Abstract

A method of temporally compressing picosecond pulses is proposed. To increase the spectral broadening, two picosecond pulses at different central wavelengths are overlapped spatiotemporally to induce a modulation on the intensity envelope, thus leading to a high temporal intensity gradient. The combined pulse is then coupled into a gas-filled hollow-core fiber (HCF) to broaden the spectrum through nonlinear propagation. After that the pulse can be compressed by chirp compensation. This method is demonstrated numerically with two 1-ps/5-mJ pulses centered at 1053- and 1064-nm, respectively, which are coupled into a 250-μm-inner-diameter, 1-m-long HCF filled with 5-bar neon. After nonlinear propagation, the spectrum of the combined pulse is broadened significantly compared with the sum of the broadened spectra of a single 1-ps/10-mJ pulse centered at 1053- and 1064-nm. Under proper initial conditions, the pulse can be compressed down to ~16-fs. The influences of the energy ratio, time delay and wavelength gap between two input pulses, as well as the energy scaling are also discussed. These results show an alternative way to obtain ultrashort laser pulses from the picosecond laser technology, which can deliver both high peak power and high average power, and thus will benefit relevant researches in high-field laser physics.

© 2017 Optical Society of America

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2017 (1)

2016 (4)

2015 (5)

J. P. Negel, A. Loescher, A. Voss, D. Bauer, D. Sutter, A. Killi, M. A. Ahmed, and T. Graf, “Ultrafast thin-disk multipass laser amplifier delivering 1.4 kW (4.7 mJ, 1030 nm) average power converted to 820 W at 515 nm and 234 W at 343 nm,” Opt. Express 23(16), 21064–21077 (2015).
[PubMed]

F. Emaury, A. Diebold, C. J. Saraceno, and U. Keller, “Compact extreme ultraviolet source at megahertz pulse repetition rate with a low-noise ultrafast thin-disk laser oscillator,” Optica 2(11), 980 (2015).

S. Hädrich, M. Krebs, A. Hoffmann, A. Klenke, J. Rothhardt, J. Limpert, and A. Tünnermann, “Exploring new avenues in high repetition rate table-top coherent extreme ultraviolet sources,” Light Sci. Appl. 4(8), e320 (2015).

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).

A. Antikainen and G. P. Agrawal, “Dual-pump frequency comb generation in normally dispersive optical fibers,” J. Opt. Soc. Am. B 32(8), 1705–1711 (2015).

2014 (3)

2013 (1)

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
[PubMed]

2011 (1)

Y. Liu, X. Liu, Y. Deng, C. Wu, H. Jiang, and Q. Gong, “Selective steering of molecular multiple dissociative channels with strong few-cycle laser pulses,” Phys. Rev. Lett. 106(7), 073004 (2011).
[PubMed]

2010 (1)

2009 (1)

F. Krausz and M. Ivanov, “Attosecond physic,” Rev. Mod. Phys. 81(1), 163–234 (2009).

2008 (1)

J. Liu, X. W. Chen, R. W. Li, and T. Kobayashi, “Polarization-dependent pulse compression in an argon-filled cell through filamentation,” Laser Phys. Lett. 5(1), 45–47 (2008).

2007 (2)

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

M. Nurhuda, A. Suda, M. Kaku, and K. Midorikawa, “Optimization of hollow fiber pulse compression using pressure gradient,” Appl. Phys. B 89(2), 209–215 (2007).

2006 (1)

2005 (2)

2004 (3)

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).

C. G. Geddes, C. S. Toth, J. Van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature 431(7008), 538–541 (2004).
[PubMed]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3 Pt 2), 036604 (2004).
[PubMed]

2001 (1)

1998 (1)

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, “Generation of monocycle-like optical pulses using induced-phase modulation between two-color femtosecond pulses with carrier phase locking,” IEEE J. Quantum Electron. 34, 2145–2149 (1998).

1997 (1)

1996 (1)

M. Nisoli, S. D. Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68(20), 2793–2795 (1996).

1988 (1)

R. R. Alfano and P. P. Ho, “Self-, cross-, and induced-phase modulations of ultrashort laser pulse propagation,” IEEE J. Quantum Electron. 24, 351–364 (1988).

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

1984 (1)

1964 (1)

E. A. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964).

Agrawal, G. P.

Ahmed, M. A.

Alfano, R. R.

R. R. Alfano and P. P. Ho, “Self-, cross-, and induced-phase modulations of ultrashort laser pulse propagation,” IEEE J. Quantum Electron. 24, 351–364 (1988).

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

Anis, H.

Antikainen, A.

Apolonski, A.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

Arisholm, G.

Bauer, D.

Beier, F.

Benabid, F.

Biegert, J.

C. Hauri, A. Guandalini, P. Eckle, W. Kornelis, J. Biegert, and U. Keller, “Generation of intense few-cycle laser pulses through filamentation - parameter dependence,” Opt. Express 13(19), 7541–7547 (2005).
[PubMed]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).

Bock, V.

Brömmel, D.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
[PubMed]

Brons, J.

Bruhwiler, D.

C. G. Geddes, C. S. Toth, J. Van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature 431(7008), 538–541 (2004).
[PubMed]

Cary, J.

C. G. Geddes, C. S. Toth, J. Van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature 431(7008), 538–541 (2004).
[PubMed]

Cavalieri, A. L.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

Cerullo, G.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).

Chen, B. H.

Chen, H. Y.

Chen, M. C.

Chen, X. W.

J. Liu, X. W. Chen, R. W. Li, and T. Kobayashi, “Polarization-dependent pulse compression in an argon-filled cell through filamentation,” Laser Phys. Lett. 5(1), 45–47 (2008).

Cheng, Y. C.

Cirmi, G.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).

Corkum, P. B.

Cormier, E.

Couairon, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).

De Silvestri, S.

Debord, B.

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

Demmler, S.

Deng, Y.

Y. Liu, X. Liu, Y. Deng, C. Wu, H. Jiang, and Q. Gong, “Selective steering of molecular multiple dissociative channels with strong few-cycle laser pulses,” Phys. Rev. Lett. 106(7), 073004 (2011).
[PubMed]

Diebold, A.

Dillner, U.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
[PubMed]

Drozdy, A.

Eberhardt, R.

Eckle, P.

Eidam, T.

Emaury, F.

Esarey, E.

C. G. Geddes, C. S. Toth, J. Van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature 431(7008), 538–541 (2004).
[PubMed]

Fang, S.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).

Ferencz, K.

Fieß, M.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

Gabler, T.

Geddes, C. G.

C. G. Geddes, C. S. Toth, J. Van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature 431(7008), 538–541 (2004).
[PubMed]

Gèrôme, F.

Ghosh, D.

Gibbon, P.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
[PubMed]

Gong, Q.

Y. Liu, X. Liu, Y. Deng, C. Wu, H. Jiang, and Q. Gong, “Selective steering of molecular multiple dissociative channels with strong few-cycle laser pulses,” Phys. Rev. Lett. 106(7), 073004 (2011).
[PubMed]

Gopal, A.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
[PubMed]

Gotschall, T.

Gottschall, T.

Goulielmakis, E.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

Graf, T.

Guandalini, A.

Hädrich, S.

Hauri, C.

Hauri, C. P.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).

Heinrich, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).

Helbing, F. W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).

Helml, W.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

Herzer, S.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
[PubMed]

Ho, P. P.

R. R. Alfano and P. P. Ho, “Self-, cross-, and induced-phase modulations of ultrashort laser pulse propagation,” IEEE J. Quantum Electron. 24, 351–364 (1988).

Hoffmann, A.

S. Hädrich, M. Krebs, A. Hoffmann, A. Klenke, J. Rothhardt, J. Limpert, and A. Tünnermann, “Exploring new avenues in high repetition rate table-top coherent extreme ultraviolet sources,” Light Sci. Appl. 4(8), e320 (2015).

J. Rothhardt, S. Hädrich, A. Klenke, S. Demmler, A. Hoffmann, T. Gotschall, T. Eidam, M. Krebs, J. Limpert, and A. Tünnermann, “53 W average power few-cycle fiber laser system generating soft x rays up to the water window,” Opt. Lett. 39(17), 5224–5227 (2014).
[PubMed]

Hoffmann, H. D.

Hong, K. H.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).

Horvath, B.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

Hsu, C. C.

Huang, S. W.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).

Ivanov, M.

F. Krausz and M. Ivanov, “Attosecond physic,” Rev. Mod. Phys. 81(1), 163–234 (2009).

Ivanov, M. Y.

A. Scrinzi, M. Y. Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B 39(1), R1–R37 (2005).

Jetschke, S.

Jiang, H.

Y. Liu, X. Liu, Y. Deng, C. Wu, H. Jiang, and Q. Gong, “Selective steering of molecular multiple dissociative channels with strong few-cycle laser pulses,” Phys. Rev. Lett. 106(7), 073004 (2011).
[PubMed]

Jójárt, P.

Kaku, M.

M. Nurhuda, A. Suda, M. Kaku, and K. Midorikawa, “Optimization of hollow fiber pulse compression using pressure gradient,” Appl. Phys. B 89(2), 209–215 (2007).

Karmakar, A.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
[PubMed]

Kärtner, F. X.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).

Keller, U.

Kienberger, R.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

A. Scrinzi, M. Y. Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B 39(1), R1–R37 (2005).

Kienel, M.

Killi, A.

Klas, R.

Klenke, A.

Kobayashi, T.

J. Liu, X. W. Chen, R. W. Li, and T. Kobayashi, “Polarization-dependent pulse compression in an argon-filled cell through filamentation,” Laser Phys. Lett. 5(1), 45–47 (2008).

Kolesik, M.

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3 Pt 2), 036604 (2004).
[PubMed]

Kornelis, W.

C. Hauri, A. Guandalini, P. Eckle, W. Kornelis, J. Biegert, and U. Keller, “Generation of intense few-cycle laser pulses through filamentation - parameter dependence,” Opt. Express 13(19), 7541–7547 (2005).
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C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).

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M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191 (1986).

Krausz, F.

F. Krausz and M. Ivanov, “Attosecond physic,” Rev. Mod. Phys. 81(1), 163–234 (2009).

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22(8), 522–524 (1997).
[PubMed]

Krebs, M.

S. Hädrich, M. Krebs, A. Hoffmann, A. Klenke, J. Rothhardt, J. Limpert, and A. Tünnermann, “Exploring new avenues in high repetition rate table-top coherent extreme ultraviolet sources,” Light Sci. Appl. 4(8), e320 (2015).

J. Rothhardt, S. Hädrich, A. Klenke, S. Demmler, A. Hoffmann, T. Gotschall, T. Eidam, M. Krebs, J. Limpert, and A. Tünnermann, “53 W average power few-cycle fiber laser system generating soft x rays up to the water window,” Opt. Lett. 39(17), 5224–5227 (2014).
[PubMed]

Kung, A. H.

Leemans, W. P.

C. G. Geddes, C. S. Toth, J. Van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature 431(7008), 538–541 (2004).
[PubMed]

Li, R. W.

J. Liu, X. W. Chen, R. W. Li, and T. Kobayashi, “Polarization-dependent pulse compression in an argon-filled cell through filamentation,” Laser Phys. Lett. 5(1), 45–47 (2008).

Liem, A.

Limpert, J.

Liu, J.

J. Liu, X. W. Chen, R. W. Li, and T. Kobayashi, “Polarization-dependent pulse compression in an argon-filled cell through filamentation,” Laser Phys. Lett. 5(1), 45–47 (2008).

Liu, X.

Y. Liu, X. Liu, Y. Deng, C. Wu, H. Jiang, and Q. Gong, “Selective steering of molecular multiple dissociative channels with strong few-cycle laser pulses,” Phys. Rev. Lett. 106(7), 073004 (2011).
[PubMed]

Liu, Y.

Y. Liu, X. Liu, Y. Deng, C. Wu, H. Jiang, and Q. Gong, “Selective steering of molecular multiple dissociative channels with strong few-cycle laser pulses,” Phys. Rev. Lett. 106(7), 073004 (2011).
[PubMed]

Loescher, A.

Lu, C. H.

Mans, T.

Mansour, B. F.

Manzoni, C.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).

Marcatili, E. A.

E. A. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964).

May, T.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
[PubMed]

Meyer, H.-G.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
[PubMed]

Midorikawa, K.

M. Nurhuda, A. Suda, M. Kaku, and K. Midorikawa, “Optimization of hollow fiber pulse compression using pressure gradient,” Appl. Phys. B 89(2), 209–215 (2007).

Moloney, J. V.

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3 Pt 2), 036604 (2004).
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Morita, R.

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, “Generation of monocycle-like optical pulses using induced-phase modulation between two-color femtosecond pulses with carrier phase locking,” IEEE J. Quantum Electron. 34, 2145–2149 (1998).

Moses, J.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).

Mücke, O. D.

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).

Müller, H.-R.

Müller, M.

Mysyrowicz, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).

Negel, J. P.

Nieter, C.

C. G. Geddes, C. S. Toth, J. Van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature 431(7008), 538–541 (2004).
[PubMed]

Nisoli, M.

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22(8), 522–524 (1997).
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M. Nisoli, S. D. Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68(20), 2793–2795 (1996).

Nurhuda, M.

M. Nurhuda, A. Suda, M. Kaku, and K. Midorikawa, “Optimization of hollow fiber pulse compression using pressure gradient,” Appl. Phys. B 89(2), 209–215 (2007).

Osvay, K.

Paulus, G. G.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
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Pervak, V.

M. Seidel, G. Arisholm, J. Brons, V. Pervak, and O. Pronin, “All solid-state spectral broadening: an average and peak power scalable method for compression of ultrashort pulses,” Opt. Express 24(9), 9412–9428 (2016).
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A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

Plötner, M.

Poprawe, R.

Pronin, O.

Reinhard, A.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
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Rothhardt, J.

Russbueldt, P.

Saraceno, C. J.

Sartania, S.

Sartorius, T.

Schmeltzer, R. A.

E. A. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964).

Schmidt, A.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
[PubMed]

Schreiber, T.

Schroeder, C. B.

C. G. Geddes, C. S. Toth, J. Van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature 431(7008), 538–541 (2004).
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Schulte, J.

Schultze, M.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

Schultze, T.

Scrinzi, A.

A. Scrinzi, M. Y. Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B 39(1), R1–R37 (2005).

Seidel, M.

Shank, C. V.

Shestaev, E.

Shigekawa, H.

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, “Generation of monocycle-like optical pulses using induced-phase modulation between two-color femtosecond pulses with carrier phase locking,” IEEE J. Quantum Electron. 34, 2145–2149 (1998).

Silvestri, S. D.

M. Nisoli, S. D. Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68(20), 2793–2795 (1996).

Singh, P.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
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Sone, H.

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, “Generation of monocycle-like optical pulses using induced-phase modulation between two-color femtosecond pulses with carrier phase locking,” IEEE J. Quantum Electron. 34, 2145–2149 (1998).

Spielmann, C.

Stolen, R. H.

Suda, A.

M. Nurhuda, A. Suda, M. Kaku, and K. Midorikawa, “Optimization of hollow fiber pulse compression using pressure gradient,” Appl. Phys. B 89(2), 209–215 (2007).

Südmeyer, T.

Sutter, D.

Svelto, O.

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22(8), 522–524 (1997).
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M. Nisoli, S. D. Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68(20), 2793–2795 (1996).

Szipöcs, R.

Tomlinson, W. J.

Toth, C. S.

C. G. Geddes, C. S. Toth, J. Van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature 431(7008), 538–541 (2004).
[PubMed]

Tsou, Y. J.

Tünnermann, A.

M. Plötner, V. Bock, T. Schultze, F. Beier, T. Schreiber, R. Eberhardt, and A. Tünnermann, “High power sub-ps pulse generation by compression of a frequency comb obtained by a nonlinear broadened two colored seed,” Opt. Express 25(14), 16476–16483 (2017).
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M. Müller, M. Kienel, A. Klenke, T. Gottschall, E. Shestaev, M. Plötner, J. Limpert, and A. Tünnermann, “1 kW 1 mJ eight-channel ultrafast fiber laser,” Opt. Lett. 41(15), 3439–3442 (2016).
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S. Hädrich, M. Kienel, M. Müller, A. Klenke, J. Rothhardt, R. Klas, T. Gottschall, T. Eidam, A. Drozdy, P. Jójárt, Z. Várallyay, E. Cormier, K. Osvay, A. Tünnermann, and J. Limpert, “Energetic sub-2-cycle laser with 216 W average power,” Opt. Lett. 41(18), 4332–4335 (2016).
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S. Hädrich, M. Krebs, A. Hoffmann, A. Klenke, J. Rothhardt, J. Limpert, and A. Tünnermann, “Exploring new avenues in high repetition rate table-top coherent extreme ultraviolet sources,” Light Sci. Appl. 4(8), e320 (2015).

J. Rothhardt, S. Hädrich, A. Klenke, S. Demmler, A. Hoffmann, T. Gotschall, T. Eidam, M. Krebs, J. Limpert, and A. Tünnermann, “53 W average power few-cycle fiber laser system generating soft x rays up to the water window,” Opt. Lett. 39(17), 5224–5227 (2014).
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J. Limpert, A. Liem, T. Gabler, H. Zellmer, A. Tünnermann, S. Unger, S. Jetschke, and H.-R. Müller, “High-average-power picosecond Yb-doped fiber amplifier,” Opt. Lett. 26(23), 1849–1851 (2001).
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Uiberacker, M.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

Unger, S.

Van Tilborg, J.

C. G. Geddes, C. S. Toth, J. Van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature 431(7008), 538–541 (2004).
[PubMed]

Várallyay, Z.

Veisz, L.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

Vernaleken, A.

Villeneuve, D. M.

Voss, A.

Weitenberg, J.

Wu, C.

Y. Liu, X. Liu, Y. Deng, C. Wu, H. Jiang, and Q. Gong, “Selective steering of molecular multiple dissociative channels with strong few-cycle laser pulses,” Phys. Rev. Lett. 106(7), 073004 (2011).
[PubMed]

Yakovlev, V. S.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

Yamashita, M.

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, “Generation of monocycle-like optical pulses using induced-phase modulation between two-color femtosecond pulses with carrier phase locking,” IEEE J. Quantum Electron. 34, 2145–2149 (1998).

Yang, S. D.

Zeidler, D.

Zellmer, H.

Ziegler, W.

A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H.-G. Meyer, and G. G. Paulus, “Observation of Gigawatt-Class THz Pulses from a Compact Laser-Driven Particle Accelerator,” Phys. Rev. Lett. 111(7), 074802 (2013).
[PubMed]

Appl. Phys. B (2)

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004).

M. Nurhuda, A. Suda, M. Kaku, and K. Midorikawa, “Optimization of hollow fiber pulse compression using pressure gradient,” Appl. Phys. B 89(2), 209–215 (2007).

Appl. Phys. Lett. (1)

M. Nisoli, S. D. Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68(20), 2793–2795 (1996).

Bell Syst. Tech. J. (1)

E. A. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43(4), 1783–1809 (1964).

IEEE J. Quantum Electron. (2)

R. R. Alfano and P. P. Ho, “Self-, cross-, and induced-phase modulations of ultrashort laser pulse propagation,” IEEE J. Quantum Electron. 24, 351–364 (1988).

M. Yamashita, H. Sone, R. Morita, and H. Shigekawa, “Generation of monocycle-like optical pulses using induced-phase modulation between two-color femtosecond pulses with carrier phase locking,” IEEE J. Quantum Electron. 34, 2145–2149 (1998).

J. Opt. Soc. Am. B (2)

J. Phys. B (1)

A. Scrinzi, M. Y. Ivanov, R. Kienberger, and D. M. Villeneuve, “Attosecond physics,” J. Phys. B 39(1), R1–R37 (2005).

Laser Photonics Rev. (1)

C. Manzoni, O. D. Mücke, G. Cirmi, S. Fang, J. Moses, S. W. Huang, K. H. Hong, G. Cerullo, and F. X. Kärtner, “Coherent pulse synthesis: towards sub-cycle optical waveforms,” Laser Photonics Rev. 9(2), 129–171 (2015).

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J. Liu, X. W. Chen, R. W. Li, and T. Kobayashi, “Polarization-dependent pulse compression in an argon-filled cell through filamentation,” Laser Phys. Lett. 5(1), 45–47 (2008).

Light Sci. Appl. (1)

S. Hädrich, M. Krebs, A. Hoffmann, A. Klenke, J. Rothhardt, J. Limpert, and A. Tünnermann, “Exploring new avenues in high repetition rate table-top coherent extreme ultraviolet sources,” Light Sci. Appl. 4(8), e320 (2015).

Nature (1)

C. G. Geddes, C. S. Toth, J. Van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature 431(7008), 538–541 (2004).
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A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9(7), 242 (2007).

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Opt. Lett. (9)

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22(8), 522–524 (1997).
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J. Schulte, T. Sartorius, J. Weitenberg, A. Vernaleken, and P. Russbueldt, “Nonlinear pulse compression in a multi-pass cell,” Opt. Lett. 41(19), 4511–4514 (2016).
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J. Rothhardt, S. Hädrich, A. Klenke, S. Demmler, A. Hoffmann, T. Gotschall, T. Eidam, M. Krebs, J. Limpert, and A. Tünnermann, “53 W average power few-cycle fiber laser system generating soft x rays up to the water window,” Opt. Lett. 39(17), 5224–5227 (2014).
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S. Hädrich, M. Kienel, M. Müller, A. Klenke, J. Rothhardt, R. Klas, T. Gottschall, T. Eidam, A. Drozdy, P. Jójárt, Z. Várallyay, E. Cormier, K. Osvay, A. Tünnermann, and J. Limpert, “Energetic sub-2-cycle laser with 216 W average power,” Opt. Lett. 41(18), 4332–4335 (2016).
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B. F. Mansour, H. Anis, D. Zeidler, P. B. Corkum, and D. M. Villeneuve, “Generation of 11 fs pulses by using hollow-core gas-filled fibers at a 100 kHz repetition rate,” Opt. Lett. 31(21), 3185–3187 (2006).
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F. Emaury, C. J. Saraceno, B. Debord, D. Ghosh, A. Diebold, F. Gèrôme, T. Südmeyer, F. Benabid, and U. Keller, “Efficient spectral broadening in the 100-W average power regime using gas-filled kagome HC-PCF and pulse compression,” Opt. Lett. 39(24), 6843–6846 (2014).
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J. Limpert, A. Liem, T. Gabler, H. Zellmer, A. Tünnermann, S. Unger, S. Jetschke, and H.-R. Müller, “High-average-power picosecond Yb-doped fiber amplifier,” Opt. Lett. 26(23), 1849–1851 (2001).
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M. Müller, M. Kienel, A. Klenke, T. Gottschall, E. Shestaev, M. Plötner, J. Limpert, and A. Tünnermann, “1 kW 1 mJ eight-channel ultrafast fiber laser,” Opt. Lett. 41(15), 3439–3442 (2016).
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P. Russbueldt, T. Mans, J. Weitenberg, H. D. Hoffmann, and R. Poprawe, “Compact diode-pumped 1.1 kW Yb:YAG Innoslab femtosecond amplifier,” Opt. Lett. 35(24), 4169–4171 (2010).
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Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

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Y. Liu, X. Liu, Y. Deng, C. Wu, H. Jiang, and Q. Gong, “Selective steering of molecular multiple dissociative channels with strong few-cycle laser pulses,” Phys. Rev. Lett. 106(7), 073004 (2011).
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Sov. Phys. JETP (1)

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G. P. Agrawal, “Ultrashort Pulse Propagation in Nonlinear Dispersive Fibers. In The Supercontinuum Laser Source (ed. R. R. Alfano,) 2nd ed,” (Springer).

https://refractiveindex.info/

C. Wandt, S. Klingebiel, M. Schultze, S. Prinz, C. Y. Teisset, S. Stark, C. Grebing, M. Häfner, R. Bessing, T. Herzig, A. Budnicki, D. Sutter, K. Michel, T. Nubbemeyer, F. Krausz, and T. Metzger, “1 kW Ultrafast Thin-Disk Amplifier System,” CLEO: Science and Innovations. Optical Society of America (2017).

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Figures (8)

Fig. 1
Fig. 1 Temporal intensity profiles of the combination of two pulses centered at 1053-nm and a varying wavelength.
Fig. 2
Fig. 2 Spectral intensity distributions during propagation for (a) a single pulse centered at 1053-nm, (b) a single pulse centered at 1064-nm, and (c) two pulses centered at 1053- and 1064-nm. (d) Output-pulse spectral intensity profiles for these three kinds of initial pulses.
Fig. 3
Fig. 3 Propagation results of the combined pulse. (a) Evolutions of normalized total energies of the combined pulse (red-dotted line) and different fiber modes (solid lines with various colors represent different fiber mode orders m of Eq. (1)) during propagation; (b) transverse energy distributions; (c) evolutions of normalized total temporal intensity during propagation; (d) spatiospectral distribution of the output combined spectrum.
Fig. 4
Fig. 4 (a) Total output-pulse temporal intensity profiles versus compensated GDDs; (b) spatiotemporal distribution of the combined pulse after compression; (c) temporal intensity and phase profiles of the compressed pulse.
Fig. 5
Fig. 5 Total output-pulse intensity profiles in (a, c) time and (b, d) frequency domains for the combined pulse with optimal chirp compensation through neon gas-filled HCFs at different gas pressure: (a, b) 2-bar and (c, d) 6-bar, and the red-dash curve represents initial-pulse spectral profiles.
Fig. 6
Fig. 6 (a)-(c) Total pulse temporal intensity profiles and (d)-(f) spectral intensity distributions along the fiber-radial direction for two pulses with (a, d) 5/5, (b, e) 7/3, and (c, f) 9/1 initial energy ratios at 1053- and 1064-nm central wavelengths.
Fig. 7
Fig. 7 (a) Combined temporal intensity profiles of two pulses at 1053-nm and a varying central wavelength. (b)-(e) Total pulse intensity profiles in time and frequency domains for pulses at different types of central wavelengths: (b, c) 1053- and 1060-nm, (d, e) 1053- and 1030-nm.
Fig. 8
Fig. 8 (a) Evolutions of normalized total energies during propagation for two 1-ps/4-mJ pulses in HCFs filled with neon at 7 bar, two 5-mJ pulses at 5 bar, and two 6-mJ pulses at 4 bar, respectively. (b, c) Total output-pulse temporal intensity profiles for two 4-mJ pulses at 7 bar, and two 6-mJ pulses at 4 bar with optimal chirp compensation. (d)-(g) Temporal intensity distributions during propagation, and spectral intensity distributions along the fiber-radial direction: (d, e) two 4-mJ pulses at 7 bar, and (d, e) two 6-mJ pulses at 4 bar.

Equations (4)

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z U m ( ω , z ) = α m 2 U m + i( β m ω v g ) U m + ω c 2 β m ( ω ) 2 a 2 0 1 r d r J 0 2 ( u m r ) e s × 0 a J 0 ( u m r / a ) [ i ω P ( r , ω ) ε 0 j ( r , ω ) ε 0 ] r d r
E ( x , y , z , t ) = 2 Re { F F T 1 [ m U m ( ω , z ) × J 0 ( u m r / a ) ] } ,
t ρ = W ( I ) ( ρ nt ρ ) + σ I ρ / U i
E ( r , t , z = 0 ) = I 1 exp ( t 2 2 T 1 2 r 2 w 1 2 ) exp ( i ω 1 t ) + I 2 exp ( t 2 2 T 2 2 r 2 w 2 2 ) exp ( i ω 2 t ) ,

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