Angularly-dispersed optical parametric amplification of optical pulses with one-octave bandwidth toward monocycle regime

We demonstrated experimentally the generation of 65-μJ, 5.8-fs optical pulses with an ultrabroad bandwidth (540 – 1000 nm) by the use of a double-pass angularly-dispersed non-collinear optical parametric amplifier. We also confirmed up to the 95-μJ output from the amplifier when seed pulses were not pre-compensated for. Furthermore, we confirmed that the broadband pump pulses brought in the broader gain bandwidth (from 520 to 1080 nm) than numerical estimation based on CW-pump approximation. To the best of our knowledge, this is the system with the broadest gain bandwidth. © 2008 Optical Society of America OCIS codes: (190.4970) Parametric oscillators and amplifiers; (320.1590) Chirping. References and links 1. A. Baltus̆ka, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch and F. Krausz, ”Attosecond control of electronic processes by intense light fields,” Nature (London) 421 611–615 (2003). 2. N. Ishii, L. Turi, V. S. Yakovlev, T. Fuji, F. Krausz, A. Baltus̆ka, 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). 3. 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 8168-8177 (2006). 4. J. A. Fülöp, Zs Major, A. Henig, S. Kruber, R. Weingartner, T. Clausnitzer, E.-B. Kley, A. Tünnermann, V. Pervak, A. Apolonski, J. Osterhoff, R. Hörlein, F. Krausz and S. Karsch, ”Short-pulse optical parametric chirped-pulse amplification for the generation of high-power few-cycle pulses,” New J, Phys. 9 438 (2007). 5. S. Adachi, H. Ishii, T. Kanai, N. Ishii, A. Kosuge and S. Watanabe, ”1.5 mJ, 6.4 fs parametric chirped-pulse amplification system at 1 kHz,” Opt. Lett. 32 2487-2489 (2007). 6. M. Schultze, E. Goulielmakis, M. Uiberacker, M. Hofstetter, J. Kim, D. Kim, F. Krausz and U. Kleineberg, ”Powerful 170-attosecond XUV pulses generated with few-cycle laser pulses and broadband multilayer optics,” New J. Phys. 9 243 (2007). 7. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. D. Silvestri and M. Nisoli, ”Isolated Single-Cycle Attosecond Pulses,” Science 314, 443–446 (2006). 8. Y. Oishi, M. Kaku, A. Suda, F. Kannari and K. Midorikawa, ”Generation of extreme ultraviolet continuum radiation driven by a sub-10-fs two-color field,” Opt. Express 14, 7230–7237 (2006). #101793 $15.00 USD Received 19 Sep 2008; revised 15 Oct 2008; accepted 18 Oct 2008; published 23 Oct 2008 (C) 2008 OSA 27 October 2008 / Vol. 16, No. 22 / OPTICS EXPRESS 18345 9. H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon and Z. Chang, ”Double Optical Gating of High-Order Harmonic Generation with Carrier-Envelope Phase Stabilized Lasers,” Phys. Rev. Lett. 100, 103906-4 (2008). 10. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz and U. Kleineberg, “Single-Cycle Nonlinear Optics,” Science, 320, 1614–1617 (2008). 11. J. J. Carrera, X. M. Tong and Shih-I Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A 74,023404-023407 (2006). 12. X. Song, Z. Zeng, Y. Fu, B. Cai, R. Li, Y. Cheng and Z. Xu “Quantum path control in few-optical-cycle regime,” Phys. Rev. A 76, 043830-043834 (2007). 13. V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz and A. Apolonski “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B 87, 5–12 (2007). 14. E. Matsubara, K. Yamane, T. Sekikawa and M. Yamashita, ”Generation of 2.6 fs optical pulses using inducedphase modulation in a gas-filled hollow fiber,” J. Opt. Soc. Am. B 24, 985–989 (2007). 15. K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita and A.Suguro, ”Optical pulse compression to 3.4fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258–2260 (2003). 16. M. Hirasawa, N. Nakagawa, K. Yamamoto, R. Morita, H. Shigekawa and M. Yamashita, ”Sensitivity improvement of spectral phase interferometry for direct electric-field reconstruction for the characterization of lowintensity femtosecond pulses,” Appl. Phys. B, 74 s225–s229 (2002). 17. A. Baltus̆ka, T. Fuji and T. Kobayashi, “Visible pulse compression to 4 fs by optical parametric amplification and programmable dispersion control,” Opt. Lett. 27, 306–308 (2002). 18. G. Arisholm, J. Biegert, P. Schlup, C. P. Hauri and U. Keller, “Ultra-broadband chirped-pulse optical parametric amplifier with angularly dispersed beams,” Opt. Express 12, 518–530 (2004). 19. L. Cardoso and G. Figueira, “Broadband amplification in non-linear crystals using controlled angular dispersion of signal beam,” Opt. Commun. 251, 405–414 (2005). 20. H. Liu, W. Zhao, Y. Yang, H. Wang, Y. Wang and G. Chen, ”Matching of both group-velocity and pulse-front for ultrabroadband three-wave-mixing with noncollinear angularly dispersed geometry,” Appl. Phys. B 82, 585–594 (2006). 21. K. Yamane, T. Kito, R. Morita and M. Yamashita, ”2.8-fs clean single transform-limited optical-pulse generation and characterization,” in Ultrafast Phenomena XIV, T. Kobayashi, T. Okada, T. Kobayashi, K. A. Nelson and S. D. Silvestri, eds, (Springer Berlin Heidelberg, 2005), pp. 13–15. 22. R. Danielius, A. Piskarskas, A. Stabinis, G. P. Banfi, P. Di Trapani and R. Righini ”Traveling-wave parametric generation of widely tunable, highly coherent femtosecond light pulses,” JOSA B 10, 2222–2232 (1993). 23. D. Eimerl, L. Davis, S. Velsko, E. K. Graham and A. Zalkin, “Optical, mechanical, and thermal properties of barium borate,” J. Appl. Phys. 62, 1968-1983 (1987) 24. K. Yamane, A. Iwasaki, T. Tanigawa, T. Sekikawa and M. Yamashita, ”Optical parametric amplification of optical pulses with a nearly one-octave bandwidth from a hollow fiber,” in Technical Digest of Conference on Lasers and Electro-Optics (CLEO), JThD1 (2007).


Introduction
Many research groups are now developing laser systems to generate extremely high-power, fewcycle pulses for high-field physics applications [1][2][3][4][5][6]. Several research groups have succeeded in the generation of isolated attosecond pulses utilizing few-cycle pulses generated by self phase modulation (SPM) in a noble-gas-filled hollow fiber [6], and utilizing multi-cycle pulses with a polarization gating technique [7]. In addition, other sophisticated techniques, such as two-color amplitude gating [8] and double optical gating [9] have been developed to generate ultrabroad XUV continuum spectra. However, in those cases, excitation sources with more than two optical cycles were employed and the durations of the generated XUV pulses were longer than 100 attoseconds. Recently, the generation of isolated sub-100-attosecond XUV pulses by the use of sub-4-fs, 300-μJ optical pulses from a hollow fiber without the above-mentioned various gating techniques has been reported [10]. This indicates that the high-power optical pulses in the monocycle regime are the most powerful candidate as a driver for the generation of shorter XUV pulses. This has been also predicted by a high-order harmonic generation theory where shorter isolated attosecond XUV pulses are generated efficiently within a half cycle of high-power, monocycle pump pulses [11,12].
However, for the generation of shorter pulses in the monocycle regime using only chirped mirrors, specially designed chirped mirrors with much broader bandwidth are required. But, ultrabroad-band chirped mirrors over the ultraviolet-visible-near-infrared region not only are difficult to fabricate but also have a low reflectivity (<∼ 90 percent) [13] (It seems that the mirrors are not used in pulse compression experiments as far as we know). Moreover, additional dispersive optics depending on the specific optical system are required for compensation of higher-order dispersion because chirped mirrors have fixed dispersion characteristics and are unsuitable for ad-hoc precise control of the dispersion. We have succeeded in generating 1.3-cycle, 2.6-fs optical pulses [14] by the use of SPM and induced phase modulation (IPM) in an argon-filled hollow fiber. The duration of the corresponding Fourier transform limited pulses was 2.5 fs, that is to say, the chirp of the generated pulses was almost completely compensated for by a feedback phase compensation system [15], which consisted of a M-SPIDER [16] (modified spectral phase interferometry for direct electric-field reconstruction) apparatus and a 4-f pulse shaper. However, the pulse energy (∼ 3.6 μJ/pulse) was too low for high field physics applications due to the low throughput of the 4-f pulse shaper.
Noncollinear optical parametric amplification (NOPA) has an ability to amplify broadband weak pulses and is considered to be a promising way to generate few-cycle high-power optical pulses, but its bandwidth is so narrow that only a fraction of the ultrabroad-band spectrum (460 -1060 nm) of the pulses we have generated [15] can be amplified. For example, its gain bandwidth is limited to ∼ 500 -∼ 800 nm for the pump wavelength of 393 nm [17]. However, it was recently predicted by some groups [18][19][20] that a much broader parametric gain will be obtained if incoming seed pulses are angularly dispersed so that their frequency components almost satisfy the phase-matching condition in the gain medium in the broader wavelength region. We call this technique angularly-dispersed noncollinear OPA (A-NOPA) after this.
In this paper, we report the first experimental demonstration of ultrabroad-band optical pulse amplification with an octave bandwidth by the use of A-NOPA. We chose the second harmonic (∼ 400 nm) of the output beam from a Ti:sapphire laser amplifier for pump pulses, not a Q-switched diode pumped solid state laser (DPSSL) which is generally used in an optical parametric chirped pulse amplification (OPCPA) system. The use of 400-nm pulses enables us to achieve a broader gain bandwidth. Moreover, synchronization between pump and seed pulses does not require additional low-jitter, high-speed electrical circuits.
Furthermore, we use relatively intense ultrabroad-band optical pulses generated in an argonfilled hollow fiber as a seed beam, because conventional white light continuum generated by SPM in a glass plate or a micro structure fiber is extremely weak and has a complicated spectral phase. Our hollow fiber technique does not need a high OPA gain so that we can suppress the superflueorescence in the gain medium. In addition, we have already succeeded in compensating for the chirp of the output from a hollow fiber almost completely [15,21]. The low throughput of our 4-f system which was used for the nonlinear chirp compensation [18] is not a problem because lost pulse energy will be easily recovered by an A-NOPA system. The A-NOPA system has the potential ability to generate precisely-phase-controlled, high-power optical pulses with an over-one-octave bandwidth.

Numerical calculation and design of A-NOPA system
First, we show numerically that an appropriately designed A-NOPA system has an over-oneoctave bandwidth, which was already shown in Ref. [18]. We also calculated numerically the phase matching angles as a function of the wavelength for a pump wavelength of 393 nm, in the plane-wave approximation with monochromatic and undepleted pump (see Fig. 1). Here, the nonlinear crystal is a type-I β -barium borate (BBO). As shown in Fig. 1(b), θ is the angle between the pump beam and the optic axis and α is the noncollinear angle between the pump In conventional NOPA, the almost flat region from ∼ 500 to ∼ 800 nm is usually used when θ = 31.7 • . On the other hand, when θ = 40 • , there is a region where the phase-matching angle increases almost linearly to the wavelength (the red solid curve in Fig. 1) [18]. Such a linearity can be easily achieved by using a diffraction grating and a lens (or a concave mirror) as shown in Fig. 1(a). The slope of such linear dependency is easily controlled by changing the distance between the grating and the lens. For example, the black solid curve shows calculated angular dispersion when the lens (a focusing length f of 100 mm) is located at the distance d of 204 mm from the diffraction grating (a groove density of 333 lines/mm). It is found that the curve almost agrees with the phase matching angle for θ = 40 • in the wavelength region from ∼ 550 to ∼ 1400 nm. Therefore, we can expect to achieve the sufficient gain in the region.
The gain profile which was numerically calculated under the same configuration is shown by a red solid curve in Fig. 2. Here, we take a pump intensity of 50 GW/cm 2 and a crystal length of 1 mm. For simplicity, we assumed that the lens refocuses the seed beam dispersed by the grating but each wavelength component of the seed has no divergence. We found that the A-NOPA has an ability to amplify the ultrabroad-band pulses with an octave-spanning spectrum and the gain bandwidth is about 1.5 times broader than that of the conventional one (a blue solid curve in Fig.2). The gain of the A-NOPA is lower than that of the conventional NOPA, but it is because the gain depends on effective nonlinear coefficient d eff [22], which is proportional to cos θ in the case of type-I BBO crystal [23]. It is not due to the configuration of the A-NOPA itself. Moreover, the pulse front of the seed beam almost matches with that of the pump in the A-NOPA configuration [18]. In our case, we numerically confirmed that the mismatch of these pulse fronts is less than several milliradian when the broadest gain bandwidth is obtained. Therefore, the pulse front tilt does not matter practically in our case.
The above simple configuration cannot be used for practical purposes. This is because we can not obtain the numerically calculated gain profile unless the divergence of each wavelength component is appropriately compensated. Figure 3 shows the practical schematic of the A-NOPA. The concave mirror CM2 (a focal length f 2 of 100 mm) and the diffraction grating (a groove density of 333 lines/mm) correspond to the lens and the grating in Fig. 1, respectively. The concave mirror CM1 (a focal length f 1 of 250 mm ) was used to reduce the beam size to f 2 / f 1 and to compensate for the beam divergence by CM2. The distance between CM1 and CM2 was set to f 1 + f 2 . The beam angularly-dispersed by these components, which goes through the gain medium (1-mm-thick type-I BBO crystal), is recombined by the symmetrically placed optical components (see Fig. 3) to get a single collimated beam [24]. We confirmed ultrabroad-band gain from 550-1000 nm (output pulse energy of 7.8 μJ) by preliminary experiments using this configuration.  Fig. 3. Schematic of angularly-dispersed NOPA (single pass geometry). CM1, CM2, CM3, CM4: silver-coated concave mirrors, FM1, FM2: silver-coated folding mirrors, GR1, GR2: silver-coated diffraction gratings Furthermore, to get higher pulse energy, we designed a new A-NOPA which enables twice the amplification. As shown in Fig. 4, the angularly-dispersed pulses were symmetrically reflected back by the use of the concave mirror CM3 ( a focal length f 3 of 250 mm) and folding mirrors when the optical path length between BBO crystal and CM3 and that between CM3 and FM3 were set to equal to f 3 . Therefore, the pulses were amplified again by the reflected pump pulses. In both configurations, the seed pulses were reflected twice by the diffraction gratings. The  Fig. 4. Schematic of angularly-dispersed NOPA (double pass geometry). CM1,CM2,CM3: silver-coated concave mirrors, FM1,FM2,FM3: silver-coated folding mirrors, FM4: dielectric mirror, GR: silver-coated diffraction grating loss in the A-NOPA system was mainly caused by diffraction gratings. Therefore, the new configuration shown in Fig. 4 is superior to the previous one in the point that it enables twice the amplification without increasing the loss.

Experiment and discussion
Our experimental setup is shown in Fig. 5. We let the split beam (300 μJ/pulse) of the output from a cryogenically-cooled Ti:sapphire laser amplifier system (Red dragon II, KMLabs inc., a pulse duration of 25 fs, a center wavelength of 786 nm, a repetition rate of 1 kHz) propagate in a hollow fiber (a length l of 370 mm, an inner diameter d of 0.1 mm) which was set in a chamber filled with 3.0-atm argon gas.  Ultrabroad-band pulses generated by SPM in the noble gas were guided into a grating-based 4-f pulse shaper with a liquid crystal spatial light modulator (SLM, a pixel number of 648, a transmission range of 400 -1300 nm, a pixel size of 102 μm) [14,15,21], and subsequently into the A-NOPA system as down-chirped seed pulses (a pulse energy of ∼0.5 μJ, a spectrum from 500 to 1100 nm, a pulse duration of ∼ 300 fs), as shown in Fig. 4. The input pulses were spatially and temporally overlapped with pump pulses (a center wavelength of 393 nm, a pulse energy of 1.2 mJ/pulse, a pulse duration of ∼ 400 fs) which were generated by frequencydoubling of the output (pulse energy of 2.8 mJ/pulse) from the Ti:sapphire laser amplifier using a 0.2-mm-thick type-I BBO crystal. The 393-nm pump pulses were temporally stretched by a 20-mm-thick fused silica plate (FS1) to avoid spontaneous optical parametric generation in the amplifying medium (type-I BBO , a thickness of 1 mm, θ = 40 degrees). The diameter of the pump beam on the BBO crystal was ∼ 2 mm, which was almost same as the seed. The intensity of the up-chirped pump beam was ∼ 75 GW/cm 2 . The seed pulses were negatively chirped by the 4-f pulse shaper before optical parametric chirped pulse amplification, and the chirp of the amplified pulses was compensated for by a 5-mm thick fused silica plate. Then, the chirp-compensated pulses were guided into the M-SPIDER apparatus for the measurement of the spectral phase. The residual chirp was further compensated for by the 4-f pulse shaper. We confirmed an ultrabroad-band amplification with nearly one-octave bandwidth ranging from ∼550 to ∼1000 nm, as shown in Fig. 6. The sensitivity of CCD was calibrated by using a calibrated light source. We found that the spectral phase is almost flattened, but higher order dispersion still remains. This is because the modulation of the spectrum made reconstruction of the spectral phase by SPIDER difficult and therefore, we could not compensate for the residual chirp with high accuracy. The output pulse energy, which was reduced by about 50 percent mainly due to diffraction losses by the gratings, was 65 μJ/pulse. Moreover, it should be noted that we also could boost pulse energy up to 95 μJ/pulse when the LC-SLM was not activated. Figure 7 shows the reconstructed temporal profile of amplified pulses. We found that the temporal profile of amplified pulses has little sub pulses and the duration of the main pulse is 5.8 fs, while the duration of the corresponding Fourier transform limited pulses is 4.0 fs.
Finally, we investigated the possibility of the further enlargement of the gain bandwidth by a broadband pumping beam. Figure 8 shows the calculated curves of gain profiles for different wavelengths of pump beams using the same configuration. We found that gain profile drastically changes with a slight shift in the pumping wavelength: the shorter wavelength shift extends both edges of the gain profile. We produced a 10-nm-FWHM (Full Width of Half Maximum) bandwidth pumping beam using a thin BBO crystal (a thickness of 200 μm). If both the seed and pump pulses are appropriately chirped, it can be expected that an enlarged gain profile will be obtained in ∼ 520 -∼ 1500 nm. In fact, we confirmed ultrabroad-band amplification in 520 -1080 nm by using the 10-nm bandwidth pump pulses and applying the phase modulation to the seed pulses by the pulse shaper in order to obtain the broader gain bandwidth (see Fig.  9). To the best of our knowledge, this is the NOPA system which has the broadest gain bandwidth. However, further optimization is required to achieve a good balance between broadband amplification and pulse compression.

Conclusion
It was demonstrated experimentally that A-NOPA is an attractive way to obtain octave-spanning broadband (520-1080 nm) pulses with high pulse energy in the monocycle region. We also could boost the seed pulses up to 95 μJ/pulse, and confirmed the generation of 5.8-fs, 65 μJ/pulse by using a pulse shaper.
However, in order to obtain higher-power shorter optical pulses, there are some problems to be solved in our present system. The first is the intensity modulation in the amplified spectrum, and the second is the optical damage on the diffraction grating. These problems are not caused  by the intrinsic limitation of the A-NOPA but is due to the design of the optical system. We are considering the following solutions.
As for the former, the modulation is due to the SLM, in addition to intrinsic characteristics of SPM. The negative GDD added by SLM for chirped pulse amplification was about -550 fs 2 . This value slightly exceeds typical limitation (-400 fs 2 ) for our 4-f system, which depends on "load per pixel" [21]. Too much load not only decreases the accuracy of pulse compression, but also causes the intensity modulation by diffraction on SLM. This problem can be solved by the use of additional dispersive optics such as a prism pair and chirped mirrors.
The latter arises from the fact that the beam size (diameter of ∼ 2 mm) on the diffraction grating is approximately the same as that on BBO crystal in the configuration shown in Fig. 4. Actually, the grating we used could not bear amplified pulses with more than 95 μJ/pulse. We are now developing an improved A-NOPA whose damage threshold is enhanced more than 5 times. Several-hundred micro-joule-level pulses in the monocycle regime will be generated in the near future.
In principle, the A-NOPA has the disadvantages that the gain is lower than the conventional one and the output pulse energy is partially lost due to the diffraction loss by a grating. However, at present, only A-NOPA can amplify the optical pulses with octave-spanning bandwidth in the monocycle regime. The A-NOPA will become the very promising candidate as a driver for application such as the generation of shorter attosecond pulses.