Abstract

In addition to subluminal solitons and superluminal conical beams, self-focusing media also support a luminal nonspreading beam with hybrid solitary–conical properties. Its existence reveals that spatial solitons may also have a conical structure, and vice versa.

© 2011 Optical Society of America

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References

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  1. R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [CrossRef]
  2. J. Durnin and J. J. Miceli, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  3. P. Johhanisson, D. Anderson, M. Lisak, and M. Marklund, Opt. Commun. 222, 107 (2003).
    [CrossRef]
  4. M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. Lett. 93, 153902 (2004).
    [CrossRef] [PubMed]
  5. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, Opt. Lett. 20, 73 (1995).
    [CrossRef] [PubMed]
  6. S. Henz and J. Herrmann, Phys. Rev. E 53, 4092 (1996).
    [CrossRef]
  7. E. Gaizauskas, A. Dubietis, V. Kudriasov, V. Sirutkaitis, A. Couairon, D. Faccio, and P. Di Trapani, Top. Appl. Phys. 114, 457 (2009).
    [CrossRef]
  8. M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
    [CrossRef] [PubMed]
  9. J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
    [CrossRef] [PubMed]
  10. E.g., the axial wavenumber of Gaussian beams is k0+dϕ(z)/dz, where ϕ(z) is Gouy’s phase.
  11. M. A. Porras and A. Parola, Opt. Commun. 282, 644 (2009).
    [CrossRef]

2009 (2)

E. Gaizauskas, A. Dubietis, V. Kudriasov, V. Sirutkaitis, A. Couairon, D. Faccio, and P. Di Trapani, Top. Appl. Phys. 114, 457 (2009).
[CrossRef]

M. A. Porras and A. Parola, Opt. Commun. 282, 644 (2009).
[CrossRef]

2004 (2)

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

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

2003 (1)

P. Johhanisson, D. Anderson, M. Lisak, and M. Marklund, Opt. Commun. 222, 107 (2003).
[CrossRef]

1996 (1)

S. Henz and J. Herrmann, Phys. Rev. E 53, 4092 (1996).
[CrossRef]

1995 (1)

1991 (1)

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

1987 (1)

J. Durnin and J. J. Miceli, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Akhmediev, N. N.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

Anderson, D.

P. Johhanisson, D. Anderson, M. Lisak, and M. Marklund, Opt. Commun. 222, 107 (2003).
[CrossRef]

Braun, A.

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Couairon, A.

E. Gaizauskas, A. Dubietis, V. Kudriasov, V. Sirutkaitis, A. Couairon, D. Faccio, and P. Di Trapani, Top. Appl. Phys. 114, 457 (2009).
[CrossRef]

Di Trapani, P.

E. Gaizauskas, A. Dubietis, V. Kudriasov, V. Sirutkaitis, A. Couairon, D. Faccio, and P. Di Trapani, Top. Appl. Phys. 114, 457 (2009).
[CrossRef]

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

Du, D.

Dubietis, A.

E. Gaizauskas, A. Dubietis, V. Kudriasov, V. Sirutkaitis, A. Couairon, D. Faccio, and P. Di Trapani, Top. Appl. Phys. 114, 457 (2009).
[CrossRef]

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

Durnin, J.

J. Durnin and J. J. Miceli, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Faccio, D.

E. Gaizauskas, A. Dubietis, V. Kudriasov, V. Sirutkaitis, A. Couairon, D. Faccio, and P. Di Trapani, Top. Appl. Phys. 114, 457 (2009).
[CrossRef]

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

Gaizauskas, E.

E. Gaizauskas, A. Dubietis, V. Kudriasov, V. Sirutkaitis, A. Couairon, D. Faccio, and P. Di Trapani, Top. Appl. Phys. 114, 457 (2009).
[CrossRef]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Heatley, D. R.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

Henz, S.

S. Henz and J. Herrmann, Phys. Rev. E 53, 4092 (1996).
[CrossRef]

Herrmann, J.

S. Henz and J. Herrmann, Phys. Rev. E 53, 4092 (1996).
[CrossRef]

Johhanisson, P.

P. Johhanisson, D. Anderson, M. Lisak, and M. Marklund, Opt. Commun. 222, 107 (2003).
[CrossRef]

Kolesik, M.

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

Korn, G.

Kudriasov, V.

E. Gaizauskas, A. Dubietis, V. Kudriasov, V. Sirutkaitis, A. Couairon, D. Faccio, and P. Di Trapani, Top. Appl. Phys. 114, 457 (2009).
[CrossRef]

Lisak, M.

P. Johhanisson, D. Anderson, M. Lisak, and M. Marklund, Opt. Commun. 222, 107 (2003).
[CrossRef]

Liu, X.

Marklund, M.

P. Johhanisson, D. Anderson, M. Lisak, and M. Marklund, Opt. Commun. 222, 107 (2003).
[CrossRef]

Miceli, J. J.

J. Durnin and J. J. Miceli, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Moloney, J. V.

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

Mourou, G.

Parola, A.

M. A. Porras and A. Parola, Opt. Commun. 282, 644 (2009).
[CrossRef]

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

Porras, M. A.

M. A. Porras and A. Parola, Opt. Commun. 282, 644 (2009).
[CrossRef]

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

Sirutkaitis, V.

E. Gaizauskas, A. Dubietis, V. Kudriasov, V. Sirutkaitis, A. Couairon, D. Faccio, and P. Di Trapani, Top. Appl. Phys. 114, 457 (2009).
[CrossRef]

Soto-Crespo, J. M.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

Squier, J.

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Wright, E. M.

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

Opt. Commun. (2)

P. Johhanisson, D. Anderson, M. Lisak, and M. Marklund, Opt. Commun. 222, 107 (2003).
[CrossRef]

M. A. Porras and A. Parola, Opt. Commun. 282, 644 (2009).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

Phys. Rev. E (1)

S. Henz and J. Herrmann, Phys. Rev. E 53, 4092 (1996).
[CrossRef]

Phys. Rev. Lett. (4)

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

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

J. Durnin and J. J. Miceli, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

Top. Appl. Phys. (1)

E. Gaizauskas, A. Dubietis, V. Kudriasov, V. Sirutkaitis, A. Couairon, D. Faccio, and P. Di Trapani, Top. Appl. Phys. 114, 457 (2009).
[CrossRef]

Other (1)

E.g., the axial wavenumber of Gaussian beams is k0+dϕ(z)/dz, where ϕ(z) is Gouy’s phase.

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Figures (5)

Fig. 1
Fig. 1

Linear and nonlinear conical geometries of wave vectors in (a) the linear BB and (b) the luminal beam.

Fig. 2
Fig. 2

Normalized amplitude (black curve) and intensity (gray curve) of the LB, approximation f l ( ρ ) J 0 [ φ ( ρ ) ] with φ ( ρ ) = ( 3 γ / 2 ) ρ 2 / 3 (dotted curve), and the normalized effective intensity ( 1 / 2 ) γ 2 / ρ 2 / 3 (dashed gray curve). The normalized radius is ρ = k 0 k NL r .

Fig. 3
Fig. 3

In fused silica ( n 0 = 1.4533 , n 2 = 6 × 10 16 cm 2 / W ) at 800 nm , (a) nonlinear BB (solid) and linear BB (dashed) with θ = 0.25 ° and I 0 = 10 10 W / cm 2 , and the LB (dotted) with the same I 0 ; (b) the same as in (a) but at I 0 = 10 13 W / cm 2 ; (c) soliton of order m = 20 and with I 0 = 10 13 W / cm 2 (solid) and the LB (dotted) with the same I 0 .

Fig. 4
Fig. 4

(a) Squared modulus of the Hänkel transform of the LB truncated at ρ t = k 0 k NL r t = 570 . The vertical line is K ( r t ) / k 0 k NL = 0.106 . (b) As functions of the truncation radius, conical-based distortion-free distance z free (dashed curve) and actual distortion-free distance evaluated numerically by solving the NSE [Eq. (1)] with δ = 0 and truncated LBs as initial conditions (solid curve).

Fig. 5
Fig. 5

(a) Normalized on-axis intensity I ( 0 , z ) (black curve), difference I ( 0 , z ) I 0 in log scale (dots) obtained by numerical integration of the NSE [Eq. (1)] with input LB truncated at ρ t = 570 , and difference I ( 0 , z ) I 0 as given by Eq. (6) with κ = ( 0.361 i 0.124 ) k NL (dashed curve); (b), (c) dominant unstable mode [ u ( r ) , v ( r ) ] of the LB, normalized such that Im u ( 0 ) = 0 .

Equations (7)

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z A = i 2 k 0 ( 2 A r 2 + 1 r A r ) + i k 0 n 2 n 0 | A | 2 A
1 2 k 0 ( d 2 a d r 2 + 1 r d a d r ) + ( k 0 n 2 n 0 a 2 δ ) a = 0 , a ( 0 ) = I 0 , ( d a / d r ) ( 0 ) = 0 , a ( ) = 0 .
K ( r ) = γ ( k 0 k NL / r ) 1 / 3 ,
a l ( r ) I 0 J 0 [ φ ( r ) ] , φ ( r ) = 3 γ 2 ( k 0 k NL r ) 2 3 ,
I eff ( r ) = γ 2 2 I 0 ( k 0 k NL r ) 2 / 3 ,
A ( r , z ) = a l ( r ) + ϵ [ u ( r ) exp ( i κ z ) + v ( r ) exp ( i κ z ) ]
[ u ( r ) , v ( r ) ] = g 1 e κ I z 1 g 2 e κ I z 2 e i κ R ( z 1 z 2 ) e ± i κ R z 1 [ 1 e 2 i κ R ( z 1 z 2 ) ] ,

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