Abstract

All-optical synchronization of 1064 nm pulses with femtosecond laser pulses at 794 nm is realized on the basis of continuous-wave laser seeded non-collinear optical parametric amplification, by using a CW laser at 632.8 nm as the seeded signal and intense frequency-doubled Ti:sapphire femtosecond laser at 396 nm as the pumping source. The generated background-free idler pulses at 1064 nm can be used as an accurately synchronized pump seed for the optical parametric amplification of ultra-broadband chirped Ti:sapphire laser pulses.

© 2006 Optical Society of America

1. Introduction

Optical parametric chirped-pulse amplification (OPCPA) [1–5] has been demonstrated recently as an alternative way to chirped-pulse amplification (CPA) [6] to generate high-intensity optical pulses of ultrabroad bandwidths. The advantages of OPCPA over CPA include ultrabroad gain bandwidth, very high pulse contrast, very good beam quality, and so on. Ultrashort laser pulses with about 10 fs pulse duration [7] or more than 16.7 TW laser power [8] have been achieved by OPCPA. The broadband signal seed can be obtained from a Ti:sapphire laser at the central wavelength of 800 nm to take the full advantage of its ultra-broad gain bandwidth [9], while the pumping beam is typically frequency-doubled Nd-doped lasers so that their high scalable single-pulse energies can be used to boost the signal pulses. Based on this consideration, high-intensity OPCPA of ultrabroad bandwidth tends to choose signal seeds from ultrabroadband Ti:sapphire fs lasers and pump pulses from high-intensity frequency-doubled Nd-doped lasers. The pulse duration of the pump lasers usually ranges from sub-nanosecond to several nanoseconds, while the chirped signal pulses are in the sub-nanosecond range in order to achieve efficient pulse energy amplification of ultrabroadband signals [1, 3, 10]. It is critically important for efficient and stable operation of such an OPCPA system to accurately synchronize pump and signal pulses. A conventional electronic synchronization method has been employed to synchronize the signal sources with the pumping pulses [10], which provides a typical timing jitter about 100 ps between the pump and signal lasers. It is still an experimental challenge to get a more accurate synchronization between independent lasers by using electronic units to control pulse delays. In order to control the timing jitter between independent lasers, e.g., Nd-doped and Ti:sapphire lasers, a hybrid method has been invented which combines phase-locked loop electronics and careful control of laser cavity length so that mode-locking of independent lasers can be synchronized [11, 12]. The timing jitters between the output pulses from two independent lasers have been recently locked within about 2 ps [11]. For picoseconds pump pulses, the timing jitter between the pump and signal can be controlled as short as 100 fs [12]. However, it is still difficult to maintain the cavity lock of independent lasers with a satisfactory long-term stability. On the other hand, various all-optical synchronization schemes have been demonstrated as simple and robust methods to reduce timing jitter of the pump pulses used in OPCPAs. The pump and seed pulses can be simply provided by the same seed, and exact synchronization can be maintained during the pump pulses are boosted to high energies. About 10 ps timing jitter has already been realized by using a Ti:sapphire oscillator operated at the central wavelength of 1064 nm as the signal and the pump sources [8, 13], which has enabled a successful operation of 16.7 TW OPCPA with the highest output power to date [8]. The narrow gain bandwidth of Ti:sapphire oscillator at 1064 nm increases the signal pulse duration up to 120 fs. It is desirable to obtain a broadband signal seed from a Ti:sapphire laser at the central wavelength of 800 nm that is all-optically synchronized with intense Nd-doped lasers. A straightforward way for this purpose is to generate seed pulses at 1064 nm with nonlinear frequency mixing, which guarantees automatic synchronization of pulses at 1064 and 800 nm. The generated seed pulses at 1064 nm can be further amplified and frequency-doubled as synchronized pump sources for OPCPA near 800 nm. All-optical synchronization of pump and signal pulses has been realized with CW laser seeded non-collinear optical parametric amplification (NOPA) pumped by 400 nm intense laser pulses from a frequency-doubled Ti:sapphire regenerative amplifier [14], where a CW Nd:GdVO4 laser is used as a signal seed in the first-stage NOPA and a second-stage NOPA is used to get pulses at 1064 nm free of CW background. C.Y.Teisset and coworkers have presented an interesting all-optical pump-seed synchronization for few-cycle OPCPA by transferring a fraction of a broadband seed pulse at 800 nm to 1064 nm by using large optical nonlinearity in photonic crystal fiber [15].

In this paper, we demonstrates that all-optical synchronization of 1064 nm pulses with the Ti:sapphire fs pulses can be realized with a quite simple and robust scheme of CW-seeded NOPA, with the CW signal seed from a He-Ne laser at 632.8 nm, and pump from frequency-doubled Ti:sapphire fs pulses at 397 nm. Compared with the design in Ref. [14], the CW background-free 1064 nm pulses can be generated in the first-stage CW-seeded NOPA rather than a CW-seeded NOPA plus a second-stage NOPA. The CW laser beam provides seeding photons within the interaction duration for optical parametric amplification so that the beam quality of the amplified signal can be controlled efficiently. The pulse contrast and spatial distribution of the 1064 nm pulses can be further improved in a second-stage NOPA, and spectral characteristics can be controlled therein. After the second-stage NOPA, the generated idler pulses have enough pulse energy that can be further amplified by multi-pass amplifiers or regenerative amplifiers. Other advantages of NOPA seeded with a He-Ne CW laser include its excellent output beam quality, high stability, and cost-effectiveness.

This paper is organized as follows. After this brief introduction, section 2 describes our experimental setup of CW-seeded NOPA. Section 3 presents our experimental measurements of temporal, spatial and spectral features of the generated idler pulses. In section 4, we mainly discuss the parametric gain of the CW-seeded NOPA. Experimental results on further amplification of the idler pulses in the second-stage NOPA are also given. A summary of our results is given in section 5.

2. Experimental setup

Our experimental setup is schematically shown in Fig. 1. A 1-kHz pulses are generated from a Ti:sapphire regenerative amplifier (Spitfire, Spectra-Physics) with a pulse duration of 45 fs and pulse energy of 0.6 mJ. The central wavelength of the output pulses is tuned around 794 nm with the bandwidth of 26 nm. After a half-wave plate, the transverse diameter of the beam is reduced to 3 mm by an afocal optical system consisting of a concave mirror M1 (HR@800 nm) and a fused-quartz lens L1. Through a 29.2°-cut 0.2-mm-thick type I phase-matched beta-barium borate (β-BBO) crystal (C1), about 35% energy of the fundamental pulses is transferred into their second harmonic pulses, corresponding to 210 mW average power. The SH beam is centered at 396.8 nm with about 6 nm bandwidth [see Fig. 2(a)]. In order to optimize the SH conversion efficiency, the dispersion induced by the wave plate and the lens L1 is pre-compensated by adjusting the grating pulse compressor of the Ti:sapphire laser system. The SH pulses are separated from their fundamental pulses by a dichronic mirror (DM) which is coated HR at 400 nm and AR at 800 nm. The 396.8 nm beam is then reflected to another 29.2°-cut 2-mm-thick type I phase-matched β-BBO crystal (C2) as the pumping beam for NOPA. A CW He-Ne laser at 632.8 nm with an output power of 20 mW is focused into the β-BBO crystal C2 by a lens with a focal length of 250 mm. The CW seed crossly overlaps with the pumping pulses inside the crystal. Within a typical duration (~60 fs) for the parametric interaction between the pumping pulses and the CW seeding beam, there are more than 3500 photons that are seeded from the CW laser beam. As compared with the spontaneous optical parametric amplification, such photon numbers are large enough to control efficiently the beam quality of the amplified signal.

 

Fig. 1. (a) Schematic of the experimental setup. λ/2: half wave plate at 800 nm; M1: mirror with 45° HR at 800 nm; M2: concave mirror with 0 ° HR at 800 nm; M3: mirror with 45° HR at 632.8 nm; M4: mirror with 45o HR at 400 nm ; M5: mirror with 0 o HR at 400 nm; M6: concave mirror with 0 ° HR at 1064 nm; M7: mirror with 45° HR at 1064 nm; DM: mirror with 45° HR at 400 nm and AR at 800 nm; L1, L2: lens; C1,C2: β-BBO crystal. (b)Alignment for measuring spatial chirp of idler pulses.

Download Full Size | PPT Slide | PDF

3. Experimental measurements

In order to get the amplified signal and idler pulses easily, the β-BBO crystal C2 for NOPA is tilted to the pumping beam so that a strong red component around 632.8 nm appears in the parametric ring. When the CW seed signal is aligned with proper polarizations to overlap with the pump pulses inside the β-BBO crystal C2 and along the propagation direction of the spectral component around 632.8 nm in the parametric ring, the idler beam appears. After a careful experimental optimization, the idler pulses are so strong that their second harmonics are observed when the incident angle of the pumping is about 13 degrees in air and the angle between the pumping and signal is about 10 degrees in air. The corresponding angle between the idler and the pumping is about 12 degree in air. Figure 2(a) is the measured spectrum of the pumping pulses centered at 396.7 nm with a bandwidth about 9.5 nm. Figure 2(b) is the spectrum of the amplified signal after the first-stage NOPA. As our prediction, it is the same as that directly from the He-Ne laser. Figure 2(c) presents the recorded spectrum of the background-free idler pulses which indicates clearly pulsed features at the central wavelength of 1064 nm with a bandwidth of 15 nm, while Fig. 2(d) shows the spectrum of its corresponding second harmonic pulses centered at 532 nm with a bandwidth of 5 nm. An elliptic spatial distribution is observed for the generated idler pulses. Figure 3 presents the measured spectra of the idler pulse with different spatial transverse positions [B, C, D and E in 1(b)] centered at 1053, 1059, 1064 and 1069nm, respectively. The separations DE, CD, and BC are approximately 2.5 mm, and the distance DO is about 100 cm. Apparently, there exists some spatial chirp in the spatial intensity distribution of the idler beam, which is mainly originated from the angular matching on optical frequency for effective optical parametric amplification pumped by the broadband laser pulses.

However, the measured bandwidth of the idler beam behind a fixed iris keeps constant in spite of different distance between the BBO crystal and observed screen, e.g. DO (100 cm) and AO (50 cm). This is originated from the fact that the spatial divergent angle of the beam with a small waist size is larger than the angular dispersion due to the phase-matching for different spectral components of the idler beam in our OPA. According to the requirement of energy conservation in OPA, the bandwidth of the idler pulses is determined by the spectrum of the ultrashort pumping pulses due to the very narrow bandwidth of the CW signal beam. From the phase matching condition, the dispersion angle of the idler pulses in our experiment is calculated about 5.0×10-4 radian/nm, while the divergent angle of the idler is about 2.2×10-3 radian, 4 times larger than the former. Here the waist radius of the idler is estimated about 0.15 mm by the focused beam size of the signal beam. Based on the calculation given above, the separations between E and D, D and C, and C and B are 3.1, 2.6 and 2.6 mm, respectively, which almost match with our measured data. In a standard OPCPA system, effective amplification requires a pump pulse temporally overlapped with the chirped signal. Therefore, before or during the amplification of the 1064 nm beam, some steps, such as spectral filtering [12] or inserting an appropriate etalon into the cavity of a regenerative amplifier [3, 15], should be taken to narrow the bandwidth thus widen the pulse duration up to hundreds of picoseconds. Our analysis indicates that the spatial chirp of the idler is too weak to degrade the spatial intensity distribution of the 1064 nm beam if it passes through an Nd-doped, e.g. Nd:YAG, amplifier. The absence of CW background from our non-collinear configuration makes the generated idler pulses at 1064 nm be used as seeding pulses of a regenerative amplifier for upscaling pulse power, improving intensity stability and spectral/temporal shaping [8, 12, 13].

 

Fig. 2. Measured spectra of (a) the pump pulses from the SH of the Ti:sapphire fs laser, (b) the 632.8 nm beam after first-stage OPA, (c) the generated idler pulses and (d) their SH pulses, (e) the 632.8 nm beam and (f) the idler pulses after the second-stage NOPA

Download Full Size | PPT Slide | PDF

The idler pulses at 1064 nm can be further amplified with Nd-doped gain materials in either regenerative amplifiers or cascade high-power amplifiers to generate the strong pump pulses for OPCPA. Here we build the second-stage NOPA for further amplification for convenience in our measurements rather than for high pulse contrast of the idler pulses by reflecting the residual pump and the generated idler pulses back into the same BBO crystal. A concave mirror M6 used as a 2f-2f image optical system makes sure that the reflected idler pulses inside the BBO crystal have the same spatial dimension as that in the first-stage NOPA. The amplification of the parametric fluorescence reflected by M6 is suppressed by inserting an iris between M6 and C2. The iris also improves the spatial intensity distribution of the 1064 nm beam after its second pass through the BBO crystal. Figure 2(e) presents the obvious spectral broadening of the 632.8 nm beam after the second-stage NOPA. The spectra of the 1064 nm pulses after the second-stage NOPA are also measured as shown in Fig. 2(f). Compared with Fig. 2(c), a slight spectral narrowing occurs. The appearance of 532 nm beam resulting from the second harmonic of the idler pulses at 1064 nm indicates that the idler pulses have a short pulse width and accordingly a high intensity. The measured autocorrelation duration is about 265 fs for the generated idler pulse after the second-stage of NOPA [see in Fig. 4(a)], which is apparently longer than the 60 fs pump pulses from the frequency-doubled Ti:sapphire laser [see in Fig. 4(b)]. According to the measured spectra in Figs. 2(a) and 2(f), it is clear that the spectral narrowing during OPA stretches the pulse autocorrelation duration from 60 to 160 fs, while the dispersion during double-passage through the crystal C2 broadens the pulse further up to 265 fs.

 

Fig. 3. The measured spectra of the idler pulses for different transverse positions

Download Full Size | PPT Slide | PDF

 

Fig. 4. The autocorrelation trace of (a) the generated 1064 nm pulse after the second-stage of NOPA and (b) the pump pulses from the frequency-doubled Ti:sapphire fs laser

Download Full Size | PPT Slide | PDF

4. Results and discussion

Neglecting pump depletion and assuming a perfect phase matching and large gain approximation, we can approximately estimate the idler beam power after a length L of the nonlinear crystal by

PiωiωsPs0exp(2ΓL)4,

where no initial idler beam is assumed, Ps0 is the initial signal power, ωs and ωi are the signal and idler frequencies, respectively. Γ is proportional to the pump intensity Ip as determined by [16]

Γ=2ωiωsdeff2Ipninsnpε0c03,

where c 0 and ε0 are the speed of light and the dielectric constant in vacuum, nj (j=i,s,p) is the refractive index at frequency ω j. deff is the so-called effective nonlinear optical coefficient, depending on the propagation direction and the polarization of the three beams. In our first-stage NOPA, when the pumping intensity is about 45 GW/cm2, the parametric gain is up to 8×105, corresponding to 0.7 nJ single-pulse energy of the idler pulse. In the second-stage NOP A, the pump intensity is 14.3 GW/cm2, the corresponding parametric gain is estimated as ~4.2×103. Consequently, the final output is about 2.8 μJ. The solid line in Fig. 4 is our theoretical prediction according to Eqs. (1) and (2), which fits very well with our measured data. The deviation of our experimental results from the theoretical calculation is partly due to the slight optical parametric gain saturation. Based on the analysis above, the output single-pulse energy from the first-stage NOPA is about 0.7 nJ, which is large enough to act as the seed of an Nd-doped regenerative amplifier.

 

Fig. 5. Dependence of the single-pulse energy of the 1064 nm pulses after the second-stage of NOPA on the power of the CW 632.8 nm seeding laser

Download Full Size | PPT Slide | PDF

The impressive advantage of our design is the inherent synchronization between the 1064 and 794 nm pulses. The 794 nm pulse can be provided from an ultrabroad bandwidth Ti:sapphire laser oscillator, whose output can be split into two parts. One is used as the seed for a Ti:sapphire fs regenerative amplifier to generate 397 nm pump pulses in NOPA, while the other as the ultrabroadband seed for OPCPA. The synchronization accuracy is mainly limited by the timing jitter in the Ti:sapphire fs regenerative amplifier, which is nearly 10 fs in a few seconds and less than 200 fs in one hour [17]. Since the time interval of the optical pulses before and after our Ti:sapphire fs regenerative amplifier is about 350 ns, the timing jitter between the broadband OPCPA signal at 794 nm and the generated 1064 nm idler from the CW seeded NOPA can be estimated as ~10 fs. The spectral stability of He-Ne laser is usually less than 1 GHz (1.33×10-3 nm), which brings about negligible influence on timing jitter of the generated 1064 nm pulses. In our experiments, the power stability of the 1064 nm beam is measured about ±8% for 16.5 mW CW He-Ne laser, which can be improved by carefully choosing and balancing the system parameters within an appreciable extent of pump variation [18].

5. Conclusion

In summary, we have demonstrated a novel method to transfer intense 397 nm pulses from frequency-doubled femtosecond Ti:sapphire laser system to 1064 nm laser pulses through a non-collinear optical parametric amplification. Using a CW 632.8 nm laser beam as the seed signal, background-free idler pulses are achieved at 1064 nm without need of any synchronizing devices. Single pulse energy of 0.7 nJ is obtainable just by use of a first-stage NOPA. After the second-stage OPA, the single-pulse energy is as high as 2.5 μJ. The pulse duration can be stretched up to tens even hundreds of picoseconds by narrowing the bandwidth of the pulses. This kind of pulses can be used as seeding pulses of the amplification chain to generate accurately synchronized pump pulses for optical parametric amplification of chirped pulses from the same Ti:sapphire laser with a timing jitter down to femtoseconds region.

Acknowledgments

This work was supported in part by Key Project from Science and Technology Commission of Shanghai Municipality (Grant 04dz14001), National Natural Science Fund (Grants 10525416, 60478011 and 10234030), key project sponsored by National Education Ministry of China (Grant 104193), and Shanghai Municipality Natural Science Fund (Grant 05ZR14044).

References and links

1. 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, 2923–2929 (2002). [CrossRef]   [PubMed]  

2. I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplification,” Opt. Commun. 144, 125–133 (1997). [CrossRef]  

3. X. Yang, Z. Xu, Y.-X. Leng, H.-H. Lu, L.-H. Lin, Z.-Q. Zhang, R.-X. Li, W.-Q. Zhang, D.-J. Yin, and B. Tang, “Multiterawatt laser system based on optical parametric chirped pulse amplification,” Opt. Lett. 27, 1135–1137(2002). [CrossRef]  

4. I. Jovanovic, C. G. Brown, C. A. Ebbers, C. P. J. Barty, N. Forget, and C. Le Blanc, “Generation of high-contrast millijoule pulses by optical parametric chirped-pulse amplification in periodically poled KTiOPO4,” Opt. Lett. 30, 1036–1038(2005). [CrossRef]   [PubMed]  

5. P. Schlup, J. Biegert, C. P. Hauri, G. Arisholm, and U. Keller, “Design of a sub-13-fs, multi-gigawatt chirped pulse optical parametric amplification system,” Appl. Phys. B 79, 285–288 (2004). [CrossRef]  

6. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221(1985). [CrossRef]  

7. N. Ishii, L. Turi, V. S. Yakovlev, T. Fuji, F. Krausz, A. Baltuška, R. Butkus, G. Veitas, V. Smilgevicius, R. Danielius, and A. Piskarskas, “Multimillijoule chirped parametric amplification of few-cycle pulses,” Opt. Lett. 30, 567–569 (2005). [CrossRef]   [PubMed]  

8. Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004). [CrossRef]  

9. S. Backus, C. G. Durfee III, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223(2002). [CrossRef]  

10. I. N. Ross, J. L. Collier, P. Matousek, C. N. Danson, D. Neely, R. M. Allott, D. A. Pepler, C. Hernandez-Gomez, and K. Osvay: Appl. Generation of terawatt pulses by use of optical parametric chirped pulse amplification,” Appl. Opt. 39, 2422–3427 (2000). [CrossRef]  

11. J. V. Rudd, R. J. Law, T. S. Luk, and S. M. Cameron, “High-power optical parametric chirped-pulse amplifier system with a 1.55 μm signal and a 1.064 μm pump,” Opt. Lett. 30, 1974 (2005). [CrossRef]   [PubMed]  

12. S. Witte, R. Th. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Generation of few-cycle terawatt light pulses using optical parametric chirped pulse amplification,” Opt. Express 13, 4903–4908 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-4903. [CrossRef]   [PubMed]  

13. Y. Leng, L. Lin, X. Yang, H. Lu, Z. Zhang, and Z. Xu, “Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping,” Opt. Eng. 42, 862–866 (2003). [CrossRef]  

14. H. Zeng, J. Wu, H. Xu, K. Wu, and E Wu, “Generation of accurately synchronized pump source for optical parametric chirped pulse amplification,” Appl. Phys. B 79, 837–839 (2004). [CrossRef]  

15. C. Y. Teisset, N. Ishii, T. Fuji, T. Metzger, S. Köhler, R. Holzwarth1, A. Baltuška1, A. M. Zheltikov, and F. Krausz, “Soliton-based pump-seed synchronization for few-cycle OPCPA,” Opt. Express 13, 6550–6557(2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6550. [CrossRef]   [PubMed]  

16. G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum 74, 1–18 (2003). [CrossRef]  

17. T. Miura, K. Kobayashi, K. Takasago, Z. Zhang, K. Torizuka, and F. Kannari, “Timing jitter in a kilohertz regenerative amplifier of a femtosecond-pulse TiAl 2 O3 laser,” Opt. Lett. 25, 1795–1797 (2000). [CrossRef]  

18. 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, 451–455 (2000). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. 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, 2923–2929 (2002).
    [CrossRef] [PubMed]
  2. I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplification,” Opt. Commun. 144, 125–133 (1997).
    [CrossRef]
  3. X. Yang, Z. Xu, Y.-X. Leng, H.-H. Lu, L.-H. Lin, Z.-Q. Zhang, R.-X. Li, W.-Q. Zhang, D.-J. Yin, and B. Tang, “Multiterawatt laser system based on optical parametric chirped pulse amplification,” Opt. Lett. 27, 1135–1137(2002).
    [CrossRef]
  4. I. Jovanovic, C. G. Brown, C. A. Ebbers, C. P. J. Barty, N. Forget, and C. Le Blanc, “Generation of high-contrast millijoule pulses by optical parametric chirped-pulse amplification in periodically poled KTiOPO4,” Opt. Lett. 30, 1036–1038(2005).
    [CrossRef] [PubMed]
  5. P. Schlup, J. Biegert, C. P. Hauri, G. Arisholm, and U. Keller, “Design of a sub-13-fs, multi-gigawatt chirped pulse optical parametric amplification system,” Appl. Phys. B 79, 285–288 (2004).
    [CrossRef]
  6. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221(1985).
    [CrossRef]
  7. N. Ishii, L. Turi, V. S. Yakovlev, T. Fuji, F. Krausz, A. Baltuška, R. Butkus, G. Veitas, V. Smilgevicius, R. Danielius, and A. Piskarskas, “Multimillijoule chirped parametric amplification of few-cycle pulses,” Opt. Lett. 30, 567–569 (2005).
    [CrossRef] [PubMed]
  8. Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004).
    [CrossRef]
  9. S. Backus, C. G. Durfee III, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223(2002).
    [CrossRef]
  10. I. N. Ross, J. L. Collier, P. Matousek, C. N. Danson, D. Neely, R. M. Allott, D. A. Pepler, C. Hernandez-Gomez, and K. Osvay: Appl. Generation of terawatt pulses by use of optical parametric chirped pulse amplification,” Appl. Opt. 39, 2422–3427 (2000).
    [CrossRef]
  11. J. V. Rudd, R. J. Law, T. S. Luk, and S. M. Cameron, “High-power optical parametric chirped-pulse amplifier system with a 1.55 μm signal and a 1.064 μm pump,” Opt. Lett. 30, 1974 (2005).
    [CrossRef] [PubMed]
  12. S. Witte, R. Th. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Generation of few-cycle terawatt light pulses using optical parametric chirped pulse amplification,” Opt. Express 13, 4903–4908 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-4903.
    [CrossRef] [PubMed]
  13. Y. Leng, L. Lin, X. Yang, H. Lu, Z. Zhang, and Z. Xu, “Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping,” Opt. Eng. 42, 862–866 (2003).
    [CrossRef]
  14. H. Zeng, J. Wu, H. Xu, K. Wu, and E Wu, “Generation of accurately synchronized pump source for optical parametric chirped pulse amplification,” Appl. Phys. B 79, 837–839 (2004).
    [CrossRef]
  15. C. Y. Teisset, N. Ishii, T. Fuji, T. Metzger, S. Köhler, R. Holzwarth1, A. Baltuška1, A. M. Zheltikov, and F. Krausz, “Soliton-based pump-seed synchronization for few-cycle OPCPA,” Opt. Express 13, 6550–6557(2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6550.
    [CrossRef] [PubMed]
  16. G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum 74, 1–18 (2003).
    [CrossRef]
  17. T. Miura, K. Kobayashi, K. Takasago, Z. Zhang, K. Torizuka, and F. Kannari, “Timing jitter in a kilohertz regenerative amplifier of a femtosecond-pulse TiAl 2 O3 laser,” Opt. Lett. 25, 1795–1797 (2000).
    [CrossRef]
  18. 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, 451–455 (2000).
    [CrossRef]

2005 (5)

2004 (3)

P. Schlup, J. Biegert, C. P. Hauri, G. Arisholm, and U. Keller, “Design of a sub-13-fs, multi-gigawatt chirped pulse optical parametric amplification system,” Appl. Phys. B 79, 285–288 (2004).
[CrossRef]

Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004).
[CrossRef]

H. Zeng, J. Wu, H. Xu, K. Wu, and E Wu, “Generation of accurately synchronized pump source for optical parametric chirped pulse amplification,” Appl. Phys. B 79, 837–839 (2004).
[CrossRef]

2003 (2)

G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum 74, 1–18 (2003).
[CrossRef]

Y. Leng, L. Lin, X. Yang, H. Lu, Z. Zhang, and Z. Xu, “Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping,” Opt. Eng. 42, 862–866 (2003).
[CrossRef]

2002 (3)

2000 (3)

1997 (1)

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplification,” Opt. Commun. 144, 125–133 (1997).
[CrossRef]

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221(1985).
[CrossRef]

Allott, R. M.

Arisholm, G.

P. Schlup, J. Biegert, C. P. Hauri, G. Arisholm, and U. Keller, “Design of a sub-13-fs, multi-gigawatt chirped pulse optical parametric amplification system,” Appl. Phys. B 79, 285–288 (2004).
[CrossRef]

Backus, S.

S. Backus, C. G. Durfee III, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223(2002).
[CrossRef]

Baltuška, A.

Baltuška1, A.

Barty, C. P. J.

Biegert, J.

P. Schlup, J. Biegert, C. P. Hauri, G. Arisholm, and U. Keller, “Design of a sub-13-fs, multi-gigawatt chirped pulse optical parametric amplification system,” Appl. Phys. B 79, 285–288 (2004).
[CrossRef]

Bonner, R. A.

Brown, C. G.

Butkus, R.

Cameron, S. M.

Cerullo, G.

G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum 74, 1–18 (2003).
[CrossRef]

Collier, J. L.

I. N. Ross, J. L. Collier, P. Matousek, C. N. Danson, D. Neely, R. M. Allott, D. A. Pepler, C. Hernandez-Gomez, and K. Osvay: Appl. Generation of terawatt pulses by use of optical parametric chirped pulse amplification,” Appl. Opt. 39, 2422–3427 (2000).
[CrossRef]

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplification,” Opt. Commun. 144, 125–133 (1997).
[CrossRef]

Comaskey, B. J.

Danielius, R.

Danson, C. N.

De Silvestri, S.

G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum 74, 1–18 (2003).
[CrossRef]

Durfee III, C. G.

S. Backus, C. G. Durfee III, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223(2002).
[CrossRef]

Ebbers, C. A.

Eikema, K. S. E.

Forget, N.

Fuji, T.

Fujita, M.

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, 451–455 (2000).
[CrossRef]

Hauri, C. P.

P. Schlup, J. Biegert, C. P. Hauri, G. Arisholm, and U. Keller, “Design of a sub-13-fs, multi-gigawatt chirped pulse optical parametric amplification system,” Appl. Phys. B 79, 285–288 (2004).
[CrossRef]

Hernandez-Gomez, C.

Hogervorst, W.

Holzwarth1, R.

Ishii, N.

Izawa, Y.

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, 451–455 (2000).
[CrossRef]

Jovanovic, I.

Kannari, F.

Kapteyn, H. C.

S. Backus, C. G. Durfee III, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223(2002).
[CrossRef]

Keller, U.

P. Schlup, J. Biegert, C. P. Hauri, G. Arisholm, and U. Keller, “Design of a sub-13-fs, multi-gigawatt chirped pulse optical parametric amplification system,” Appl. Phys. B 79, 285–288 (2004).
[CrossRef]

Kobayashi, K.

Köhler, S.

Krausz, F.

Langley, A. J.

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplification,” Opt. Commun. 144, 125–133 (1997).
[CrossRef]

Law, R. J.

Le Blanc, C.

Leng, Y.

Y. Leng, L. Lin, X. Yang, H. Lu, Z. Zhang, and Z. Xu, “Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping,” Opt. Eng. 42, 862–866 (2003).
[CrossRef]

Leng, Y. X.

Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004).
[CrossRef]

Leng, Y.-X.

Li, R X.

Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004).
[CrossRef]

Li, R.-X.

Lin, L.

Y. Leng, L. Lin, X. Yang, H. Lu, Z. Zhang, and Z. Xu, “Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping,” Opt. Eng. 42, 862–866 (2003).
[CrossRef]

Lin, L. H.

Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004).
[CrossRef]

Lin, L.-H.

Lu, H.

Y. Leng, L. Lin, X. Yang, H. Lu, Z. Zhang, and Z. Xu, “Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping,” Opt. Eng. 42, 862–866 (2003).
[CrossRef]

Lu, H. H.

Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004).
[CrossRef]

Lu, H.-H.

Luk, T. S.

Matousek, P.

I. N. Ross, J. L. Collier, P. Matousek, C. N. Danson, D. Neely, R. M. Allott, D. A. Pepler, C. Hernandez-Gomez, and K. Osvay: Appl. Generation of terawatt pulses by use of optical parametric chirped pulse amplification,” Appl. Opt. 39, 2422–3427 (2000).
[CrossRef]

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplification,” Opt. Commun. 144, 125–133 (1997).
[CrossRef]

Metzger, T.

Miura, T.

Morse, E. C.

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221(1985).
[CrossRef]

Murnane, M. M.

S. Backus, C. G. Durfee III, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223(2002).
[CrossRef]

Nakatsuka, M.

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, 451–455 (2000).
[CrossRef]

Neely, D.

Osvay, K.

Pennington, D. M.

Pepler, D. A.

Piskarskas, A.

Ross, I. N.

I. N. Ross, J. L. Collier, P. Matousek, C. N. Danson, D. Neely, R. M. Allott, D. A. Pepler, C. Hernandez-Gomez, and K. Osvay: Appl. Generation of terawatt pulses by use of optical parametric chirped pulse amplification,” Appl. Opt. 39, 2422–3427 (2000).
[CrossRef]

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplification,” Opt. Commun. 144, 125–133 (1997).
[CrossRef]

Rudd, J. V.

Schlup, P.

P. Schlup, J. Biegert, C. P. Hauri, G. Arisholm, and U. Keller, “Design of a sub-13-fs, multi-gigawatt chirped pulse optical parametric amplification system,” Appl. Phys. B 79, 285–288 (2004).
[CrossRef]

Smilgevicius, V.

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221(1985).
[CrossRef]

Takasago, K.

Tang, B.

Teisset, C. Y.

Torizuka, K.

Towrie, M.

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplification,” Opt. Commun. 144, 125–133 (1997).
[CrossRef]

Turi, L.

Veitas, G.

Witte, S.

Wu, E

H. Zeng, J. Wu, H. Xu, K. Wu, and E Wu, “Generation of accurately synchronized pump source for optical parametric chirped pulse amplification,” Appl. Phys. B 79, 837–839 (2004).
[CrossRef]

Wu, J.

H. Zeng, J. Wu, H. Xu, K. Wu, and E Wu, “Generation of accurately synchronized pump source for optical parametric chirped pulse amplification,” Appl. Phys. B 79, 837–839 (2004).
[CrossRef]

Wu, K.

H. Zeng, J. Wu, H. Xu, K. Wu, and E Wu, “Generation of accurately synchronized pump source for optical parametric chirped pulse amplification,” Appl. Phys. B 79, 837–839 (2004).
[CrossRef]

Xu, H.

H. Zeng, J. Wu, H. Xu, K. Wu, and E Wu, “Generation of accurately synchronized pump source for optical parametric chirped pulse amplification,” Appl. Phys. B 79, 837–839 (2004).
[CrossRef]

Xu, Z.

Y. Leng, L. Lin, X. Yang, H. Lu, Z. Zhang, and Z. Xu, “Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping,” Opt. Eng. 42, 862–866 (2003).
[CrossRef]

X. Yang, Z. Xu, Y.-X. Leng, H.-H. Lu, L.-H. Lin, Z.-Q. Zhang, R.-X. Li, W.-Q. Zhang, D.-J. Yin, and B. Tang, “Multiterawatt laser system based on optical parametric chirped pulse amplification,” Opt. Lett. 27, 1135–1137(2002).
[CrossRef]

Xu, Z. Z.

Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004).
[CrossRef]

Yakovlev, V. S.

Yamanaka, C.

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, 451–455 (2000).
[CrossRef]

Yamanaka, M.

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, 451–455 (2000).
[CrossRef]

Yang, X.

Y. Leng, L. Lin, X. Yang, H. Lu, Z. Zhang, and Z. Xu, “Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping,” Opt. Eng. 42, 862–866 (2003).
[CrossRef]

X. Yang, Z. Xu, Y.-X. Leng, H.-H. Lu, L.-H. Lin, Z.-Q. Zhang, R.-X. Li, W.-Q. Zhang, D.-J. Yin, and B. Tang, “Multiterawatt laser system based on optical parametric chirped pulse amplification,” Opt. Lett. 27, 1135–1137(2002).
[CrossRef]

Yang, X. D.

Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004).
[CrossRef]

Yin, D. J.

Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004).
[CrossRef]

Yin, D.-J.

Zeng, H.

H. Zeng, J. Wu, H. Xu, K. Wu, and E Wu, “Generation of accurately synchronized pump source for optical parametric chirped pulse amplification,” Appl. Phys. B 79, 837–839 (2004).
[CrossRef]

Zhang, S. K.

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, 451–455 (2000).
[CrossRef]

Zhang, W.-Q.

Zhang, Z.

Y. Leng, L. Lin, X. Yang, H. Lu, Z. Zhang, and Z. Xu, “Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping,” Opt. Eng. 42, 862–866 (2003).
[CrossRef]

T. Miura, K. Kobayashi, K. Takasago, Z. Zhang, K. Torizuka, and F. Kannari, “Timing jitter in a kilohertz regenerative amplifier of a femtosecond-pulse TiAl 2 O3 laser,” Opt. Lett. 25, 1795–1797 (2000).
[CrossRef]

Zhang, Z. Q.

Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004).
[CrossRef]

Zhang, Z.-Q.

Zheltikov, A. M.

Zinkstok, R. Th.

Appl. Opt. (2)

Appl. Phys. B (2)

P. Schlup, J. Biegert, C. P. Hauri, G. Arisholm, and U. Keller, “Design of a sub-13-fs, multi-gigawatt chirped pulse optical parametric amplification system,” Appl. Phys. B 79, 285–288 (2004).
[CrossRef]

H. Zeng, J. Wu, H. Xu, K. Wu, and E Wu, “Generation of accurately synchronized pump source for optical parametric chirped pulse amplification,” Appl. Phys. B 79, 837–839 (2004).
[CrossRef]

Opt. Commun. (3)

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplification,” Opt. Commun. 144, 125–133 (1997).
[CrossRef]

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221(1985).
[CrossRef]

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, 451–455 (2000).
[CrossRef]

Opt. Eng. (2)

Y. X. Leng, X. D. Yang, H. H. Lu, L. H. Lin, Z. Q. Zhang, R X. Li, D. J. Yin, and Z. Z. Xu, “Temporal synchronization in optical parametric chirped pulse amplification laser system,” Opt. Eng. 43, 2994–2997(2004).
[CrossRef]

Y. Leng, L. Lin, X. Yang, H. Lu, Z. Zhang, and Z. Xu, “Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping,” Opt. Eng. 42, 862–866 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Rev. Sci. Instrum (1)

G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum 74, 1–18 (2003).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Backus, C. G. Durfee III, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223(2002).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of the experimental setup. λ/2: half wave plate at 800 nm; M1: mirror with 45° HR at 800 nm; M2: concave mirror with 0 ° HR at 800 nm; M3: mirror with 45° HR at 632.8 nm; M4: mirror with 45o HR at 400 nm ; M5: mirror with 0 o HR at 400 nm; M6: concave mirror with 0 ° HR at 1064 nm; M7: mirror with 45° HR at 1064 nm; DM: mirror with 45° HR at 400 nm and AR at 800 nm; L1, L2: lens; C1,C2: β-BBO crystal. (b)Alignment for measuring spatial chirp of idler pulses.

Fig. 2.
Fig. 2.

Measured spectra of (a) the pump pulses from the SH of the Ti:sapphire fs laser, (b) the 632.8 nm beam after first-stage OPA, (c) the generated idler pulses and (d) their SH pulses, (e) the 632.8 nm beam and (f) the idler pulses after the second-stage NOPA

Fig. 3.
Fig. 3.

The measured spectra of the idler pulses for different transverse positions

Fig. 4.
Fig. 4.

The autocorrelation trace of (a) the generated 1064 nm pulse after the second-stage of NOPA and (b) the pump pulses from the frequency-doubled Ti:sapphire fs laser

Fig. 5.
Fig. 5.

Dependence of the single-pulse energy of the 1064 nm pulses after the second-stage of NOPA on the power of the CW 632.8 nm seeding laser

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

P i ω i ω s P s 0 exp ( 2 Γ L ) 4 ,
Γ = 2 ω i ω s d eff 2 I p n i n s n p ε 0 c 0 3 ,

Metrics