Abstract

Collapse of a Gaussian beam in self-focusing Kerr media arrested by nonlinear losses may lead to the spontaneous formation of a quasi-stationary nonlinear unbalanced Bessel beam with finite energy, which can propagate without significant distortion over tens of diffraction lengths, and without peak intensity attenuation while the beam power is drastically diminishing.

© 2008 Optical Society of America

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References

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  1. M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. Lett. 93, 153902 (2004).
    [Crossref] [PubMed]
  2. P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. E 73, 056612 (2006).
    [Crossref]
  3. P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Phys. Rev. Lett. 99, 223902 (2007).
    [Crossref]
  4. S. Polyakov, F. Yashino, and G. Stegeman, J. Opt. Soc. Am. B 18, 1891 (2001).
    [Crossref]
  5. This quantity corresponds to 2α, α=1.8962 given in G. Fibich and A. Gaeta, Opt. Lett. 25, 335 (2000).
    [Crossref]
  6. B. J. LeMesurier, Physica D 138, 334 (2000).
    [Crossref]

2007 (1)

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

2006 (1)

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. E 73, 056612 (2006).
[Crossref]

2004 (1)

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

2001 (1)

2000 (2)

Couairon, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. E 73, 056612 (2006).
[Crossref]

Di Trapani, P.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. E 73, 056612 (2006).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Dubietis, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. E 73, 056612 (2006).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Faccio, D.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. E 73, 056612 (2006).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Fibich, G.

Gaeta, A.

Kucinskas, E.

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. E 73, 056612 (2006).
[Crossref]

LeMesurier, B. J.

B. J. LeMesurier, Physica D 138, 334 (2000).
[Crossref]

Parola, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Piskarskas, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

Polesana, P.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. E 73, 056612 (2006).
[Crossref]

Polyakov, S.

Porras, M. A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. E 73, 056612 (2006).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Stegeman, G.

Yashino, F.

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

Opt. Lett. (1)

Phys. Rev. E (1)

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. E 73, 056612 (2006).
[Crossref]

Phys. Rev. Lett. (2)

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Phys. Rev. Lett. 99, 223902 (2007).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Physica D (1)

B. J. LeMesurier, Physica D 138, 334 (2000).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

(a) A ̃ ( 0 , ξ ) 2 for input Gaussian with g = 60 and increasing γ ( K = 8 ) . (b) A ̃ ( ρ , ξ ) 2 for g = 60 and γ = 10 3 ( K = 8 ) (in logarithmic scale).

Fig. 2
Fig. 2

Beam power 2 π 0 d ρ ρ A ̃ ( ρ , ξ ) 2 as a function of propagation distance ξ for g = 60 and increasing γ ( K = 8 ) .

Fig. 3
Fig. 3

(a) For g = 60 , γ = 10 3 , and K = 8 , region of existence of NL-UBBs in their parameter space ( I , δ ) . (b) Radial intensity profiles a 2 ( ρ ) and inward radial energy fluxes 2 π ρ a 2 ( ρ ) d ϕ ( ρ ) d ρ for NL-UBBs with fixed I = 6.575 and decreasing δ down to 0 + , as indicated by the arrow in (a).

Fig. 4
Fig. 4

For g = 60 , γ = 10 1 , K = 8 , and input Gaussian (dotted curve), radial intensity profiles of the propagated field at increasing distances beyond collapse (solid curves), and radial intensity profiles of NL-UBBs with same peak intensities I = 3.15 , 2.82 , 2.23 as those of the propagated field at each distance, and δ = 0 + (dashed curves).

Fig. 5
Fig. 5

For g = 60 , γ = 10 3 , K = 8 , (a) radial intensity profiles of input Gaussian, propagated field, and NL-UBB with same peak intensity I = 6.61 as the propagated field, and δ = 0 + . (b) Inward radial energy flux F ρ (black curves) and NLL N ρ (gray curves) at increasing propagation distances ξ. For the NL-UBB, inward flux and NLL are equal at any ρ.

Equations (5)

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z A = i 2 k 1 r r ( r r A ) + i k n 2 n A 2 A β ( K ) 2 A 2 K 2 A ,
ξ A ̃ = i 2 1 ρ ρ ( ρ ρ A ̃ ) + i g A ̃ 2 A ̃ γ A ̃ 2 K 2 A ̃ ,
1 ρ d d ρ ( ρ d a d ρ ) a ( d ϕ d ρ ) 2 + 2 δ a + 2 g a 3 = 0 ,
2 π ρ a 2 d ϕ d ρ = 2 γ 2 π 0 ρ d ρ ρ a 2 K .
d d ξ 2 π 0 ρ d ρ ρ a 2 = 2 π ρ a 2 ρ φ 2 γ 2 π 0 ρ d ρ ρ a 2 K ,

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