Abstract

In this paper the results of the theoretical and experimental study of spatiotemporal distortions emerging in noncollinear optical parametric chirped-pulse amplifiers are presented. In a noncollinear parametric amplifier, when the pulse fronts of the pump and signal are not matched, the signal pulse becomes tilted and, aside from angular dispersion, has a spatial chirp. The expressions relating the magnitudes of the acquired spatial chirp and angular dispersion to the temporal chirp of the signal pulse are derived. It is shown that the magnitudes of the induced spatial chirp and angular dispersion decrease at different rates with the increase of the signal pulse temporal chirp and, for the large temporal chirp, the spatial chirp mainly contributes to the pulse-front tilt of the signal, whereas the induced signal pulse tilt is independent of the signal pulse temporal chirp, but is always smaller than the tilt of the pump pulse.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 437–440 (1992).
    [CrossRef]
  4. G. Cerullo, M. Nisoli, S. Stagira, and S. D. Silvestri, “Sub-8-fs pulses from an ultrabroadband optical parametric amplifier in the visible,” Opt. Lett. 23, 1283–1285 (1998).
    [CrossRef]
  5. T. Kobayashi and A. Shirakawa, “Tunable visible and near-infrared pulse generator in a 5 fs regime,” Appl. Phys. B 70, S239–S246 (2000).
    [CrossRef]
  6. A. Baltuška, 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).
    [CrossRef]
  7. S. Witte, R. T. 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).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. 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, 2459–2461 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  16. P. Tzankov, J. Zheng, M. Mero, D. Polli, C. Manzoni, and G. Cerullo, “300 μJ noncollinear optical parametric amplifier in the visible at 1 kHz repetition rate,” Opt. Lett. 31, 3629–3631(2006).
    [CrossRef] [PubMed]
  17. A. Shirakawa, I. Sakane, and T. Kobayashi, “Pulse-front-matched optical parametric amplification for sub-10-fs pulse generation tunable in the visible and near infrared,” Opt. Lett. 23, 1292–1294 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  23. V. Pyragaite, A. Stabinis, R. Butkus, R. Antipenkov, and A. Varanavicius, “Parametric amplification of chirped optical pulses under pump depletion,” Opt. Commun. 283, 1144–1151(2010).
    [CrossRef]
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    [CrossRef]
  26. J. Bromage, C. Dorrer, and J. D. Zuegel, “Angular-dispersion-induced spatiotemporal aberrations in noncollinear optical parametric amplifiers,” Opt. Lett. 35, 2251–2253 (2010).
    [CrossRef] [PubMed]
  27. K. Kato, “Second-harmonic generation to 2048 Å in β-BaB2O4,” IEEE J. Quantum Electron. 22, 1013–1014 (1986).
    [CrossRef]
  28. R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
    [CrossRef]
  29. R. Antipenkov, A. Varanavičius, A. Zaukevičius, and A. P. Piskarskas, “Femtosecond Yb:KGW MOPA driven broadband NOPA as a frontend for TW few-cycle pulse systems,” Opt. Express 19, 3519–3524 (2011).
    [CrossRef] [PubMed]
  30. K. Osvay, A. Kovcs, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209(2005).
    [CrossRef]

2011 (1)

2010 (4)

2009 (3)

2007 (4)

2006 (2)

2005 (2)

S. Akturk, X. Gu, P. Gabolde, and R. Trebino, “The general theory of first-order spatiotemporal distortions of Gaussian pulses and beams,” Opt. Express 13, 8642–8661 (2005).
[CrossRef] [PubMed]

K. Osvay, A. Kovcs, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209(2005).
[CrossRef]

2004 (2)

2002 (1)

2000 (1)

T. Kobayashi and A. Shirakawa, “Tunable visible and near-infrared pulse generator in a 5 fs regime,” Appl. Phys. B 70, S239–S246 (2000).
[CrossRef]

1998 (3)

1997 (1)

1996 (1)

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

1995 (1)

1992 (1)

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

1986 (1)

K. Kato, “Second-harmonic generation to 2048 Å in β-BaB2O4,” IEEE J. Quantum Electron. 22, 1013–1014 (1986).
[CrossRef]

1985 (1)

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

Adachi, S.

Akturk, S.

Akutsu, A.

Antipenkov, R.

R. Antipenkov, A. Varanavičius, A. Zaukevičius, and A. P. Piskarskas, “Femtosecond Yb:KGW MOPA driven broadband NOPA as a frontend for TW few-cycle pulse systems,” Opt. Express 19, 3519–3524 (2011).
[CrossRef] [PubMed]

V. Pyragaite, A. Stabinis, R. Butkus, R. Antipenkov, and A. Varanavicius, “Parametric amplification of chirped optical pulses under pump depletion,” Opt. Commun. 283, 1144–1151(2010).
[CrossRef]

Arisholm, G.

Baltuška, A.

Borguet, E.

Boyd, R.

R. Boyd, Nonlinear Optics (Academic, 2008).

Bromage, J.

Butkus, R.

V. Pyragaite, A. Stabinis, R. Butkus, R. Antipenkov, and A. Varanavicius, “Parametric amplification of chirped optical pulses under pump depletion,” Opt. Commun. 283, 1144–1151(2010).
[CrossRef]

Cavallari, M.

Cerullo, G.

Daido, H.

DeSalvo, R.

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

Divall, M.

K. Osvay, A. Kovcs, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209(2005).
[CrossRef]

Dorrer, C.

Driscoll, T. J.

Dubietis, A.

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

Düsterer, S.

Eikema, K.

S. Witte, R. Zinkstok, W. Hogervorst, and K. Eikema, “Numerical simulations for performance optimization of a few-cycle terawatt NOPCPA system,” Appl. Phys. B 87, 677–684 (2007).
[CrossRef]

Eikema, K. S. E.

Feldhaus, J.

Ferincz, I.

K. Osvay, A. Kovcs, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209(2005).
[CrossRef]

Fuji, T.

Gabolde, P.

Gale, G. M.

Gu, X.

Hache, F.

Hädrich, S.

Hagan, D.

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

Hanna, D. C.

Heiner, Z.

K. Osvay, A. Kovcs, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209(2005).
[CrossRef]

Herrmann, D.

Hogervorst, W.

S. Witte, R. Zinkstok, W. Hogervorst, and K. Eikema, “Numerical simulations for performance optimization of a few-cycle terawatt NOPCPA system,” Appl. Phys. B 87, 677–684 (2007).
[CrossRef]

S. Witte, R. T. 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).
[CrossRef] [PubMed]

Isaienko, O.

Ishii, H.

Ishii, N.

Jonusauskas, G.

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

Kanai, T.

Kanazawa, S.

Kato, K.

K. Kato, “Second-harmonic generation to 2048 Å in β-BaB2O4,” IEEE J. Quantum Electron. 22, 1013–1014 (1986).
[CrossRef]

Kimura, T.

Kiriyama, H.

Klebniczki, J.

K. Osvay, A. Kovcs, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209(2005).
[CrossRef]

Kobayashi, T.

A. Baltuška, 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).
[CrossRef]

T. Kobayashi and A. Shirakawa, “Tunable visible and near-infrared pulse generator in a 5 fs regime,” Appl. Phys. B 70, S239–S246 (2000).
[CrossRef]

A. Shirakawa, I. Sakane, and T. Kobayashi, “Pulse-front-matched optical parametric amplification for sub-10-fs pulse generation tunable in the visible and near infrared,” Opt. Lett. 23, 1292–1294 (1998).
[CrossRef]

A. Shirakawa and T. Kobayashi, “Noncollinearly phase-matched femtosecond optical parametric amplification with a 2000 cm−1 bandwidth,” Appl. Phys. Lett. 72, 147–149 (1998).
[CrossRef]

Kondo, S.

Kosuge, A.

Kovcs, A.

K. Osvay, A. Kovcs, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209(2005).
[CrossRef]

Krausz, F.

Krebs, M.

Kurdi, G.

K. Osvay, A. Kovcs, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209(2005).
[CrossRef]

Limpert, J.

Manzoni, C.

Mero, M.

Miyanaga, N.

Mori, M.

Mourou, G.

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

Nakai, Y.

Nisoli, M.

Osvay, K.

K. Osvay, A. Kovcs, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209(2005).
[CrossRef]

Pervak, V.

Piskarskas, A.

A. Piskarskas, A. Stabinis, and V. Pyragaite, “Ultrabroad bandwidth of optical parametric amplifiers,” IEEE J. Quantum Electron. 46, 1031–1038 (2010).
[CrossRef]

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

Piskarskas, A. P.

Polli, D.

Pyragaite, V.

V. Pyragaite, A. Stabinis, R. Butkus, R. Antipenkov, and A. Varanavicius, “Parametric amplification of chirped optical pulses under pump depletion,” Opt. Commun. 283, 1144–1151(2010).
[CrossRef]

A. Piskarskas, A. Stabinis, and V. Pyragaite, “Ultrabroad bandwidth of optical parametric amplifiers,” IEEE J. Quantum Electron. 46, 1031–1038 (2010).
[CrossRef]

Radzewicz, C.

Rossbach, J.

Rothhardt, J.

Said, A.

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

Sakane, I.

Schimpf, D. N.

Schlarb, H.

Schmid, K.

Seise, E.

Sheik-Bahae, M.

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

Shimomura, T.

Shirakawa, A.

T. Kobayashi and A. Shirakawa, “Tunable visible and near-infrared pulse generator in a 5 fs regime,” Appl. Phys. B 70, S239–S246 (2000).
[CrossRef]

A. Shirakawa and T. Kobayashi, “Noncollinearly phase-matched femtosecond optical parametric amplification with a 2000 cm−1 bandwidth,” Appl. Phys. Lett. 72, 147–149 (1998).
[CrossRef]

A. Shirakawa, I. Sakane, and T. Kobayashi, “Pulse-front-matched optical parametric amplification for sub-10-fs pulse generation tunable in the visible and near infrared,” Opt. Lett. 23, 1292–1294 (1998).
[CrossRef]

Silvestri, S. D.

Stabinis, A.

A. Piskarskas, A. Stabinis, and V. Pyragaite, “Ultrabroad bandwidth of optical parametric amplifiers,” IEEE J. Quantum Electron. 46, 1031–1038 (2010).
[CrossRef]

V. Pyragaite, A. Stabinis, R. Butkus, R. Antipenkov, and A. Varanavicius, “Parametric amplification of chirped optical pulses under pump depletion,” Opt. Commun. 283, 1144–1151(2010).
[CrossRef]

Stagira, S.

Stepanenko, Y.

Strickland, D.

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

Tanoue, M.

Tautz, R.

Tavella, F.

Trebino, R.

Tünnermann, A.

Tzankov, P.

Ubachs, W.

Van Stryland, E.

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

Varanavicius, A.

R. Antipenkov, A. Varanavičius, A. Zaukevičius, and A. P. Piskarskas, “Femtosecond Yb:KGW MOPA driven broadband NOPA as a frontend for TW few-cycle pulse systems,” Opt. Express 19, 3519–3524 (2011).
[CrossRef] [PubMed]

V. Pyragaite, A. Stabinis, R. Butkus, R. Antipenkov, and A. Varanavicius, “Parametric amplification of chirped optical pulses under pump depletion,” Opt. Commun. 283, 1144–1151(2010).
[CrossRef]

Veisz, L.

Watanabe, S.

Willner, A.

Witte, S.

S. Witte, R. Zinkstok, W. Hogervorst, and K. Eikema, “Numerical simulations for performance optimization of a few-cycle terawatt NOPCPA system,” Appl. Phys. B 87, 677–684 (2007).
[CrossRef]

S. Witte, R. T. 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).
[CrossRef] [PubMed]

Wnuk, P.

Wolf, A. L.

Yamamoto, Y.

Zaukevicius, A.

Zeek, E.

Zheng, J.

Zinkstok, R.

S. Witte, R. Zinkstok, W. Hogervorst, and K. Eikema, “Numerical simulations for performance optimization of a few-cycle terawatt NOPCPA system,” Appl. Phys. B 87, 677–684 (2007).
[CrossRef]

Zinkstok, R. T.

Zuegel, J. D.

Appl. Phys. B (2)

T. Kobayashi and A. Shirakawa, “Tunable visible and near-infrared pulse generator in a 5 fs regime,” Appl. Phys. B 70, S239–S246 (2000).
[CrossRef]

S. Witte, R. Zinkstok, W. Hogervorst, and K. Eikema, “Numerical simulations for performance optimization of a few-cycle terawatt NOPCPA system,” Appl. Phys. B 87, 677–684 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

A. Shirakawa and T. Kobayashi, “Noncollinearly phase-matched femtosecond optical parametric amplification with a 2000 cm−1 bandwidth,” Appl. Phys. Lett. 72, 147–149 (1998).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. Piskarskas, A. Stabinis, and V. Pyragaite, “Ultrabroad bandwidth of optical parametric amplifiers,” IEEE J. Quantum Electron. 46, 1031–1038 (2010).
[CrossRef]

K. Kato, “Second-harmonic generation to 2048 Å in β-BaB2O4,” IEEE J. Quantum Electron. 22, 1013–1014 (1986).
[CrossRef]

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (5)

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

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

K. Osvay, A. Kovcs, G. Kurdi, Z. Heiner, M. Divall, J. Klebniczki, and I. Ferincz, “Measurement of non-compensated angular dispersion and the subsequent temporal lengthening of femtosecond pulses in a CPA laser,” Opt. Commun. 248, 201–209(2005).
[CrossRef]

X. Gu, S. Akturk, and R. Trebino, “Spatial chirp in ultrafast optics,” Opt. Commun. 242, 599–604 (2004).
[CrossRef]

V. Pyragaite, A. Stabinis, R. Butkus, R. Antipenkov, and A. Varanavicius, “Parametric amplification of chirped optical pulses under pump depletion,” Opt. Commun. 283, 1144–1151(2010).
[CrossRef]

Opt. Express (6)

Opt. Lett. (9)

G. M. Gale, M. Cavallari, T. J. Driscoll, and F. Hache, “Sub-20-fs tunable pulses in the visible from an 82 mhz optical parametric oscillator,” Opt. Lett. 20, 1562–1564 (1995).
[CrossRef] [PubMed]

P. Tzankov, J. Zheng, M. Mero, D. Polli, C. Manzoni, and G. Cerullo, “300 μJ noncollinear optical parametric amplifier in the visible at 1 kHz repetition rate,” Opt. Lett. 31, 3629–3631(2006).
[CrossRef] [PubMed]

A. Shirakawa, I. Sakane, and T. Kobayashi, “Pulse-front-matched optical parametric amplification for sub-10-fs pulse generation tunable in the visible and near infrared,” Opt. Lett. 23, 1292–1294 (1998).
[CrossRef]

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).
[CrossRef] [PubMed]

H. Kiriyama, M. Mori, Y. Nakai, Y. Yamamoto, M. Tanoue, A. Akutsu, T. Shimomura, S. Kondo, S. Kanazawa, H. Daido, T. Kimura, and N. Miyanaga, “High-energy, high-contrast, multiterawatt laser pulses by optical parametric chirped-pulse amplification,” Opt. Lett. 32, 2315–2317 (2007).
[CrossRef] [PubMed]

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, 2459–2461 (2009).
[CrossRef] [PubMed]

G. Cerullo, M. Nisoli, S. Stagira, and S. D. Silvestri, “Sub-8-fs pulses from an ultrabroadband optical parametric amplifier in the visible,” Opt. Lett. 23, 1283–1285 (1998).
[CrossRef]

A. Baltuška, 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).
[CrossRef]

J. Bromage, C. Dorrer, and J. D. Zuegel, “Angular-dispersion-induced spatiotemporal aberrations in noncollinear optical parametric amplifiers,” Opt. Lett. 35, 2251–2253 (2010).
[CrossRef] [PubMed]

Other (1)

R. Boyd, Nonlinear Optics (Academic, 2008).

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Figures (7)

Fig. 1
Fig. 1

Noncollinear interaction scheme (a) when the pump and signal fronts are not matched and (b) when the pump front is tilted to match the signal front. Wave vectors k 1 and k 3 denote the propagation directions of the signal and pump pulses, respectively, O denotes the optical axis of the nonlinear crystal, θ is the phase-matching angle, and α is the noncollinearity angle.

Fig. 2
Fig. 2

Variation of the isointensity lines of normalized spectra defined by conditions (a)  F ( 2 π ν , x ) = 1 2 and (b)  G ( 2 π ν , 2 π f x ) = 1 2 when increasing the temporal chirp parameter γ of the signal pulse: γ 1 = 0 , γ 2 = 5 , γ 3 = 10 . Filled circles correspond to the most-distant points of isointensity lines along the frequency axis. τ 3 = 300 fs (FWHM), u 3 = 0.2 μm / fs , ρ 3 = 1 mm (FWHM), Γ z = 9 , α = 2.6 deg , τ 1 = 100 fs (FWHM), ρ 1 = ρ 3 .

Fig. 3
Fig. 3

Dependences of (a) pulse tilt, (b) spatial dispersion, and (c) angular dispersion of the amplified signal on the pump pulse duration (FWHM) for the three different pump beam diameters (FWHM): ρ 3 = 2 mm (solid curve), ρ 3 = 1 mm (dashed curve), ρ 3 = 0.2 mm (dotted curve). u 3 = 0.2 μm / fs , Γ z = 9 , α = 2.6 deg , τ 1 = τ 3 / Γ z , ρ 1 = ρ 3 , τ TL = 10 fs (FWHM), and γ = τ 1 2 / τ TL 2 1 . Note the logarithmic scale of the x axis.

Fig. 4
Fig. 4

Calculated phase-matching curve at the magic phase- matching angle of θ = 24.67 deg in Type I BBO crystal pumped by λ 3 = 512 nm (solid black curve). The signal pulse spectrum corresponding to a 10 fs transform-limited Gaussian pulse is depicted by the gray solid curve.

Fig. 5
Fig. 5

Normalized intensity profiles of amplified signal pulse in three different domains (see text) for the three different input conditions: (a)–(c) when the signal pulse is temporally chirped ( γ = 20 ), (d)–(f) when the signal pulse is transform limited ( γ = 0 ), and (g)–(i) when the fronts of the signal and pump pulses are matched ( γ = 20 ). Note that the scale interval of the frequency axis is reduced 10 times in (e) and (f) due to the narrow bandwidth of the transform-limited signal.

Fig. 6
Fig. 6

Dependences of the FWHM bandwidth of the amplified signal pulse (solid curve) and the pump-to-signal energy conversion efficiency (dashed curve) on pump beam diameter (FWHM) in the case when the fronts are not matched.

Fig. 7
Fig. 7

(a) and (c) Spatiospectral intensity distributions F ( λ , x ) and (b) and (d) far-field intensity distributions G ( λ , β ) of the amplified signal pulse in the case of non-matched fronts (first row) and in the case of matched fronts (second row).

Equations (24)

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A 1 ( t , x , z ) = A 1 ( t , x , z = 0 ) cosh ( A 3 ( t , x ) σ z ) ,
σ = ω 1 ω 2 2 c 2 χ eff k 1 k 2 ,
A 1 ( t , x , z ) 1 2 A 1 ( t , x , z = 0 ) exp ( A 3 ( t , x ) σ z ) .
A 1 ( t , x , z = 0 ) = A 10 exp ( t 2 τ 1 2 ( 1 i γ ) x 2 ρ 1 2 ) ,
A 3 ( t , x ) = A 30 exp ( t 2 τ 3 2 x 2 ρ 3 2 ) ,
A 3 ( t , x ) = A 30 exp [ ( t u 3 cos α x sin α ) 2 τ 3 2 u 3 2 ( t u 3 sin α + x cos α ) 2 ρ 3 2 ] ,
A 3 ( t , x ) = A 30 exp [ ( t p 0 x ) 2 τ 2 x 2 ρ 2 ] ,
τ = τ 3 ρ 3 ρ ,
ρ = ρ 3 2 cos 2 ( α ) + τ 3 2 u 3 2 sin 2 ( α ) ,
p 0 = ( ρ 3 2 τ 3 2 u 3 2 ) cos ( α ) sin ( α ) ρ 2 u 3 .
A 3 ( t , x ) = A 30 [ 1 ( t p 0 x ) 2 τ 2 x 2 ρ 2 ] .
A 1 ( t , x , z ) A 0 exp [ t 2 τ 1 2 ( 1 i γ ) x 2 ρ 1 2 ( t p 0 x ) 2 τ 2 Γ z x 2 ρ 2 Γ z ] ,
F ( ω , x ) = | A 1 ( t , x ) exp ( i ω t ) d t | 2 ,
G ( ω , k x ) = | A 1 ( t , x ) exp ( i ω t i k x x ) d t d x | 2 .
d x 0 d ω = γ A sd γ 2 B + C ,
d k x 0 d ω = A ad γ 2 B + C ,
A sd = 1 2 p 0 τ 1 2 ρ 1 2 τ 3 2 ρ 3 2 ,
A ad = p 0 τ 1 2 ( ( τ 1 2 + τ 3 2 ) ( ρ 1 2 + ρ 3 2 ) + p 0 2 ρ 1 2 ρ 3 2 ) ,
B = τ 3 2 ( τ 3 2 ( ρ 1 2 + ρ 3 2 ) + p 0 2 ρ 1 2 ρ 3 2 ) , C = ( τ 1 2 + τ 3 2 ) ( ( τ 1 2 + τ 3 2 ) ( ρ 1 2 + ρ 3 2 ) + p 0 2 ρ 1 2 ρ 3 2 ) .
p = d t 0 d x = p 0 1 + τ 3 2 / τ 1 2 ,
A j = F 1 { S j ( ω , k x , k y ) exp ( i k ( ω ) 2 k x 2 k y 2 z ) } ,
A 1 z = i w 1 2 2 k 1 c 2 χ eff A 3 A 2 * , A 2 z = i w 2 2 2 k 2 c 2 χ eff A 3 A 1 * , A 3 z = i w 3 2 2 k 3 c 2 χ eff A 1 A 2 .
cos ( α ) = k 1 2 + k 3 2 k 2 2 2 k 1 k 3 .
α λ 1 | λ 1 = 800 nm = 0.

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