Abstract

A Gaussian beam propagating in a photopolymer undergoes self-phase modulation to form diffraction rings and then transforms into a single ring, which in turn ruptures into a necklace of stable self-trapped multimode filaments. The transitions of the beam between the three distinct nonlinear forms only occur at intensities where the beam-induced refractive index profile in the medium slowly evolves from a Gaussian to a flattened Gaussian.

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  1. M. Soljačić, S. Sears, and M. Segev, “Self-Trapping of “Necklace” Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81(22), 48511–48514 (1998).
    [CrossRef]
  2. T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
    [CrossRef] [PubMed]
  3. A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
    [CrossRef] [PubMed]
  4. J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94(11), 113902 (2005).
    [CrossRef] [PubMed]
  5. L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
    [CrossRef] [PubMed]
  6. M. S. Bigelow, P. Zerom, and R. W. Boyd, “Breakup of ring beams carrying orbital angular momentum in sodium vapor,” Phys. Rev. Lett. 92(8), 083902 (2004).
    [CrossRef] [PubMed]
  7. V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable Nonlinear Medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
    [CrossRef] [PubMed]
  8. J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
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    [CrossRef]
  11. T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. K. Saravanamuttu, X. M. Du, S. I. Najafi, and M. P. Andrews, “Photoinduced structural relaxation and densification in sol-gel-derived nanocomposite thin films: implications for integrated optics device fabrication,” Rev. Can. Chim. 76(11), 1717–1729 (1998).
    [CrossRef]
  15. A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21(1), 24–26 (1996).
    [CrossRef] [PubMed]
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  20. R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. Quantum Electron. 2(9), 467–469 (1966).
    [CrossRef]
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2009

A. B. Villafranca and K. Saravanamuttu, “Diffraction rings due to spatial self-phase modulation in a photopolymerizable medium,” J. Opt. A, Pure Appl. Opt. 11(12), 125202 (2009).
[CrossRef]

2008

A. B. Villafranca and K. Saravanamuttu, “An Experimental Study of the Dynamics and Temporal Evolution of Self-Trapped Laser Beams in a Photopolymerizable Organosiloxane,” J. Phys. Chem. C 112(44), 17388–17396 (2008).
[CrossRef]

2007

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef] [PubMed]

2006

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[CrossRef] [PubMed]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

2005

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94(11), 113902 (2005).
[CrossRef] [PubMed]

2004

M. S. Bigelow, P. Zerom, and R. W. Boyd, “Breakup of ring beams carrying orbital angular momentum in sodium vapor,” Phys. Rev. Lett. 92(8), 083902 (2004).
[CrossRef] [PubMed]

2001

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
[CrossRef] [PubMed]

T. M. Monro, C. M. De Sterke, and L. J. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

1998

K. Saravanamuttu, X. M. Du, S. I. Najafi, and M. P. Andrews, “Photoinduced structural relaxation and densification in sol-gel-derived nanocomposite thin films: implications for integrated optics device fabrication,” Rev. Can. Chim. 76(11), 1717–1729 (1998).
[CrossRef]

M. Soljačić, S. Sears, and M. Segev, “Self-Trapping of “Necklace” Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81(22), 48511–48514 (1998).
[CrossRef]

1996

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable Nonlinear Medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21(1), 24–26 (1996).
[CrossRef] [PubMed]

1991

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

1988

1981

1966

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. Quantum Electron. 2(9), 467–469 (1966).
[CrossRef]

’t Hooft, G. W.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[CrossRef] [PubMed]

Akhmediev, N. N.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

Andrews, M. P.

K. Saravanamuttu, X. M. Du, S. I. Najafi, and M. P. Andrews, “Photoinduced structural relaxation and densification in sol-gel-derived nanocomposite thin films: implications for integrated optics device fabrication,” Rev. Can. Chim. 76(11), 1717–1729 (1998).
[CrossRef]

Arakelian, S. M.

Bigelow, M. S.

M. S. Bigelow, P. Zerom, and R. W. Boyd, “Breakup of ring beams carrying orbital angular momentum in sodium vapor,” Phys. Rev. Lett. 92(8), 083902 (2004).
[CrossRef] [PubMed]

Boyd, R. W.

M. S. Bigelow, P. Zerom, and R. W. Boyd, “Breakup of ring beams carrying orbital angular momentum in sodium vapor,” Phys. Rev. Lett. 92(8), 083902 (2004).
[CrossRef] [PubMed]

Chen, Z.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94(11), 113902 (2005).
[CrossRef] [PubMed]

Chiao, R. Y.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. Quantum Electron. 2(9), 467–469 (1966).
[CrossRef]

Christou, J.

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable Nonlinear Medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

De Sterke, C. M.

T. M. Monro, C. M. De Sterke, and L. J. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

Desyatnikov, A. S.

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
[CrossRef] [PubMed]

Du, X. M.

K. Saravanamuttu, X. M. Du, S. I. Najafi, and M. P. Andrews, “Photoinduced structural relaxation and densification in sol-gel-derived nanocomposite thin films: implications for integrated optics device fabrication,” Rev. Can. Chim. 76(11), 1717–1729 (1998).
[CrossRef]

Durbin, S. D.

Eliel, E. R.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[CrossRef] [PubMed]

Feit, M. D.

Fibich, G.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[CrossRef] [PubMed]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

Fleck, J. A.

Frantzeskakis, D. J.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94(11), 113902 (2005).
[CrossRef] [PubMed]

Gaeta, A. L.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[CrossRef] [PubMed]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

Garmire, E.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. Quantum Electron. 2(9), 467–469 (1966).
[CrossRef]

Gavish, N.

Grow, T. D.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[CrossRef] [PubMed]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

Heatley, D. R.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

Ishaaya, A.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[CrossRef] [PubMed]

Ishaaya, A. A.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef] [PubMed]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

Johnson, M. A.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. Quantum Electron. 2(9), 467–469 (1966).
[CrossRef]

Kevrekidis, P. G.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94(11), 113902 (2005).
[CrossRef] [PubMed]

Kewitsch, A. S.

Kivshar, Y. S.

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
[CrossRef] [PubMed]

Krinsky, S.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. Quantum Electron. 2(9), 467–469 (1966).
[CrossRef]

Luther-Davies, B.

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable Nonlinear Medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

Makasyuk, I.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94(11), 113902 (2005).
[CrossRef] [PubMed]

Malomed, B. A.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94(11), 113902 (2005).
[CrossRef] [PubMed]

Martin, H.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94(11), 113902 (2005).
[CrossRef] [PubMed]

Monro, T. M.

T. M. Monro, C. M. De Sterke, and L. J. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

Najafi, S. I.

K. Saravanamuttu, X. M. Du, S. I. Najafi, and M. P. Andrews, “Photoinduced structural relaxation and densification in sol-gel-derived nanocomposite thin films: implications for integrated optics device fabrication,” Rev. Can. Chim. 76(11), 1717–1729 (1998).
[CrossRef]

Poladian, L. J.

T. M. Monro, C. M. De Sterke, and L. J. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

Saravanamuttu, K.

A. B. Villafranca and K. Saravanamuttu, “Diffraction rings due to spatial self-phase modulation in a photopolymerizable medium,” J. Opt. A, Pure Appl. Opt. 11(12), 125202 (2009).
[CrossRef]

A. B. Villafranca and K. Saravanamuttu, “An Experimental Study of the Dynamics and Temporal Evolution of Self-Trapped Laser Beams in a Photopolymerizable Organosiloxane,” J. Phys. Chem. C 112(44), 17388–17396 (2008).
[CrossRef]

K. Saravanamuttu, X. M. Du, S. I. Najafi, and M. P. Andrews, “Photoinduced structural relaxation and densification in sol-gel-derived nanocomposite thin films: implications for integrated optics device fabrication,” Rev. Can. Chim. 76(11), 1717–1729 (1998).
[CrossRef]

Sears, S.

M. Soljačić, S. Sears, and M. Segev, “Self-Trapping of “Necklace” Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81(22), 48511–48514 (1998).
[CrossRef]

Segev, M.

M. Soljačić, S. Sears, and M. Segev, “Self-Trapping of “Necklace” Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81(22), 48511–48514 (1998).
[CrossRef]

Shen, Y. R.

Smith, H. A.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. Quantum Electron. 2(9), 467–469 (1966).
[CrossRef]

Soljacic, M.

M. Soljačić, S. Sears, and M. Segev, “Self-Trapping of “Necklace” Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81(22), 48511–48514 (1998).
[CrossRef]

Soto-Crespo, J. M.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

Tikhonenko, V.

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable Nonlinear Medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

Townes, C. H.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. Quantum Electron. 2(9), 467–469 (1966).
[CrossRef]

Villafranca, A. B.

A. B. Villafranca and K. Saravanamuttu, “Diffraction rings due to spatial self-phase modulation in a photopolymerizable medium,” J. Opt. A, Pure Appl. Opt. 11(12), 125202 (2009).
[CrossRef]

A. B. Villafranca and K. Saravanamuttu, “An Experimental Study of the Dynamics and Temporal Evolution of Self-Trapped Laser Beams in a Photopolymerizable Organosiloxane,” J. Phys. Chem. C 112(44), 17388–17396 (2008).
[CrossRef]

Vuong, L. T.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[CrossRef] [PubMed]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-Gaussian Beams,” Opt. Express 14(12), 5468–5475 (2006).
[CrossRef] [PubMed]

Wright, E. M.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

Yang, J.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94(11), 113902 (2005).
[CrossRef] [PubMed]

Yariv, A.

Zerom, P.

M. S. Bigelow, P. Zerom, and R. W. Boyd, “Breakup of ring beams carrying orbital angular momentum in sodium vapor,” Phys. Rev. Lett. 92(8), 083902 (2004).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. Quantum Electron. 2(9), 467–469 (1966).
[CrossRef]

J. Mod. Opt.

T. M. Monro, C. M. De Sterke, and L. J. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

J. Opt. A, Pure Appl. Opt.

A. B. Villafranca and K. Saravanamuttu, “Diffraction rings due to spatial self-phase modulation in a photopolymerizable medium,” J. Opt. A, Pure Appl. Opt. 11(12), 125202 (2009).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Chem. C

A. B. Villafranca and K. Saravanamuttu, “An Experimental Study of the Dynamics and Temporal Evolution of Self-Trapped Laser Beams in a Photopolymerizable Organosiloxane,” J. Phys. Chem. C 112(44), 17388–17396 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, “Stability of the higher-bound states in a saturable self-focusing medium,” Phys. Rev. A 44(1), 636–644 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett.

M. Soljačić, S. Sears, and M. Segev, “Self-Trapping of “Necklace” Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81(22), 48511–48514 (1998).
[CrossRef]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99(13), 133902 (2007).
[CrossRef] [PubMed]

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike solitons in optically induced photonic lattices,” Phys. Rev. Lett. 94(11), 113902 (2005).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[CrossRef] [PubMed]

M. S. Bigelow, P. Zerom, and R. W. Boyd, “Breakup of ring beams carrying orbital angular momentum in sodium vapor,” Phys. Rev. Lett. 92(8), 083902 (2004).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable Nonlinear Medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

Rev. Can. Chim.

K. Saravanamuttu, X. M. Du, S. I. Najafi, and M. P. Andrews, “Photoinduced structural relaxation and densification in sol-gel-derived nanocomposite thin films: implications for integrated optics device fabrication,” Rev. Can. Chim. 76(11), 1717–1729 (1998).
[CrossRef]

Other

J. A. Buck, Fundamentals of Optical Fibers (Wiley and Sons, Inc., New York, 2004).

S. Trillo and W. Torruellas, eds., Spatial Solitons (Springer, New York, 2001)

G. Fibich, N. Gavish, and X. P. Wang, “New singular solutions of the nonlinear Schrodinger equation,” in Physica D: Nonlinear Phenomena (2005), pp. 193–220.

A. J. Campillo, “Small-Scale Self-focusing,” in Self-Focusing: Past and Present, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds. (Springer Science, 2009), pp. 157–173.

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Figures (7)

Fig. 1
Fig. 1

Temporal evolution of 2D and 3D intensity profiles of a laser beam (532 nm; input intensity = 80 Wcm−2) at the exit face (propagation distance (z) = 6.00 mm) in the organosiloxane photopolymer. Profiles at 1 s, 8 s, 26 s, 37 s, 46 s, 61 s, 100 s, 138 s, 227 s, 253 s and 509 s are shown. 2D intensity profiles were scaled to peak for clarity. Maximum peak intensities are given in % with respect to the saturation value of the CCD camera.

Fig. 2
Fig. 2

Calculated temporal variation of refractive index profiles induced by a Gaussian beam in a photopolymer. Time is represented by steps, which correspond to each iteration of the calculation.

Fig. 3
Fig. 3

Simulated temporal evolution of a Gaussian beam at the output (z = 6.00 mm) of a photopolymer that had a flattened-Gaussian refractive index profile at z = 0.00 mm. Time is represented in arbitrary units (steps), which correspond to each iteration of the simulation.

Fig. 4
Fig. 4

Comparison between the profiles of a flattened Gaussian beam (step 20 of Fig. 3) and a super-Gaussian beam plotted with A = 0.006, n = 3 and ωSG = 12.5 in Eq. (4).

Fig. 5
Fig. 5

Temporal evolution of a single filament (contained within white square) in a circular array of filaments induced by a Gaussian beam (532 nm, 80 Wcm−2) in the organosiloxane photopolymer. 2D intensity profiles of two separate sequences of oscillations (312 s–318 s; 385 s–393 s) are shown.

Fig. 6
Fig. 6

Transition of the single ring to circular array of filaments at different input intensities of the Gaussian beam (532 nm). For each input intensity, 2D spatial intensity profiles of the single ring and corresponding filament array are shown. For clarity, 3D intensity profiles of the ring of filaments are also presented.

Fig. 7
Fig. 7

Optical micrographs of permanent self-inscribed circular array of waveguides at various input intensities. Micrographs were obtained at an angle with waveguides projecting out of the page. Samples were not subjected to any post-experimental treatment and waveguides remained embedded within the photopolymer monolith. Imaging was possible due to the contrast in refractive index between the waveguides and surrounding medium. 2D spatial intensity profiles of the ring of filaments corresponding to the waveguides are shown for comparison. Note that although four waveguides are observed at 40Wcm−2, the number of filaments generally reduced to 2 over time (also see Table 1).

Tables (1)

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Table 1 Intensity Dependence of

Equations (4)

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Δ n ( r , z , t ) = Δ n s { 1 exp [ 1 U 0 0 t τ | E ( t ) | 2 d t ] }
I ( r ) = I max exp ( 2 r 2 ω 2 )
Δ ψ ( r ) = 2 π λ z 0 z 0 + L Δ n ( r , z ) d z
I ( r ) = A exp [ ( r ω S G ) n ]

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