Abstract

We simulate a four-channel coherent beam combination (CBC) system designed for femtosecond petawatt lasers. Typical behavior characteristics of the CBC system are revealed. Key parameters relevant to engineering are identified. A simple automatic alignment method is also demonstrated with the virtual CBC system. This work may benefit relevant projects around the world.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (2)

C. Danson, C. Haefner, J. Bromage, T. Butcher, J. Chanteloup, E. Chowdhury, A. Galvanauskas, L. Gizzi, J. Hein, D. Hillier, N. Hopps, Y. Kato, E. Khazanov, R. Kodama, G. Korn, R. Li, Y. Li, J. Limpert, J. Ma, C. Nam, D. Neely, D. Papadopoulos, R. Penman, L. Qian, J. Rocca, A. Shaykin, C. Siders, C. Spindloe, S. Szatmari, R. Trines, J. Zhu, P. Zhu, and J. Zuegel, “Petawatt and exawatt class lasers worldwide,” High Power Laser Sci. Eng. 7, e54 (2019).
[Crossref]

C. Peng, X. Liang, R. Liu, W. Li, and R. Li, “Two-beam coherent combining based on Ti:Sapphire chirped-pulse amplification at repetition of 1 Hz,” Opt. Lett. 44(17), 4379–4382 (2019).
[Crossref]

2018 (4)

J. Kim, Y. Wang, and X. Zhang, “Calculation of vectorial diffraction in optical systems,” J. Opt. Soc. Am. A 35(4), 526–535 (2018).
[Crossref]

B. Shen, Z. Bu, J. Xu, T. Xu, L. Ji, R. Li, and Z. Xu, “Exploring vacuum birefringence based on a 100 PW laser and an x-ray free electron laser beam,” Plasma Phys. Controlled Fusion 60(4), 044002 (2018).
[Crossref]

H. Kiriyama, A. Pirozhkov, M. Nishiuchi, Y. Fukuda, K. Ogura, A. Sagisaka, Y. Miyasaka, M. Mori, H. Sakaki, N. Dover, K. Kondo, J. Koga, T. Esirkepov, M. Kando, and K. Kondo, “High-contrast high-intensity repetitive petawatt laser,” Opt. Lett. 43(11), 2595–2598 (2018).
[Crossref]

J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Sci. Eng. 6, e29 (2018).
[Crossref]

2017 (5)

2016 (1)

2015 (4)

V. Leshchenko, “Coherent combining efficiency in tiled and filled aperture approaches,” Opt. Express 23(12), 15944–15970 (2015).
[Crossref]

Z. Zhao, Y. Gao, Y. Cui, Z. Xu, N. An, D. Liu, T. Wang, D. Rao, M. Chen, W. Feng, L. Ji, Z. Cao, X. Yang, and W. Ma, “Investigation of phase effects of coherent beam combining for large-aperture ultrashort ultrahigh intensity laser systems,” Appl. Opt. 54(33), 9939–9948 (2015).
[Crossref]

V. Leshchenko, V. Vasiliev, N. Kvashnin, and E. Pestryakov, “Coherent combining of relativistic-intensity femtosecond laser pulses,” Appl. Phys. B: Lasers Opt. 118(4), 511–516 (2015).
[Crossref]

S. Bulanov, T. Esirkepov, M. Kando, J. Koga, K. Kondo, and G. Korn, “On the problems of relativistic laboratory astrophysics and fundamental physics with super powerful lasers,” Plasma Phys. Rep. 41(1), 1–51 (2015).
[Crossref]

2014 (3)

V. Leshchenko, V. Trunov, S. Frolov, E. Pestryakov, V. Vasiliev, N. Kvashnin, and S. Bagayev, “Coherent combining of multimillijoule parametric-amplified femtosecond pulses,” Laser Phys. Lett. 11(9), 095301 (2014).
[Crossref]

S. Bagayev, V. Leshchenko, V. Trunov, E. Pestryakov, and S. Frolov, “Coherent combining of femtosecond pulses parametrically amplified in BBO crystals,” Opt. Lett. 39(6), 1517–1519 (2014).
[Crossref]

S. Bagayev, V. Trunov, E. Pestryakov, S. Frolov, V. Leshchenko, A. Kokh, and V. Vasiliev, “Super-intense femtosecond multichannel laser system with coherent beam combining,” Laser Phys. 24(7), 074016 (2014).
[Crossref]

2013 (2)

B. Rus, P. Bakule, D. Kramer, G. Korn, J. Green, J. Novak, M. Fibrich, F. Batysta, J. Thoma, and J. Naylon, “ELI-Beamlines laser systems: status and design options,” Proc. SPIE 8780, 87801T (2013).
[Crossref]

Y. Chu, X. Liang, L. Yu, Y. Xu, L. Xu, L. Ma, X. Lu, Y. Liu, Y. Leng, R. Li, and Z. Xu, “High-contrast 2.0 Petawatt Ti:Sapphire laser system,” Opt. Express 21(24), 29231–29239 (2013).
[Crossref]

2012 (2)

2011 (1)

2010 (4)

2009 (1)

E. Esarey, C. Schroeder, and W. Leemans, “Physics of laser-driven plasma based electron accelerators,” Rev. Mod. Phys. 81(3), 1229–1285 (2009).
[Crossref]

2008 (2)

J. Qiao, A. Kalb, T. Nguyen, J. Bunkenburg, D. Canning, and J. Kelly, “Demonstration of large-aperture tiled-grating compressors for high-energy, petawatt-class, chirped-pulse amplification systems,” Opt. Lett. 33(15), 1684–1686 (2008).
[Crossref]

N. Blanchot, G. Behar, T. Berthier, E. Bignon, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, J. Ebrardt, O. Flour, Y. Gautheron, P. Gibert, O. Hartmann, E. Hugonnot, F. Laborde, D. Lebeaux, J. Luce, S. Montant, S. Noailles, J. Neauport, D. Raffestin, A. Roques, F. Sautarel, M. Sautet, C. Sauteret, and C. Rouyer, “Overview of PETAL, the multi-Petawatt project on the LIL facility,” Plasma Phys. Controlled Fusion 50(12), 124045 (2008).
[Crossref]

2007 (2)

2006 (1)

M. Dunne, “A high-power laser fusion facility for Europe,” Nat. Phys. 2(1), 2–5 (2006).
[Crossref]

2005 (3)

M. Tabak, D. Clark, S. Hatchett, M. Key, B. Lasinski, R. Snavely, S. Wilks, R. Town, R. Stephens, E. Campbell, R. Kodama, K. Mima, K. Tanaka, S. Atzeni, and R. Freeman, “Review of progress in fast ignition,” Phys. Plasmas 12(5), 057305 (2005).
[Crossref]

H. Nguyen, J. Britten, T. Carlson, J. Nissen, L. Summers, C. Hoaglan, M. Aasen, J. Peterson, and I. Jovanovic, “Gratings for high-energy petawatt lasers,” Proc. SPIE 5991, 59911M (2005).
[Crossref]

T. Y. Fan, “Laser beam combining for high-power, high radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
[Crossref]

2004 (3)

T. Kessler, J. Bunkenburg, H. Huang, A. Kozlov, and D. Meyerhofer, “Demonstration of coherent addition of multiple gratings for high-energy chirped-pulse-amplified lasers,” Opt. Lett. 29(6), 635–637 (2004).
[Crossref]

C. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Crane, J. Dawson, A. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Nguyen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44(12), S266–S275 (2004).
[Crossref]

S. Bahk, P. Rousseau, T. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Generation and characterization of the highest laser intensities (1022 W/cm2),” Opt. Lett. 29(24), 2837–2839 (2004).
[Crossref]

2003 (1)

2001 (1)

M. Roth, T. Cowan, M. Key, S. Hatchett, C. Brown, W. Fountain, J. Johnson, D. Pennington, R. Snavely, S. Wilks, K. Yasuike, H. Ruhl, F. Pegoraro, S. Bulanov, E. Campbell, M. Perry, and H. Powell, “Fast ignition by intense laser-accelerated proton beams,” Phys. Rev. Lett. 86(3), 436–439 (2001).
[Crossref]

1999 (1)

1998 (1)

T. Zhang, M. Yonemura, and Y. Kato, “An array-grating compressor for high-power chirped-pulse amplification lasers,” Opt. Commun. 145(1-6), 367–376 (1998).
[Crossref]

1993 (1)

Lifeng Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40(4), 553–573 (1993).
[Crossref]

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(4-6), 437–440 (1992).
[Crossref]

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
[Crossref]

1979 (1)

T. Tajima and J. Dawson, “Laser-electron accelerator,” Phys. Rev. Lett. 43(4), 267–270 (1979).
[Crossref]

1965 (1)

J. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7(4), 308–313 (1965).
[Crossref]

1962 (1)

1960 (1)

T. Maiman, “Stimulated optical radiation,” Nature 187(4736), 493–494 (1960).
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Aasen, M.

H. Nguyen, J. Britten, T. Carlson, J. Nissen, L. Summers, C. Hoaglan, M. Aasen, J. Peterson, and I. Jovanovic, “Gratings for high-energy petawatt lasers,” Proc. SPIE 5991, 59911M (2005).
[Crossref]

J. Britten, H. Nguyen, L. Jones, T. Carlson, C. Hoaglan, L. Summers, M. Aasen, A. Rigatti, and J. Oliver, “First demonstration of a meter-scale multilayer dielectric reflection grating for high-energy petawatt-class lasers,” Lawrence Livermore National Laboratory, UCRL-JRNL-205887 (2004).

Akahane, Y.

Alexander, N.

M. Dunne, N. Alexander, and F. Amiranoff, “Technical Background and Conceptual Design Report 2007,” http://www.hiper-laser.org/overview/tdr/tdr.asp .

Amiranoff, F.

M. Dunne, N. Alexander, and F. Amiranoff, “Technical Background and Conceptual Design Report 2007,” http://www.hiper-laser.org/overview/tdr/tdr.asp .

An, N.

Aoyama, M.

Atzeni, S.

M. Tabak, D. Clark, S. Hatchett, M. Key, B. Lasinski, R. Snavely, S. Wilks, R. Town, R. Stephens, E. Campbell, R. Kodama, K. Mima, K. Tanaka, S. Atzeni, and R. Freeman, “Review of progress in fast ignition,” Phys. Plasmas 12(5), 057305 (2005).
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Audebert, P.

Bagayev, S.

V. Leshchenko, V. Trunov, S. Frolov, E. Pestryakov, V. Vasiliev, N. Kvashnin, and S. Bagayev, “Coherent combining of multimillijoule parametric-amplified femtosecond pulses,” Laser Phys. Lett. 11(9), 095301 (2014).
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S. Bagayev, V. Trunov, E. Pestryakov, S. Frolov, V. Leshchenko, A. Kokh, and V. Vasiliev, “Super-intense femtosecond multichannel laser system with coherent beam combining,” Laser Phys. 24(7), 074016 (2014).
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S. Bagayev, V. Leshchenko, V. Trunov, E. Pestryakov, and S. Frolov, “Coherent combining of femtosecond pulses parametrically amplified in BBO crystals,” Opt. Lett. 39(6), 1517–1519 (2014).
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Bahk, S.

Bakule, P.

B. Rus, P. Bakule, D. Kramer, G. Korn, J. Green, J. Novak, M. Fibrich, F. Batysta, J. Thoma, and J. Naylon, “ELI-Beamlines laser systems: status and design options,” Proc. SPIE 8780, 87801T (2013).
[Crossref]

Bar, E.

Barty, C.

H. Habara, G. Xu, T. Jitsuno, R. Kodama, K. Suzuki, K. Sawai, K. Kondo, N. Miyanaga, K. Tanaka, K. Mima, M. Rushford, J. Britten, and C. Barty, “Pulse compression and beam focusing with segmented diffraction gratings in a high-power chirped-pulse amplification glass laser system,” Opt. Lett. 35(11), 1783–1785 (2010).
[Crossref]

C. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Crane, J. Dawson, A. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Nguyen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44(12), S266–S275 (2004).
[Crossref]

Batysta, F.

B. Rus, P. Bakule, D. Kramer, G. Korn, J. Green, J. Novak, M. Fibrich, F. Batysta, J. Thoma, and J. Naylon, “ELI-Beamlines laser systems: status and design options,” Proc. SPIE 8780, 87801T (2013).
[Crossref]

Beach, R.

C. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Crane, J. Dawson, A. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Nguyen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44(12), S266–S275 (2004).
[Crossref]

Beer, G.

C. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Crane, J. Dawson, A. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Nguyen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44(12), S266–S275 (2004).
[Crossref]

Behar, G.

N. Blanchot, E. Bar, G. Behar, C. Bellet, D. Bigourd, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, O. Flour, O. Hartmann, L. Hilsz, E. Hugonnot, E. Lavastre, J. Luce, E. Mazataud, J. Neauport, S. Noailles, B. Remy, F. Sautarel, M. Sautet, and C. Rouyer, “Experimental demonstration of a synthetic aperture compression scheme for multi-Petawatt high-energy lasers,” Opt. Express 18(10), 10088–10097 (2010).
[Crossref]

N. Blanchot, G. Behar, T. Berthier, E. Bignon, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, J. Ebrardt, O. Flour, Y. Gautheron, P. Gibert, O. Hartmann, E. Hugonnot, F. Laborde, D. Lebeaux, J. Luce, S. Montant, S. Noailles, J. Neauport, D. Raffestin, A. Roques, F. Sautarel, M. Sautet, C. Sauteret, and C. Rouyer, “Overview of PETAL, the multi-Petawatt project on the LIL facility,” Plasma Phys. Controlled Fusion 50(12), 124045 (2008).
[Crossref]

Bellet, C.

Berthier, T.

N. Blanchot, G. Behar, T. Berthier, E. Bignon, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, J. Ebrardt, O. Flour, Y. Gautheron, P. Gibert, O. Hartmann, E. Hugonnot, F. Laborde, D. Lebeaux, J. Luce, S. Montant, S. Noailles, J. Neauport, D. Raffestin, A. Roques, F. Sautarel, M. Sautet, C. Sauteret, and C. Rouyer, “Overview of PETAL, the multi-Petawatt project on the LIL facility,” Plasma Phys. Controlled Fusion 50(12), 124045 (2008).
[Crossref]

Bignon, E.

N. Blanchot, G. Behar, T. Berthier, E. Bignon, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, J. Ebrardt, O. Flour, Y. Gautheron, P. Gibert, O. Hartmann, E. Hugonnot, F. Laborde, D. Lebeaux, J. Luce, S. Montant, S. Noailles, J. Neauport, D. Raffestin, A. Roques, F. Sautarel, M. Sautet, C. Sauteret, and C. Rouyer, “Overview of PETAL, the multi-Petawatt project on the LIL facility,” Plasma Phys. Controlled Fusion 50(12), 124045 (2008).
[Crossref]

Bigourd, D.

Blanchot, N.

N. Blanchot, E. Bar, G. Behar, C. Bellet, D. Bigourd, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, O. Flour, O. Hartmann, L. Hilsz, E. Hugonnot, E. Lavastre, J. Luce, E. Mazataud, J. Neauport, S. Noailles, B. Remy, F. Sautarel, M. Sautet, and C. Rouyer, “Experimental demonstration of a synthetic aperture compression scheme for multi-Petawatt high-energy lasers,” Opt. Express 18(10), 10088–10097 (2010).
[Crossref]

N. Blanchot, G. Behar, T. Berthier, E. Bignon, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, J. Ebrardt, O. Flour, Y. Gautheron, P. Gibert, O. Hartmann, E. Hugonnot, F. Laborde, D. Lebeaux, J. Luce, S. Montant, S. Noailles, J. Neauport, D. Raffestin, A. Roques, F. Sautarel, M. Sautet, C. Sauteret, and C. Rouyer, “Overview of PETAL, the multi-Petawatt project on the LIL facility,” Plasma Phys. Controlled Fusion 50(12), 124045 (2008).
[Crossref]

Bodefeld, R.

Boubault, F.

N. Blanchot, E. Bar, G. Behar, C. Bellet, D. Bigourd, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, O. Flour, O. Hartmann, L. Hilsz, E. Hugonnot, E. Lavastre, J. Luce, E. Mazataud, J. Neauport, S. Noailles, B. Remy, F. Sautarel, M. Sautet, and C. Rouyer, “Experimental demonstration of a synthetic aperture compression scheme for multi-Petawatt high-energy lasers,” Opt. Express 18(10), 10088–10097 (2010).
[Crossref]

N. Blanchot, G. Behar, T. Berthier, E. Bignon, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, J. Ebrardt, O. Flour, Y. Gautheron, P. Gibert, O. Hartmann, E. Hugonnot, F. Laborde, D. Lebeaux, J. Luce, S. Montant, S. Noailles, J. Neauport, D. Raffestin, A. Roques, F. Sautarel, M. Sautet, C. Sauteret, and C. Rouyer, “Overview of PETAL, the multi-Petawatt project on the LIL facility,” Plasma Phys. Controlled Fusion 50(12), 124045 (2008).
[Crossref]

Breitkopf, S.

Britten, J.

H. Habara, G. Xu, T. Jitsuno, R. Kodama, K. Suzuki, K. Sawai, K. Kondo, N. Miyanaga, K. Tanaka, K. Mima, M. Rushford, J. Britten, and C. Barty, “Pulse compression and beam focusing with segmented diffraction gratings in a high-power chirped-pulse amplification glass laser system,” Opt. Lett. 35(11), 1783–1785 (2010).
[Crossref]

H. Nguyen, J. Britten, T. Carlson, J. Nissen, L. Summers, C. Hoaglan, M. Aasen, J. Peterson, and I. Jovanovic, “Gratings for high-energy petawatt lasers,” Proc. SPIE 5991, 59911M (2005).
[Crossref]

C. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Crane, J. Dawson, A. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Nguyen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44(12), S266–S275 (2004).
[Crossref]

M. Perry, D. Pennington, B. Stuart, G. Tietbohl, J. Britten, C. Brown, S. Herman, B. Golick, M. Kartz, J. Miller, H. Powell, M. Vergino, and V. Yanovsky, “Petawatt laser pulses,” Opt. Lett. 24(3), 160–162 (1999).
[Crossref]

J. Britten, H. Nguyen, L. Jones, T. Carlson, C. Hoaglan, L. Summers, M. Aasen, A. Rigatti, and J. Oliver, “First demonstration of a meter-scale multilayer dielectric reflection grating for high-energy petawatt-class lasers,” Lawrence Livermore National Laboratory, UCRL-JRNL-205887 (2004).

Bromage, J.

C. Danson, C. Haefner, J. Bromage, T. Butcher, J. Chanteloup, E. Chowdhury, A. Galvanauskas, L. Gizzi, J. Hein, D. Hillier, N. Hopps, Y. Kato, E. Khazanov, R. Kodama, G. Korn, R. Li, Y. Li, J. Limpert, J. Ma, C. Nam, D. Neely, D. Papadopoulos, R. Penman, L. Qian, J. Rocca, A. Shaykin, C. Siders, C. Spindloe, S. Szatmari, R. Trines, J. Zhu, P. Zhu, and J. Zuegel, “Petawatt and exawatt class lasers worldwide,” High Power Laser Sci. Eng. 7, e54 (2019).
[Crossref]

Brown, C.

C. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Crane, J. Dawson, A. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Nguyen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44(12), S266–S275 (2004).
[Crossref]

M. Roth, T. Cowan, M. Key, S. Hatchett, C. Brown, W. Fountain, J. Johnson, D. Pennington, R. Snavely, S. Wilks, K. Yasuike, H. Ruhl, F. Pegoraro, S. Bulanov, E. Campbell, M. Perry, and H. Powell, “Fast ignition by intense laser-accelerated proton beams,” Phys. Rev. Lett. 86(3), 436–439 (2001).
[Crossref]

M. Perry, D. Pennington, B. Stuart, G. Tietbohl, J. Britten, C. Brown, S. Herman, B. Golick, M. Kartz, J. Miller, H. Powell, M. Vergino, and V. Yanovsky, “Petawatt laser pulses,” Opt. Lett. 24(3), 160–162 (1999).
[Crossref]

Bryan, S.

C. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Crane, J. Dawson, A. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Nguyen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44(12), S266–S275 (2004).
[Crossref]

Bu, Z.

B. Shen, Z. Bu, J. Xu, T. Xu, L. Ji, R. Li, and Z. Xu, “Exploring vacuum birefringence based on a 100 PW laser and an x-ray free electron laser beam,” Plasma Phys. Controlled Fusion 60(4), 044002 (2018).
[Crossref]

Bulanov, S.

S. Bulanov, T. Esirkepov, M. Kando, J. Koga, K. Kondo, and G. Korn, “On the problems of relativistic laboratory astrophysics and fundamental physics with super powerful lasers,” Plasma Phys. Rep. 41(1), 1–51 (2015).
[Crossref]

M. Roth, T. Cowan, M. Key, S. Hatchett, C. Brown, W. Fountain, J. Johnson, D. Pennington, R. Snavely, S. Wilks, K. Yasuike, H. Ruhl, F. Pegoraro, S. Bulanov, E. Campbell, M. Perry, and H. Powell, “Fast ignition by intense laser-accelerated proton beams,” Phys. Rev. Lett. 86(3), 436–439 (2001).
[Crossref]

Bunkenburg, J.

Butcher, T.

C. Danson, C. Haefner, J. Bromage, T. Butcher, J. Chanteloup, E. Chowdhury, A. Galvanauskas, L. Gizzi, J. Hein, D. Hillier, N. Hopps, Y. Kato, E. Khazanov, R. Kodama, G. Korn, R. Li, Y. Li, J. Limpert, J. Ma, C. Nam, D. Neely, D. Papadopoulos, R. Penman, L. Qian, J. Rocca, A. Shaykin, C. Siders, C. Spindloe, S. Szatmari, R. Trines, J. Zhu, P. Zhu, and J. Zuegel, “Petawatt and exawatt class lasers worldwide,” High Power Laser Sci. Eng. 7, e54 (2019).
[Crossref]

Caird, J.

C. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Crane, J. Dawson, A. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Nguyen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44(12), S266–S275 (2004).
[Crossref]

Campbell, E.

M. Tabak, D. Clark, S. Hatchett, M. Key, B. Lasinski, R. Snavely, S. Wilks, R. Town, R. Stephens, E. Campbell, R. Kodama, K. Mima, K. Tanaka, S. Atzeni, and R. Freeman, “Review of progress in fast ignition,” Phys. Plasmas 12(5), 057305 (2005).
[Crossref]

M. Roth, T. Cowan, M. Key, S. Hatchett, C. Brown, W. Fountain, J. Johnson, D. Pennington, R. Snavely, S. Wilks, K. Yasuike, H. Ruhl, F. Pegoraro, S. Bulanov, E. Campbell, M. Perry, and H. Powell, “Fast ignition by intense laser-accelerated proton beams,” Phys. Rev. Lett. 86(3), 436–439 (2001).
[Crossref]

Canning, D.

Cao, Z.

Carlson, T.

H. Nguyen, J. Britten, T. Carlson, J. Nissen, L. Summers, C. Hoaglan, M. Aasen, J. Peterson, and I. Jovanovic, “Gratings for high-energy petawatt lasers,” Proc. SPIE 5991, 59911M (2005).
[Crossref]

C. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Crane, J. Dawson, A. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Nguyen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44(12), S266–S275 (2004).
[Crossref]

J. Britten, H. Nguyen, L. Jones, T. Carlson, C. Hoaglan, L. Summers, M. Aasen, A. Rigatti, and J. Oliver, “First demonstration of a meter-scale multilayer dielectric reflection grating for high-energy petawatt-class lasers,” Lawrence Livermore National Laboratory, UCRL-JRNL-205887 (2004).

Chanteloup, J.

C. Danson, C. Haefner, J. Bromage, T. Butcher, J. Chanteloup, E. Chowdhury, A. Galvanauskas, L. Gizzi, J. Hein, D. Hillier, N. Hopps, Y. Kato, E. Khazanov, R. Kodama, G. Korn, R. Li, Y. Li, J. Limpert, J. Ma, C. Nam, D. Neely, D. Papadopoulos, R. Penman, L. Qian, J. Rocca, A. Shaykin, C. Siders, C. Spindloe, S. Szatmari, R. Trines, J. Zhu, P. Zhu, and J. Zuegel, “Petawatt and exawatt class lasers worldwide,” High Power Laser Sci. Eng. 7, e54 (2019).
[Crossref]

Chappuis, C.

N. Blanchot, E. Bar, G. Behar, C. Bellet, D. Bigourd, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, O. Flour, O. Hartmann, L. Hilsz, E. Hugonnot, E. Lavastre, J. Luce, E. Mazataud, J. Neauport, S. Noailles, B. Remy, F. Sautarel, M. Sautet, and C. Rouyer, “Experimental demonstration of a synthetic aperture compression scheme for multi-Petawatt high-energy lasers,” Opt. Express 18(10), 10088–10097 (2010).
[Crossref]

N. Blanchot, G. Behar, T. Berthier, E. Bignon, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, J. Ebrardt, O. Flour, Y. Gautheron, P. Gibert, O. Hartmann, E. Hugonnot, F. Laborde, D. Lebeaux, J. Luce, S. Montant, S. Noailles, J. Neauport, D. Raffestin, A. Roques, F. Sautarel, M. Sautet, C. Sauteret, and C. Rouyer, “Overview of PETAL, the multi-Petawatt project on the LIL facility,” Plasma Phys. Controlled Fusion 50(12), 124045 (2008).
[Crossref]

Chen, M.

Chowdhury, E.

C. Danson, C. Haefner, J. Bromage, T. Butcher, J. Chanteloup, E. Chowdhury, A. Galvanauskas, L. Gizzi, J. Hein, D. Hillier, N. Hopps, Y. Kato, E. Khazanov, R. Kodama, G. Korn, R. Li, Y. Li, J. Limpert, J. Ma, C. Nam, D. Neely, D. Papadopoulos, R. Penman, L. Qian, J. Rocca, A. Shaykin, C. Siders, C. Spindloe, S. Szatmari, R. Trines, J. Zhu, P. Zhu, and J. Zuegel, “Petawatt and exawatt class lasers worldwide,” High Power Laser Sci. Eng. 7, e54 (2019).
[Crossref]

Chu, Y.

Chvykov, V.

Clark, D.

M. Tabak, D. Clark, S. Hatchett, M. Key, B. Lasinski, R. Snavely, S. Wilks, R. Town, R. Stephens, E. Campbell, R. Kodama, K. Mima, K. Tanaka, S. Atzeni, and R. Freeman, “Review of progress in fast ignition,” Phys. Plasmas 12(5), 057305 (2005).
[Crossref]

Coic, H.

N. Blanchot, E. Bar, G. Behar, C. Bellet, D. Bigourd, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, O. Flour, O. Hartmann, L. Hilsz, E. Hugonnot, E. Lavastre, J. Luce, E. Mazataud, J. Neauport, S. Noailles, B. Remy, F. Sautarel, M. Sautet, and C. Rouyer, “Experimental demonstration of a synthetic aperture compression scheme for multi-Petawatt high-energy lasers,” Opt. Express 18(10), 10088–10097 (2010).
[Crossref]

N. Blanchot, G. Behar, T. Berthier, E. Bignon, F. Boubault, C. Chappuis, H. Coic, C. Damiens-Dupont, J. Ebrardt, O. Flour, Y. Gautheron, P. Gibert, O. Hartmann, E. Hugonnot, F. Laborde, D. Lebeaux, J. Luce, S. Montant, S. Noailles, J. Neauport, D. Raffestin, A. Roques, F. Sautarel, M. Sautet, C. Sauteret, and C. Rouyer, “Overview of PETAL, the multi-Petawatt project on the LIL facility,” Plasma Phys. Controlled Fusion 50(12), 124045 (2008).
[Crossref]

Cotel, A.

Cowan, T.

M. Roth, T. Cowan, M. Key, S. Hatchett, C. Brown, W. Fountain, J. Johnson, D. Pennington, R. Snavely, S. Wilks, K. Yasuike, H. Ruhl, F. Pegoraro, S. Bulanov, E. Campbell, M. Perry, and H. Powell, “Fast ignition by intense laser-accelerated proton beams,” Phys. Rev. Lett. 86(3), 436–439 (2001).
[Crossref]

Crane, J.

C. Barty, M. Key, J. Britten, R. Beach, G. Beer, C. Brown, S. Bryan, J. Caird, T. Carlson, J. Crane, J. Dawson, A. Erlandson, D. Fittinghoff, M. Hermann, C. Hoaglan, A. Iyer, L. Jones, I. Jovanovic, A. Komashko, O. Landen, Z. Liao, W. Molander, S. Mitchell, E. Moses, N. Nielsen, H-H. Nguyen, J. Nissen, S. Payne, D. Pennington, L. Risinger, M. Rushford, K. Skulina, M. Spaeth, B. Stuart, G. Tietbohl, and B. Wattellier, “An overview of LLNL high-energy short pulse technology for advanced radiography of laser fusion experiments,” Nucl. Fusion 44(12), S266–S275 (2004).
[Crossref]

Crotti, C.

Cui, Y.

Cui, Z.

J. Zhu, X. Xie, M. Sun, J. Kang, Q. Yang, A. Guo, H. Zhu, P. Zhu, Q. Gao, X. Liang, Z. Cui, S. Yang, C. Zhang, and Z. Lin, “Analysis and construction status of SG II-5PW laser facility,” High Power Laser Sci. Eng. 6, e29 (2018).
[Crossref]

Dai, G.

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Figures (13)

Fig. 1.
Fig. 1. Input pulse parameters. (a, b) Beam transverse intensity profile; (c) Spectrum; (d) Fourier-transform-limited temporal intensity profile.
Fig. 2.
Fig. 2. (a) Configuration of the coherent combination system; (b) beam splitting module; (c) pulse compressor module. ‘BS’ indicates beam splitter; ‘M’ reflective mirror; ‘GP’ glass plate for chirp compensation; ‘G’ optical grating; ‘P’ path; ‘FP’ focusing parabola; ‘#’ indicates the path number from 1 to 4.
Fig. 3.
Fig. 3. (a) Cross section of beam envelops after combination; (b) ray matrix distribution on a spherical plane before the focal point; (c) spectral phase induced by the beam combination system.
Fig. 4.
Fig. 4. (a-c) Fluence distributions of 4-beam combination at the focus with different polarizations; (d) isosurfaces (50% of peak intensity) of the spatiotemporal intensity of the 4-beam-combined pulse at from −10um to 10um along propagation axis relative to the focal point at 0um; (e) fluence distribution of 4-beam at the focus obtain with scalar Fourier transform method; (f-h) fluence distributions of the dominant component at the focus with different number of beams. The values of the fluence are normalized to the peak number of the ideal 4-beam combination at the focus.
Fig. 5.
Fig. 5. Spatiotemporal field distributions at the focal point under different input pointing deviations. (a) no deviation; (b) 0.5urad; (c) 0.9urad; (d) 1.8urad. Three isosurfaces in each figure corresponds to 20%, 50% and 80% of the peak intensity in (a).
Fig. 6.
Fig. 6. (a) Mirror surface curvature based on the 4th order polynomial; (b) beam wavefront at 910 nm induced by the mirror surface curvature; (c) focusing efficiency of different curvatures with RMS values. The curvatures are represented with orthonormal polynomials on square aperture from 4th order to 11th order and indicated by S4 to S11.
Fig. 7.
Fig. 7. (a) Change of focusing efficiency with mirror translations d mismatch among four paths; [0, d, 0, 0] indicates that mirror M23 moves d along X direction while other paths are fixed; the 1st (2nd) and 4th (3rd) beams are diagonal; (b) spatiotemporal distribution of the worst situation in (a); (c-f) histograms of 500 samples in which M#3 locations in the four paths are randomly chosen on the condition that the differences among the paths are within 50 nm, 100 nm, 150 nm, and 240 nm, respectively.
Fig. 8.
Fig. 8. (a) Peak location of a single path versus pointing deviation of a reflective mirror; (b) change of peak intensity with pointing deviation of a reflective mirror in path 1 while the other three paths are fixed. Blue-dotted line indicates results induced by mirror M11 alone; red-circle line by M13; black-star line by M15. (c, d) Histograms of 500 samples in which pointing directions of all four paths are randomly chosen revolving Z or Y axis within +/− 0.3urad and +/− 0.5urad, respectively.
Fig. 9.
Fig. 9. (a) Focusing efficiency versus increase of curvature RMS values for four kinds of deformations specified by single Zernike polynomials on rectangular aperture from 4th order to 7th order, indicated by S4 to S7; the curvatures on the four mirrors M#1 are the same. (b-d) Histograms of 500 samples in which surface curvature is generated using combination of 8 polynomials with random coefficients while keeping RMS fixed at 0.02$\lambda$, 0.04$\lambda$ and 0.06$\lambda$, respectively.
Fig. 10.
Fig. 10. (a) Focusing efficiency dependence of the first grating translation along its normal; (b) different angular changes of the first grating on efficiency; (c, d) effects of different surface deformations of the first (c) and second (d) grating on efficiency. The surface deformations are represented by single orthonormal polynomials on rectangular aperture from the 4th order to 11th order (indicated by S4 to S11).
Fig. 11.
Fig. 11. Histograms of 500 samples in which (a) the first grating in four paths randomly shift in [−50 nm, 50 nm]; (b) the first grating in four paths randomly tilt, tip or rotate in [−0.3urad, 0.3urad]; (c, d) surface curvature of the first (c) and second (d) gratings in four paths are generated using combination of 8 polynomials with random coefficients while keeping RMS fixed at 0.06$\lambda$.
Fig. 12.
Fig. 12. Field distributions before (1st row) and after (2nd and 3rd row) optimization. The first 4 columns show the fluence distributions of the four paths separately (units in micrometer); the last column shows the coherently-combined spatiotemporal field distribution. The isosurfaces in the last column corresponds to 10% and 50% of the ideal peak intensity.
Fig. 13.
Fig. 13. Evolutions of relevant parameters of each path during optimization process: (a) peak fluence normalized by the ideal value; (b) RMS of surface deformations; (c-d) normalized coefficients of the first eight square Zernike polynomials used to synthesize the deformations for each path.

Equations (2)

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E ( x ) = i k 4 π Σ G [ k ^ Σ ( N ^ E Σ ) E Σ ( N ^ k ^ Σ ) + N ^ ( R ^ E Σ ) E Σ ( R ^ N ^ ) ( N ^ E Σ ) R ^ ] d 2 x ,
E ( x ) i k exp ( i k f ) 4 π f exp [ i k ( N ^ x ) ] [ k ^ Σ ( N ^ E Σ ) E Σ ( N ^ k ^ Σ ) E Σ ] Δ s ,

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