Abstract

We investigate numerically and experimentally the spatial collapse dynamics and polarization stability of radially and azimuthally polarized vortex beams in pure Kerr medium. These beams are unstable to azimuthal modulation instabilities and break up into distinct collapsing filaments. The polarization of the filaments is primarily linear with weak circular components at the filaments’ boundaries. This unique hybrid linear–circular polarization collapse pattern persists to advanced stages of collapse and appears to be a general feature of beams with spatially variant linear polarization.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2007 (1)

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (1)

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 94, 073902 (2005).
[CrossRef] [PubMed]

2003 (4)

D. P. Biss and T. G. Brown, Opt. Lett. 28, 923 (2003).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

G. Fibich and B. Ilan, Phys. Rev. E 67, 036622 (2003).
[CrossRef]

K. D. Moll, A. L. Gaeta, and G. Fibich, Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

2001 (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

2000 (1)

A. V. Nesterov and V. G. Niziev, J. Phys. D 33, 1817 (2000).
[CrossRef]

1998 (1)

M. Soljacic, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998).
[CrossRef]

1997 (1)

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

1992 (1)

E. J. Bochove, G. T. Moore, and M. O. Scully, Phys. Rev. A 46, 6640 (1992).
[CrossRef] [PubMed]

1990 (1)

M. O. Scully, Appl. Phys. B 51, 238 (1990).
[CrossRef]

1972 (1)

D. Pohl, Phys. Rev. A 5, 1906 (1972).
[CrossRef]

Appl. Phys. B (1)

M. O. Scully, Appl. Phys. B 51, 238 (1990).
[CrossRef]

J. Phys. D (1)

A. V. Nesterov and V. G. Niziev, J. Phys. D 33, 1817 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (2)

D. Pohl, Phys. Rev. A 5, 1906 (1972).
[CrossRef]

E. J. Bochove, G. T. Moore, and M. O. Scully, Phys. Rev. A 46, 6640 (1992).
[CrossRef] [PubMed]

Phys. Rev. E (1)

G. Fibich and B. Ilan, Phys. Rev. E 67, 036622 (2003).
[CrossRef]

Phys. Rev. Lett. (8)

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

M. Soljacic, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998).
[CrossRef]

K. D. Moll, A. L. Gaeta, and G. Fibich, Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef] [PubMed]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, Phys. Rev. Lett. 86, 5251 (2001).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. A. Ishaaya, A. L. Gaeta, G. W. 't Hooft, E. R. Eliel, and G. Fibich, Phys. Rev. Lett. 96, 133901 (2006).
[CrossRef] [PubMed]

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 94, 073902 (2005).
[CrossRef] [PubMed]

Other (1)

E. Collett, Polarized Light: Fundamentals and Applications (Dekker, 1993).

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Figures (4)

Fig. 1
Fig. 1

Numerical propagation of an AP TEM 01 Laguerre-Gaussian donut beam in Kerr medium. (a) Ideal azimuthal polarization without noise, (b) ideal azimuthal polarization with 10 % random amplitude and phase noise in the input beam. The total power is 10 P cr , where P cr is the critical power for self-focusing of a Gaussian, and ζ propagation distance in units of diffraction length. Online, blue (red) shades indicate low (high) intensities.

Fig. 2
Fig. 2

Numerical calculation of the Stokes polarization parameters for an initial AP beam with 10 % random amplitude and phase noise. Results are shown for three input powers at different propagation distances. Gradient bars (colorbars online) indicate the values of the Stokes parameters.

Fig. 3
Fig. 3

Schematic setup for converting a linearly polarized Gaussian beam to a RP donut beam. Time and phase alignment is achieved by controlling the delay with a high-precision stage. Elements in red (online) are in a different plane.

Fig. 4
Fig. 4

Experimental intensity distributions and Stokes matrices of the RP beam at the output face of the glass sample. (a) Intensity distribution at low power, (b) intensity distribution at high power ( 15 μ J , 90 fs pulses), (c) positive (negative) S1 Stokes values represent horizontal (vertical) linear polarization components, (d) positive and negative S3 values represent opposite circular components. Online, red (purple) shades in (a) and (b) indicate high (low) intensity; colorbars in (c) and (d) indicate values of the Stokes parameters, and black circles indicate the corresponding locations of the filaments.

Equations (3)

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i ψ ± ζ + 1 4 2 ψ ± + 2 3 L df L nl [ ψ ± 2 + 2 ψ 2 ] ψ ± = 0 ,
ψ RP ( μ , ν , 0 ) = E ( ρ ) [ e i θ σ ̂ + e i θ σ ̂ + ] ,
ψ AP ( μ , ν , 0 ) = i E ( ρ ) [ e i θ σ ̂ e i θ σ ̂ + ] ,

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