.opticsinfobase.org/abstract.cfm?URI=ol-21-6-414 . [CrossRef] [PubMed]

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