Abstract

The propagation of high peak-power laser beams in real atmospheres will be affected by both linear and nonlinear effects contained therein. Atmospheric turbulence usually will induce decreases in the filamentation self-focusing collapse distance for refractive index structure parameter increases. This paper provided the first validated analytical equation for predicting the nonlinear self-focusing collapse distance based on a modification of Petrishchev’s and Marburger’s theories. It shows that the estimate of the peak power to critical power at range in turbulence is modified to be the product of the transmitted peak power to critical power ratio times a multiplicative factor derived from Petrishchev’s turbulence equations. This estimate is used in the Marburger distance equation to yield a predicted self-focusing collapse distance. This approach was compared to previous NRL’s HELCAP computer simulation results and showed good agreement. The HELCAP simulations capability has shown good agreement between its results and a previously published laboratory-scale experiment. The analytical approach in this paper may provide a guide for further numerical simulations, more formal theoretical developments and field experiments.

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

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References

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  1. J. Peñano, J. P. Palastro, B. Hafizi, M. H. Helle, and G. P. DiComo, “Self-channeling of high-power laser pulses through strong atmospheric turbulence,” Phys. Rev. A (Coll. Park) 96(1), 013829 (2017).
    [Crossref]
  2. C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions, “in Proceedings of the OSA Conference on Propagation Through and Characterization of Atmospheric and Oceanic Phenomena (Optical Society of America, 2016), paper Tu2A.
    [Crossref]
  3. A. Schmitt-Sody, H. G. Kurz, L. Bergé, S. Skupin, and P. Polynkin, “Picosecond laser filamentation in air,” New J. Phys. 18(9), 093005 (2016).
    [Crossref]
  4. M. Durand, A. Houard, B. Prade, A. Mysyrowicz, A. Durécu, B. Moreau, D. Fleury, O. Vasseur, H. Borchert, K. Diener, R. Schmitt, F. Théberge, M. Chateauneuf, J. F. Daigle, and J. Dubois, “Kilometer Range Filamentation,” Opt. Express 21(22), 26836–26845 (2013).
    [Crossref] [PubMed]
  5. S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
    [Crossref]
  6. A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).
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    [Crossref]
  8. D. Eeltink, N. Berti, N. Marchiando, S. Hermelin, J. Gateau, M. Brunetti, J. P. Wolf, and J. Kasparian, “Triggering filamentation using turbulence,” Phys. Rev. A (Coll. Park) 94(3), 033806 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  11. F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultra-intense light filaments transmitted through clouds<,” Appl. Phys. Lett. 83(2), 213–215 (2003).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2018 (2)

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Engineering Equations for Characterizing Non-Linear Laser Intensity Propagation in air with loss,” Opt. Express 26(4), 3974–3987 (2018).
[Crossref] [PubMed]

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Propagation of infrared ultrashort pulses in the air,” Proc. SPIE 10684, 1068414 (2018).

2017 (1)

J. Peñano, J. P. Palastro, B. Hafizi, M. H. Helle, and G. P. DiComo, “Self-channeling of high-power laser pulses through strong atmospheric turbulence,” Phys. Rev. A (Coll. Park) 96(1), 013829 (2017).
[Crossref]

2016 (2)

A. Schmitt-Sody, H. G. Kurz, L. Bergé, S. Skupin, and P. Polynkin, “Picosecond laser filamentation in air,” New J. Phys. 18(9), 093005 (2016).
[Crossref]

D. Eeltink, N. Berti, N. Marchiando, S. Hermelin, J. Gateau, M. Brunetti, J. P. Wolf, and J. Kasparian, “Triggering filamentation using turbulence,” Phys. Rev. A (Coll. Park) 94(3), 033806 (2016).
[Crossref]

2014 (1)

2013 (1)

2009 (1)

S. A. Shlenov and A. I. Markov, “Control of filamentation of femtosecond laser pulses in a turbulent atmosphere,” Quantum Electron. 39(7), 658−662 (2009).

2008 (1)

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

2007 (1)

S. A. Shlenov, V. P. Kandidov, O. G. Kosareva, A. E. Bezborodov, and V. Yu. Fedorov, “Spatio-temporal control of femtosecond laser pulse filamentation in the atmosphere,” Proc. SPIE 6733, 67332M (2007).

2006 (1)

2004 (2)

M. Kolesik and J. V. Moloney, “Self-healing femtosecond light filaments,” Opt. Lett. 29(6), 590–592 (2004).
[Crossref] [PubMed]

J. R. Penano, P. Sprangle, B. Hazafi, A. Ting, D. F. Gordon, and C. A. Kapetanakos, “Propagation of ultra-short, intense laser pulses in air,” Phys. Plasmas 11(5), 2865–2874 (2004).
[Crossref]

2003 (1)

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultra-intense light filaments transmitted through clouds<,” Appl. Phys. Lett. 83(2), 213–215 (2003).
[Crossref]

2002 (2)

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

1999 (1)

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

1991 (1)

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30(8), 1228 (1991).
[Crossref]

1971 (1)

V. Petrishchev, “Application of the Method of Moments to Certain Problems in the Propagation of Partially Coherent Light Beams, Izvestiya Vysshikh Uchebnykh Zavedenii,” Radiofizika 14(9), 1416–1426 (1971).

1969 (1)

E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179(3), 862–868 (1969).
[Crossref]

Ackermann, R.

Baudelet, M.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions, “in Proceedings of the OSA Conference on Propagation Through and Characterization of Atmospheric and Oceanic Phenomena (Optical Society of America, 2016), paper Tu2A.
[Crossref]

Bergé, L.

A. Schmitt-Sody, H. G. Kurz, L. Bergé, S. Skupin, and P. Polynkin, “Picosecond laser filamentation in air,” New J. Phys. 18(9), 093005 (2016).
[Crossref]

Berti, N.

D. Eeltink, N. Berti, N. Marchiando, S. Hermelin, J. Gateau, M. Brunetti, J. P. Wolf, and J. Kasparian, “Triggering filamentation using turbulence,” Phys. Rev. A (Coll. Park) 94(3), 033806 (2016).
[Crossref]

Bezborodov, A. E.

S. A. Shlenov, V. P. Kandidov, O. G. Kosareva, A. E. Bezborodov, and V. Yu. Fedorov, “Spatio-temporal control of femtosecond laser pulse filamentation in the atmosphere,” Proc. SPIE 6733, 67332M (2007).

Borchert, H.

Bourdon, P.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Boutou, V.

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultra-intense light filaments transmitted through clouds<,” Appl. Phys. Lett. 83(2), 213–215 (2003).
[Crossref]

Brodeur, A.

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

Brunetti, M.

D. Eeltink, N. Berti, N. Marchiando, S. Hermelin, J. Gateau, M. Brunetti, J. P. Wolf, and J. Kasparian, “Triggering filamentation using turbulence,” Phys. Rev. A (Coll. Park) 94(3), 033806 (2016).
[Crossref]

Chateauneuf, M.

Chin, S.

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

Chin, S. L.

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

Courairon, A.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Courvoisier, F.

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultra-intense light filaments transmitted through clouds<,” Appl. Phys. Lett. 83(2), 213–215 (2003).
[Crossref]

Daigle, J. F.

Dawes, E. L.

E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179(3), 862–868 (1969).
[Crossref]

DiComo, G. P.

J. Peñano, J. P. Palastro, B. Hafizi, M. H. Helle, and G. P. DiComo, “Self-channeling of high-power laser pulses through strong atmospheric turbulence,” Phys. Rev. A (Coll. Park) 96(1), 013829 (2017).
[Crossref]

Diener, K.

Dubois, J.

Durand, M.

Durécu, A.

M. Durand, A. Houard, B. Prade, A. Mysyrowicz, A. Durécu, B. Moreau, D. Fleury, O. Vasseur, H. Borchert, K. Diener, R. Schmitt, F. Théberge, M. Chateauneuf, J. F. Daigle, and J. Dubois, “Kilometer Range Filamentation,” Opt. Express 21(22), 26836–26845 (2013).
[Crossref] [PubMed]

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Eeltink, D.

D. Eeltink, N. Berti, N. Marchiando, S. Hermelin, J. Gateau, M. Brunetti, J. P. Wolf, and J. Kasparian, “Triggering filamentation using turbulence,” Phys. Rev. A (Coll. Park) 94(3), 033806 (2016).
[Crossref]

Fedorov, V. Yu.

S. A. Shlenov, V. P. Kandidov, O. G. Kosareva, A. E. Bezborodov, and V. Yu. Fedorov, “Spatio-temporal control of femtosecond laser pulse filamentation in the atmosphere,” Proc. SPIE 6733, 67332M (2007).

Fleury, B.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Fleury, D.

Franco, M.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Gateau, J.

D. Eeltink, N. Berti, N. Marchiando, S. Hermelin, J. Gateau, M. Brunetti, J. P. Wolf, and J. Kasparian, “Triggering filamentation using turbulence,” Phys. Rev. A (Coll. Park) 94(3), 033806 (2016).
[Crossref]

Gordon, D. F.

J. R. Penano, P. Sprangle, B. Hazafi, A. Ting, D. F. Gordon, and C. A. Kapetanakos, “Propagation of ultra-short, intense laser pulses in air,” Phys. Plasmas 11(5), 2865–2874 (2004).
[Crossref]

Hafizi, B.

J. Peñano, J. P. Palastro, B. Hafizi, M. H. Helle, and G. P. DiComo, “Self-channeling of high-power laser pulses through strong atmospheric turbulence,” Phys. Rev. A (Coll. Park) 96(1), 013829 (2017).
[Crossref]

J. Peñano, B. Hafizi, A. Ting, and M. H. Helle, “Theoretical and numerical investigation of Filament onset distance in atmospheric turbulence,” J. Opt. Soc. Am. B 31(5), 963–971 (2014).
[Crossref]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30(8), 1228 (1991).
[Crossref]

Hazafi, B.

J. R. Penano, P. Sprangle, B. Hazafi, A. Ting, D. F. Gordon, and C. A. Kapetanakos, “Propagation of ultra-short, intense laser pulses in air,” Phys. Plasmas 11(5), 2865–2874 (2004).
[Crossref]

Helle, M. H.

J. Peñano, J. P. Palastro, B. Hafizi, M. H. Helle, and G. P. DiComo, “Self-channeling of high-power laser pulses through strong atmospheric turbulence,” Phys. Rev. A (Coll. Park) 96(1), 013829 (2017).
[Crossref]

J. Peñano, B. Hafizi, A. Ting, and M. H. Helle, “Theoretical and numerical investigation of Filament onset distance in atmospheric turbulence,” J. Opt. Soc. Am. B 31(5), 963–971 (2014).
[Crossref]

Hermelin, S.

D. Eeltink, N. Berti, N. Marchiando, S. Hermelin, J. Gateau, M. Brunetti, J. P. Wolf, and J. Kasparian, “Triggering filamentation using turbulence,” Phys. Rev. A (Coll. Park) 94(3), 033806 (2016).
[Crossref]

Houard, A.

M. Durand, A. Houard, B. Prade, A. Mysyrowicz, A. Durécu, B. Moreau, D. Fleury, O. Vasseur, H. Borchert, K. Diener, R. Schmitt, F. Théberge, M. Chateauneuf, J. F. Daigle, and J. Dubois, “Kilometer Range Filamentation,” Opt. Express 21(22), 26836–26845 (2013).
[Crossref] [PubMed]

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Jeon, C.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions, “in Proceedings of the OSA Conference on Propagation Through and Characterization of Atmospheric and Oceanic Phenomena (Optical Society of America, 2016), paper Tu2A.
[Crossref]

Kandidov, V. P.

S. A. Shlenov, V. P. Kandidov, O. G. Kosareva, A. E. Bezborodov, and V. Yu. Fedorov, “Spatio-temporal control of femtosecond laser pulse filamentation in the atmosphere,” Proc. SPIE 6733, 67332M (2007).

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

Kapetanakos, C. A.

J. R. Penano, P. Sprangle, B. Hazafi, A. Ting, D. F. Gordon, and C. A. Kapetanakos, “Propagation of ultra-short, intense laser pulses in air,” Phys. Plasmas 11(5), 2865–2874 (2004).
[Crossref]

Karr, T.

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Engineering Equations for Characterizing Non-Linear Laser Intensity Propagation in air with loss,” Opt. Express 26(4), 3974–3987 (2018).
[Crossref] [PubMed]

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Propagation of infrared ultrashort pulses in the air,” Proc. SPIE 10684, 1068414 (2018).

Kasparian, J.

D. Eeltink, N. Berti, N. Marchiando, S. Hermelin, J. Gateau, M. Brunetti, J. P. Wolf, and J. Kasparian, “Triggering filamentation using turbulence,” Phys. Rev. A (Coll. Park) 94(3), 033806 (2016).
[Crossref]

R. Ackermann, G. Méjean, J. Kasparian, J. Yu, E. Salmon, and J.-P. Wolf, “Laser filaments generated and transmitted in highly turbulent air,” Opt. Lett. 31(1), 86–88 (2006).
[Crossref] [PubMed]

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultra-intense light filaments transmitted through clouds<,” Appl. Phys. Lett. 83(2), 213–215 (2003).
[Crossref]

Kolesik, M.

Kosareva, O. G.

S. A. Shlenov, V. P. Kandidov, O. G. Kosareva, A. E. Bezborodov, and V. Yu. Fedorov, “Spatio-temporal control of femtosecond laser pulse filamentation in the atmosphere,” Proc. SPIE 6733, 67332M (2007).

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

Kurz, H. G.

A. Schmitt-Sody, H. G. Kurz, L. Bergé, S. Skupin, and P. Polynkin, “Picosecond laser filamentation in air,” New J. Phys. 18(9), 093005 (2016).
[Crossref]

Lane, J.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions, “in Proceedings of the OSA Conference on Propagation Through and Characterization of Atmospheric and Oceanic Phenomena (Optical Society of America, 2016), paper Tu2A.
[Crossref]

Lombard, L.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Mansell, J. D.

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Propagation of infrared ultrashort pulses in the air,” Proc. SPIE 10684, 1068414 (2018).

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Engineering Equations for Characterizing Non-Linear Laser Intensity Propagation in air with loss,” Opt. Express 26(4), 3974–3987 (2018).
[Crossref] [PubMed]

Marburger, J. H.

E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179(3), 862–868 (1969).
[Crossref]

Marchiando, N.

D. Eeltink, N. Berti, N. Marchiando, S. Hermelin, J. Gateau, M. Brunetti, J. P. Wolf, and J. Kasparian, “Triggering filamentation using turbulence,” Phys. Rev. A (Coll. Park) 94(3), 033806 (2016).
[Crossref]

Markov, A. I.

S. A. Shlenov and A. I. Markov, “Control of filamentation of femtosecond laser pulses in a turbulent atmosphere,” Quantum Electron. 39(7), 658−662 (2009).

Méjean, G.

R. Ackermann, G. Méjean, J. Kasparian, J. Yu, E. Salmon, and J.-P. Wolf, “Laser filaments generated and transmitted in highly turbulent air,” Opt. Lett. 31(1), 86–88 (2006).
[Crossref] [PubMed]

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultra-intense light filaments transmitted through clouds<,” Appl. Phys. Lett. 83(2), 213–215 (2003).
[Crossref]

Michau, V.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Moloney, J. V.

Moreau, B.

Mysyrowicz, A.

M. Durand, A. Houard, B. Prade, A. Mysyrowicz, A. Durécu, B. Moreau, D. Fleury, O. Vasseur, H. Borchert, K. Diener, R. Schmitt, F. Théberge, M. Chateauneuf, J. F. Daigle, and J. Dubois, “Kilometer Range Filamentation,” Opt. Express 21(22), 26836–26845 (2013).
[Crossref] [PubMed]

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Palastro, J. P.

J. Peñano, J. P. Palastro, B. Hafizi, M. H. Helle, and G. P. DiComo, “Self-channeling of high-power laser pulses through strong atmospheric turbulence,” Phys. Rev. A (Coll. Park) 96(1), 013829 (2017).
[Crossref]

Penano, J. R.

J. R. Penano, P. Sprangle, B. Hazafi, A. Ting, D. F. Gordon, and C. A. Kapetanakos, “Propagation of ultra-short, intense laser pulses in air,” Phys. Plasmas 11(5), 2865–2874 (2004).
[Crossref]

Peñano, J.

J. Peñano, J. P. Palastro, B. Hafizi, M. H. Helle, and G. P. DiComo, “Self-channeling of high-power laser pulses through strong atmospheric turbulence,” Phys. Rev. A (Coll. Park) 96(1), 013829 (2017).
[Crossref]

J. Peñano, B. Hafizi, A. Ting, and M. H. Helle, “Theoretical and numerical investigation of Filament onset distance in atmospheric turbulence,” J. Opt. Soc. Am. B 31(5), 963–971 (2014).
[Crossref]

Petit, S.

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

Petrishchev, V.

V. Petrishchev, “Application of the Method of Moments to Certain Problems in the Propagation of Partially Coherent Light Beams, Izvestiya Vysshikh Uchebnykh Zavedenii,” Radiofizika 14(9), 1416–1426 (1971).

Polynkin, P.

A. Schmitt-Sody, H. G. Kurz, L. Bergé, S. Skupin, and P. Polynkin, “Picosecond laser filamentation in air,” New J. Phys. 18(9), 093005 (2016).
[Crossref]

Prade, B.

M. Durand, A. Houard, B. Prade, A. Mysyrowicz, A. Durécu, B. Moreau, D. Fleury, O. Vasseur, H. Borchert, K. Diener, R. Schmitt, F. Théberge, M. Chateauneuf, J. F. Daigle, and J. Dubois, “Kilometer Range Filamentation,” Opt. Express 21(22), 26836–26845 (2013).
[Crossref] [PubMed]

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Richardson, M.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions, “in Proceedings of the OSA Conference on Propagation Through and Characterization of Atmospheric and Oceanic Phenomena (Optical Society of America, 2016), paper Tu2A.
[Crossref]

Robert, C.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Rostami, S.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions, “in Proceedings of the OSA Conference on Propagation Through and Characterization of Atmospheric and Oceanic Phenomena (Optical Society of America, 2016), paper Tu2A.
[Crossref]

Said, A. A.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30(8), 1228 (1991).
[Crossref]

Salmon, E.

R. Ackermann, G. Méjean, J. Kasparian, J. Yu, E. Salmon, and J.-P. Wolf, “Laser filaments generated and transmitted in highly turbulent air,” Opt. Lett. 31(1), 86–88 (2006).
[Crossref] [PubMed]

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultra-intense light filaments transmitted through clouds<,” Appl. Phys. Lett. 83(2), 213–215 (2003).
[Crossref]

Schmidt, J. D.

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Propagation of infrared ultrashort pulses in the air,” Proc. SPIE 10684, 1068414 (2018).

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Engineering Equations for Characterizing Non-Linear Laser Intensity Propagation in air with loss,” Opt. Express 26(4), 3974–3987 (2018).
[Crossref] [PubMed]

Schmitt, R.

Schmitt-Sody, A.

A. Schmitt-Sody, H. G. Kurz, L. Bergé, S. Skupin, and P. Polynkin, “Picosecond laser filamentation in air,” New J. Phys. 18(9), 093005 (2016).
[Crossref]

Shah, L.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions, “in Proceedings of the OSA Conference on Propagation Through and Characterization of Atmospheric and Oceanic Phenomena (Optical Society of America, 2016), paper Tu2A.
[Crossref]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30(8), 1228 (1991).
[Crossref]

Shlenov, S. A.

S. A. Shlenov and A. I. Markov, “Control of filamentation of femtosecond laser pulses in a turbulent atmosphere,” Quantum Electron. 39(7), 658−662 (2009).

S. A. Shlenov, V. P. Kandidov, O. G. Kosareva, A. E. Bezborodov, and V. Yu. Fedorov, “Spatio-temporal control of femtosecond laser pulse filamentation in the atmosphere,” Proc. SPIE 6733, 67332M (2007).

Skupin, S.

A. Schmitt-Sody, H. G. Kurz, L. Bergé, S. Skupin, and P. Polynkin, “Picosecond laser filamentation in air,” New J. Phys. 18(9), 093005 (2016).
[Crossref]

Soileau, M. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30(8), 1228 (1991).
[Crossref]

Sprangle, P.

J. R. Penano, P. Sprangle, B. Hazafi, A. Ting, D. F. Gordon, and C. A. Kapetanakos, “Propagation of ultra-short, intense laser pulses in air,” Phys. Plasmas 11(5), 2865–2874 (2004).
[Crossref]

Stotts, L. B.

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Propagation of infrared ultrashort pulses in the air,” Proc. SPIE 10684, 1068414 (2018).

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Engineering Equations for Characterizing Non-Linear Laser Intensity Propagation in air with loss,” Opt. Express 26(4), 3974–3987 (2018).
[Crossref] [PubMed]

Talebpour, A.

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

Tamarov, M. P.

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

Tellez, J. A.

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Engineering Equations for Characterizing Non-Linear Laser Intensity Propagation in air with loss,” Opt. Express 26(4), 3974–3987 (2018).
[Crossref] [PubMed]

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Propagation of infrared ultrashort pulses in the air,” Proc. SPIE 10684, 1068414 (2018).

Théberge, F.

Ting, A.

J. Peñano, B. Hafizi, A. Ting, and M. H. Helle, “Theoretical and numerical investigation of Filament onset distance in atmospheric turbulence,” J. Opt. Soc. Am. B 31(5), 963–971 (2014).
[Crossref]

J. R. Penano, P. Sprangle, B. Hazafi, A. Ting, D. F. Gordon, and C. A. Kapetanakos, “Propagation of ultra-short, intense laser pulses in air,” Phys. Plasmas 11(5), 2865–2874 (2004).
[Crossref]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30(8), 1228 (1991).
[Crossref]

Vasseur, O

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Vasseur, O.

Wolf, J. P.

D. Eeltink, N. Berti, N. Marchiando, S. Hermelin, J. Gateau, M. Brunetti, J. P. Wolf, and J. Kasparian, “Triggering filamentation using turbulence,” Phys. Rev. A (Coll. Park) 94(3), 033806 (2016).
[Crossref]

Wolf, J.-P.

R. Ackermann, G. Méjean, J. Kasparian, J. Yu, E. Salmon, and J.-P. Wolf, “Laser filaments generated and transmitted in highly turbulent air,” Opt. Lett. 31(1), 86–88 (2006).
[Crossref] [PubMed]

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultra-intense light filaments transmitted through clouds<,” Appl. Phys. Lett. 83(2), 213–215 (2003).
[Crossref]

Yang, J.

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

Yu, J.

R. Ackermann, G. Méjean, J. Kasparian, J. Yu, E. Salmon, and J.-P. Wolf, “Laser filaments generated and transmitted in highly turbulent air,” Opt. Lett. 31(1), 86–88 (2006).
[Crossref] [PubMed]

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultra-intense light filaments transmitted through clouds<,” Appl. Phys. Lett. 83(2), 213–215 (2003).
[Crossref]

Appl. Phys. B (2)

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

S. Chin, A. Talebpour, J. Yang, S. Petit, V. P. Kandidov, O. G. Kosareva, and M. P. Tamarov, “Filamentation of femtosecond laser pulses in turbulent air,” Appl. Phys. B 74(1), 67–76 (2002).
[Crossref]

Appl. Phys. Lett. (1)

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultra-intense light filaments transmitted through clouds<,” Appl. Phys. Lett. 83(2), 213–215 (2003).
[Crossref]

J. Opt. Soc. Am. B (1)

New J. Phys. (1)

A. Schmitt-Sody, H. G. Kurz, L. Bergé, S. Skupin, and P. Polynkin, “Picosecond laser filamentation in air,” New J. Phys. 18(9), 093005 (2016).
[Crossref]

Opt. Eng. (1)

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30(8), 1228 (1991).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Plasmas (1)

J. R. Penano, P. Sprangle, B. Hazafi, A. Ting, D. F. Gordon, and C. A. Kapetanakos, “Propagation of ultra-short, intense laser pulses in air,” Phys. Plasmas 11(5), 2865–2874 (2004).
[Crossref]

Phys. Rev. (1)

E. L. Dawes and J. H. Marburger, “Computer studies in self-focusing,” Phys. Rev. 179(3), 862–868 (1969).
[Crossref]

Phys. Rev. A (1)

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O Vasseur, B. Fleury, C. Robert, V. Michau, A. Courairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78, 033804 (2008).

Phys. Rev. A (Coll. Park) (2)

D. Eeltink, N. Berti, N. Marchiando, S. Hermelin, J. Gateau, M. Brunetti, J. P. Wolf, and J. Kasparian, “Triggering filamentation using turbulence,” Phys. Rev. A (Coll. Park) 94(3), 033806 (2016).
[Crossref]

J. Peñano, J. P. Palastro, B. Hafizi, M. H. Helle, and G. P. DiComo, “Self-channeling of high-power laser pulses through strong atmospheric turbulence,” Phys. Rev. A (Coll. Park) 96(1), 013829 (2017).
[Crossref]

Proc. SPIE (2)

T. Karr, L. B. Stotts, J. A. Tellez, J. D. Schmidt, and J. D. Mansell, “Propagation of infrared ultrashort pulses in the air,” Proc. SPIE 10684, 1068414 (2018).

S. A. Shlenov, V. P. Kandidov, O. G. Kosareva, A. E. Bezborodov, and V. Yu. Fedorov, “Spatio-temporal control of femtosecond laser pulse filamentation in the atmosphere,” Proc. SPIE 6733, 67332M (2007).

Quantum Electron. (2)

S. A. Shlenov and A. I. Markov, “Control of filamentation of femtosecond laser pulses in a turbulent atmosphere,” Quantum Electron. 39(7), 658−662 (2009).

V. P. Kandidov, O. G. Kosareva, M. P. Tamarov, A. Brodeur, and S. L. Chin, “Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere,” Quantum Electron. 29(10), 911–915 (1999).
[Crossref]

Radiofizika (1)

V. Petrishchev, “Application of the Method of Moments to Certain Problems in the Propagation of Partially Coherent Light Beams, Izvestiya Vysshikh Uchebnykh Zavedenii,” Radiofizika 14(9), 1416–1426 (1971).

Other (7)

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions, “in Proceedings of the OSA Conference on Propagation Through and Characterization of Atmospheric and Oceanic Phenomena (Optical Society of America, 2016), paper Tu2A.
[Crossref]

L. B. Stotts, Free Space Optical Systems Engineering (John Wiley and Sons, 2017), Chap. 7.

L. C. Andrews, R. L. Phillips, Z. C. Bagley, N. D. Plasson, and L. B. Stotts, Advanced Free Space Optics (FSO) A Systems Approach, Springer Series in Optical Sciences, Volume 186, William T. Rhodes, ed. (Springer, 2014), Chap. 9.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, 2nd Edition (SPIE, 2005).

Sherman Karp and Larry B. Stotts, Fundamentals of Electro-Optic Systems Design: Communications, Lidar, and Imaging (Cambridge Press, 2013), Chap. 10.

R. W. Boyd, Nonlinear Optics, 3rd Edition (Academic Press, 2008).

J. H. Marburger, “Self-Focusing Theory,” in R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., Self-Focusing: Past and Present / Fundamentals and Prospects (Springer Science+Business Media, 1975).

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Figures (10)

Fig. 1
Fig. 1 Kolmogorov cascade theory of turbulence.
Fig. 2
Fig. 2 Qualitative comparison between USPL filamentation and lens focusing in turbulence.
Fig. 3
Fig. 3 Observed scintillation versus predicted scintillation [19].
Fig. 4
Fig. 4 Plot of the ratio of the Spatial Coherence Radius and the Diffractive Beam Diameter versus the Fresnel Ratio Λ 0 for converging, collimated and divergent beams assuming q=0.2.
Fig. 5
Fig. 5 Ground level Cn2 values at Hollister Airport during June 7-9, 2011 measured by a BLS 900 Scintec scintillometer [20].
Fig. 6
Fig. 6 Plot of the Houard et al’s MI Distance Estimate, the classical Marburger self-focusing distance and Eq. (6) solutions as a function of Peak Power to Critical Power Ratio.
Fig. 7
Fig. 7 Comparison of median self-focusing distance with modified Petrishchev Equation, Eq. (22).
Fig. 8
Fig. 8 Rytov Standard Deviation versus Link Range for the Peñano, et. al. Computer Simulations [7].
Fig. 9
Fig. 9 Comparison of Peñano, et. al. median self-focusing distances with modified Petrishchev Equation, Eq. (24) with m 0 = 0.02.
Fig. 10
Fig. 10 Comparison of Peñano, et. al. median self-focusing distance with modified Petrishchev Equation, Eq. (24) with m 0 = 0.008.

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

n(r)= n 0 + n 1 (r)1+( 0.79x 10 6 millibars/ Kelvin )[ P(r)/ T(r) ]
D n ( r 1 , r 2 )= | n( r 1 )n( r 2 ) | 2 ,
D n ( r 1 , r 2 )= D n (| r 1 r 2 |)= D n (ρ),
D n (ρ)= C n 2 ( h ) ρ 2/3 for l 0 <ρ< L 0 ,
W ST ={ W 1+1.33 σ R 2 Λ 5/6 [ 10.66 ( Λ 0 2 / 1+ Λ 0 2 ) 1/6 ] W 1+0.35 σ R 2 Λ 5/6 CollimatedBeam FocusedBeam
W= W 0 2 [ ( λL/ π W 0 2 ) 2 + ( 1L/f ) 2 ] = W 0 2 [ Λ 0 2 + Θ 0 2 ] ,
Λ= Λ 0 / ( Λ 0 2 + Θ 0 2 ) ,
σ R 2 =1.23 C n 2 k 7/6 L 11/6
Weakirradiancefluctuations: σ R 2 <1and σ R 2 Λ 5/6 <1 Strongirradiancefluctuations: σ R 2 >1and σ R 2 Λ 5/6 >1 .
Q 2 ( z )=4( P peak / P crit ) ( ρ 0 / 2W ) 2
ρ 0 2W =0.35 Λ q [ 8 3( a TH +0.62 Λ 11/6 ) ] 3/5 l 0 ρ 0 L 0 ,
a TH ={ ( 1 Θ 8/3 )/ [ 1Θ ] ( 1 | Θ | 8/3 )/ [ 1Θ ] Θ0 Θ<0 ,
Θ= Θ 0 / ( Λ 0 2 + Θ 0 2 ) ,
q=1.22 ( σ R 2 ) 6/5
Q 2 ( z )1/q 1/ ( 1.5 C n 2 k 7/6 L 11/6 )
1+(1 P peak / P crit )(z/ z r ) 2 +( k 3 W 0 4 C/8 ) ( z/ z r ) 3 =0
C=4.38 l 0 1/3 C n 2 ( h )[ 1 { 1+17.5 ( a/ l 0 ) 2 } 1/6 ].
(z/ z r ) 2 +(1[ P peak / P crit ] ( z/ z r ) 2 )+( k 3 W 0 4 C/8 ) ( z/ z r ) 3 =
(z/ z r ) 2 +(1 ( z/ { z r / [ P peak / P crit ] } ) 2 )+( k 3 W 0 4 C/8 ) ( z/ z r ) 3 =0.
(z/ z r ) 2 +(1 ( z/ z sf ) 2 )+( k 3 W 0 4 C/8 ) ( z/ z r ) 3 0
z sf = 0.367 z r ( P peak / P crit 0.852 ) ,
P peak / P crit =1+0.75 k 2 a 2 ( aC/ l 0 ) 2/3 .
P peak * / P crit =( P Peak / P crit )[ 1+0.75 k 2 a 2 ( aC/ l 0 ) 2/3 ].
P peak * / P crit =( P Peak / P crit )[ 1+ m 0 k 2 a 2 ( aC/ l 0 ) 2/3 ].

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