Abstract

We show that small negative fourth-order dispersion can arrest spatiotemporal collapse of ultrashort pulses with anomalous dispersion in a planar waveguide with pure Kerr nonlinearity, resulting in 2+1D optical bullets. Similarly to solitons, these bullets undergo elastic collisions. Since these bullets can self-trap from noisy Gaussian input beams and propagate without any power losses, this result may be used to realize experimentally stable, nondissipative optical bullets.

© 2004 Optical Society of America

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  1. Y. Silberberg, Opt. Lett. 15, 1282 (1990).
    [CrossRef] [PubMed]
  2. K. J. Blow, N. J. Doran, and D. Wood, IEEE J. Quantum Electron. 27, 2060 (1991).
    [CrossRef]
  3. H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
    [CrossRef]
  4. X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
    [CrossRef]
  5. I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, Phys. Rev. Lett. 84, 3847 (2000).
    [CrossRef] [PubMed]
  6. I. N. Towers, B. A. Malomed, and F. W. Wise, Phys. Rev. Lett. 90, 123902 (2003).
    [CrossRef]
  7. G. Fibich, B. Ilan, and S. Schochet, Nonlinearity 16, 1809 (2003).
    [CrossRef]
  8. G. Fibich and G. C. Papanicolaou, Opt. Lett. 22, 1379 (1997).
    [CrossRef]
  9. A. Höök and M. Karlsson, Opt. Lett. 18, 1388 (1993).
    [CrossRef]
  10. I. H. Malitson, J. Opt. Soc. Am. 55, 1205 (1965).
  11. C. B. Schaffer, A. Brodeur, and E. Mazur, Meas. Sci. Technol. 12, 1784 (2001).
    [CrossRef]
  12. D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
    [CrossRef]

2003 (3)

I. N. Towers, B. A. Malomed, and F. W. Wise, Phys. Rev. Lett. 90, 123902 (2003).
[CrossRef]

G. Fibich, B. Ilan, and S. Schochet, Nonlinearity 16, 1809 (2003).
[CrossRef]

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

2001 (2)

C. B. Schaffer, A. Brodeur, and E. Mazur, Meas. Sci. Technol. 12, 1784 (2001).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

2000 (1)

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, Phys. Rev. Lett. 84, 3847 (2000).
[CrossRef] [PubMed]

1999 (1)

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

1997 (1)

1993 (1)

1991 (1)

K. J. Blow, N. J. Doran, and D. Wood, IEEE J. Quantum Electron. 27, 2060 (1991).
[CrossRef]

1990 (1)

1965 (1)

Aitchison, J. S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Bar-Ad, S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Blow, K. J.

K. J. Blow, N. J. Doran, and D. Wood, IEEE J. Quantum Electron. 27, 2060 (1991).
[CrossRef]

Brodeur, A.

C. B. Schaffer, A. Brodeur, and E. Mazur, Meas. Sci. Technol. 12, 1784 (2001).
[CrossRef]

Cheskis, D.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

Doran, N. J.

K. J. Blow, N. J. Doran, and D. Wood, IEEE J. Quantum Electron. 27, 2060 (1991).
[CrossRef]

Eisenberg, H. S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Fibich, G.

G. Fibich, B. Ilan, and S. Schochet, Nonlinearity 16, 1809 (2003).
[CrossRef]

G. Fibich and G. C. Papanicolaou, Opt. Lett. 22, 1379 (1997).
[CrossRef]

Höök, A.

Ilan, B.

G. Fibich, B. Ilan, and S. Schochet, Nonlinearity 16, 1809 (2003).
[CrossRef]

Karlsson, M.

Koprinkov, I. G.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, Phys. Rev. Lett. 84, 3847 (2000).
[CrossRef] [PubMed]

Liu, X.

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

Malitson, I. H.

Malomed, B. A.

I. N. Towers, B. A. Malomed, and F. W. Wise, Phys. Rev. Lett. 90, 123902 (2003).
[CrossRef]

Mazur, E.

C. B. Schaffer, A. Brodeur, and E. Mazur, Meas. Sci. Technol. 12, 1784 (2001).
[CrossRef]

Midorikawa, K.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, Phys. Rev. Lett. 84, 3847 (2000).
[CrossRef] [PubMed]

Morandotti, R.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Papanicolaou, G. C.

Qian, L. J.

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

Ross, D.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Schaffer, C. B.

C. B. Schaffer, A. Brodeur, and E. Mazur, Meas. Sci. Technol. 12, 1784 (2001).
[CrossRef]

Schochet, S.

G. Fibich, B. Ilan, and S. Schochet, Nonlinearity 16, 1809 (2003).
[CrossRef]

Silberberg, Y.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Y. Silberberg, Opt. Lett. 15, 1282 (1990).
[CrossRef] [PubMed]

Suda, A.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, Phys. Rev. Lett. 84, 3847 (2000).
[CrossRef] [PubMed]

Towers, I. N.

I. N. Towers, B. A. Malomed, and F. W. Wise, Phys. Rev. Lett. 90, 123902 (2003).
[CrossRef]

Wang, P. Q.

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, Phys. Rev. Lett. 84, 3847 (2000).
[CrossRef] [PubMed]

Wise, F. W.

I. N. Towers, B. A. Malomed, and F. W. Wise, Phys. Rev. Lett. 90, 123902 (2003).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

Wood, D.

K. J. Blow, N. J. Doran, and D. Wood, IEEE J. Quantum Electron. 27, 2060 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. J. Blow, N. J. Doran, and D. Wood, IEEE J. Quantum Electron. 27, 2060 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

C. B. Schaffer, A. Brodeur, and E. Mazur, Meas. Sci. Technol. 12, 1784 (2001).
[CrossRef]

Nonlinearity (1)

G. Fibich, B. Ilan, and S. Schochet, Nonlinearity 16, 1809 (2003).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (5)

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

I. G. Koprinkov, A. Suda, P. Q. Wang, and K. Midorikawa, Phys. Rev. Lett. 84, 3847 (2000).
[CrossRef] [PubMed]

I. N. Towers, B. A. Malomed, and F. W. Wise, Phys. Rev. Lett. 90, 123902 (2003).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Amplitude of the solution of Eq. (5) with γ2=-1, and γ4=0 (dashed curve), γ4=-0.04 (solid curve), γ4=-0.04 with focusing, chirping, and input noise (dashed–dotted curve), and γ4=0.04 (dotted curve).

Fig. 2
Fig. 2

Isointensity plot of the solid curve solution from Fig. 1.

Fig. 3
Fig. 3

Elastic collision of two bullets.

Fig. 4
Fig. 4

Amplitude of the solution of Eq. (6) with γ2=-1 and γ4=0 (dashed curve), γ4=-0.05 (solid curve), and γ4=0.05 (dashed–dotted curve).

Fig. 5
Fig. 5

Optical bullet at 1.8 µm.

Fig. 6
Fig. 6

Same as Fig. 5 with the addition of a shock term.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

iψzz,x+Δψ+ψ2σψ=0,    ψ0,x=ψ0x,
iψzz,x+Δψ-α2ψxDxDxDxD+ψ2σψ=0,
Azzz,x,y,t+2ik0Az+ΔA+m=11m!mk2ωmitmA+4n2n0ω02c2A2A=0,
iψzz,x,y,t+Δψ+ψ2ψ-γ2ψtt-iγ3ψttt+γ4ψtttt=0,
iψzz,x,t+ψxx+ψ2ψ-γ2ψtt-iγ3ψttt+γ4ψtttt=0.
iψzz,x,t+ψxx+ψ2ψ-γ2ψtt+γ4ψtttt=0.
iψzt,x,y,z+ψxx+ψyy+ψ2ψ-γ2ψtt+γ4ψtttt=0.
ddztψ2dxdt=2γ2Imψ0ψ0,t*dxdt+3γ3ψt2dxdt.

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