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.

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]

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).

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).

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]

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

[Crossref]

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).

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]

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]

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

[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]

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.

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.

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]

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).

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.

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]

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.

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]

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.

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).

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).

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.

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]

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.

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.

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).

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).

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.

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]

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]

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]

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

[Crossref]

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]

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]

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.

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]

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).

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).

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]

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).

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).

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

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

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).

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]

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.

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]

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]

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).

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.

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.

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]

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.

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]

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

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

[Crossref]

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).

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

[Crossref]

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).

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

[Crossref]
[PubMed]

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

[Crossref]
[PubMed]

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]

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]

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 H. A. Rose, “Instability versus equilibrium propagation of laser beam in plasma,” Phys. Rev. Lett. 92, 255003 (2004).

[Crossref]

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]

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]

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

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.