Abstract

Recent theoretical researches reveal that the self-focusing critical power in the fiber waveguide is identical to that in the bulk medium. However, the delivery of peak power much higher than the self-focusing critical power has been demonstrated experimentally in ultra-large-mode-area fiber (ULMAF). And no experimental observation of self-focusing effect has been reported in recent pulsed fiber laser system whose peak power has reached or even exceeded the critical power. In this paper, we try to address this issue by studying the self-focusing length theoretically in the ULMAF which is highly multimode. Nonlinear beam propagation method employing PÁDE(2,2) approximation is applied in the numerical simulation. The results show that the self-focusing length of the fundamental mode is typically a few millimeters which is almost identical to that in the bulk medium. However, the self-focusing length of the summation of numerous modes can be as long as a few meters.

© 2012 OSA

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2010 (1)

2009 (2)

L. Ming-Jun, C. Xin, L. Anping, S. Gray, W. Ji, D. T. Walton, and L. A. Zenteno, “Limit of effective area for single-mode operation in step-index large mode area laser fibers,” J. Lightwave Technol. 27(15), 3010–3016 (2009).
[CrossRef]

A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
[CrossRef]

2008 (2)

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

J. Boullet, Y. Zaouter, R. Desmarchelier, M. Cazaux, F. Salin, J. Saby, R. Bello-Doua, and E. Cormier, “High power ytterbium-doped rod-type three-level photonic crystal fiber laser,” Opt. Express 16(22), 17891–17902 (2008).
[CrossRef] [PubMed]

2007 (2)

A. Galvanauskas, M.-Y. Cheng, K.-C. Hou, and K.-H. Liao, “High peak power pulse amplification in large-core Yb-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 559–566 (2007).
[CrossRef]

G. R. Hadley and A. V. Smith, “Self-focusing in high-power optical fibers,” Proc. SPIE 6475, 64750G, 64750G-11 (2007).
[CrossRef]

2006 (3)

2005 (2)

2001 (1)

T. Schmidt-Uhlig, P. Karlitschek, G. Marowsky, and Y. Sano, “New simplified coupling scheme for the delivery of 20 MW Nd:YAG laser pulses by large core optical fibers,” Appl. Phys. B 72(2), 183–186 (2001).
[CrossRef]

2000 (1)

1998 (1)

1997 (1)

1996 (1)

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8(5), 649–651 (1996).
[CrossRef]

1992 (1)

Anping, L.

Baets, R.

P. Vandersteegen, B. Maes, P. Bienstman, and R. Baets, “Using the complex Jacobi method to simulate Kerr non-linear photonic components,” Opt. Quantum Electron. 38(1-3), 35–44 (2006).
[CrossRef]

Bello-Doua, R.

Bienstman, P.

P. Vandersteegen, B. Maes, P. Bienstman, and R. Baets, “Using the complex Jacobi method to simulate Kerr non-linear photonic components,” Opt. Quantum Electron. 38(1-3), 35–44 (2006).
[CrossRef]

Boullet, J.

Bowers, M. W.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Brooks, C. D.

Cazaux, M.

Chang, Y.-C.

Changkakoti, R.

Cheng, M.-Y.

Clarkson, W. A.

Cormier, E.

Desmarchelier, R.

Di Teodoro, F.

Dixit, S. N.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Do, B. T.

A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
[CrossRef]

Erbert, G. V.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Farrow, R. L.

A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
[CrossRef]

R. L. Farrow, D. A. V. Kliner, G. R. Hadley, and A. V. Smith, “Peak-power limits on fiber amplifiers imposed by self-focusing,” Opt. Lett. 31(23), 3423–3425 (2006).
[CrossRef] [PubMed]

Fibich, G.

Frasca, M.

Gaeta, A. L.

Galvanauskas, A.

Garavaglia, A.

Gatchell, P.

Gobin, I.

Gray, S.

Hadley, G. R.

A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
[CrossRef]

G. R. Hadley and A. V. Smith, “Self-focusing in high-power optical fibers,” Proc. SPIE 6475, 64750G, 64750G-11 (2007).
[CrossRef]

R. L. Farrow, D. A. V. Kliner, G. R. Hadley, and A. V. Smith, “Peak-power limits on fiber amplifiers imposed by self-focusing,” Opt. Lett. 31(23), 3423–3425 (2006).
[CrossRef] [PubMed]

G. R. Hadley, “Wide-angle beam propagation using Padé approximant operators,” Opt. Lett. 17(20), 1426–1428 (1992).
[CrossRef] [PubMed]

Haynam, C. A.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Heestand, G. M.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Henesian, M. A.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Hermann, M. R.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Hou, K.-C.

A. Galvanauskas, M.-Y. Cheng, K.-C. Hou, and K.-H. Liao, “High peak power pulse amplification in large-core Yb-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 559–566 (2007).
[CrossRef]

Huang, W. P.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8(5), 649–651 (1996).
[CrossRef]

Jancaitis, K. S.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Ji, W.

Karlitschek, P.

T. Schmidt-Uhlig, P. Karlitschek, G. Marowsky, and Y. Sano, “New simplified coupling scheme for the delivery of 20 MW Nd:YAG laser pulses by large core optical fibers,” Appl. Phys. B 72(2), 183–186 (2001).
[CrossRef]

Kliner, D. A. V.

Liao, K.-H.

A. Galvanauskas, M.-Y. Cheng, K.-C. Hou, and K.-H. Liao, “High peak power pulse amplification in large-core Yb-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 559–566 (2007).
[CrossRef]

Lui, W.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8(5), 649–651 (1996).
[CrossRef]

Maes, B.

P. Vandersteegen, B. Maes, P. Bienstman, and R. Baets, “Using the complex Jacobi method to simulate Kerr non-linear photonic components,” Opt. Quantum Electron. 38(1-3), 35–44 (2006).
[CrossRef]

Mamidipudi, P.

Manes, K. R.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Mansuripur, M.

Marowsky, G.

T. Schmidt-Uhlig, P. Karlitschek, G. Marowsky, and Y. Sano, “New simplified coupling scheme for the delivery of 20 MW Nd:YAG laser pulses by large core optical fibers,” Appl. Phys. B 72(2), 183–186 (2001).
[CrossRef]

Marshall, C. D.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Martinelli, M.

Mehta, N. C.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Melloni, A.

Menapace, J.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Ming-Jun, L.

Nilsson, J.

Nostrand, M. C.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Orth, C. D.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Polynkin, P.

Richardson, D. J.

Richou, B.

Richou, J.

Saby, J.

Sacks, R. A.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Salin, F.

Sano, Y.

T. Schmidt-Uhlig, P. Karlitschek, G. Marowsky, and Y. Sano, “New simplified coupling scheme for the delivery of 20 MW Nd:YAG laser pulses by large core optical fibers,” Appl. Phys. B 72(2), 183–186 (2001).
[CrossRef]

Schertz, I.

Schmidt-Uhlig, T.

T. Schmidt-Uhlig, P. Karlitschek, G. Marowsky, and Y. Sano, “New simplified coupling scheme for the delivery of 20 MW Nd:YAG laser pulses by large core optical fibers,” Appl. Phys. B 72(2), 183–186 (2001).
[CrossRef]

Shaw, M. J.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Smith, A. V.

A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
[CrossRef]

G. R. Hadley and A. V. Smith, “Self-focusing in high-power optical fibers,” Proc. SPIE 6475, 64750G, 64750G-11 (2007).
[CrossRef]

R. L. Farrow, D. A. V. Kliner, G. R. Hadley, and A. V. Smith, “Peak-power limits on fiber amplifiers imposed by self-focusing,” Opt. Lett. 31(23), 3423–3425 (2006).
[CrossRef] [PubMed]

Sutton, S. B.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Tonini, A.

Vandersteegen, P.

P. Vandersteegen, B. Maes, P. Bienstman, and R. Baets, “Using the complex Jacobi method to simulate Kerr non-linear photonic components,” Opt. Quantum Electron. 38(1-3), 35–44 (2006).
[CrossRef]

Walton, D. T.

Wegner, P. J.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

White, R. K.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Widmayer, C. C.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Williams, W. H.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Wonterghem, B. M. V.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Xin, C.

Xu, C. L.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8(5), 649–651 (1996).
[CrossRef]

Yang, S. T.

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Yoda, H.

Yokoyama, K.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8(5), 649–651 (1996).
[CrossRef]

Zaouter, Y.

Zenteno, L. A.

Appl. Opt. (1)

Appl. Phys. B (1)

T. Schmidt-Uhlig, P. Karlitschek, G. Marowsky, and Y. Sano, “New simplified coupling scheme for the delivery of 20 MW Nd:YAG laser pulses by large core optical fibers,” Appl. Phys. B 72(2), 183–186 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

A. Galvanauskas, M.-Y. Cheng, K.-C. Hou, and K.-H. Liao, “High peak power pulse amplification in large-core Yb-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 559–566 (2007).
[CrossRef]

A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 153–158 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer (PML) boundary condition for the beam propagation method,” IEEE Photon. Technol. Lett. 8(5), 649–651 (1996).
[CrossRef]

J. Lightwave Technol. (2)

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

J. Phys.: Conf. Ser. (1)

C. A. Haynam, R. A. Sacks, P. J. Wegner, M. W. Bowers, S. N. Dixit, G. V. Erbert, G. M. Heestand, M. A. Henesian, M. R. Hermann, K. S. Jancaitis, K. R. Manes, C. D. Marshall, N. C. Mehta, J. Menapace, M. C. Nostrand, C. D. Orth, M. J. Shaw, S. B. Sutton, W. H. Williams, C. C. Widmayer, R. K. White, S. T. Yang, and B. M. V. Wonterghem, “The National Ignition Facility 2007 laser performance status,” J. Phys.: Conf. Ser. 112(3), 032004 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Opt. Quantum Electron. (1)

P. Vandersteegen, B. Maes, P. Bienstman, and R. Baets, “Using the complex Jacobi method to simulate Kerr non-linear photonic components,” Opt. Quantum Electron. 38(1-3), 35–44 (2006).
[CrossRef]

Proc. SPIE (1)

G. R. Hadley and A. V. Smith, “Self-focusing in high-power optical fibers,” Proc. SPIE 6475, 64750G, 64750G-11 (2007).
[CrossRef]

Other (4)

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

E. Stiles, “New developments in IPG fiber laser technology,” in Proceedings of the 5th International Workshop on Fiber Lasers, 2009.

R. W. Boyd, S. G. Lukishova, and Y. R. Shen, Self-Focusing: Past and Present. (Springer, 2009).

K. Okamoto, Fundamentals of Optical Waveguides (Adademic Press, 2000).

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Figures (8)

Fig. 1
Fig. 1

Normalized intensity profiles of the LP01 mode and its Gaussian fit in the (a) 80μm-core and (b) 200μm-core fiber.

Fig. 2
Fig. 2

The evolution of the peak intensity along the propagation direction for Gaussian fit beam in the bulk (black), LP01 mode in the bulk (blue) and LP01 mode in the waveguide (red) in the (a) 80μm-core and (b) 200μm-core fiber.

Fig. 3
Fig. 3

The SFLs for LP01 mode in the bulk (blue diamond) and the waveguide (red square) in the (a) 80μm-core and (b) 200μm-core fiber.

Fig. 4
Fig. 4

The radius of the central lobe (blue) and ratio of the peak intensity (green) of LP0m mode to that of the LP01 mode under the same power versus the order m in the (a) 80μm-core and (b) 200μm-core fiber.

Fig. 5
Fig. 5

Nonlinear propagation of LP0m mode in ULMAFs under beam power of 2Pcr. x-z intensity cross section for (a) LP02 mode in 80μm-core fiber, (b) LP02 mode in 200μm-core fiber, (c) LP04 mode in 80μm-core fiber and (d) LP04 mode in 200μm-core fiber.

Fig. 6
Fig. 6

Nonlinear propagation of the LP11 mode under the power of 2Pcr in the (a) 80μm-core and (b)200μm-core fiber.

Fig. 7
Fig. 7

The summation of multimode in the 80μm-core fiber under the power of (a) 2Pcr and (c) 6MW. The x-z intensity cross sections in the 80μm-core fiber under the power of (b) 2Pcr and (d) 6MW.

Fig. 8
Fig. 8

The nonlinear beam propagation in 200μm-core fiber under the power 2Pcr. (a) input field, (b) output field, (c) beam power, (d) peak intensity, (e) beam quality factor, (f) x-z intensity cross section.

Tables (1)

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Table 1 Parameters of the Fibers and the Numerical Simulation

Equations (8)

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2i k 0 n r ϕ z = 2 ϕ z 2 + 1 s x x ( 1 s x ϕ x )+ 1 s y y ( 1 s y ϕ y )+ k 0 2 ( n 2 n r 2 )ϕ
s i ={ 1 1j ( m+1 )λ 4πd n L ( r d ) q ln( 1 R ) outsidePML insidePML
n= n L + n NL = n L +γ | ϕ | 2
n NL =α | 1 2 ( ϕ l + ϕ l+1 ( i ) ) | 2
ϕ lm ( r,θ )={ A× J m ( ur )×f( lθ ) B× K m ( vr )×f( lθ ) ra ra
P cr = π ( 0.61 ) 2 λ 2 8 n L n 2
L sf = 2 n L w 2 λ 1 P/ P cr 1
ϕ( r,z=0 )= j=1 N | c j |exp( i φ j ) ϕ j ( r )

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