We report on an OPCPA system delivering CEP-stable pulses with a pulse duration of only 1.7 optical cycles at 880 nm wavelength. This pulse duration is achieved by the generation, optical parametric amplification and compression of a full optical octave of bandwidth. The system is pumped by a high average power Yb-fiber laser system, which allows for operation of the OPCPA at up to 1 MHz repetition rate and 22 W of average output power. Further scaling towards single-cycle pulses, higher energy and output power is discussed.
©2012 Optical Society of America
Optical parametric amplifiers (OPAs) have attracted huge interest due to their unique properties. One of them, i.e. the enormous gain bandwidth, has triggered a remarkable development in few-cycle laser technology. By employing the concept of optical parametric chirped pulse amplification (OPCPA) , the peak power of few-cycle OPCPA has recently been boosted beyond 10 TW , giving such lasers the potential to push the frontiers in laser based particle acceleration  and attoscience .
In addition, the lack of energy storage and the low residual absorption of nonlinear crystals has allowed for scaling of few-cycle OPCPAs to high average output powers. Today, several watts of average output power are routinely generated, while achieving sufficient peak power for high field physics [5,6]. Such systems are for example ideally suited for high repetition rate high harmonic generation . It is expected that high repetition rate HHG sources will help to increase the signal to noise ratio of subsequent applications, such as XUV- imaging . A high laser repetition rate is in particular advantageous for applications that have to avoid space charge effects, such as photoelectron spectroscopy .
Since the first demonstration of broadband non-collinear optical parametric amplification , there has been an ongoing interest in enhancing the gain bandwidth in order to achieve the shortest possible pulse durations. By using broadband and angularly dispersed pump waves, pulses as short as 3.9 fs (~1.9 optical cycles) have been generated in the visible with OPA . Later work was focused on extending the OPAs gain bandwidth further towards a full optical octave . However, pulse compression could not be demonstrated in the latter experiment due to the complex phase structure of the broadband signal. By temporal chirping of a broadband pump pulse half an octave of spectral bandwidth has been achieved at degeneracy , without the need of additional angular chirp of the signal. An alternative approach of gain bandwidth engineering is two-color pumping, which has been successfully demonstrated recently . However, this approach neither demonstrated octave spanning amplification nor pulse compression to few-cycle durations, so far.
In this paper we present a different approach to octave spanning optical parametric amplification. We utilize only a single narrow bandwidth pump beam. However, we optimize the non-collinear geometry and operation conditions of a BBO based OPA in order to obtain the largest possible amplification bandwidth. To provide an adequate signal bandwidth we utilized an all-normal-dispersion (ANDi) photonic crystal fiber for octave spanning continuum generation . Amplification of a full optical octave ranging from 600 nm to beyond 1200 nm and pulse compression to only 1.7 optical cycles is achieved. To our knowledge this represents the largest bandwidth and shortest pulse duration (measured in optical cycles) of any CEP-stable OPCPA system reported today. Furthermore, measurements of the carrier-envelope-phase drifts reveal excellent stability even without a slow loop feedback. In addition, the system delivers unprecedented high average output powers of up to 22 W at 1 MHz repetition rate by employing a high power femtosecond Yb-doped fiber chirped pulse amplification system as pump laser. This holds promise to address the generation of isolated attosecond pulses at megahertz repetition rate in the near future.
The manuscript is organized as follows. First the experimental setup is introduced and the design of the octave spanning optical parametric amplifier is presented. Afterwards a detailed characterization of the OPCPA output at 150 kHz repetition rate will be shown including measurements of the CEP stability. Finally we present the results on average power scaling of the OPCPA system up to 1 MHz repetition rate and 22 W of compressed output power.
2. Experimental setup
The experimental setup of the OPCPA system is outlined in Fig. 1 . A broadband 76 MHz Ti:Sa oscillator (Femtolasers Rainbow) serves as the seeder for the fiber-based pump laser and the OPA stages as well. In order to generate sufficient seed for the pump laser, a fraction of the oscillator pulses (~0.5 nJ) is coupled into a piece of photonic crystal fiber (PCF) and frequency shifted to the Yb-gain region. Recent numerical optimizations revealed that the amplitude stability of the synchronization can be significantly improved and timing jitter can be reduced to the sub-fs scale by choice of a fiber with a zero dispersion wavelength around 850 nm . In consequence a 20 cm long NKT NL-890 (ZDW 890 nm) fiber is employed in the setup for improved stability.
The pump laser itself is an Yb-doped fiber chirped pulse amplification system (FCPA), which is described elsewhere [17,18]. It utilizes a novel large-pitch PCF with a mode field diameter of 45 µm (at 300W of average output power) as main amplifier . The FCPA system delivers nearly transform limited 470 fs pulses with 200 µJ of pulse energy at 1030 nm wavelength and repetition rates of up to 1 MHz (200W average power) . Subsequent frequency doubling (SHG in Fig. 1) in a 1 mm BBO crystal to ~120 µJ pulse energy at 515 nm wavelength generates the pump pulses for the OPA stages.
In order to generate an octave-spanning signal, the remaining fraction of the oscillators output pulses is coupled to a 14 mm long ANDi-type (all normal dispersive fiber) photonic crystal fiber via an aspheric lens . The dispersion of the coupling lens has been pre-compensated via chirped mirrors. As a result we obtain a coherent continuum, which spans from below 600 nm to beyond 1300 nm. In previous experiments it was already shown that, due to the smooth spectral phase and high stability, this continuum can be recompressed to nearly its Fourier limit . The continuum is then collimated by means of an off-axis parabolic mirror and sent through a grating based phase shaper, which is designed to image a wavelength range of ~600 nm to ~1230 nm onto the 128 pixel SLM in the Fourier-plane. Subsequently, 8 bounces (−36 fs2 each) on an ultra-broadband chirped mirror pair partially compensate for the positive chirp of the continuum in order to match the signal and pump pulse duration. The optical parametric amplifier consists of two-stages (Fig. 1) in order to achieve high conversion efficiency . Finally, ultra-broadband chirped mirrors compress the pulses.
3. Design of the octave-spanning optical parametric amplifier
Previous numerical investigations have shown that BBO can exhibit an extremely large gain bandwidth in an optimized non-collinear geometry and consequently supports sub-two optical cycle pulses . In this regard it became obvious that a certain wave vector mismatch, which leads to a reduced gain, can be tolerated. As a matter of fact, shorter crystals result in smaller accumulated phase mismatch of the interacting waves, hence larger gain bandwidths and smoother gain spectra. However, the pump intensity has to be increased accordingly in order to maintain the same parametric gain. An ultimate limit to the applicable pump intensity is given by the damage threshold intensity of the nonlinear crystal, which approximately scales with the square-root of the pulse duration . Hence, shorter pump pulses can be focused to higher intensities and allow for shorter crystals and a larger gain bandwidth, which is a great advantage of femtosecond pump pulses as delivered by FCPA systems.
In the presented experiments we focus the ~500 fs pump pulses to a peak intensity of ~300 GW/cm2 in the first and ~200 GW/cm2 in the second OPA stage. Hence, only 2 mm short BBO crystals need to be used in both stages.
In combination with optimized phase matching condition (phase matching angle θ = (23.9 ± 0.2)° and non-collinear angle α = (2.1 ± 0.1)°) this results in octave spanning optical parametric amplification.
The measured amplified spectra after the first OPA stage and the seed spectrum (black) are displayed together with the wave vector mismatch (grey dashed line) in Fig. 2 . For measurement of the blue curve the pump intensity has been reduced in order to avoid saturation effects. It can be clearly seen that only in regions of small wave vector mismatch efficient parametric amplification is observed. In contrast saturation favors the wavelength range between 900 nm and 1000 nm as well as the spectral wings with low seed intensities (<700 nm and >1100 nm), when the full pump intensity (~300 GW/cm2) is applied (red curve). In this case, efficient parametric amplification is observed over the full optical octave, spanning from 600 nm to beyond 1200 nm.
4. Characterization of the OPCPA system
The optimized geometry presented in the previous section has been employed for both OPA stages. The first amplification stage has a high gain factor of ~6∙104 increasing the pulse energy from ~200 pJ to 12 µJ. The second stage is optimized for energy extraction resulting in 29 µJ pulse energy.
Careful fine tuning of the non-collinear angle, the phase matching angle and the temporal delay of signal and pump pulses in both stages results in an octave spanning output spectrum (−10 dB bandwidth: >500 nm), which is displayed in Fig. 3 . The spectrum supports a Fourier limited pulse duration of only 3.8 fs (1.3 optical cycles). After amplification the beam is collimated and sent through a chirped mirror compressor (6 bounces, −36 fs2 each), which removes all remaining second order dispersion from the pulses. The throughput efficiency was measured to be as high as 90%, resulting in up to 26 µJ of pulse energy.
In order to compensate for the remaining higher order dispersion, the spectral phase of the unamplified pulses is measured with a SPIDER device and iteratively compensated by means of the phase shaper. After a few iterations, a flat residual spectral phase with deviations smaller than 0.5 rad is measured with the SPIDER over the entire bandwidth resulting in pulse compression close to the Fourier limit. However, the SPIDER measurement of the amplified pulses was severely disturbed due to the strongly modulated spectrum, parasitic nonlinear effects  and superfluorescence.
In order to avoid phase-matched parasitic second harmonic generation and sum-frequency-generation (SFG) of signal and idler at around 800 nm signal wavelength, we employ the non walkoff-compensating geometry for both OPA stages . Nevertheless, due to the octave-spanning bandwidth, phase matched SHG of 1120 nm signal is observed, which cannot be avoided . Although measurements with a band pass filter revealed that the energy fraction transferred to the second harmonic (580 nm) is below 2.5% of the total signal energy, this effect leads to spectral modulations as such observed in the amplified spectrum.
The amount of parametric fluorescence is estimated by cutting small fractions of the seed spectrum in the Fourier plane of the phase shaper and measuring the power content in this particular spectral region, which can only originate from fluorescence. Although, 8% of the output energy are found to be fluorescence, a sufficient pulse contrast of ~30 dB can be expected, since the signal pulses are shortened in time by two orders of magnitude due to the compressor, while the fluorescence is not. Summarizing, we expect to have 24 µJ of energy in the few-cycle pulse.
Due to the fact that a SPIDER measurement of the amplified pulses was not possible an interferometric autocorrelator is utilized for temporal characterization instead. Pulse compression has been optimized for the shortest pulse duration by a pair of fused silica wedges in the setup. The measured interferometric autocorrelation is displayed in Fig. 4 (blue dots) together with the autocorrelation trace of the Fourier-limited pulses (black line).
Although the measurement suffers from some background signal, it confirms a pulse duration of only 5.0 fs (assuming the deconvolution factor for Gaussian pulses), which corresponds to only 1.7 optical cycles at ~880 nm mean wavelength. The measured pulses (5.0 fs) are slightly longer than the Fourier-limited pulses (3.8 fs), which can be partly attributed to the phase imposed by the optical parametric amplifier itself . A detailed analysis and measurements of this optical parametric phase is subject of ongoing research and will potentially allow for compensation of this phase and pulse compression close to single-cycle durations in the near future. The peak power of the pulses is estimated to be about 2 GW.
Finally, the stability of the pulse energy was monitored with a photodiode at the OPCPA output. On a short timescale of ~1 s, we find the deviations to be below ± 5% (peak-to-peak). However, on longer timescales periodic variations of up to ± 10% (peak-to-peak) are observed, with cycle times between 15 and 20 seconds. These periodic deviations can be attributed to the cooling cycle of the pump diodes of the FCPA (also see section 5). This technical issue can be avoided if higher stability is required in future.
5. Carrier-envelope-phase measurements
Having an octave-spanning spectrum allows for direct measurement of the carrier-envelope-phase (CEP) stability without the need of additional spectral broadening. For this ambition the CE beat frequency of the oscillator is stabilized to one fourth of the repetition rate. The repetition rate of the pump laser is set to a fraction of one fourth of the oscillator’s repetition rate (~150 kHz). Hence, we obtain the same CEP for subsequent pulses amplified within the OPCPA system.
The pulses are fed into a modified f-2f interferometer (MENLO systems, APS800) and stable interference fringes around 605 nm are observed at 10 ms spectrometer integration time (Fig. 5(a) ). Please note that the second OPA stage is not pumped during these measurements, since the fringe visibility has been significantly reduced in this case by parasitic SHG and SFG of the signal and fluorescence located in the vicinity of 600 nm. The interference pattern vanishes immediately when switching off the oscillators CEP stabilization. Furthermore, the fringe pattern moved when inserting fused silica wedges into the beam (Time = 1.5 s to 5.8 s in Fig. 5(a) and returned to the initial position when removing the wedges from the beam (Time = 5.8 s to 9.2 s in Fig. 5(a)).
The measurements on the CEP stability are performed with 0.5 ms integration time, containing 75 pulses. They reveal excellent short-term stability with a standard deviation of only 0.15 rad (Fig. 5(b)). However, periodic deviations up to ± 1 rad are observed on a longer timescale, increasing the standard deviation to 0.41 rad for 95 s of measurement time (Fig. 5(c)). These drifts can be clearly attributed to the energy drifts of the OPCPA output, due to the cooling cycle of the pump diode of the FCPA. However, by using a stable cooling system for the pump diodes we expect to reach significantly lower values over the timescale of minutes in the near future. Furthermore, a slow loop feedback could be easily implemented in order to achieve active CEP stabilization of the OPCPA system over the timescale of hours.
6. Average power scaling
All measurements presented until this point of the manuscript have been carried out at 150 kHz repetition rate. As mentioned earlier the FCPA system can be operated up to 200 W of average output power and 1 MHz repetition rate. In accordance to earlier experiments on high average power SHG  we find the SHG efficiency of 60% to be independent of the repetition rate, which indicates absence of any thermo-optical problems. At 1 MHz repetition rate this results in 120 W of pump power at 515 nm for the OPA stages.
In order to investigate the thermo-optical behavior of the OPAs at very high average output power, we operate the system at 500 kHz and 1 MHz repetition rate, respectively. In both cases the same laser conversion efficiency and pulse energies are measured. Furthermore, similar beam profiles are achieved (see Fig. 6(b) ) with only small differences, which can be attributed to slightly different alignment of the OPA stages. Hence, thermal de-phasing and other thermo-optical effects do not influence the performance of the nonlinear amplifier so far. Note that an average output power as high as 22 W is achieved with the compressed pulses in the case of 1 MHz repetition rate. The measured output spectrum at 1 MHz repetition rate is displayed in Fig. 6(a) together with the spectrum at 150 kHz which is shown for comparison. Although the two spectra do not perfectly match they both show amplification over the full bandwidth and the spectrum measured at 1 MHz repetition rate supports Fourier-limited pulse durations of 4.6 fs. Hence, the pulse duration is expected to be slightly longer but still in the few-cycle range at 1 MHz repetition rate. Note that both the spatial and the spectral quality could be further improved by iterative alignment of the pump beam, phase matching angles and pump-signal delay in both stages. Since one deals with 120 W of average pump power this alignment procedure has been reduced to a minimum so far in order to avoid damage of the nonlinear crystals or other optics.
Although the performance of the OPAs was not significantly impaired, it must be mentioned that a tuning of the phase matching angle was required to maintain phase matching with increasing repetition rate. This indicates that the heat generated in the nonlinear crystal is not negligible anymore. This fact is confirmed by measurements of the crystal temperatures with a thermal imaging camera yielding up to 200 °C of crystal temperature at 1 MHz repetition rate. Part of the generated heat can be attributed to absorption of the idler wave, caused by the rapidly increasing absorption coefficient of BBO beyond 2 µm (2090 nm: 0,07 cm−1, 2550 nm: 0,5 cm−1 ). Indeed, avoiding of idler generation in this wavelength range reduced the crystal temperature significantly. Experimentally this has been achieved by blocking the corresponding signal wavelength range (<700 nm) in the Fourier-plane of the phase shaper. Further scaling of the average output power of OPCPA systems requires attention to residual absorption and crystal heating. Although optical parametric amplification in BBO exhibits a huge temperature bandwidth, which is calculated to be ~130 K in the presented case , idler absorption should be avoided in future high power OPCPA systems. This can be achieved by a proper selection of the wavelength range for the signal, hence keeping the generated idler far from the IR-absorption. In the presented system, this could be easily achieved e.g. by shifting of the signal wavelength range to longer wavelengths. Alternatively, configurations with a broadband signal around degeneracy could be considered .
7. Conclusion and outlook
In conclusion we presented an OPCPA system, which is capable of octave-wide amplification and delivers CEP-stable pulses as short as 1.7 cycles (5.0 fs). To our knowledge this is the first demonstration of octave-spanning optical parametric amplification and subsequent pulse compression close to the Fourier-limit so far. In consequence, the achieved pulse duration is the shortest reported from any CEP-stable OPCPA system up to now. Both the compressed pulse energy of 24 µJ and the resulting pulse peak power of ~2 GW are sufficient e.g. for high harmonic generation. This performance is achieved by the generation of an octave-spanning signal in an ANDi photonic crystal fiber, optical parametric amplification in only 2 mm long BBO crystals with optimized broadband phase matching and subsequent compression with ultra-broadband chirped mirrors. The presented approach holds promise for the generation of single-cycle pulses in the near future and represents a less complex alternative to coherent pulse synthesis .
In addition, excellent CEP stability with a standard deviation below 0.15 rad on a 1s timescale has been measured. The stability on a timescale of minutes is currently limited to 0.41 rad (95 s) by periodic amplitude deviations caused by the cooling cycle of the pump laser system. By avoiding these deviations with a proper cooling system of the laser diodes and a slow loop feedback system, improved CEP stability on the timescale of hours is expected in future.
Furthermore, we presented experimental results on scaling of the OPCPA system to exceptionally high repetition rates and average output powers. Although significant heating of the nonlinear crystals is observed during high power operation, the performance of the optical parametric amplifiers is not affected thanks to the huge temperature bandwidth of the employed nonlinear material. As a result the system delivers an average output power as high as 22 W, which represents a record value for OPCPA systems.
This unique source of CEP-stable high average- and peak power pulses will find numerous applications. Especially the short pulse duration holds promise to push isolated attosecond pulse generation to megahertz repetition rates. Since fiber technology already demonstrated multi-millijoule femtosecond pulses from single-  and coherently combined  amplifiers, mJ-class pulse energies and even higher average powers can be expected from fiber laser driven CEP-stable few-cycle OPCPA in the future.
Jan Rothhardt grateful acknowledges the support of the German Academic Exchange Service (DAAD). This work has also been partly supported by the German Federal Ministry of Education and Research (BMBF), Grant 05 ES7GU1, the Helmholtz Institute Jena and the European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013)/ERC Grant agreement no .
References and links
1. A. Dubietis, R. Butkus, and A. Piskarskas, “Trends in chirped pulse optical parametric amplification,” IEEE J. Sel. Top. Quantum Electron. 12(2), 163–172 (2006). [CrossRef]
2. D. Herrmann, L. Veisz, R. Tautz, F. Tavella, K. Schmid, V. Pervak, and F. Krausz, “Generation of sub-three-cycle, 16 TW light pulses by using noncollinear optical parametric chirped-pulse amplification,” Opt. Lett. 34(16), 2459–2461 (2009). [CrossRef] [PubMed]
3. K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevičius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009). [CrossRef] [PubMed]
4. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009). [CrossRef]
5. J. Rothhardt, S. Hädrich, E. Seise, M. Krebs, F. Tavella, A. Willner, S. Düsterer, H. Schlarb, J. Feldhaus, J. Limpert, J. Rossbach, and A. Tünnermann, “High average and peak power few-cycle laser pulses delivered by fiber pumped OPCPA system,” Opt. Express 18(12), 12719–12726 (2010). [CrossRef] [PubMed]
6. S. Hädrich, S. Demmler, J. Rothhardt, C. Jocher, J. Limpert, and A. Tünnermann, “High-repetition-rate sub-5-fs pulses with 12 GW peak power from fiber-amplifier-pumped optical parametric chirped-pulse amplification,” Opt. Lett. 36(3), 313–315 (2011). [CrossRef] [PubMed]
7. S. Hädrich, J. Rothhardt, M. Krebs, F. Tavella, A. Willner, J. Limpert, and A. Tünnermann, “High harmonic generation by novel fiber amplifier based sources,” Opt. Express 18(19), 20242–20250 (2010). [CrossRef] [PubMed]
8. M. D. Seaberg, D. E. Adams, E. L. Townsend, D. A. Raymondson, W. F. Schlotter, Y. Liu, C. S. Menoni, L. Rong, C.-C. Chen, J. Miao, H. C. Kapteyn, and M. M. Murnane, “Ultrahigh 22 nm resolution coherent diffractive imaging using a desktop 13 nm high harmonic source,” Opt. Express 19(23), 22470–22479 (2011). [CrossRef] [PubMed]
9. T. Rohwer, S. Hellmann, M. Wiesenmayer, C. Sohrt, A. Stange, B. Slomski, A. Carr, Y. Liu, L. M. Avila, M. Kalläne, S. Mathias, L. Kipp, K. Rossnagel, and M. Bauer, “Collapse of long-range charge order tracked by time-resolved photoemission at high momenta,” Nature 471(7339), 490–493 (2011). [CrossRef] [PubMed]
10. T. Wilhelm, J. Piel, and E. Riedle, “Sub-20-fs pulses tunable across the visible from a blue-pumped single-pass noncollinear parametric converter,” Opt. Lett. 22(19), 1494–1496 (1997). [CrossRef] [PubMed]
11. A. Baltuška, T. Fuji, and T. Kobayashi, “Visible pulse compression to 4 fs by optical parametric amplification and programmable dispersion control,” Opt. Lett. 27(5), 306–308 (2002). [CrossRef] [PubMed]
12. C. Aguergaray, O. Schmidt, J. Rothhardt, D. Schimpf, D. Decamps, S. Petit, J. Limpert, and E. Cormier, “Ultra-wide parametric amplification at 800 nm toward octave spanning,” Opt. Express 17(7), 5153–5162 (2009). [CrossRef] [PubMed]
13. J. Limpert, C. Aguergaray, S. Montant, I. Manek-Hönninger, S. Petit, D. Descamps, E. Cormier, and F. Salin, “Ultra-broad bandwidth parametric amplification at degeneracy,” Opt. Express 13(19), 7386–7392 (2005). [CrossRef] [PubMed]
14. D. Herrmann, C. Homann, R. Tautz, M. Scharrer, P. St. J. Russell, F. Krausz, L. Veisz, and E. Riedle, “Approaching the full octave: noncollinear optical parametric chirped pulse amplification with two-color pumping,” Opt. Express 18(18), 18752–18762 (2010). [CrossRef] [PubMed]
15. S. Demmler, J. Rothhardt, A. M. Heidt, A. Hartung, E. G. Rohwer, H. Bartelt, J. Limpert, and A. Tünnermann, “Generation of high quality, 1.3 cycle pulses by active phase control of an octave spanning supercontinuum,” Opt. Express 19(21), 20151–20158 (2011). [CrossRef] [PubMed]
16. J. Rothhardt, A. M. Heidt, S. Hädrich, S. Demmler, J. Limpert, and A. Tünnermann, “High stability soliton frequency-shifting mechanisms for laser synchronization applications,” J. Opt. Soc. Am. B [to be published (doc ID: 159349)].
17. F. Röser, T. Eidam, J. Rothhardt, O. Schmidt, D. N. Schimpf, J. Limpert, and A. Tünnermann, “Millijoule pulse energy high repetition rate femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 32(24), 3495–3497 (2007). [CrossRef] [PubMed]
18. J. Rothhardt, S. Hädrich, H. Carstens, N. Herrick, S. Demmler, J. Limpert, and A. Tünnermann, “1 MHz repetition rate hollow fiber pulse compression to sub-100-fs duration at 100 W average power,” Opt. Lett. 36(23), 4605–4607 (2011). [CrossRef] [PubMed]
19. F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (2011). [CrossRef] [PubMed]
20. J. Rothhardt, S. Hädrich, F. Röser, J. Limpert, and A. Tünnermann, “500 MW peak power degenerated optical parametric amplifier delivering 52 fs pulses at 97 kHz repetition rate,” Opt. Express 16(12), 8981–8988 (2008). [CrossRef] [PubMed]
21. D. N. Schimpf, J. Rothhardt, J. Limpert, A. Tünnermann, and D. C. Hanna, “Theoretical analysis of the gain bandwidth for noncollinear parametric amplification of ultrafast pulses,” J. Opt. Soc. Am. B 24(11), 2837–2846 (2007). [CrossRef]
22. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter 53(4), 1749–1761 (1996). [CrossRef] [PubMed]
23. J. Bromage, J. Rothhardt, S. Hädrich, C. Dorrer, C. Jocher, S. Demmler, J. Limpert, A. Tünnermann, and J. D. Zuegel, “Analysis and suppression of parasitic processes in noncollinear optical parametric amplifiers,” Opt. Express 19(18), 16797–16808 (2011). [CrossRef] [PubMed]
24. I. N. Ross, P. Matousek, G. H. C. New, and K. Osvay, “Analysis and optimization of optical parametric chirped pulse amplification,” J. Opt. Soc. Am. B 19(12), 2945–2956 (2002). [CrossRef]
25. J. Rothhardt, T. Eidam, S. Hädrich, F. Jansen, F. Stutzki, T. Gottschall, T. V. Andersen, J. Limpert, and A. Tünnermann, “135 W average-power femtosecond pulses at 520 nm from a frequency-doubled fiber laser system,” Opt. Lett. 36(3), 316–318 (2011). [CrossRef] [PubMed]
26. D. N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey (Springer Berlin, 2005).
27. SNLO nonlinear optics code available from A. V. Smith, AS-Photonics, Albuquerque.
28. S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kärtner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5(8), 475–479 (2011). [CrossRef]
29. T. Eidam, J. Rothhardt, F. Stutzki, F. Jansen, S. Hädrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Fiber chirped-pulse amplification system emitting 3.8 GW peak power,” Opt. Express 19(1), 255–260 (2011). [CrossRef] [PubMed]
30. A. Klenke, E. Seise, S. Demmler, J. Rothhardt, S. Breitkopf, J. Limpert, and A. Tünnermann, “Coherently-combined two channel femtosecond fiber CPA system producing 3 mJ pulse energy,” Opt. Express 19(24), 24280–24285 (2011). [CrossRef] [PubMed]