Abstract

The uniform irradiation generated by beam self-focusing in the inhomogeneous atmosphere is studied. It is found that the uniform irradiation may appear on propagation of an initial flat-topped beam from the ground to space orbits because of the phase modulation caused by self-focusing in the inhomogeneous atmosphere. This may offer a way to achieve the uniform irradiation under the effect of inhomogeneous nonlinearity. The uniform irradiation on the target is interesting for the laser space-debris clearing. To achieve the uniform irradiation on the debris target, we present the fitting formula of the modified focal length, which presents an effective design rule for the uniform irradiation on the debris target. In addition, the influence of the beam order on the beam quality due to self-focusing is also investigated.

© 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. NASA, “Satellite Box Score,” Orbital Debris Q. News 22(1), 12 (2018).
  2. D. K. Monroe, “Space debris removal using a high-power ground-based laser,” in Space Programs and Technologies Conference and Exhibit (American Institute of Aeronautics and Astronautics, 1993), paper AIAA-93-4238.
  3. C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
    [Crossref]
  4. J. W. Campbell, “Project Orion: orbital debris removal using ground-based sensors and lasers,” NASA Technical Memorandum 108522 (2002).
  5. A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “The effect of self-focusing on laser space-debris cleaning,” Light Sci. Appl. 3(4), e159 (2014).
    [Crossref]
  6. A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Laser beam self-focusing in the atmosphere,” Phys. Rev. Lett. 102(23), 233902 (2009).
    [Crossref] [PubMed]
  7. H. Deng, X. Ji, X. Li, and X. Wang, “Effect of spherical aberration on laser beam self-focusing in the atmosphere,” Opt. Lett. 40(16), 3881–3884 (2015).
    [Crossref] [PubMed]
  8. I. A. Vaseva, M. P. Fedoruk, A. M. Rubenchik, and S. K. Turitsyn, “Light self-focusing in the atmosphere: thin window model,” Sci. Rep. 6(1), 30697 (2016).
    [Crossref] [PubMed]
  9. Y. Zhang, X. Ji, H. Zhang, X. Li, T. Wang, H. Wang, and Y. Deng, “Self-focusing and group-velocity dispersion of pulsed laser beams in the inhomogeneous atmosphere,” Opt. Express 26(11), 14617–14625 (2018).
    [Crossref] [PubMed]
  10. F. M. Dickey, Laser Beam Shaping Theory and Techniques (Chemical Rubber Company, 2001), pp. 390–391.
  11. F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Chemical Rubber Company, 2005).
  12. D. L. Shealy, “Historical perspective of laser beam shaping,” in Laser Beam Shaping III (International Society for Optics and Photonics, 2002), Vol. 4770, pp. 28–48.
  13. S. Pfalzner, An Introduction to Inertial Confinement Fusion (Chemical Rubber Company, 2006).
  14. C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
    [Crossref]
  15. G. P. Agrawal, Nonlinear Fiber Optics. (Academic Press, 1995), Vol. II, Chap. 2.
  16. Y. Li, “Light beams with flat-topped profiles,” Opt. Lett. 27(12), 1007–1009 (2002).
    [Crossref] [PubMed]
  17. R. H. Hardin and F. D. Tappert, “Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equation,” SIAM Rev. Chronicles 15(2), 805–809 (1973).
  18. A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–15 (1990).
    [Crossref]
  19. S. V. Chekalin and V. P. Kandidov, “From self-focusing light beams to femtosecond laser pulse filamentation,” Phys. Uspekhi 56(2), 123–140 (2013).
    [Crossref]
  20. C. A. Palla, C. Pacheco, and M. E. Carrín, “Production of structured lipids by acidolysis with immobilized Rhizomucor miehei lipases: selection of suitable reaction conditions,” J. Mol. Catal., B Enzym. 76, 106–115 (2012).
    [Crossref]

2018 (2)

2016 (1)

I. A. Vaseva, M. P. Fedoruk, A. M. Rubenchik, and S. K. Turitsyn, “Light self-focusing in the atmosphere: thin window model,” Sci. Rep. 6(1), 30697 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (1)

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “The effect of self-focusing on laser space-debris cleaning,” Light Sci. Appl. 3(4), e159 (2014).
[Crossref]

2013 (1)

S. V. Chekalin and V. P. Kandidov, “From self-focusing light beams to femtosecond laser pulse filamentation,” Phys. Uspekhi 56(2), 123–140 (2013).
[Crossref]

2012 (2)

C. A. Palla, C. Pacheco, and M. E. Carrín, “Production of structured lipids by acidolysis with immobilized Rhizomucor miehei lipases: selection of suitable reaction conditions,” J. Mol. Catal., B Enzym. 76, 106–115 (2012).
[Crossref]

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

2009 (1)

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Laser beam self-focusing in the atmosphere,” Phys. Rev. Lett. 102(23), 233902 (2009).
[Crossref] [PubMed]

2002 (1)

1996 (1)

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

1990 (1)

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–15 (1990).
[Crossref]

1973 (1)

R. H. Hardin and F. D. Tappert, “Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equation,” SIAM Rev. Chronicles 15(2), 805–809 (1973).

Albrecht, G.

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

Baker, K. L.

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

Carrín, M. E.

C. A. Palla, C. Pacheco, and M. E. Carrín, “Production of structured lipids by acidolysis with immobilized Rhizomucor miehei lipases: selection of suitable reaction conditions,” J. Mol. Catal., B Enzym. 76, 106–115 (2012).
[Crossref]

Chekalin, S. V.

S. V. Chekalin and V. P. Kandidov, “From self-focusing light beams to femtosecond laser pulse filamentation,” Phys. Uspekhi 56(2), 123–140 (2013).
[Crossref]

Deng, H.

Deng, Y.

Dickey, F. M.

F. M. Dickey, Laser Beam Shaping Theory and Techniques (Chemical Rubber Company, 2001), pp. 390–391.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Chemical Rubber Company, 2005).

Fedoruk, M. P.

I. A. Vaseva, M. P. Fedoruk, A. M. Rubenchik, and S. K. Turitsyn, “Light self-focusing in the atmosphere: thin window model,” Sci. Rep. 6(1), 30697 (2016).
[Crossref] [PubMed]

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “The effect of self-focusing on laser space-debris cleaning,” Light Sci. Appl. 3(4), e159 (2014).
[Crossref]

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Laser beam self-focusing in the atmosphere,” Phys. Rev. Lett. 102(23), 233902 (2009).
[Crossref] [PubMed]

Friedman, H.

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

Gavel, D.

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

George, E. V.

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

Hardin, R. H.

R. H. Hardin and F. D. Tappert, “Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equation,” SIAM Rev. Chronicles 15(2), 805–809 (1973).

Ho, C.

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

Holswade, S. C.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Chemical Rubber Company, 2005).

Ji, X.

Kandidov, V. P.

S. V. Chekalin and V. P. Kandidov, “From self-focusing light beams to femtosecond laser pulse filamentation,” Phys. Uspekhi 56(2), 123–140 (2013).
[Crossref]

Li, X.

Li, Y.

Libby, S. B.

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

Liedahl, D. A.

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

Marcovici, B.

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

Michaelis, M. M.

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

Murray, J.

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

Olivier, S. S.

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

Pacheco, C.

C. A. Palla, C. Pacheco, and M. E. Carrín, “Production of structured lipids by acidolysis with immobilized Rhizomucor miehei lipases: selection of suitable reaction conditions,” J. Mol. Catal., B Enzym. 76, 106–115 (2012).
[Crossref]

Palla, C. A.

C. A. Palla, C. Pacheco, and M. E. Carrín, “Production of structured lipids by acidolysis with immobilized Rhizomucor miehei lipases: selection of suitable reaction conditions,” J. Mol. Catal., B Enzym. 76, 106–115 (2012).
[Crossref]

Pfalzner, S.

S. Pfalzner, An Introduction to Inertial Confinement Fusion (Chemical Rubber Company, 2006).

Phipps, C. R.

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

Pleasance, L. D.

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

Priedhorsky, W.

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

Reilly, J. P.

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

Rubenchik, A. M.

I. A. Vaseva, M. P. Fedoruk, A. M. Rubenchik, and S. K. Turitsyn, “Light self-focusing in the atmosphere: thin window model,” Sci. Rep. 6(1), 30697 (2016).
[Crossref] [PubMed]

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “The effect of self-focusing on laser space-debris cleaning,” Light Sci. Appl. 3(4), e159 (2014).
[Crossref]

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Laser beam self-focusing in the atmosphere,” Phys. Rev. Lett. 102(23), 233902 (2009).
[Crossref] [PubMed]

Shealy, D. L.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Chemical Rubber Company, 2005).

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–15 (1990).
[Crossref]

Tappert, F. D.

R. H. Hardin and F. D. Tappert, “Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equation,” SIAM Rev. Chronicles 15(2), 805–809 (1973).

Trebes, J. E.

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

Turitsyn, S. K.

I. A. Vaseva, M. P. Fedoruk, A. M. Rubenchik, and S. K. Turitsyn, “Light self-focusing in the atmosphere: thin window model,” Sci. Rep. 6(1), 30697 (2016).
[Crossref] [PubMed]

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “The effect of self-focusing on laser space-debris cleaning,” Light Sci. Appl. 3(4), e159 (2014).
[Crossref]

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Laser beam self-focusing in the atmosphere,” Phys. Rev. Lett. 102(23), 233902 (2009).
[Crossref] [PubMed]

Valley, M. T.

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

Vaseva, I. A.

I. A. Vaseva, M. P. Fedoruk, A. M. Rubenchik, and S. K. Turitsyn, “Light self-focusing in the atmosphere: thin window model,” Sci. Rep. 6(1), 30697 (2016).
[Crossref] [PubMed]

Wang, H.

Wang, T.

Wang, X.

Zhang, H.

Zhang, Y.

Adv. Space Res. (1)

C. R. Phipps, K. L. Baker, S. B. Libby, D. A. Liedahl, S. S. Olivier, L. D. Pleasance, A. M. Rubenchik, J. E. Trebes, E. V. George, B. Marcovici, J. P. Reilly, and M. T. Valley, “Removing orbital debris with lasers,” Adv. Space Res. 49(9), 1283–1300 (2012).
[Crossref]

J. Mol. Catal., B Enzym. (1)

C. A. Palla, C. Pacheco, and M. E. Carrín, “Production of structured lipids by acidolysis with immobilized Rhizomucor miehei lipases: selection of suitable reaction conditions,” J. Mol. Catal., B Enzym. 76, 106–115 (2012).
[Crossref]

Laser Part. Beams (1)

C. R. Phipps, G. Albrecht, H. Friedman, D. Gavel, E. V. George, J. Murray, C. Ho, W. Priedhorsky, M. M. Michaelis, and J. P. Reilly, “ORION: Clearing near-Earth space debris using a 20-kW, 530-nm, Earth-based, repetitively pulsed laser,” Laser Part. Beams 14(1), 1–44 (1996).
[Crossref]

Light Sci. Appl. (1)

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “The effect of self-focusing on laser space-debris cleaning,” Light Sci. Appl. 3(4), e159 (2014).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Orbital Debris Q. News (1)

NASA, “Satellite Box Score,” Orbital Debris Q. News 22(1), 12 (2018).

Phys. Rev. Lett. (1)

A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Laser beam self-focusing in the atmosphere,” Phys. Rev. Lett. 102(23), 233902 (2009).
[Crossref] [PubMed]

Phys. Uspekhi (1)

S. V. Chekalin and V. P. Kandidov, “From self-focusing light beams to femtosecond laser pulse filamentation,” Phys. Uspekhi 56(2), 123–140 (2013).
[Crossref]

Proc. SPIE (1)

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–15 (1990).
[Crossref]

Sci. Rep. (1)

I. A. Vaseva, M. P. Fedoruk, A. M. Rubenchik, and S. K. Turitsyn, “Light self-focusing in the atmosphere: thin window model,” Sci. Rep. 6(1), 30697 (2016).
[Crossref] [PubMed]

SIAM Rev. Chronicles (1)

R. H. Hardin and F. D. Tappert, “Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equation,” SIAM Rev. Chronicles 15(2), 805–809 (1973).

Other (7)

G. P. Agrawal, Nonlinear Fiber Optics. (Academic Press, 1995), Vol. II, Chap. 2.

F. M. Dickey, Laser Beam Shaping Theory and Techniques (Chemical Rubber Company, 2001), pp. 390–391.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Chemical Rubber Company, 2005).

D. L. Shealy, “Historical perspective of laser beam shaping,” in Laser Beam Shaping III (International Society for Optics and Photonics, 2002), Vol. 4770, pp. 28–48.

S. Pfalzner, An Introduction to Inertial Confinement Fusion (Chemical Rubber Company, 2006).

D. K. Monroe, “Space debris removal using a high-power ground-based laser,” in Space Programs and Technologies Conference and Exhibit (American Institute of Aeronautics and Astronautics, 1993), paper AIAA-93-4238.

J. W. Campbell, “Project Orion: orbital debris removal using ground-based sensors and lasers,” NASA Technical Memorandum 108522 (2002).

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Figures (10)

Fig. 1
Fig. 1 Initial 3D intensity distributions of flat-topped beams with different beam order N, P = 1400Pcr.
Fig. 2
Fig. 2 (a) Beam width wlin for linear propagation in free space and (b) beam width w for nonlinear propagation in the atmosphere versus the propagation distance z, P = 1400Pcr.
Fig. 3
Fig. 3 Relative beam width w/ wlin versus the propagation distance z, P = 1400Pcr.
Fig. 4
Fig. 4 On-axis intensity I(r = 0, z) versus the propagation distance z, P = 1400Pcr.
Fig. 5
Fig. 5 Relative intensity distribution I(r, z)/I0 versus the propagation distance z, P = 2250Pcr.
Fig. 6
Fig. 6 B integral versus the beam order N, P = 1500Pcr.
Fig. 7
Fig. 7 Intensity distribution I(r, z) versus the propagation distance z. Uniform irradiation on the debris target.
Fig. 8
Fig. 8 (a) intensity distribution I(r, z) and (b) phase distribution Ф(r, z) at the plane z = 20km, (c) relative intensity distribution I(r, z)/Ipea on the debris target (z = 1000km), N = 10, P = 8050Pcr.
Fig. 9
Fig. 9 For the uniform irradiation on the debris target, (a) required beam power Pfla and (b) B integral Bfla versus the beam order N, F = 1000km.
Fig. 10
Fig. 10 For the uniform irradiation on the debris target, (a) modified focal length Fmod versus the beam order N and the beam power P (black dots: numerical simulation results; Curve surface: fitting surface by using Eq. (10)), and (b) the range of N and P in Eq. (10).

Tables (1)

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Table 1 Values of the coefficients in Eq. (10)

Equations (10)

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2i k 0 A z + 2 A+2 k 0 2 n 2 n 0 | A | 2 A=0,
A( r, z j+1 )=exp( i 4 k 0 Δz 2 )exp(is)exp( i 4 k 0 Δz 2 )A(r, z j ),
i A z + k 0 n 2 n 0 | A 2 |A=0.
A( r, z j +Δz )=A( r, z j )exp[ i k 0 n 2 | A( r, z j ) | 2 n 0 Δz ].
A( r,z=0 )= A 0 exp( i C 0 w 0 2 r 2 ) m=1 N ( 1 ) m1 N ( N m )exp( m r 2 w 0 2 ) ,
A 0 = P/ π w 0 2 m N n N ( 1 ) m+n N 2 ( N m )( N n ) 1 m+n .
w 2 = 2 P 0 2π 0 r 2 A( r,z ) A * ( r,z )rdrdθ .
B= k 0 0 z 0 I( r=0,z ) n 2 ( z )dz .
B= k 0 n 20 Ph[ 1exp( z 0 /h) ] π w 0 2 m=1 N n=1 N (1) m+n ( N m ) ( N n ) m=1 N n=1 N (1) m+n ( N m )( N n ) 1 m+n .
F mod = F 0 + A 01 N +B 01 (P/ P cr )+ B 02 (P/ P cr ) 2 + B 03 (P/ P cr ) 3 1+ A 1 N+ A 2 N 2 + A 3 N 3 + B 1 (P/ P cr )+ B 2 (P/ P cr ) 2 ,

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