Abstract

We developed a theory of optimization of amplifier bandwidth and conversion efficiency in ultrabroadband optical parametric chirped pulse amplification based on the principle of making the optimal conversion length uniform in time through pulse shaping. Conformal profiles, ideal combinations of pump intensity, seed intensity, and wave-vector mismatch temporal profiles can be found analytically by use of the exact Jacobi elliptic function solutions for signal gain and pump depletion in optical parametric amplification. We derive and investigate these gain equations for the general purpose of aiding the design of optical parametric amplifiers. Using these analytics, through an extensive analysis of conformal profile methods, we find conformal profile pulse shaping can significantly boost amplifier bandwidth as well as conversion efficiency, allowing in some amplifiers a severalfold increase in obtainable peak power. Pump pulse shaping is found to be particularly effective and flexible.

© 2011 Optical Society of America

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  3. 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]
  4. F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14, 12822–12827 (2006).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  43. We used MATLAB to find the roots of Eq. , using bounds for Ip0 defined by Δk2/41−ωp/ωs*Is0/Ip0*<Γ2<Δk24+Γ*2, where Ip0* and Γ* are the pump intensity and nonlinear drive, respectively, which set our choice of L equal to Lpeak when Δk=0. We have found that in actuality, the transition between regimes of the OPA does not take place exactly at Δκ=1, but rather at |Δk|/2Γ=(1−ωp/ωs*Is0/Ip0)1/2. This small correction becomes important when looking for the correct root of Eq.  when Δk is large.
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    [CrossRef]
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    [CrossRef]
  49. J. Limpert, C. Aguergaray, S. Montant, I. Manek-Honninger, S. Petit, D. Descamps, E. Cormier, and F. Salin, “Ultra-broad bandwidth parametric amplification at degeneracy,” Opt. Express 13, 7386–7392 (2005).
    [CrossRef] [PubMed]
  50. S. Zeng, B. Zhang, Y. Dan, X. Li, N. Sun, and Z. Sui, “Analysis and optimization of chirp-compensation OPCPA scheme,” Opt. Commun. 283, 4054–4058 (2010).
    [CrossRef]
  51. T. Fuji, N. Ishii, C. Y. Teisset, X. Gu, T. Metzger, A. Baltuska, N. Forget, D. Kaplan, A. Galvanauskas, and F. Krausz, “Parametric amplification of few-cycle carrier-envelope phase-stable pulses at 2.1 μm,” Opt. Lett. 31, 1103–1105 (2006).
    [CrossRef] [PubMed]
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  54. F. Tavella, A. Marcinkevicius, and F. Krausz, “Investigation of the superfluorescence and signal amplification in an ultrabroadband multiterawatt optical parametric chirped pulse amplifier system,” New J. Phys. 8, 219 (2006).
    [CrossRef]
  55. F. Tavella, K. Schmid, N. Ishii, A. Marcinkevicius, L. Veisz, and F. Krausz, “High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier,” Appl. Phys. B 81, 753–756 (2005).
    [CrossRef]
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2010 (3)

E. W. Gaul, M. Martinez, J. Blakeney, A. Jochmann, M. Ringuette, D. Hammond, T. Borger, R. Escamilla, S. Douglas, W. Henderson, G. Dyer, A. Erlandson, R. Cross, J. Caird, C. Ebbers, and T. Ditmire, “Demonstration of a 1.1 petawatt laser based on a hybrid optical parametric chirped pulse amplification/mixed Nd:glass amplifier,” Appl. Opt. 49, 1676–1681(2010).
[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]

S. Zeng, B. Zhang, Y. Dan, X. Li, N. Sun, and Z. Sui, “Analysis and optimization of chirp-compensation OPCPA scheme,” Opt. Commun. 283, 4054–4058 (2010).
[CrossRef]

2009 (4)

2008 (4)

2007 (4)

S. Zhou, D. Ouzounov, H. Li, I. Bazarov, B. Dunham, C. Sinclair, and F. W. Wise, “Efficient temporal shaping of ultrashort pulses with birefringent crystals,” Appl. Opt. 46, 8488–8492 (2007).
[CrossRef] [PubMed]

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

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

J. A. Fueloep, Z. Major, B. Horvath, F. Tavella, A. Baltuska, and F. Krausz, “Shaping of picosecond pulses for pumping optical parametric amplification,” Appl. Phys. B 87, 79–84 (2007).
[CrossRef]

2006 (8)

E. J. Grace, C. L. Tsangaris, and G. H. C. New, “Competing processes in optical parametric chirped pulse amplification,” Opt. Commun. 261, 225–230 (2006).
[CrossRef]

A. Dubietis, R. Butkus, and A. Piskarskas, “Trends in chirped pulse optical parametric amplification,” IEEE J. Sel. Top. Quantum Electron. 12, 163–172 (2006).
[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]

F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14, 12822–12827 (2006).
[CrossRef] [PubMed]

J. D. Zuegel, V. Bagnoud, J. Bromage, I. A. Begishev, and J. Puth, “High-performance OPCPA laser system,” J. Phys. IV 133, 701–703 (2006).
[CrossRef]

O. V. Chekhlov, J. L. Collier, I. N. Ross, P. K. Bates, M. Notley, C. Hernandez-Gomez, W. Shaikh, C. N. Danson, D. Neely, P. Matousek, S. Hancock, and L. Cardoso, “35 J broadband femtosecond optical parametric chirped pulse amplification system,” Opt. Lett. 31, 3665–3667 (2006).
[CrossRef] [PubMed]

F. Tavella, A. Marcinkevicius, and F. Krausz, “Investigation of the superfluorescence and signal amplification in an ultrabroadband multiterawatt optical parametric chirped pulse amplifier system,” New J. Phys. 8, 219 (2006).
[CrossRef]

T. Fuji, N. Ishii, C. Y. Teisset, X. Gu, T. Metzger, A. Baltuska, N. Forget, D. Kaplan, A. Galvanauskas, and F. Krausz, “Parametric amplification of few-cycle carrier-envelope phase-stable pulses at 2.1 μm,” Opt. Lett. 31, 1103–1105 (2006).
[CrossRef] [PubMed]

2005 (4)

J. Limpert, C. Aguergaray, S. Montant, I. Manek-Honninger, S. Petit, D. Descamps, E. Cormier, and F. Salin, “Ultra-broad bandwidth parametric amplification at degeneracy,” Opt. Express 13, 7386–7392 (2005).
[CrossRef] [PubMed]

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevicius, L. Veisz, and F. Krausz, “High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier,” Appl. Phys. B 81, 753–756 (2005).
[CrossRef]

V. Bagnoud, I. A. Begishev, M. J. Guardalben, J. Puth, and J. D. Zuegel, “5 Hz, >250 mJ optical parametric chirped-pulse amplifier at 1053 nm,” Opt. Lett. 30, 1843–1845 (2005).
[CrossRef] [PubMed]

Y.-L. Jiang, Y.-X. Leng, B.-Z. Zhao, C. Wang, X.-Y. Liang, H.-H. Lu, and Z.-Z. Xu, “High and stable conversion efficiency obtaining in single-stage multi-crystal optical parametric chirped pulse amplification system,” Chin. Phys. Lett. 22, 2840–2842 (2005).
[CrossRef]

2004 (1)

P. Baum, S. Lochbrunner, and E. Riedle, “Generation of tunable 7 fs ultraviolet pulses: achromatic phase matching and chirp management,” Appl. Phys. B 79, 1027–1032 (2004).
[CrossRef]

2003 (5)

2002 (2)

2000 (1)

P. Matousek, B. Rus, and I. N. Ross, “Design of a multi-petawatt optical parametric chirped pulse amplifier for the iodine laser ASTERIX IV,” IEEE J. Quantum Electron. 36, 158–163 (2000).
[CrossRef]

1997 (2)

G. D’Aguanno, C. Sibilia, E. Fazio, and M. Bertolotti, “Three-wave mixing in a quadratic material under perfect phase-matching,” Opt. Commun. 142, 75–78 (1997).
[CrossRef]

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

1996 (5)

A. Kobyakov, U. Peschel, and F. Lederer, “Vectorial type-II interaction in cascaded quadratic nonlinearities—an analytical approach,” Opt. Commun. 124, 184–194 (1996).
[CrossRef]

P. J. Wegner and M. D. Feit, “High-power narrow-band pulses with wavelengths tunable about 1.053 μm from a synchronously pumped optical parametric oscillator,” Appl. Opt. 35, 890–902(1996).
[CrossRef] [PubMed]

I. N. Ross and K. Osvay, “Efficient broad-bandwidth frequency mixing in dispersive media,” Opt. Quantum Electron. 28, 83–86(1996).
[CrossRef]

A. C. L. Boscheron, C. J. Sauteret, and A. Migus, “Efficient broadband sum frequency based on controlled phase-modulated input fields: theory for 351 nm ultrabroadband or ultrashort-pulse generation,” J. Opt. Soc. Am. B 13, 818–826 (1996).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

1992 (2)

M. J. Milton, “General expression for the efficiency of phase-matched and nonphase-matched second-order nonlinear interactions between plane waves,” IEEE J. Quantum Electron. 28, 739–749 (1992).
[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]

1990 (3)

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. I. Optimization of the profiles of interacting waves in parametric amplification,” Sov. J. Quantum Electron. 20, 1100–1103 (1990).
[CrossRef]

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. II. Parametric interaction of waves with conformal profiles,” Sov. J. Quantum Electron. 20, 1104–1106 (1990).
[CrossRef]

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear-optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
[CrossRef] [PubMed]

1986 (1)

K. Kato, “Second-harmonic generation to 2048Å in β-Ba2O4,” IEEE J. Quantum Electron. 22, 1013–1014 (1986).
[CrossRef]

1981 (1)

J. Katriel and D. G. Hummer, “Analytic solutions for three- and four-wave mixing via generalised bose operators,” J. Phys. A 14, 1211–1224 (1981).
[CrossRef]

1979 (1)

R. Baumgartner and R. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. 15, 432–444 (1979).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Aguergaray, C.

Antipenkov, 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]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Atherton, B.

J. Schwarz, P. Rambo, M. Geissel, M. Kimmel, E. Brambrink, B. Atherton, and J. Glassman, “A hybrid OPCPA/Nd:phosphate glass multi-terawatt laser system for seeding of a petawatt laser,” Opt. Commun. 281, 4984–4992 (2008).
[CrossRef]

Bagnoud, V.

Bakker, H. J.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear-optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
[CrossRef] [PubMed]

Baltuska, A.

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J. Schwarz, P. Rambo, M. Geissel, M. Kimmel, E. Brambrink, B. Atherton, and J. Glassman, “A hybrid OPCPA/Nd:phosphate glass multi-terawatt laser system for seeding of a petawatt laser,” Opt. Commun. 281, 4984–4992 (2008).
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Brida, D.

Bromage, J.

J. D. Zuegel, V. Bagnoud, J. Bromage, I. A. Begishev, and J. Puth, “High-performance OPCPA laser system,” J. Phys. IV 133, 701–703 (2006).
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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).
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R. Baumgartner and R. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. 15, 432–444 (1979).
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J. Moses, C. Manzoni, S.-W. Huang, G. Cerullo, and F. X. Kaertner, “Temporal optimization of ultrabroadband high-energy OPCPA,” Opt. Express 17, 5540–5555 (2009).
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Chekhlov, O. V.

Cirmi, G.

Collier, J. L.

Cormier, E.

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G. D’Aguanno, C. Sibilia, E. Fazio, and M. Bertolotti, “Three-wave mixing in a quadratic material under perfect phase-matching,” Opt. Commun. 142, 75–78 (1997).
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S. Zeng, B. Zhang, Y. Dan, X. Li, N. Sun, and Z. Sui, “Analysis and optimization of chirp-compensation OPCPA scheme,” Opt. Commun. 283, 4054–4058 (2010).
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A. Dubietis, R. Butkus, and A. Piskarskas, “Trends in chirped pulse optical parametric amplification,” IEEE J. Sel. Top. Quantum Electron. 12, 163–172 (2006).
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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).
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J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Dunham, B.

Dyer, G.

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Eggleton, B. J.

Eikema, K. S. E.

S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. 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).
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Erlandson, A.

Erofeev, E. A.

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. II. Parametric interaction of waves with conformal profiles,” Sov. J. Quantum Electron. 20, 1104–1106 (1990).
[CrossRef]

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. I. Optimization of the profiles of interacting waves in parametric amplification,” Sov. J. Quantum Electron. 20, 1100–1103 (1990).
[CrossRef]

Escamilla, R.

Falcao-Filho, E. L.

Fazio, E.

G. D’Aguanno, C. Sibilia, E. Fazio, and M. Bertolotti, “Three-wave mixing in a quadratic material under perfect phase-matching,” Opt. Commun. 142, 75–78 (1997).
[CrossRef]

Feit, M. D.

Forget, N.

Freidman, G. I.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Fueloep, J. A.

J. A. Fueloep, Z. Major, B. Horvath, F. Tavella, A. Baltuska, and F. Krausz, “Shaping of picosecond pulses for pumping optical parametric amplification,” Appl. Phys. B 87, 79–84 (2007).
[CrossRef]

Fuji, T.

Galvanauskas, A.

Garanin, S. G.

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Gaul, E. W.

Geissel, M.

J. Schwarz, P. Rambo, M. Geissel, M. Kimmel, E. Brambrink, B. Atherton, and J. Glassman, “A hybrid OPCPA/Nd:phosphate glass multi-terawatt laser system for seeding of a petawatt laser,” Opt. Commun. 281, 4984–4992 (2008).
[CrossRef]

Ginzburg, V. N.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Glassman, J.

J. Schwarz, P. Rambo, M. Geissel, M. Kimmel, E. Brambrink, B. Atherton, and J. Glassman, “A hybrid OPCPA/Nd:phosphate glass multi-terawatt laser system for seeding of a petawatt laser,” Opt. Commun. 281, 4984–4992 (2008).
[CrossRef]

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E. J. Grace, C. L. Tsangaris, and G. H. C. New, “Competing processes in optical parametric chirped pulse amplification,” Opt. Commun. 261, 225–230 (2006).
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Gu, X.

Guardalben, M. J.

Gulamov, A. A.

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. I. Optimization of the profiles of interacting waves in parametric amplification,” Sov. J. Quantum Electron. 20, 1100–1103 (1990).
[CrossRef]

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. II. Parametric interaction of waves with conformal profiles,” Sov. J. Quantum Electron. 20, 1104–1106 (1990).
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G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
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Hancock, S.

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S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. 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]

Hong, K.

Horvath, B.

J. A. Fueloep, Z. Major, B. Horvath, F. Tavella, A. Baltuska, and F. Krausz, “Shaping of picosecond pulses for pumping optical parametric amplification,” Appl. Phys. B 87, 79–84 (2007).
[CrossRef]

Huang, S.-W.

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J. Katriel and D. G. Hummer, “Analytic solutions for three- and four-wave mixing via generalised bose operators,” J. Phys. A 14, 1211–1224 (1981).
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Ibragimov, E. A.

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. I. Optimization of the profiles of interacting waves in parametric amplification,” Sov. J. Quantum Electron. 20, 1100–1103 (1990).
[CrossRef]

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. II. Parametric interaction of waves with conformal profiles,” Sov. J. Quantum Electron. 20, 1104–1106 (1990).
[CrossRef]

Ilday, F. O.

Ishii, N.

T. Fuji, N. Ishii, C. Y. Teisset, X. Gu, T. Metzger, A. Baltuska, N. Forget, D. Kaplan, A. Galvanauskas, and F. Krausz, “Parametric amplification of few-cycle carrier-envelope phase-stable pulses at 2.1 μm,” Opt. Lett. 31, 1103–1105 (2006).
[CrossRef] [PubMed]

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevicius, L. Veisz, and F. Krausz, “High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier,” Appl. Phys. B 81, 753–756 (2005).
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Y.-L. Jiang, Y.-X. Leng, B.-Z. Zhao, C. Wang, X.-Y. Liang, H.-H. Lu, and Z.-Z. Xu, “High and stable conversion efficiency obtaining in single-stage multi-crystal optical parametric chirped pulse amplification system,” Chin. Phys. Lett. 22, 2840–2842 (2005).
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Jochmann, A.

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]

Kaertner, F. X.

Kamalov, S. R.

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. II. Parametric interaction of waves with conformal profiles,” Sov. J. Quantum Electron. 20, 1104–1106 (1990).
[CrossRef]

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. I. Optimization of the profiles of interacting waves in parametric amplification,” Sov. J. Quantum Electron. 20, 1100–1103 (1990).
[CrossRef]

Kaplan, D.

Katin, E. V.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Kato, K.

K. Kato, “Second-harmonic generation to 2048Å in β-Ba2O4,” IEEE J. Quantum Electron. 22, 1013–1014 (1986).
[CrossRef]

Katriel, J.

J. Katriel and D. G. Hummer, “Analytic solutions for three- and four-wave mixing via generalised bose operators,” J. Phys. A 14, 1211–1224 (1981).
[CrossRef]

Kedrov, A. I.

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Keegan, J.

Khadzhaev, A. D.

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. I. Optimization of the profiles of interacting waves in parametric amplification,” Sov. J. Quantum Electron. 20, 1100–1103 (1990).
[CrossRef]

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. II. Parametric interaction of waves with conformal profiles,” Sov. J. Quantum Electron. 20, 1104–1106 (1990).
[CrossRef]

Khazanov, E. A.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Kimmel, M.

J. Schwarz, P. Rambo, M. Geissel, M. Kimmel, E. Brambrink, B. Atherton, and J. Glassman, “A hybrid OPCPA/Nd:phosphate glass multi-terawatt laser system for seeding of a petawatt laser,” Opt. Commun. 281, 4984–4992 (2008).
[CrossRef]

Kirsanov, A. V.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Klemz, G.

Kobyakov, A.

A. Kobyakov, U. Peschel, and F. Lederer, “Vectorial type-II interaction in cascaded quadratic nonlinearities—an analytical approach,” Opt. Commun. 124, 184–194 (1996).
[CrossRef]

Krausz, F.

J. A. Fueloep, Z. Major, B. Horvath, F. Tavella, A. Baltuska, and F. Krausz, “Shaping of picosecond pulses for pumping optical parametric amplification,” Appl. Phys. B 87, 79–84 (2007).
[CrossRef]

T. Fuji, N. Ishii, C. Y. Teisset, X. Gu, T. Metzger, A. Baltuska, N. Forget, D. Kaplan, A. Galvanauskas, and F. Krausz, “Parametric amplification of few-cycle carrier-envelope phase-stable pulses at 2.1 μm,” Opt. Lett. 31, 1103–1105 (2006).
[CrossRef] [PubMed]

F. Tavella, A. Marcinkevicius, and F. Krausz, “Investigation of the superfluorescence and signal amplification in an ultrabroadband multiterawatt optical parametric chirped pulse amplifier system,” New J. Phys. 8, 219 (2006).
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F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14, 12822–12827 (2006).
[CrossRef] [PubMed]

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevicius, L. Veisz, and F. Krausz, “High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier,” Appl. Phys. B 81, 753–756 (2005).
[CrossRef]

Kuipers, L.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear-optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
[CrossRef] [PubMed]

L’vov, L. V.

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Lagendijk, A.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear-optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
[CrossRef] [PubMed]

Langley, A. J.

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

Lederer, F.

A. Kobyakov, U. Peschel, and F. Lederer, “Vectorial type-II interaction in cascaded quadratic nonlinearities—an analytical approach,” Opt. Commun. 124, 184–194 (1996).
[CrossRef]

Leng, Y.-X.

Y.-L. Jiang, Y.-X. Leng, B.-Z. Zhao, C. Wang, X.-Y. Liang, H.-H. Lu, and Z.-Z. Xu, “High and stable conversion efficiency obtaining in single-stage multi-crystal optical parametric chirped pulse amplification system,” Chin. Phys. Lett. 22, 2840–2842 (2005).
[CrossRef]

Li, H.

Li, X.

S. Zeng, B. Zhang, Y. Dan, X. Li, N. Sun, and Z. Sui, “Analysis and optimization of chirp-compensation OPCPA scheme,” Opt. Commun. 283, 4054–4058 (2010).
[CrossRef]

Liang, X.-Y.

Y.-L. Jiang, Y.-X. Leng, B.-Z. Zhao, C. Wang, X.-Y. Liang, H.-H. Lu, and Z.-Z. Xu, “High and stable conversion efficiency obtaining in single-stage multi-crystal optical parametric chirped pulse amplification system,” Chin. Phys. Lett. 22, 2840–2842 (2005).
[CrossRef]

Limpert, J.

Lin, Z.

P. Zhu, L. Qian, S. Xue, and Z. Lin, “Numerical studies of optical parametric chirped pulse amplification,” Opt. Laser Technol. 35, 13–19 (2003).
[CrossRef]

Liu, X.

Lochbrunner, S.

P. Baum, S. Lochbrunner, and E. Riedle, “Generation of tunable 7 fs ultraviolet pulses: achromatic phase matching and chirp management,” Appl. Phys. B 79, 1027–1032 (2004).
[CrossRef]

Lozhkarev, V. V.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Lu, H.-H.

Y.-L. Jiang, Y.-X. Leng, B.-Z. Zhao, C. Wang, X.-Y. Liang, H.-H. Lu, and Z.-Z. Xu, “High and stable conversion efficiency obtaining in single-stage multi-crystal optical parametric chirped pulse amplification system,” Chin. Phys. Lett. 22, 2840–2842 (2005).
[CrossRef]

Luchinin, G. A.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Major, Z.

J. A. Fueloep, Z. Major, B. Horvath, F. Tavella, A. Baltuska, and F. Krausz, “Shaping of picosecond pulses for pumping optical parametric amplification,” Appl. Phys. B 87, 79–84 (2007).
[CrossRef]

Mal’shakov, A. N.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Manek-Honninger, I.

Manzoni, C.

J. Moses, C. Manzoni, S.-W. Huang, G. Cerullo, and F. X. Kaertner, “Temporal optimization of ultrabroadband high-energy OPCPA,” Opt. Express 17, 5540–5555 (2009).
[CrossRef] [PubMed]

D. Brida, G. Cirmi, C. Manzoni, S. Bonora, P. Villoresi, S. De Silvestri, and G. Cerullo, “Sub-two-cycle light pulses at 1.6 μm from an optical parametric amplifier,” Opt. Lett. 33, 741–743(2008).
[CrossRef] [PubMed]

C. Manzoni, J. Moses, F. X. Kaertner, and G. Cerullo, “The evolution of signal-to-noise ratio in superfluorescence-contaminated optical parametric chirped-pulse amplification,” presented at the 17th International Conference on Ultrafast Phenomena, Snowmass Village, Colorado, 19–23 July 2010.

Marcinkevicius, A.

F. Tavella, A. Marcinkevicius, and F. Krausz, “Investigation of the superfluorescence and signal amplification in an ultrabroadband multiterawatt optical parametric chirped pulse amplifier system,” New J. Phys. 8, 219 (2006).
[CrossRef]

F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14, 12822–12827 (2006).
[CrossRef] [PubMed]

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevicius, L. Veisz, and F. Krausz, “High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier,” Appl. Phys. B 81, 753–756 (2005).
[CrossRef]

Marcus, G.

Martinez, M.

Martyanov, M. A.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Matousek, P.

Metzger, T.

Migus, A.

Milton, M. J.

M. J. Milton, “General expression for the efficiency of phase-matched and nonphase-matched second-order nonlinear interactions between plane waves,” IEEE J. Quantum Electron. 28, 739–749 (1992).
[CrossRef]

Montant, S.

Moses, J.

Muecke, O. D.

Musgrave, I.

Neely, D.

New, G. H. C.

Notley, M.

Osin, V. A.

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Osvay, K.

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, 2945–2956 (2002).
[CrossRef]

I. N. Ross and K. Osvay, “Efficient broad-bandwidth frequency mixing in dispersive media,” Opt. Quantum Electron. 28, 83–86(1996).
[CrossRef]

Ouzounov, D.

Palashov, O. V.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Peschel, U.

A. Kobyakov, U. Peschel, and F. Lederer, “Vectorial type-II interaction in cascaded quadratic nonlinearities—an analytical approach,” Opt. Commun. 124, 184–194 (1996).
[CrossRef]

Petit, S.

Piskarskas, A.

A. Dubietis, R. Butkus, and A. Piskarskas, “Trends in chirped pulse optical parametric amplification,” IEEE J. Sel. Top. Quantum Electron. 12, 163–172 (2006).
[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]

Planken, P. C. M.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order nonlinear-optical processes,” Phys. Rev. A 42, 4085–4101 (1990).
[CrossRef] [PubMed]

Poteomkin, A. K.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Puth, J.

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]

Qian, L.

P. Zhu, L. Qian, S. Xue, and Z. Lin, “Numerical studies of optical parametric chirped pulse amplification,” Opt. Laser Technol. 35, 13–19 (2003).
[CrossRef]

Rambo, P.

J. Schwarz, P. Rambo, M. Geissel, M. Kimmel, E. Brambrink, B. Atherton, and J. Glassman, “A hybrid OPCPA/Nd:phosphate glass multi-terawatt laser system for seeding of a petawatt laser,” Opt. Commun. 281, 4984–4992 (2008).
[CrossRef]

Riedle, E.

P. Baum, S. Lochbrunner, and E. Riedle, “Generation of tunable 7 fs ultraviolet pulses: achromatic phase matching and chirp management,” Appl. Phys. B 79, 1027–1032 (2004).
[CrossRef]

Ringuette, M.

Romanov, V. V.

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Ross, I. N.

Y. Tang, I. N. Ross, C. Hernandez-Gomez, G. H. C. New, I. Musgrave, O. V. Chekhlov, P. Matousek, and J. L. Collier, “Optical parametric chirped-pulse amplification source suitable for seeding high-energy systems,” Opt. Lett. 33, 2386–2388 (2008).
[CrossRef] [PubMed]

O. V. Chekhlov, J. L. Collier, I. N. Ross, P. K. Bates, M. Notley, C. Hernandez-Gomez, W. Shaikh, C. N. Danson, D. Neely, P. Matousek, S. Hancock, and L. Cardoso, “35 J broadband femtosecond optical parametric chirped pulse amplification system,” Opt. Lett. 31, 3665–3667 (2006).
[CrossRef] [PubMed]

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, 2945–2956 (2002).
[CrossRef]

P. Matousek, B. Rus, and I. N. Ross, “Design of a multi-petawatt optical parametric chirped pulse amplifier for the iodine laser ASTERIX IV,” IEEE J. Quantum Electron. 36, 158–163 (2000).
[CrossRef]

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

I. N. Ross and K. Osvay, “Efficient broad-bandwidth frequency mixing in dispersive media,” Opt. Quantum Electron. 28, 83–86(1996).
[CrossRef]

Rukavishnikov, N. N.

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Rus, B.

P. Matousek, B. Rus, and I. N. Ross, “Design of a multi-petawatt optical parametric chirped pulse amplifier for the iodine laser ASTERIX IV,” IEEE J. Quantum Electron. 36, 158–163 (2000).
[CrossRef]

Salin, F.

Sauteret, C. J.

Savkin, A. V.

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Schmid, K.

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevicius, L. Veisz, and F. Krausz, “High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier,” Appl. Phys. B 81, 753–756 (2005).
[CrossRef]

Schwarz, J.

J. Schwarz, P. Rambo, M. Geissel, M. Kimmel, E. Brambrink, B. Atherton, and J. Glassman, “A hybrid OPCPA/Nd:phosphate glass multi-terawatt laser system for seeding of a petawatt laser,” Opt. Commun. 281, 4984–4992 (2008).
[CrossRef]

Sergeev, A. M.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Shaikh, W.

Shaykin, A. A.

V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Sibilia, C.

G. D’Aguanno, C. Sibilia, E. Fazio, and M. Bertolotti, “Three-wave mixing in a quadratic material under perfect phase-matching,” Opt. Commun. 142, 75–78 (1997).
[CrossRef]

Sinclair, C.

Stabinis, A.

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]

Stegeman, G. I.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Sui, Z.

S. Zeng, B. Zhang, Y. Dan, X. Li, N. Sun, and Z. Sui, “Analysis and optimization of chirp-compensation OPCPA scheme,” Opt. Commun. 283, 4054–4058 (2010).
[CrossRef]

Sukharev, S. A.

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Sun, N.

S. Zeng, B. Zhang, Y. Dan, X. Li, N. Sun, and Z. Sui, “Analysis and optimization of chirp-compensation OPCPA scheme,” Opt. Commun. 283, 4054–4058 (2010).
[CrossRef]

Tang, Y.

Tavella, F.

J. A. Fueloep, Z. Major, B. Horvath, F. Tavella, A. Baltuska, and F. Krausz, “Shaping of picosecond pulses for pumping optical parametric amplification,” Appl. Phys. B 87, 79–84 (2007).
[CrossRef]

F. Tavella, A. Marcinkevicius, and F. Krausz, “Investigation of the superfluorescence and signal amplification in an ultrabroadband multiterawatt optical parametric chirped pulse amplifier system,” New J. Phys. 8, 219 (2006).
[CrossRef]

F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14, 12822–12827 (2006).
[CrossRef] [PubMed]

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevicius, L. Veisz, and F. Krausz, “High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier,” Appl. Phys. B 81, 753–756 (2005).
[CrossRef]

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Teisset, C. Y.

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

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

Trikanova, O. V.

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

Tsangaris, C. L.

E. J. Grace, C. L. Tsangaris, and G. H. C. New, “Competing processes in optical parametric chirped pulse amplification,” Opt. Commun. 261, 225–230 (2006).
[CrossRef]

Ubachs, W.

Usmanov, T.

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. I. Optimization of the profiles of interacting waves in parametric amplification,” Sov. J. Quantum Electron. 20, 1100–1103 (1990).
[CrossRef]

I. A. Begishev, A. A. Gulamov, E. A. Erofeev, E. A. Ibragimov, S. R. Kamalov, T. Usmanov, and A. D. Khadzhaev, “Highly efficient parametric amplification of optical beams. II. Parametric interaction of waves with conformal profiles,” Sov. J. Quantum Electron. 20, 1104–1106 (1990).
[CrossRef]

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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).
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F. Tavella, K. Schmid, N. Ishii, A. Marcinkevicius, L. Veisz, and F. Krausz, “High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier,” Appl. Phys. B 81, 753–756 (2005).
[CrossRef]

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Voronich, I. N.

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

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[CrossRef]

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Wegner, P. J.

Will, I.

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[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]

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Xu, Z.-Z.

Y.-L. Jiang, Y.-X. Leng, B.-Z. Zhao, C. Wang, X.-Y. Liang, H.-H. Lu, and Z.-Z. Xu, “High and stable conversion efficiency obtaining in single-stage multi-crystal optical parametric chirped pulse amplification system,” Chin. Phys. Lett. 22, 2840–2842 (2005).
[CrossRef]

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P. Zhu, L. Qian, S. Xue, and Z. Lin, “Numerical studies of optical parametric chirped pulse amplification,” Opt. Laser Technol. 35, 13–19 (2003).
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V. V. Lozhkarev, G. I. Freidman, V. N. Ginzburg, E. V. Katin, E. A. Khazanov, A. V. Kirsanov, G. A. Luchinin, A. N. Mal’shakov, M. A. Martyanov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, and I. V. Yakovlev, “Compact 0.56 petawatt laser system based on optical parametric chirped pulse amplification in KD*P crystals,” Laser Phys. Lett. 4, 421–427 (2007).
[CrossRef]

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J. Zheng and H. Zacharias, “Non-collinear optical parametric chirped-pulse amplifier for few-cycle pulses,” Appl. Phys. B 97, 765–779 (2009).
[CrossRef]

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S. Zeng, B. Zhang, Y. Dan, X. Li, N. Sun, and Z. Sui, “Analysis and optimization of chirp-compensation OPCPA scheme,” Opt. Commun. 283, 4054–4058 (2010).
[CrossRef]

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S. Zeng, B. Zhang, Y. Dan, X. Li, N. Sun, and Z. Sui, “Analysis and optimization of chirp-compensation OPCPA scheme,” Opt. Commun. 283, 4054–4058 (2010).
[CrossRef]

Zhang, H.

Zhang, M.

Zhao, B.-Z.

Y.-L. Jiang, Y.-X. Leng, B.-Z. Zhao, C. Wang, X.-Y. Liang, H.-H. Lu, and Z.-Z. Xu, “High and stable conversion efficiency obtaining in single-stage multi-crystal optical parametric chirped pulse amplification system,” Chin. Phys. Lett. 22, 2840–2842 (2005).
[CrossRef]

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J. Zheng and H. Zacharias, “Non-collinear optical parametric chirped-pulse amplifier for few-cycle pulses,” Appl. Phys. B 97, 765–779 (2009).
[CrossRef]

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Zhu, P.

P. Zhu, L. Qian, S. Xue, and Z. Lin, “Numerical studies of optical parametric chirped pulse amplification,” Opt. Laser Technol. 35, 13–19 (2003).
[CrossRef]

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A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

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S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. 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).
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Other (4)

F. Bowman, Introduction to Elliptic Functions with Applications (Dover, 1961).

A. A. Shaykin, G. I. Freidman, S. G. Garanin, V. N. Ginzburg, E. V. Katin, A. I. Kedrov, E. A. Khazanov, A. V. Kirsanov, V. V. Lozhkarev, G. A. Luchinin, L. V. L’vov, A. N. Mal’shakov, M. A. Martyanov, V. A. Osin, O. V. Palashov, A. K. Poteomkin, N. N. Rukavishnikov, V. V. Romanov, A. V. Savkin, A. M. Sergeev, S. A. Sukharev, O. V. Trikanova, I. N. Voronich, I. V. Yakovlev, and B. G. Zimalin, “1 petawatt OPCPA laser in Russia: status and expectations,” presented at the European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, 14–19 June 2009.

We used MATLAB to find the roots of Eq. , using bounds for Ip0 defined by Δk2/41−ωp/ωs*Is0/Ip0*<Γ2<Δk24+Γ*2, where Ip0* and Γ* are the pump intensity and nonlinear drive, respectively, which set our choice of L equal to Lpeak when Δk=0. We have found that in actuality, the transition between regimes of the OPA does not take place exactly at Δκ=1, but rather at |Δk|/2Γ=(1−ωp/ωs*Is0/Ip0)1/2. This small correction becomes important when looking for the correct root of Eq.  when Δk is large.

C. Manzoni, J. Moses, F. X. Kaertner, and G. Cerullo, “The evolution of signal-to-noise ratio in superfluorescence-contaminated optical parametric chirped-pulse amplification,” presented at the 17th International Conference on Ultrafast Phenomena, Snowmass Village, Colorado, 19–23 July 2010.

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Figures (26)

Fig. 1
Fig. 1

Functions F = cn [ u , k ] , F = cn 2 [ u , k ] , and F = cn 2 [ u + K ( k ) , k ] versus u for k = 0.999 . F = cn [ u , k ] has period 4 K , while F = cn 2 [ u , k ] has period 2 K .

Fig. 2
Fig. 2

Behavior of the cn 2 [ u + K ( k ) , k ] function for various values of k (see legend). Here, for each value k, u is normalized to the half-period K ( k ) to aid visualization of the function’s shape.

Fig. 3
Fig. 3

Exact solution for signal gain, I s ( z ) , compared with solutions derived using the undepleted-pump approximation. In these examples, Δ k = 0 , ω s = ω i = ω p / 2 , and I p 0 / I s 0 = 10 2 . The abbreviations cn 2 , sinh 2 , and exp refer to Eqs. (1, 8, 9), respectively. The exact solution for the pump intensity, Eq. (3), is also shown.

Fig. 4
Fig. 4

Same as Fig. 3, but for I p 0 / I s 0 = 10 4 .

Fig. 5
Fig. 5

Conversion efficiency versus propagation length for various values of wave-vector mismatch. Propagation length is normalized to the location of the first peak of I s ( z ) + I i ( z ) when Δ k = 0 , L peak ( Δ k = 0 ) . The normalized wave-vector mismatch, Δ κ = | Δ k | / 2 Γ , is indicated for each curve. Additionally, the loci of the maximum signal plus idler intensities I p 0 ( Δ κ ) is plotted (dashed curve).

Fig. 6
Fig. 6

Parameters I p 0 , γ, K, and L peak are plotted as a function of normalized wave-vector mismatch, Δ κ = | Δ k | / 2 Γ .

Fig. 7
Fig. 7

Same as Fig. 3, but for I p 0 / I s 0 = 10 4 and | Δ k | = 1.6 Γ ( Δ κ = 0.8 ).

Fig. 8
Fig. 8

Same as Fig. 3, but for I p 0 / I s 0 = 10 4 and | Δ k | = 2.4 Γ ( Δ κ = 1.2 ).

Fig. 9
Fig. 9

(a) Signal plus idler intensity after amplification in BBO, I s ( t ; L ) + I i ( t ; L ) , calculated by means of Eqs. (1, 2, 3, 4). The parameters of the OPCPA stage are ω s = ω i = 1.6 μm , ω p = 0.8 μm , L = 5.0 mm , with pump and seed pulse widths of 12 ps (1/e half-width), and Gaussian and super-Gaussian shapes, respectively. The peak pump intensity, I p 0 ( 0 ) = 13.1 GW / cm 2 , and I p 0 ( 0 ) / I s 0 ( 0 ) = 10 4 . The seed bandwidth covers 2 π * 75 THz (1/e full width) (a relative bandwidth Δ ω / ω s = 0.4 ) and corresponds to a wavelength range of 1.33 2.00 μm . Δ k ( ω ) is calculated from the Sellmeier equations for BBO, and translated to Δ k ( t ) by means of the chirp, t = ( 24 ps ) / ( 2 π * 75 THz ) * ( ω ω s ) . I p 0 is shown as a function of time, and I s 0 and Δ κ = | Δ k | / 2 Γ are shown as functions of time and signal wavelength. (b) Signal plus idler intensity plotted as a function of longitudinal distance in the same BBO amplifier, I s ( z ) + I i ( z ) , for temporal coordinates t = 0 ps , 4 ps , 8 ps , and 12 ps . These curves correspond to the temporal coordinates indicated by arrows in (a). The vertical bar indicates the crystal length, L = L peak ( 0 ) = 5.0 mm , corresponding to (a). (c) I s ( t ; L ) + I i ( t ; L ) , calculated for L = 5.0 mm , L = 5.3 mm , L = 6.2 mm , and L = 14.1 mm , corresponding to L peak , 1 ( t = 0 ) , L peak , 1 ( t = 4 ps ) , L peak , 1 ( t = 8 ps ) , and L peak , 1 ( t = 12 ps ) .

Fig. 10
Fig. 10

(a) Same as Fig. 9a, but with the Gaussian pump pulse replaced by the conformal pump profile determined by finding the roots of Eq. (5) with the left-hand side set to L = L peak ( 0 ) = 5.0 mm . (b)  I s ( z ) + I i ( z ) for various temporal coordinates corresponding to (a). L peak ( t ) is now uniform.

Fig. 11
Fig. 11

L peak as a function of I p 0 , I s 0 , or Δ κ . Each curve is generated while keeping the other two parameters constant. I p 0 and I s 0 are each scaled from their initial values corresponding to (a)  I p 0 * / I s 0 * = 10 2 and (b)  I p 0 * / I s 0 * = 10 6 . Δ κ is scaled through Δ k ( I p 0 is kept constant).

Fig. 12
Fig. 12

(Solid curves) Signal plus idler intensity, I s ( z ) + I i ( z ) , versus crystal length for varying initial pump intensities, I p 0 ( Δ k and I s 0 are fixed). The black curves indicate the amplification curves that peak at the desired crystal length, i.e., L = L peak . There are two such curves. The upper curve corresponds to the desired conformal value of I p 0 , which maximizes I s + I i at z = L , and for which Δ κ < 1 . The bottom curve corresponds to a I p 0 for which Δ κ > 1 and I p 0 is several orders of magnitude lower. (Dashed curve) Locus of points I p 0 [peak value of I s ( z ) + I i ( z ) ] versus L peak [length at which I s ( z ) + I i ( z ) peaks]. The curve folds at a value of I p 0 corresponding to Δ κ 1.0 (see [43]).

Fig. 13
Fig. 13

(Dark solid curves) (a) and (b) Gaussian, (c) and (d) flattop, and (e) and (f) conformal pump intensity profiles, I p 0 G ( t ) , I p 0 F ( t ) , and I p 0 C ( t ) , respectively. In the left column, (a), (c), and (e) have a seed bandwidth δ ω s = 1.4 δ ω pm , and thus share the same Δ k ( t ) . In the right column, (b), (d), and (f) have a seed bandwidth δ ω s = 2.2 δ ω pm , and also share the same Δ k ( t ) . Signal frequency ( ω ω s ) is indexed on the top axis. The larger seed bandwidth in (f) versus (e) requires taller I p 0 C ( t ) wings to compensate for the larger | Δ k | , and thus the corresponding pump profiles have different shapes. [Note, in (e) and (f), the dotted curves indicate the exact conformal profile solution, without super-Gaussian edges.] In each panel, signal plus idler gain is calculated using Eqs. (1, 2). All cases share the same seed profile, I s 0 (dashed curve), plotted here on a scale 100 × higher than I p 0 . In each case, I s ( L ) + I i ( L ) (light solid curve) is plotted at the length that provides the highest obtainable EBP, requiring L = L peak ( 0 ) for the conformal profiles, L = 1.04 * L peak ( 0 ) for the flattop profiles, and L = 1.09 * L peak ( 0 ) for the Gaussian profiles. The Gaussian and flattop cases are thus slightly oversaturated. In each case, I p 0 ( 0 ) / I s 0 ( 0 ) = 10 3 .

Fig. 14
Fig. 14

Efficiency ( η ) , amplified signal bandwidth ( Δ ω ) , and EBP ( η Δ ω ) versus seed bandwidth compared for (a) conformal and Gaussian pump profiles and (b) conformal and flattop pump profiles. For each type of pump profile, we choose the crystal length that provides the highest obtainable EBP for each case, requiring L = L peak ( 0 ) for the conformal profiles, L = 1.04 * L peak ( 0 ) for the flattop profiles, and L = 1.09 * L peak ( 0 ) for the Gaussian profiles.

Fig. 15
Fig. 15

EBP versus amplified signal bandwidth for Gaussian, flattop, and conformal profiles. For Gaussian and flattop cases, the darker lines represent the choice of L (i.e., degree of saturation) that maximizes the EBP, while the lighter curves are performance curves for longer crystal lengths. The crystal lengths plotted for the flattop case are L / L peak ( 0 ) = 1.04 , 1.1, 1.2, 1.4, 1.8, and for the Gaussian case are L / L peak ( 0 ) = 1.09 , 1.2, 1.4, 1.8.

Fig. 16
Fig. 16

Same as Fig. 15, but with Δ k ( t ) now defined for a group-velocity-unmatched amplifier. Here, the crystal lengths plotted for the flattop case are L / L peak ( 0 ) = 1.07 , 1.2, 1.4, 1.8, and for the Gaussian case are L / L peak ( 0 ) = 1.10 , 1.2, 1.4, 1.8.

Fig. 17
Fig. 17

(Dark solid curves) Conformal pump intensity profiles, as in Figs. 13e, 13f, but solved for I p 0 ( ± τ 0 ) = 1 and L = L peak ( ± τ 0 ) . As in Fig. 13, the seed bandwidth of (b) is 1.6 × larger than (a). Also plotted: I s 0 ( t ) (dashed curve), plotted on a scale 100 × higher, and I s ( L ) + I i ( L ) (light solid curves).

Fig. 18
Fig. 18

EBP versus amplified signal bandwidth for Gaussian, flattop, and conformal profiles, where all profiles (including conformal) share the same peak intensity, I p 0 = 1 . Each pane shows the results for a different seed profile, (a) having the least variation in I s 0 , and (c) having the greatest.

Fig. 19
Fig. 19

Study of tolerance to errors in I p 0 C ( t ) (solid curves). Figures 19a, 19b correspond to the same amplifier depicted in Fig. 13e, while Figs. 19c, 19d correspond to the amplifier depicted in Fig. 13f. The two dashed curves, I p 0 , 90 % ( t ) , are the upper and lower bounds of I p 0 ( t ) that result in I s ( L ) + I i ( L ) = 0.9 I p 0 ( t ) at L = L peak ( 0 ) . Therefore, they represent the tolerances in I p 0 ( t ) for obtaining 90% of the maximum conformal profile con version efficiency. I p 0 , Approx ( t ) , Eq. (15), (dotted curve) approxi mates I p 0 C ( t ) well enough to stay within the bounds delineated by I p 0 , 90 % ( t ) .

Fig. 20
Fig. 20

(Solid curve) Corresponding to Fig. 12, signal plus idler intensity, I s + I i , versus pump intensity, I p 0 , after amplification in a crystal of length L. Arrows with index n refer to values of I p 0 at which L = L peak , n . There are two values of I p 0 corresponding to each L peak , n = L : one for Δ κ < 1 and one for Δ κ > 1 . The vertical lines mark the boundary at Δ κ = 1 . (Dot-dashed curve) Same as the solid curve, but with Δ k reduced to half the value.

Fig. 21
Fig. 21

Same as Fig. 12, but with Δ k set at 4 × the value. There is no longer a solution to Eq. (12) (i.e., to L = L peak , 1 )

Fig. 22
Fig. 22

Signal plus idler intensity, I s ( z ) + I i ( z ) , versus crystal length for varying seed intensities, I s 0 ( Δ k and I p 0 are fixed). The darker curve indicates the amplification curve that peaks at the desired crystal length, i.e., L = L peak , and thus solves Eq. (12).

Fig. 23
Fig. 23

(a) Conformal profile (solid curve), and constant intensity “flattop” seed profiles with intensity corresponding to the conformal profile minimum (dashed curve, “Flattop 1”) and maximum (dot-dashed curve, “Flattop 2”). (b)  I s ( L ) + I i ( L ) for the conformal profile at L = L peak ( t = 0 ) , and the flattop profiles at an optimally oversaturated length L = 1.09 * L peak ( t = 0 ) . The initial pump profile (dotted curve) is Gaussian with 1/e half-width τ 0 . For each profile type, we pick the seed chirp that maximizes the EBP. The peak pump intensity, I p 0 ( 0 ) , is 10 3 higher than I s 0 C ( 0 ) . Thus, I p 0 ( 0 ) / I s 0 ( 0 ) = 10 3 and 80 for Flattop 1 and Flattop 2, respectively.

Fig. 24
Fig. 24

Corresponding to Fig. 23, I s ( z ) + I i ( z ) for temporal coordinates t / τ 0 = 0 , 0.2, 0.4, 0.6, 0.8, 1.0, and 1.08, where L = L peak ( t = 0 ) . (a) Corresponds to a flattop I s 0 profile (“Flattop 1” of Fig. 23) and (b) corresponds to the conformal profile of Fig. 23. Unlike the flattop case, the conformal seed profile sets L = L peak ( t ) for all t.

Fig. 25
Fig. 25

Corresponding to the I s 0 profiles of Fig. 23, EBP versus amplified signal bandwidth. The flattop curves correspond to the degree of saturation ( L = 1.09 * L peak ( t = 0 ) ) that maximizes the EBP.

Fig. 26
Fig. 26

Conformal seed profiles for a Gaussian pump pulse and I p 0 ( t = 0 ) / I s 0 ( t = 0 ) = 10 2 (a) and 10 5 (b).

Tables (1)

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Table 1 Limits to Conformal Pump Profiles a

Equations (47)

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I s ( z ) = I s 0 + ω s ω p I p 0 cn 2 [ I p 0 I p 0 Γ γ z + K ( γ ) , γ ] ,
I i ( z ) = ω i ω p I p 0 cn 2 [ I p 0 I p 0 Γ γ z + K ( γ ) , γ ] ,
I p ( z ) = I p 0 I p 0 cn 2 [ I p 0 I p 0 Γ γ z + K ( γ ) , γ ] ,
I p 0 = I p 0 ( α β ) / 2 , γ = I p 0 β , β = [ α 2 Δ k 2 Γ 2 I p 0 2 ] 1 / 2 , α = ω p ω s I s 0 + ( 1 + Δ k 2 4 Γ 2 ) I p 0 , Γ = 2 ω s ω i I p 0 d eff 2 n s n i n p c 3 ϵ 0 .
L peak , n = ( 2 n 1 ) K ( γ ) I p 0 I p 0 γ Γ .
I s ( z ) = I s 0 + ω s ω p I p 0 cn 2 [ Γ γ z + K ( γ ) , γ ] ,
γ 2 = I p 0 / [ I p 0 + ( ω p / ω s ) I s 0 ] .
I s ( z ) = I s 0 [ 1 + ( Γ 2 / g 2 ) sinh 2 ( g z ) ] ,
I s ( z ) I s 0 4 exp ( 2 g z ) .
η = d t I s ( L ) + I i ( L ) I p 0 ,
η = d t I p 0 I p 0 ,
L K ( γ ) I p 0 I p 0 γ Γ = 0 ,
Δ k ( ω ) = k ( ω s + δ ω ) + k ( ω i δ ω ) k ( ω p ) = Δ k ( ω s ) + ( 1 / v s 1 / v i ) δ ω + ( 2 k s ω 2 | ω s + 2 k i ω 2 | ω i ) δ ω 2 +
Δ ω = ( ω 2 I s ( ω ) d ω I s ( ω ) d ω ) 1 / 2 ,
I p 0 , Approx ( t ) = I p 0 ( t = 0 ) Γ ( t = 0 ) ( 1 + Δ k ( t ) 2 4 ) ,
d A 1 d z = i ω 1 d eff n 1 c A 2 * A 3 e i Δ k z , d A 2 d z = i ω 2 d eff n 2 c A 1 * A 3 e i Δ k z , d A 3 d z = i ω 3 d eff n 3 c A 1 A 2 e i Δ k z ,
d ρ 1 d z = ω 1 d eff n 1 c ρ 2 ρ 3 sin θ , d ρ 2 d z = ω 2 d eff n 2 c ρ 1 ρ 3 sin θ , d ρ 3 d z = ω 3 d eff n 3 c ρ 1 ρ 2 sin θ , d ϕ 1 d z = ω 1 d eff n 1 c ρ 2 ρ 3 ρ 1 cos θ , d ϕ 2 d z = ω 2 d eff n 2 c ρ 1 ρ 3 ρ 2 cos θ , d ϕ 3 d z = ω 3 d eff n 3 c ρ 1 ρ 2 ρ 3 cos θ , d θ d z = Δ k + d eff c [ ω 3 n 3 ρ 1 ρ 2 ρ 3 ω 1 n 1 ρ 2 ρ 3 ρ 1 ω 2 n 2 ρ 1 ρ 3 ρ 2 ] cos θ .
d ζ u 1 = u 2 u 3 sin θ ,
d ζ u 2 = u 3 u 1 sin θ ,
d ζ u 3 = u 1 u 2 sin θ ,
d ζ ϕ 1 = u 2 u 3 u 1 cos θ ,
d ζ ϕ 2 = u 3 u 1 u 2 cos θ ,
d ζ ϕ 3 = u 1 u 2 u 3 cos θ ,
d ζ θ = Δ S + cot θ d ζ [ ln ( u 1 u 2 u 3 ) ] ,
u i = ( n i c 8 π ω i ) 1 / 2 ρ i ,
ζ = ( 8 π ω 1 ω 2 ω 3 d eff 2 c 3 n 1 n 2 n 3 ) 1 / 2 z ,
( u 1 u 2 u 3 ) d ζ cos θ + cos θ d ζ ( u 1 u 2 u 3 ) = Δ S ( u 1 u 2 u 3 ) sin θ .
cos θ = ( C + Δ S u 3 2 / 2 ) u 1 u 2 u 3 ,
d ζ u 3 2 = 2 u 3 d ζ u 3 = 2 u 1 u 2 u 3 sin θ .
sin θ = ( 1 ( C + Δ S u 3 2 / 2 ) 2 u 1 2 u 2 2 u 3 2 ) 1 / 2 .
d ζ u 3 2 = ± 2 [ ( u 1 u 2 u 3 ) 2 ( C + Δ S u 3 2 / 2 ) 2 ] 1 / 2 .
ζ = ± 1 2 u 3 2 ( 0 ) u 3 2 ( ζ ) d u 3 2 [ ( u 1 u 2 u 3 ) 2 ( C + Δ S u 3 2 / 2 ) 2 ] 1 / 2 .
ζ = ± 1 2 u 3 2 ( 0 ) u 3 2 ( ζ ) d u 3 2 [ ( m 2 u 3 2 ) ( m 1 u 3 2 ) u 3 2 ( C + Δ S u 3 2 / 2 ) 2 ] 1 / 2 .
ζ = ± 1 2 u 3 2 ( 0 ) u 3 2 ( ζ ) d u 3 2 [ ( u 3 c 2 u 3 2 ) ( u 3 b 2 u 3 2 ) ( u 3 a 2 u 3 2 ) ] 1 / 2 .
± ( u 3 c 2 u 3 a 2 ) 1 / 2 ζ = y ( 0 ) y ( ζ ) d y [ ( 1 y 2 ) ( 1 γ 2 y 2 ) ] 1 / 2 ,
γ 2 = ( u 3 b 2 u 3 a 2 ) / ( u 3 c 2 u 3 a 2 ) .
y 2 ( ζ ) = sn 2 [ ( u 3 c 2 u 3 a 2 ) 1 / 2 ζ + ζ 0 , γ ] ,
u 1 2 ( ζ ) = u 1 2 ( 0 ) + u 3 2 ( 0 ) u 3 a 2 ( u 3 b 2 u 3 a 2 ) sn 2 [ ( u 3 c 2 u 3 a 2 ) 1 / 2 ζ + ζ 0 , γ ] ,
[ ( u 3 2 ( 0 ) u 3 2 ) ( u 3 2 ( 0 ) + u 1 2 ( 0 ) u 3 2 ) u 3 2 Δ S 2 ( u 3 2 u 3 2 ( 0 ) ) 2 / 4 ] 1 / 2 .
u 1 2 ( ζ ) = u 1 2 ( 0 ) + u 3 2 ( 0 ) ( 1 sn 2 [ β 1 / 2 ( ζ + ζ 0 ) , γ ] ) ,
sn [ β 1 / 2 ζ 0 , γ ] = 1 ,
β 1 / 2 ζ 0 = K ( γ ) .
I s ( z ) = I s 0 + ω s ω p I p 0 ( 1 sn 2 [ I p 0 I p 0 Γ γ z + K ( γ ) , γ ] ) ,
I i ( z ) = ω i ω p I p 0 ( 1 sn 2 [ I p 0 I p 0 Γ γ z + K ( γ ) , γ ] ) ,
I p ( z ) = I p 0 I p 0 ( 1 sn 2 [ I p 0 I p 0 Γ γ z + K ( γ ) , γ ] ) .
d ϕ i d ζ = Δ S 2 ( u 3 2 ( 0 ) u 3 2 u i 2 ) ,
d ϕ s d z = Δ k 2 ( 1 I s 0 I s ( z ) ) , d ϕ i d z = Δ k 2 , d ϕ p d z = Δ k 2 ( I p 0 ω p / ω s ( I s 0 I s ( z ) ) + I p 0 1 ) ,

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