Abstract

We model combining of multiple laser beams into a single near diffraction-limited beam by beam self-focusing (collapse) in a Kerr medium. The beams with the total power above critical are combined in the near field and then propagated in the Kerr medium. Nonlinearity results in self-focusing event, combining multiple beams into nearly a diffraction-limited beam that carries the critical power. Beam quality of the combined beam is analyzed as a function of the number of combining beams and the level of random fluctuations of the combining beams phases.

© 2015 Optical Society of America

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References

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  1. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, B63–B92 (2010).
    [Crossref]
  2. C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7, 861 (2013).
    [Crossref]
  3. V. Gapontsev, F. A. Fomin, and M. Abramov, “Diffraction limited ultra-high-power fibre lasers,”, in Proceedings of Advanced Solid-State Photonics, OSA Topical Meeting (2010), Paper AWA1.
  4. http://www.ipgphotonics.com .
  5. C. Jauregui, H.-J. Otto, N. Modsching, J. Limpert, and A. Tünnermann, “Recent progress in the understanding of mode instabilities,” in Proceedings of the SPIE Conference on Fiber Lasers XII - Technology, Systems, and Applications, 9344, L. Shaw and J. Ballato, eds. (2015), p. 93440J.
  6. T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
    [Crossref]
  7. T. Weyrauch, M. Vorontsov, V. Ovchinnikov, E. Polnau, G. Wu, T. Ryan, and M. Maynard, “Atmospheric turbulence compensation and coherent beam combining over a 7 km propagation path using a fiber-array system with 21 sub-apertures,” in “Imaging and Applied Optics 2014,” (Optical Society of America, 2014), p. PW2E.3.
  8. A. Brignon, ed., Coherent Laser Beam Combining (Wiley, 2013).
    [Crossref]
  9. S. M. Redmond, D. J. Ripin, C. X. Yu, S. J. Augst, T. Y. Fan, P. A. Thielen, J. E. Rothenberg, and G. D. Goodno, “Diffractive coherent combining of a 2.5 kw fiber laser array into a 1.9 kw gaussian beam,” Opt. Lett. 37, 2832–2834 (2012).
    [Crossref] [PubMed]
  10. P. M. Lushnikov and N. Vladimirova, “Nonlinear combining of laser beams,” Opt. Lett. 39, 3429–3432 (2014).
    [Crossref] [PubMed]
  11. O. V. Shtyrina, A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability,” Phys. Rev. A 91, 033810 (2015).
    [Crossref]
  12. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
    [Crossref]
  13. S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media,” Izv. Vys. Uchebn. Zaved. Radiofizika 14, 1353 (1971).
  14. V. E. Zakharov, “Collapse of langmuir waves,” Sov. Phys. JETP 35, 908 (1972).
  15. C. Sulem and P. L. Sulem, Nonlinear Schrödinger Equations: Self-Focusing and Wave Collapse (World Scientific, 1999).
  16. P. M. Lushnikov, S. A. Dyachenko, and N. Vladimirova, “Beyond leading-order logarithmic scaling in the catastrophic self-focusing of a laser beam in Kerr media,” Phys. Rev. A 88, 013845 (2013).
    [Crossref]
  17. P. M. Lushnikov and H. A. Rose, “Instability versus equilibrium propagation of laser beam in plasma,” Phys. Rev. Lett. 92, 255003 (2004).
    [Crossref]
  18. P. M. Lushnikov and H. A. Rose, “How much laser power can propagate through fusion plasma?”; Plasma Phys. Control. Fusion 48, 1501–1513 (2006).
    [Crossref]
  19. P. M. Lushnikov and N. Vladimirova, “Non-gaussian statistics of multiple filamentation,” Opt. Lett. 35, 1965–1967 (2010).
    [Crossref] [PubMed]
  20. Y. Chung and P. M. Lushnikov, “Strong collapse turbulence in quintic nonlinear schrödinger equation,” Phys. Rev. E 84, 036602 (2011).
    [Crossref]
  21. T. S. Ross, Laser Beam Quality Metrics (SPIE, 2013).
    [Crossref]
  22. A. V. Smith and B. T. Do, “Bulk and surface laser damage of silica by picosecond and nanosecond pulses at 1064 nm,” Appl. Opt. 47, 4812–4832 (2008).
    [Crossref] [PubMed]
  23. J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

2015 (1)

O. V. Shtyrina, A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability,” Phys. Rev. A 91, 033810 (2015).
[Crossref]

2014 (1)

2013 (2)

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7, 861 (2013).
[Crossref]

P. M. Lushnikov, S. A. Dyachenko, and N. Vladimirova, “Beyond leading-order logarithmic scaling in the catastrophic self-focusing of a laser beam in Kerr media,” Phys. Rev. A 88, 013845 (2013).
[Crossref]

2012 (1)

2011 (1)

Y. Chung and P. M. Lushnikov, “Strong collapse turbulence in quintic nonlinear schrödinger equation,” Phys. Rev. E 84, 036602 (2011).
[Crossref]

2010 (2)

2008 (2)

A. V. Smith and B. T. Do, “Bulk and surface laser damage of silica by picosecond and nanosecond pulses at 1064 nm,” Appl. Opt. 47, 4812–4832 (2008).
[Crossref] [PubMed]

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

2007 (1)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

2006 (1)

P. M. Lushnikov and H. A. Rose, “How much laser power can propagate through fusion plasma?”; Plasma Phys. Control. Fusion 48, 1501–1513 (2006).
[Crossref]

2005 (1)

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

2004 (1)

P. M. Lushnikov and H. A. Rose, “Instability versus equilibrium propagation of laser beam in plasma,” Phys. Rev. Lett. 92, 255003 (2004).
[Crossref]

1972 (1)

V. E. Zakharov, “Collapse of langmuir waves,” Sov. Phys. JETP 35, 908 (1972).

1971 (1)

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media,” Izv. Vys. Uchebn. Zaved. Radiofizika 14, 1353 (1971).

Abramov, M.

V. Gapontsev, F. A. Fomin, and M. Abramov, “Diffraction limited ultra-high-power fibre lasers,”, in Proceedings of Advanced Solid-State Photonics, OSA Topical Meeting (2010), Paper AWA1.

Augst, S. J.

Barty, C.

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Beach, R. J.

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Bergé, L.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Chung, Y.

Y. Chung and P. M. Lushnikov, “Strong collapse turbulence in quintic nonlinear schrödinger equation,” Phys. Rev. E 84, 036602 (2011).
[Crossref]

Clarkson, W. A.

Dawson, J. W.

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Do, B. T.

Dyachenko, S. A.

P. M. Lushnikov, S. A. Dyachenko, and N. Vladimirova, “Beyond leading-order logarithmic scaling in the catastrophic self-focusing of a laser beam in Kerr media,” Phys. Rev. A 88, 013845 (2013).
[Crossref]

Fan, T. Y.

Fedoruk, M. P.

O. V. Shtyrina, A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability,” Phys. Rev. A 91, 033810 (2015).
[Crossref]

Fomin, F. A.

V. Gapontsev, F. A. Fomin, and M. Abramov, “Diffraction limited ultra-high-power fibre lasers,”, in Proceedings of Advanced Solid-State Photonics, OSA Topical Meeting (2010), Paper AWA1.

Gapontsev, V.

V. Gapontsev, F. A. Fomin, and M. Abramov, “Diffraction limited ultra-high-power fibre lasers,”, in Proceedings of Advanced Solid-State Photonics, OSA Topical Meeting (2010), Paper AWA1.

Goodno, G. D.

Heebner, J. E.

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Jauregui, C.

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7, 861 (2013).
[Crossref]

C. Jauregui, H.-J. Otto, N. Modsching, J. Limpert, and A. Tünnermann, “Recent progress in the understanding of mode instabilities,” in Proceedings of the SPIE Conference on Fiber Lasers XII - Technology, Systems, and Applications, 9344, L. Shaw and J. Ballato, eds. (2015), p. 93440J.

Kasparian, J.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Limpert, J.

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7, 861 (2013).
[Crossref]

C. Jauregui, H.-J. Otto, N. Modsching, J. Limpert, and A. Tünnermann, “Recent progress in the understanding of mode instabilities,” in Proceedings of the SPIE Conference on Fiber Lasers XII - Technology, Systems, and Applications, 9344, L. Shaw and J. Ballato, eds. (2015), p. 93440J.

Lushnikov, P. M.

P. M. Lushnikov and N. Vladimirova, “Nonlinear combining of laser beams,” Opt. Lett. 39, 3429–3432 (2014).
[Crossref] [PubMed]

P. M. Lushnikov, S. A. Dyachenko, and N. Vladimirova, “Beyond leading-order logarithmic scaling in the catastrophic self-focusing of a laser beam in Kerr media,” Phys. Rev. A 88, 013845 (2013).
[Crossref]

Y. Chung and P. M. Lushnikov, “Strong collapse turbulence in quintic nonlinear schrödinger equation,” Phys. Rev. E 84, 036602 (2011).
[Crossref]

P. M. Lushnikov and N. Vladimirova, “Non-gaussian statistics of multiple filamentation,” Opt. Lett. 35, 1965–1967 (2010).
[Crossref] [PubMed]

P. M. Lushnikov and H. A. Rose, “How much laser power can propagate through fusion plasma?”; Plasma Phys. Control. Fusion 48, 1501–1513 (2006).
[Crossref]

P. M. Lushnikov and H. A. Rose, “Instability versus equilibrium propagation of laser beam in plasma,” Phys. Rev. Lett. 92, 255003 (2004).
[Crossref]

Maynard, M.

T. Weyrauch, M. Vorontsov, V. Ovchinnikov, E. Polnau, G. Wu, T. Ryan, and M. Maynard, “Atmospheric turbulence compensation and coherent beam combining over a 7 km propagation path using a fiber-array system with 21 sub-apertures,” in “Imaging and Applied Optics 2014,” (Optical Society of America, 2014), p. PW2E.3.

Messerly, M. J.

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Miroslav,

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Modsching, N.

C. Jauregui, H.-J. Otto, N. Modsching, J. Limpert, and A. Tünnermann, “Recent progress in the understanding of mode instabilities,” in Proceedings of the SPIE Conference on Fiber Lasers XII - Technology, Systems, and Applications, 9344, L. Shaw and J. Ballato, eds. (2015), p. 93440J.

Nilsson, J.

Nuter, R.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Otto, H.-J.

C. Jauregui, H.-J. Otto, N. Modsching, J. Limpert, and A. Tünnermann, “Recent progress in the understanding of mode instabilities,” in Proceedings of the SPIE Conference on Fiber Lasers XII - Technology, Systems, and Applications, 9344, L. Shaw and J. Ballato, eds. (2015), p. 93440J.

Ovchinnikov, V.

T. Weyrauch, M. Vorontsov, V. Ovchinnikov, E. Polnau, G. Wu, T. Ryan, and M. Maynard, “Atmospheric turbulence compensation and coherent beam combining over a 7 km propagation path using a fiber-array system with 21 sub-apertures,” in “Imaging and Applied Optics 2014,” (Optical Society of America, 2014), p. PW2E.3.

Pax, P. H.

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Petrishchev, V. A.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media,” Izv. Vys. Uchebn. Zaved. Radiofizika 14, 1353 (1971).

Polnau, E.

T. Weyrauch, M. Vorontsov, V. Ovchinnikov, E. Polnau, G. Wu, T. Ryan, and M. Maynard, “Atmospheric turbulence compensation and coherent beam combining over a 7 km propagation path using a fiber-array system with 21 sub-apertures,” in “Imaging and Applied Optics 2014,” (Optical Society of America, 2014), p. PW2E.3.

Redmond, S. M.

Richardson, D. J.

Ripin, D. J.

Rose, H. A.

P. M. Lushnikov and H. A. Rose, “How much laser power can propagate through fusion plasma?”; Plasma Phys. Control. Fusion 48, 1501–1513 (2006).
[Crossref]

P. M. Lushnikov and H. A. Rose, “Instability versus equilibrium propagation of laser beam in plasma,” Phys. Rev. Lett. 92, 255003 (2004).
[Crossref]

Ross, T. S.

T. S. Ross, Laser Beam Quality Metrics (SPIE, 2013).
[Crossref]

Rothenberg, J. E.

Rubenchik, A. M.

O. V. Shtyrina, A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability,” Phys. Rev. A 91, 033810 (2015).
[Crossref]

Ryan, T.

T. Weyrauch, M. Vorontsov, V. Ovchinnikov, E. Polnau, G. Wu, T. Ryan, and M. Maynard, “Atmospheric turbulence compensation and coherent beam combining over a 7 km propagation path using a fiber-array system with 21 sub-apertures,” in “Imaging and Applied Optics 2014,” (Optical Society of America, 2014), p. PW2E.3.

Shtyrina, O. V.

O. V. Shtyrina, A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability,” Phys. Rev. A 91, 033810 (2015).
[Crossref]

Shverdin, Y.

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Siders, C. W.

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Skupin, S.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Smith, A. V.

Sridharan, A. K.

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Stappaerts, E. A.

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Sulem, C.

C. Sulem and P. L. Sulem, Nonlinear Schrödinger Equations: Self-Focusing and Wave Collapse (World Scientific, 1999).

Sulem, P. L.

C. Sulem and P. L. Sulem, Nonlinear Schrödinger Equations: Self-Focusing and Wave Collapse (World Scientific, 1999).

Talanov, V. I.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media,” Izv. Vys. Uchebn. Zaved. Radiofizika 14, 1353 (1971).

Thielen, P. A.

Tünnermann, A.

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7, 861 (2013).
[Crossref]

C. Jauregui, H.-J. Otto, N. Modsching, J. Limpert, and A. Tünnermann, “Recent progress in the understanding of mode instabilities,” in Proceedings of the SPIE Conference on Fiber Lasers XII - Technology, Systems, and Applications, 9344, L. Shaw and J. Ballato, eds. (2015), p. 93440J.

Turitsyn, S. K.

O. V. Shtyrina, A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability,” Phys. Rev. A 91, 033810 (2015).
[Crossref]

Vladimirova, N.

P. M. Lushnikov and N. Vladimirova, “Nonlinear combining of laser beams,” Opt. Lett. 39, 3429–3432 (2014).
[Crossref] [PubMed]

P. M. Lushnikov, S. A. Dyachenko, and N. Vladimirova, “Beyond leading-order logarithmic scaling in the catastrophic self-focusing of a laser beam in Kerr media,” Phys. Rev. A 88, 013845 (2013).
[Crossref]

P. M. Lushnikov and N. Vladimirova, “Non-gaussian statistics of multiple filamentation,” Opt. Lett. 35, 1965–1967 (2010).
[Crossref] [PubMed]

Vlasov, S. N.

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media,” Izv. Vys. Uchebn. Zaved. Radiofizika 14, 1353 (1971).

Vorontsov, M.

T. Weyrauch, M. Vorontsov, V. Ovchinnikov, E. Polnau, G. Wu, T. Ryan, and M. Maynard, “Atmospheric turbulence compensation and coherent beam combining over a 7 km propagation path using a fiber-array system with 21 sub-apertures,” in “Imaging and Applied Optics 2014,” (Optical Society of America, 2014), p. PW2E.3.

Weyrauch, T.

T. Weyrauch, M. Vorontsov, V. Ovchinnikov, E. Polnau, G. Wu, T. Ryan, and M. Maynard, “Atmospheric turbulence compensation and coherent beam combining over a 7 km propagation path using a fiber-array system with 21 sub-apertures,” in “Imaging and Applied Optics 2014,” (Optical Society of America, 2014), p. PW2E.3.

Wolf, J.-P.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Wu, G.

T. Weyrauch, M. Vorontsov, V. Ovchinnikov, E. Polnau, G. Wu, T. Ryan, and M. Maynard, “Atmospheric turbulence compensation and coherent beam combining over a 7 km propagation path using a fiber-array system with 21 sub-apertures,” in “Imaging and Applied Optics 2014,” (Optical Society of America, 2014), p. PW2E.3.

Yu, C. X.

Zakharov, V. E.

V. E. Zakharov, “Collapse of langmuir waves,” Sov. Phys. JETP 35, 908 (1972).

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

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

Izv. Vys. Uchebn. Zaved. Radiofizika (1)

S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, “Averaged description of wave beams in linear and nonlinear media,” Izv. Vys. Uchebn. Zaved. Radiofizika 14, 1353 (1971).

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

Nat. Photonics (1)

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7, 861 (2013).
[Crossref]

Opt. Commun. (1)

J. W. Dawson, M. J. Messerly, R. J. Beach, Miroslav, Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Commun. 16, 13240–13266 (2008).

Opt. Lett. (3)

Phys. Rev. A (2)

P. M. Lushnikov, S. A. Dyachenko, and N. Vladimirova, “Beyond leading-order logarithmic scaling in the catastrophic self-focusing of a laser beam in Kerr media,” Phys. Rev. A 88, 013845 (2013).
[Crossref]

O. V. Shtyrina, A. M. Rubenchik, M. P. Fedoruk, and S. K. Turitsyn, “Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability,” Phys. Rev. A 91, 033810 (2015).
[Crossref]

Phys. Rev. E (1)

Y. Chung and P. M. Lushnikov, “Strong collapse turbulence in quintic nonlinear schrödinger equation,” Phys. Rev. E 84, 036602 (2011).
[Crossref]

Phys. Rev. Lett. (1)

P. M. Lushnikov and H. A. Rose, “Instability versus equilibrium propagation of laser beam in plasma,” Phys. Rev. Lett. 92, 255003 (2004).
[Crossref]

Plasma Phys. Control. Fusion (1)

P. M. Lushnikov and H. A. Rose, “How much laser power can propagate through fusion plasma?”; Plasma Phys. Control. Fusion 48, 1501–1513 (2006).
[Crossref]

Rep. Prog. Phys. (1)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Sov. Phys. JETP (1)

V. E. Zakharov, “Collapse of langmuir waves,” Sov. Phys. JETP 35, 908 (1972).

Other (7)

C. Sulem and P. L. Sulem, Nonlinear Schrödinger Equations: Self-Focusing and Wave Collapse (World Scientific, 1999).

T. S. Ross, Laser Beam Quality Metrics (SPIE, 2013).
[Crossref]

T. Weyrauch, M. Vorontsov, V. Ovchinnikov, E. Polnau, G. Wu, T. Ryan, and M. Maynard, “Atmospheric turbulence compensation and coherent beam combining over a 7 km propagation path using a fiber-array system with 21 sub-apertures,” in “Imaging and Applied Optics 2014,” (Optical Society of America, 2014), p. PW2E.3.

A. Brignon, ed., Coherent Laser Beam Combining (Wiley, 2013).
[Crossref]

V. Gapontsev, F. A. Fomin, and M. Abramov, “Diffraction limited ultra-high-power fibre lasers,”, in Proceedings of Advanced Solid-State Photonics, OSA Topical Meeting (2010), Paper AWA1.

http://www.ipgphotonics.com .

C. Jauregui, H.-J. Otto, N. Modsching, J. Limpert, and A. Tünnermann, “Recent progress in the understanding of mode instabilities,” in Proceedings of the SPIE Conference on Fiber Lasers XII - Technology, Systems, and Applications, 9344, L. Shaw and J. Ballato, eds. (2015), p. 93440J.

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Figures (1)

Fig. 1
Fig. 1 (a) A schematic of 3-beam combining setup. (b) Amplitude and phase at the entrance surface for 3, 7 and 127 beams. (c) z-dependence of the beam width w. Solid lines are for propagation of self-focused beams in vacuum after exiting the Kerr medium at z = zexit. Dotted lines of the same colors are for the propagation of input beams without Kerr medium (zexit = 0 in that case). A black dashed line is for propagation of Gaussian beam in vacuum with the beam quality factor M2 = 1. (d) A cross-section of amplitude of the self-focused beam propagating in vacuum for z > zexit (corresponds to solid lines in (c)) at the location where w(z) = 2w(zexit). (e) A cross section of amplitude for beams propagating in vacuum (corresponds to dotted lines in (c) with zexit = 0) at the location where w(z) = 2w(0).

Tables (1)

Tables Icon

Table 1 Properties of self-focused beams formed by combining 3, 7, or 127 beams with total input power P = 2Pc: radial component of the wave vector, k (for the 3-beam and 7-beam cases) or phase shift parameter χ (for the 127-beam case); maximum amplitude at the exit from nonlinear medium, |ψexit||ψ(0,zexit)|; ratio of exit amplitude to input amplitude, |ψexit/ψ0| |ψexit|/maxr|ψ(r,0); quality of the exit beam filtered by the diaphragm of radius rd = 3L(zexit), measured at short distances M short 2 and at long distances M long 2; power of the exit beam filtered by the diaphragm, Pd; thickness of the slab of the medium, z exit, and total diameter of input beams, D , both in physical units. Here z exit = ( 0.1376 cm ) z exit | ψ exit | 2 and D = ( 0.0090 mm ) D | ψ exit | for the intensity maximum I = 5 · 1011W/cm2 at z = zexit.

Equations (6)

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i z ψ + 1 2 k 2 ψ + k n 2 n 0 | ψ | 2 ψ = 0 ,
i z ψ + 2 ψ + | ψ | 2 ψ = 0 ,
P c = N c λ 0 2 8 π 2 n 2 n 0 11.70 λ 0 2 8 π 2 n 2 n 0 .
R + 2 R + R 3 = 0
| ψ ( r , z ) | L ( z ) 1 R ( ρ ) , ρ r / L ( z ) , | r | r ,
w 2 ( z ) = w 0 2 + ( 2 M 2 k 0 w 0 ) 2 ( z z 0 ) 2 , where w ( z ) = 2 | ψ | 2 r 2 d 2 r | ψ | 2 d 2 r .

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