Abstract

The propagation of high peak-power laser beams in real atmospheres has been an active research area for a couple of decades. Atmospheric turbulence and loss will induce decreases in the filamentation self-focusing collapse distance as the refractive index structure parameter and volume extinction coefficient, respectively, increase. This paper provides a validated analytical method for predicting the filamentation onset distance in lossy, turbulent, nonlinear media. It is based on a modification of Petrishchev’s and Marburger theories. It postulates that the ratio of the peak power to critical power at range in turbulence is modified by a multiplicative, rather than additive, gain factor. Specifically, this new approach modifies the Petrishchev’s turbulence equation to create the required multiplicative factor. This is necessary to create the shortened filamentation onset distance that occurs when a laser beam propagates through the cited nonlinear medium. This equation then is used with the Marburger distance and the Karr et al loss equations to yield the filamentation onset distance estimate in lossy, turbulent, nonlinear environment. Theory validation is done against two independent sets of computer simulation results. One comes from the NRL’s HELCAP software and the other from MZA’s Wave Train modeling software package. This paper also shows that once the zero-turbulence onset distance is set based on link loss, the addition of turbulence creates essentially the same PDFs at similar median distances for each loss case. This result had not been previously reported. This is the first quantitative comparison between closed form equations and computer simulation results characterizing filament generation in a lossy, turbulent, nonlinear medium.

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

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References

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    [Crossref]
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    [Crossref]
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2019 (2)

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

L. B. Stotts, J. Peñano, and V. Urick, “Engineering equation for filamentation self-focusing collapse distance in atmospheric turbulence,” Opt. Express 27(11), 15159–15171 (2019).
[Crossref]

2018 (3)

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 96(1), 013829 (2017).
[Crossref]

2016 (3)

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 94(3), 033806 (2016).
[Crossref]

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]

A. Houard, V. Jukna, G. Point, Y.-B. André, S. Klingebiel, M. Schultze, K. Michel, T. Metzger, and A. Mysyrowicz, “Study of filamentation with a high-power high repetition rate ps laser at 1.03 µm,” Opt. Express 24(7), 7437–7448 (2016).
[Crossref]

2015 (1)

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[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).
[Crossref]

2008 (2)

A. A. Zemlyanov and Y. É. Geints, “Evolution of Effective Characteristics of Laser Beam of Femtosecond Duration upon Self-Action in a Gas Medium,” Opt. Spectrosc. 104(5), 772–783 (2008).
[Crossref]

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[Crossref]

2006 (1)

2004 (1)

J. R. Peñano, P. Sprangle, B. Hafizi, 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]

2002 (2)

P. Sprangle, J. R. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66(4), 046418 (2002).
[Crossref]

P. Sprangle, J. R. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66(4), 046418 (2002).
[Crossref]

1971 (1)

V. Petrishchev, “Application of the Method of Moments to Certain Problems in the Propagation of Partially Coherent Light Beams,” Radiophys. Quantum Electron. 14(9), 1112–1119 (1971).
[Crossref]

1970 (1)

V. I. Talanov, “Focusing of light in cubic media,” JETP Lett. 11, 199–201 (1970).

1969 (1)

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

Ackermann, R.

Ališauskas, S.

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

André, Y.-B.

Andrews, L. C.

L. C. Andrews, A Field Guide to Atmospheric Optics, 2nd Edition, 17 (SPIE Press, 2019).

Andriukaitis, G.

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

Baltuška, A.

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

Baudelet, M.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions,” in Propagation Through and Characterization of Atmospheric and Oceanic Phenomena, OSA Technical Digest (online) (Optical Society of America, 2016), paper Tu2A.3 (2016).

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 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, International Conference on Lasers, Applications, and Technologies 2007: Environmental Monitoring and Ecological Applications; Optical Sensors in Biological, Chemical, and Engineering Technologies; and Femtosecond Laser Pulse Filamentation, 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. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[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 94(3), 033806 (2016).
[Crossref]

Chateauneuf, M.

Coffaro, J.

Couairon, A.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[Crossref]

Crabbs, R. F.

Daigle, J.

Davis, C. C.

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 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. Daigle, and J. Dubois, “Kilometer range filamentation,” Opt. Express 21, 26836–26845 (2013).
[Crossref]

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[Crossref]

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 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, International Conference on Lasers, Applications, and Technologies 2007: Environmental Monitoring and Ecological Applications; Optical Sensors in Biological, Chemical, and Engineering Technologies; and Femtosecond Laser Pulse Filamentation, 67332M (2007).

Fedotov, A. B.

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

Fleury, B.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[Crossref]

Fleury, D.

Flöry, T.

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

Franco, M.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[Crossref]

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 94(3), 033806 (2016).
[Crossref]

Geints, Y. É.

A. A. Zemlyanov and Y. É. Geints, “Evolution of Effective Characteristics of Laser Beam of Femtosecond Duration upon Self-Action in a Gas Medium,” Opt. Spectrosc. 104(5), 772–783 (2008).
[Crossref]

Gordon, D. F.

J. R. Peñano, P. Sprangle, B. Hafizi, 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 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]

J. R. Peñano, P. Sprangle, B. Hafizi, 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]

P. Sprangle, J. R. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66(4), 046418 (2002).
[Crossref]

P. Sprangle, J. R. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66(4), 046418 (2002).
[Crossref]

P. Spangle, J. R. Pefiano, and B. Hafizi, “Optimum Wavelength and Power for Efficient Laser Propagation in Various Atmospheric Environments,” NRL/MR/6790-05-8907.

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 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 94(3), 033806 (2016).
[Crossref]

Houard, A.

Jeon, C.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions,” in Propagation Through and Characterization of Atmospheric and Oceanic Phenomena, OSA Technical Digest (online) (Optical Society of America, 2016), paper Tu2A.3 (2016).

Joshi, C.

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

Jukna, V.

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, International Conference on Lasers, Applications, and Technologies 2007: Environmental Monitoring and Ecological Applications; Optical Sensors in Biological, Chemical, and Engineering Technologies; and Femtosecond Laser Pulse Filamentation, 67332M (2007).

Kapetanakos, C. A.

J. R. Peñano, P. Sprangle, B. Hafizi, 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.

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 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]

Klingebiel, S.

Ko, J.

Koch, S. W.

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

Kolesik, M.

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

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, International Conference on Lasers, Applications, and Technologies 2007: Environmental Monitoring and Ecological Applications; Optical Sensors in Biological, Chemical, and Engineering Technologies; and Femtosecond Laser Pulse Filamentation, 67332M (2007).

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 Propagation Through and Characterization of Atmospheric and Oceanic Phenomena, OSA Technical Digest (online) (Optical Society of America, 2016), paper Tu2A.3 (2016).

Lombard, L.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[Crossref]

Mansell, J. D.

Marburger, J. H.

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

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 (Topics in Applied Optics, Springer Science + Business Media, 1975) Chap. 2.

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 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).
[Crossref]

Méjean, G.

Metzger, T.

Michau, V.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[Crossref]

Michel, K.

Mitrofanov, A. V.

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

Moloney, J. V.

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

Moreau, B.

Mysyrowicz, A.

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 96(1), 013829 (2017).
[Crossref]

Panagiotopoulos, P.

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

Paulson, D. A.

Pefiano, J. R.

P. Spangle, J. R. Pefiano, and B. Hafizi, “Optimum Wavelength and Power for Efficient Laser Propagation in Various Atmospheric Environments,” NRL/MR/6790-05-8907.

Peñano, J.

Peñano, J. R.

J. R. Peñano, P. Sprangle, B. Hafizi, 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]

P. Sprangle, J. R. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66(4), 046418 (2002).
[Crossref]

P. Sprangle, J. R. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66(4), 046418 (2002).
[Crossref]

Petrishchev, V.

V. Petrishchev, “Application of the Method of Moments to Certain Problems in the Propagation of Partially Coherent Light Beams,” Radiophys. Quantum Electron. 14(9), 1112–1119 (1971).
[Crossref]

Pigeon, J.

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

Pogorelsky, I.

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

Point, G.

Polyanskiy, M.

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

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. Daigle, and J. Dubois, “Kilometer range filamentation,” Opt. Express 21, 26836–26845 (2013).
[Crossref]

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[Crossref]

Pugžlys, A.

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

Richardson, M.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions,” in Propagation Through and Characterization of Atmospheric and Oceanic Phenomena, OSA Technical Digest (online) (Optical Society of America, 2016), paper Tu2A.3 (2016).

Robert, C.

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[Crossref]

Rostami, S.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions,” in Propagation Through and Characterization of Atmospheric and Oceanic Phenomena, OSA Technical Digest (online) (Optical Society of America, 2016), paper Tu2A.3 (2016).

Rzasa, J. R.

Salmon, E.

Schmidt, J. D.

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]

Schultze, M.

Shah, L.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions,” in Propagation Through and Characterization of Atmospheric and Oceanic Phenomena, OSA Technical Digest (online) (Optical Society of America, 2016), paper Tu2A.3 (2016).

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).
[Crossref]

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, International Conference on Lasers, Applications, and Technologies 2007: Environmental Monitoring and Ecological Applications; Optical Sensors in Biological, Chemical, and Engineering Technologies; and Femtosecond Laser Pulse Filamentation, 67332M (2007).

Sidorov-Biryukov, D. A.

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

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]

Spangle, P.

P. Spangle, J. R. Pefiano, and B. Hafizi, “Optimum Wavelength and Power for Efficient Laser Propagation in Various Atmospheric Environments,” NRL/MR/6790-05-8907.

Sprangle, P.

J. R. Peñano, P. Sprangle, B. Hafizi, 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]

P. Sprangle, J. R. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66(4), 046418 (2002).
[Crossref]

P. Sprangle, J. R. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66(4), 046418 (2002).
[Crossref]

Spychalsky, J.

Stepanov, E. A.

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

Stotts, L. B.

Talanov, V. I.

V. I. Talanov, “Focusing of light in cubic media,” JETP Lett. 11, 199–201 (1970).

Tellez, J. A.

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. Peñano, P. Sprangle, B. Hafizi, 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]

Tochitsky, S.

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

Urick, V.

Vasseur, O.

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. Daigle, and J. Dubois, “Kilometer range filamentation,” Opt. Express 21, 26836–26845 (2013).
[Crossref]

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[Crossref]

Voroninl, A. A.

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

Welch, E.

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

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 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]

Wright, E. M.

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

Wu, C.

Yu, J.

Zemlyanov, A. A.

A. A. Zemlyanov and Y. É. Geints, “Evolution of Effective Characteristics of Laser Beam of Femtosecond Duration upon Self-Action in a Gas Medium,” Opt. Spectrosc. 104(5), 772–783 (2008).
[Crossref]

Zheltikov, A. M.

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

Appl. Opt. (1)

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

J. Sci. Res. Rev. (1)

A. V. Mitrofanov, A. A. Voroninl, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” J. Sci. Res. Rev. 5(1), 1–5 (2015).
[Crossref]

JETP Lett. (1)

V. I. Talanov, “Focusing of light in cubic media,” JETP Lett. 11, 199–201 (1970).

Nat. Photonics (1)

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13(1), 41–46 (2019).
[Crossref]

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. Express (4)

Opt. Lett. (1)

Opt. Spectrosc. (1)

A. A. Zemlyanov and Y. É. Geints, “Evolution of Effective Characteristics of Laser Beam of Femtosecond Duration upon Self-Action in a Gas Medium,” Opt. Spectrosc. 104(5), 772–783 (2008).
[Crossref]

Phys. Plasmas (1)

J. R. Peñano, P. Sprangle, B. Hafizi, 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 (3)

A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, “Femtosecond filamentation in turbulent air,” Phys. Rev. A 78(3), 033804 (2008).
[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 96(1), 013829 (2017).
[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 94(3), 033806 (2016).
[Crossref]

Phys. Rev. E (2)

P. Sprangle, J. R. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66(4), 046418 (2002).
[Crossref]

P. Sprangle, J. R. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66(4), 046418 (2002).
[Crossref]

Proc. SPIE (1)

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).
[Crossref]

Quantum Electron. (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).
[Crossref]

Radiophys. Quantum Electron. (1)

V. Petrishchev, “Application of the Method of Moments to Certain Problems in the Propagation of Partially Coherent Light Beams,” Radiophys. Quantum Electron. 14(9), 1112–1119 (1971).
[Crossref]

Other (5)

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 (Topics in Applied Optics, Springer Science + Business Media, 1975) Chap. 2.

C. Jeon, J. Lane, S. Rostami, L. Shah, M. Baudelet, and M. Richardson, “Laser Induced Filament Propagation Through Adverse Conditions,” in Propagation Through and Characterization of Atmospheric and Oceanic Phenomena, OSA Technical Digest (online) (Optical Society of America, 2016), paper Tu2A.3 (2016).

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, International Conference on Lasers, Applications, and Technologies 2007: Environmental Monitoring and Ecological Applications; Optical Sensors in Biological, Chemical, and Engineering Technologies; and Femtosecond Laser Pulse Filamentation, 67332M (2007).

P. Spangle, J. R. Pefiano, and B. Hafizi, “Optimum Wavelength and Power for Efficient Laser Propagation in Various Atmospheric Environments,” NRL/MR/6790-05-8907.

L. C. Andrews, A Field Guide to Atmospheric Optics, 2nd Edition, 17 (SPIE Press, 2019).

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Figures (19)

Fig. 1.
Fig. 1. Extinction Rate versus Hour of the Day Measured on the Kennedy Space Center runway in mid-October 2017 [18]. (Figure published with permission from Originator, Dr. Chris C. Davis, and the Optical Society of America.)
Fig. 2.
Fig. 2. Refractive Index Structure Parameter versus Hour of the Day Measured on the Kennedy Space Center runway in mid-October 2017 [18]. (Figure published with permission from Originator, Dr. Chris C. Davis, and the Optical Society of America.)
Fig. 3.
Fig. 3. Fluence contours generated by the HELCAP code for beams with (a) ${P \mathord{\left/ {\vphantom {P {{P_{crit}} = 1.5}}} \right.} {{P_{crit}} = 1.5}}$ and b) ${P \mathord{\left/ {\vphantom {P {{P_{crit}} = 20}}} \right.} {{P_{crit}} = 20}}$ near the onset of filamentation. Taken from Ref. [22].
Fig. 4.
Fig. 4. Filamentation Onset Distance Probability Density Function as a function of propagation distance and various values of the Refractive Index Structure Parameter for a lossless medium and a Zero Turbulence Collapse Distance of 4 km.
Fig. 5.
Fig. 5. Filamentation Onset Distance Probability Density Function as a function of propagation distance and various values of the Refractive Index Structure Parameter and a volume Extinction Coefficient of 0.1 inverse-kilometers and a Zero Turbulence Collapse Distance of 4 km.
Fig. 6.
Fig. 6. Filamentation Onset Distance Probability Density Function as a function of propagation distance and various values of the Refractive Index Structure Parameter and a volume Extinction Coefficient of 0.2 inverse-kilometers and Zero Turbulence Collapse Distance of 4 km.
Fig. 7.
Fig. 7. Comparison of Median Collapse Distances from Eqs. (6), (8) [LHS] and (9), and HELCAP Computer Simulation Results.
Fig. 8.
Fig. 8. Filamentation Onset Distance Probability Density Function as a function of propagation distance and various values of the Refractive Index Structure Parameter and a volume Extinction Coefficient of 0.0 inverse-kilometers and a Zero Turbulence Collapse Distance of 3.6 km.
Fig. 9.
Fig. 9. Filamentation Onset Distance Probability Density Function as a function of propagation distance and various values of the Refractive Index Structure Parameter and a volume Extinction Coefficient of 0.1 inverse-kilometers and a Zero Turbulence Collapse Distance of 3.8 km.
Fig. 10.
Fig. 10. Comparison of Median Collapse Distances from Eqs. (6), (8) [LHS] and (9), and HELCAP Computer Simulation Results
Fig. 11.
Fig. 11. Comparison of Hard Aperture (red) versus Super Gaussian Beam (blue) Profiles.
Fig. 12.
Fig. 12. Wave Train component layout for modeling propagation in turbulent, non-linear atmospheres.
Fig. 13.
Fig. 13. Graph for the Filamentation Onset Distance Probability Density Function as a function of propagation distance for various ratios of Peak Power to Critical Power for $C_n^2 = 1x{10^{ - 17}}\,{m^{ - {2 \mathord{\left/ {\vphantom {2 3}} \right.} 3}}}.$
Fig. 14.
Fig. 14. Graph for the Filamentation Onset Distance Probability Density Function as a function of propagation distance for various ratios of Peak Power to Critical Power for $C_n^2 = 1x{10^{ - 16}}\,{m^{ - {2 \mathord{\left/ {\vphantom {2 3}} \right.} 3}}}.$
Fig. 15.
Fig. 15. Comparison of Average Collapse Distances from Eqs. (6), (8) [LHS] and (9), and Wave Train Computer Simulation Results
Fig. 16.
Fig. 16. Filamentation Onset Distance Probability Density Function as a function of propagation distance and various values of the Refractive Index Structure Parameter and a volume Extinction Coefficient of 0.1 inverse-kilometers and a Zero Turbulence Collapse Distance of 4 km and Peak Power to Critical Power Ratios of 5 and 10.
Fig. 17.
Fig. 17. Filamentation Onset Distance Probability Density Function as a function of propagation distance and various values of the Refractive Index Structure Parameter and a volume Extinction Coefficient of 0.1 inverse-kilometers and a Zero Turbulence Collapse Distance of 1 km and Peak Power to Critical Power Ratios of 1.5 and 8.
Fig. 18.
Fig. 18. Comparison of Average Collapse Distances from Eqs. (6) and (8) [LHS], and Wave Train Computer Simulation Results using Figs. 16 and 17 Data.
Fig. 19.
Fig. 19. Comparison of Average Collapse Distances from Eqs. (6) and (8) [LHS], and Wave Train Computer Simulation Results using Fig. 17 Data Only.

Tables (2)

Tables Icon

Table 1. Average filamentation self-focusing collapse distances from the plots in Figs. 13 and 14.

Tables Icon

Table 2. Average filamentation self-focusing collapse distances from the plots in Figs. 16 and 17.

Equations (17)

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

A z = i c 2 ω 0 2 A + [ i ω 0 c ( δ n T + δ n T B ) 1 2 ( α T B + β ) ] A + j S j
z s f = 0.367 z r ( P p e a k / P p e a k P c r i t P c r i t 0.852 ) 2 0.0219 ,
z r = k a 0 2
z s f = z s f f / z s f f ( z s f + f ) ( z s f + f )
a 16 ( z ) = a L 16 ( z ) { 1 ( 2 α 2 z s f 2 ) [ 1 ( 1 + α z ) exp { α z } ] }
P p e a k / P c r i t = ( P P e a k / P c r i t ) [ 1 + m 0 k 2 a 0 2 ( a 0 C / a 0 C 0 0 ) 2 / 2 3 3 ] ,
C = 4.38 0 1 / 1 3 3 C n 2 ( h ) [ 1 { 1 + 17.5 ( a 0 / a 0 0 0 ) 2 } 1 / 1 6 6 ] ,
z s f = 0.367 z r ( P p e a k / P p e a k P c r i t P c r i t 0.852 ) 2 0.0219 ,
0.367 z r ( P p e a k / P p e a k P c r i t P c r i t 0.852 )
z s f = z s f f z s f + f ,
I ( r ) = I p e a k e 2 ( r 2 / r 2 W 0 2 W 0 2 ) N
W 0 = D a p / D a p 2 3 / 3 2 2 2 3 / 3 2 2
P p e a k / P c r i t = ( P P e a k / P c r i t ) [ 1 + m 0 k 2 a 0 2 ( a 0 C / a 0 C 0 0 ) 2 / 2 3 3 ] ,
C = 4.38 0 1 / 1 3 3 C n 2 ( h ) [ 1 { 1 + 17.5 ( a 0 / a 0 0 0 ) 2 } 1 / 1 6 6 ] ,
z s f = 0.367 z r ( P p e a k / P p e a k P c r i t P c r i t 0.852 ) 2 0.0219 ,
a 16 ( z ) = a L 16 ( z ) { 1 ( 2 α 2 z s f 2 ) [ 1 ( 1 + α z ) exp { α z } ] }
z s f = { z s f ; w i t h o u t a t r a n s m i t t e r l e n s z s f f / z s f f ( z s f + f ) ; w i t h a t r a n s m i t t e r l e n s ( z s f + f ) ; w i t h a t r a n s m i t t e r l e n s .

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