Abstract

Using computer simulations we explore the dynamics of nonlinear pulsed Bessel-like beams arising from axicon-focused Gaussian beams and circularly apodized beams propagating in air. These pulses exhibit similar self-action. We also note that noninear behavior can occur for these pulses in the absence of significant plasma density. This is especially interesting in light of recent experimental observations of self-guiding without plasma.

© 2007 Optical Society of America

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References

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    [CrossRef]
  12. K. Dholakia and D. McGloin, "Bessel beams: Diffraction in a new light," Contemporary Physics 46, 15-28 (2005).
    [CrossRef]
  13. Z. Bouchal, J. Wagner, and M. Chlup, "Self-reconstruction of a distorted nondiffracting beam," Opt. Commun. 151, 207-211 (1998).
    [CrossRef]
  14. R. Gadonas, V. Jarutis, R. Paskauskas, V. Smilgevivcius, A. Stabinis, and V. Vaicaitis, "Self-action of Bessel beam in nonlinear medium," Opt. Commun. 196, 309-316 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  21. T. Grow, A. Ishaaya, L. Vuong, A. Gaeta, N. Gavish, and G. Fibich, "Collapse dynamics of super-Gaussian beams," Opt. Express 14, 5468-5475 (2006).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2007 (1)

D. Roskey, M. Kolesik, J. Moloney, and E. Wright, "The role of linear power partitioning in filamentation," Appl. Phys. B 86, 249-258 (2007).
[CrossRef]

2006 (2)

P. Polesana, A. Dubietis, M. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, "Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity," Phys. Rev. E 73(056612) (2006).
[CrossRef]

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

2005 (5)

P. Polesana, P. Faccio, D. Di Trapani, A. Dubietis, A. Piskarskas, A. Couairon, and M. Porras, "High localization, focal depth and contrast by means of nonlinear Bessel Beams," Opt. Express 13, 6160-6167 (2005).
[CrossRef] [PubMed]

C. Ruiz, J. San Román, C. Méndez, V. Diáz, L. Plaja, I. Arias, and L. Roso, "Observation of Spontaneous Self-Channeling of Light in Air below the Collapse Threshold," Phys. Rev. Lett. 95(053905) (2005).
[CrossRef] [PubMed]

K. Cook, A. Kar, and R. Lamb, "White-light filaments induced by diffraction effects," Optics Express 13, 2025-2031 (2005).
[CrossRef] [PubMed]

K. Dholakia and D. McGloin, "Bessel beams: Diffraction in a new light," Contemporary Physics 46, 15-28 (2005).
[CrossRef]

V. Pyragaite, K. Regelskis, V. Smilgevicius, and A. Stabinis, "Self-action of Bessel light beams in medium with large nonlinearity," Opt. Commun. 257, 139-145 (2005).
[CrossRef]

2004 (2)

G. Mechain, A. Couairon, M. Franco, B. Prode, and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93(035003) (2004).
[CrossRef] [PubMed]

M. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, "Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses," Phys. Rev. Lett. 93(153902) (2004).
[CrossRef] [PubMed]

2003 (1)

P. Johannisson, D. Anderson, M. Lisak, and M. Marklund, "Nonlinear Bessel beams," Opt. Commun. 222, 107-115 (2003).
[CrossRef]

2001 (1)

R. Gadonas, V. Jarutis, R. Paskauskas, V. Smilgevivcius, A. Stabinis, and V. Vaicaitis, "Self-action of Bessel beam in nonlinear medium," Opt. Commun. 196, 309-316 (2001).
[CrossRef]

2000 (1)

J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297-301 (2000).
[CrossRef]

1998 (3)

1997 (1)

1996 (2)

1995 (1)

1992 (2)

1987 (1)

J. Durnin, J. J. Miceli, and J. Eberly, "Diffraction-Free Beams," Phys. Rev. Lett 58, 1499-1501 (1987).
[CrossRef] [PubMed]

1975 (1)

J. Marburger, "Self-Focusing: Theory," Prog. Quant. Electr. 4, 35-110 (1975).
[CrossRef]

Appl. Phys. B (1)

D. Roskey, M. Kolesik, J. Moloney, and E. Wright, "The role of linear power partitioning in filamentation," Appl. Phys. B 86, 249-258 (2007).
[CrossRef]

Contemporary Physics (1)

K. Dholakia and D. McGloin, "Bessel beams: Diffraction in a new light," Contemporary Physics 46, 15-28 (2005).
[CrossRef]

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

Opt. Commun. (5)

Z. Bouchal, J. Wagner, and M. Chlup, "Self-reconstruction of a distorted nondiffracting beam," Opt. Commun. 151, 207-211 (1998).
[CrossRef]

R. Gadonas, V. Jarutis, R. Paskauskas, V. Smilgevivcius, A. Stabinis, and V. Vaicaitis, "Self-action of Bessel beam in nonlinear medium," Opt. Commun. 196, 309-316 (2001).
[CrossRef]

V. Pyragaite, K. Regelskis, V. Smilgevicius, and A. Stabinis, "Self-action of Bessel light beams in medium with large nonlinearity," Opt. Commun. 257, 139-145 (2005).
[CrossRef]

P. Johannisson, D. Anderson, M. Lisak, and M. Marklund, "Nonlinear Bessel beams," Opt. Commun. 222, 107-115 (2003).
[CrossRef]

J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297-301 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (6)

Optics Express (1)

K. Cook, A. Kar, and R. Lamb, "White-light filaments induced by diffraction effects," Optics Express 13, 2025-2031 (2005).
[CrossRef] [PubMed]

Phys. Rev. E (1)

P. Polesana, A. Dubietis, M. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, "Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity," Phys. Rev. E 73(056612) (2006).
[CrossRef]

Phys. Rev. Lett (1)

J. Durnin, J. J. Miceli, and J. Eberly, "Diffraction-Free Beams," Phys. Rev. Lett 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

J. Ranka, R. Schirmer, and A. Gaeta, "Observation of pulse splitting in nonlinear dispersive media," Phys. Rev. Lett. 77, 3783-3786 (1996).
[CrossRef] [PubMed]

M. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, "Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses," Phys. Rev. Lett. 93(153902) (2004).
[CrossRef] [PubMed]

G. Mechain, A. Couairon, M. Franco, B. Prode, and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93(035003) (2004).
[CrossRef] [PubMed]

C. Ruiz, J. San Román, C. Méndez, V. Diáz, L. Plaja, I. Arias, and L. Roso, "Observation of Spontaneous Self-Channeling of Light in Air below the Collapse Threshold," Phys. Rev. Lett. 95(053905) (2005).
[CrossRef] [PubMed]

Prog. Quant. Electr. (1)

J. Marburger, "Self-Focusing: Theory," Prog. Quant. Electr. 4, 35-110 (1975).
[CrossRef]

Other (2)

R. Boyd, Nonlinear Optics (Academic Press,Inc., 1991).

P. DeVries, A First Course in Computational Physics (John Wiley and Sons, Inc., 1994).

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Figures (11)

Fig. 1.
Fig. 1.

Maximum normalized intensity as a function of normalized propagation distance for axicon-focused Gaussian beams in linear (solid) and nonlinear (dashed) media. The propagation distance is normalized by the focal length of the axicon (zax =w 0 k/kr ).

Fig. 2.
Fig. 2.

Fraction of power contained in the central spot (solid) and the first ring (dashed) of a CW nonlinear axicon-focused Gaussian beam as a function of normalized propagation distance (z/zax ,zax =w 0 k/kr ).

Fig. 3.
Fig. 3.

Integrated plasma density from a 1.1 mJ axicon-focused, pulsed Gaussian beam (solid), a 0.86 mJ axicon-focused, pulsed Gaussian beam (dashed) and a 1.0 mJ non-focused, pulsed Gaussian beam (dot-dashed). The propagation distance is normalized by the axicon focal length, zax =w 0 k/kr , for each pulsed axicon-focused Gaussian beam and by the Rayleigh range for the nonfocused pulsed Gaussian beam. Here the nonfocused Gaussian has a Rayleigh range of 2.0 m and zax =22 cm.

Fig. 4.
Fig. 4.

Maximum intensity as a function of propagation distance for nonlinear CW (solid, without plasma) and pulsed (dashed, with plasma) axicon-focused Gaussian beams. The pulse is a 0.86 mJ pulse with a duration of 120 fs. The peak power gets as high as Ppk =900 MW (Ppk /Pcr ≈0.5). The propagation distance is normalized by the axicon focal length, zax =w 0 k/kr . Here, zax =22cm.

Fig. 5.
Fig. 5.

Maximum intensity as a function of propagation distance for nonlinear CW (solid, without plasma) and pulsed (dashed, with plasma) axicon-focused Gaussian beams. The pulse is a 1.1mJ pulse with a duration of 120 fs. The peak power of the initial pulse is 7.4GW and the unclamped peak power contained in the central core could get as high as Ppk =1.1GW(Ppk /Pcr ≈0.6). The propagation distance is normalized by the axicon focal length, zax =w 0 k/kr . Here, zax =22cm.

Fig. 6.
Fig. 6.

Field profile at several locations along the propagation axis for the 0.86mJ pulsed axicon-focused Gaussian beam. (a) z/zax =0.45, (b) z/zax =0.62, (c) z/zax =0.74, (d) z/zax =0.87, (e) z/zax =1.4, (f) z/zax =1.8.

Fig. 7.
Fig. 7.

Integrated plasma density for the 0.56mJ super-Gaussian pulse. The propagation distance is normalized by the focal length of the lens 2.2m.

Fig. 8.
Fig. 8.

Maximum intensity as a function of normalized propagation distance for a CW super-Gaussian beam (solid, without plasma) and a 0.56mJ, 120 fs super-Gaussian pulse (dashed, with plasma). The propagation distance is normalized by the focal length of the lens 2.2m. The peak power of the pulse was Ppk ≈3.0GW(Ppk /Pcr ≈1)

Fig. 9.
Fig. 9.

Field profile at several locations along the propagation axis for the 0.56mJ focused super-Gaussian pulse. (a) z/f=1.0, (b) z/f=1.1, (c) z/f=1.2, (d) z/f=1.4.

Fig. 10.
Fig. 10.

Integrated angular spectrum for a nonlinear axicon-focused, pulsed Gaussian beam. The solid line is the initial spectrum and the dashed line is the spectrum after nonlinear propagation. On the abscissa, unity corresponds to a transverse wavenumber of 3.4×104 m -1.

Fig. 11.
Fig. 11.

The evolution of the integrated spectrum of a focused, pulsed super-Gaussian beam in a nonlinear medium. Solid: z=0 m, Dotted: z=1.5 m, Dashed: z=2.1 m, Dotted-dashed: z=2.2 m. On the abscissa, unity corresponds to a transverse wavenumber of 8.0×103 m -1.

Equations (11)

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E ( r , z , t ) = A ( r , z ) exp [ i ( k z z ω t ) ] ,
A z = i 2 k T 2 A i k " 2 2 A t 2 i 1 2 σ ω τ ρ A
+ i k 0 n 2 A 2 A 1 2 κ h ¯ ω B ( κ ) A 2 κ 2 A .
ρ t = B ( κ ) A 2 κ α ρ 2 .
A ( r , z = 0 , t ) = A 0 exp ( i k r r ) × exp [ ( r w 0 ) 2 ( t t p ) 2 ] ,
k r = k γ ( n 1 )
A ( r , z ax , t ) ( π exp ( 1 2 ) k r w 0 ) 1 2 A 0 J 0 ( k r r )
× exp [ ( 4 r 2 w 0 2 ) ( t t p ) 2 ] ,
A ( r , z = 0 , t ) = A 0 exp ( i k r 2 2 f )
× exp [ ( r w 0 ) 2 m ( t t p ) 2 ] ,
A ( r , z = f ) J 1 ( k w 0 r f ) r ,

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