Abstract

We study the propagation of intense optical beams in layered Kerr media. With appropriate shapes, beams with a power close to the self-focusing threshold are shown to propagate over long distances as quasi-stationary waveguides in cubic media supporting a periodic nonlinear refractive index.

© 2000 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); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
    [CrossRef]
  2. J. J. Rasmussen and K. Rypdal, Phys. Scr. 33, 481 (1986).
    [CrossRef]
  3. E. Esarey, P. Sprangle, J. Krall, and A. Ting, IEEE J. Quantum Electron. 33, 1879 (1997).
    [CrossRef]
  4. A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Reading, Mass., 1991).
  5. S. K. Turitsyn, T. Schäfer, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999). See for a review: S. K. Turitsyn, V. K. Mezentsev, and E. G. Shapiro, Opt. Fiber Technol. 4, 384 (1998), and references therein.
    [CrossRef]
  6. G. Fibich and G. C. Papanicolaou, SIAM J. Appl. Math. 60, 183 (1999).
    [CrossRef]
  7. L. Bergé, Phys. Rep. 303, 259 (1998).
    [CrossRef]
  8. M. Desaix, D. Anderson, and M. Lisak, J. Opt. Soc. Am. B 8, 2082 (1991).
    [CrossRef]
  9. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1727 (1997).
    [CrossRef]
  10. S. Manoeuf, A. Barthelemy, and C. Froehly, J. Opt. 17, 139 (1986); V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
    [CrossRef] [PubMed]

1999 (2)

S. K. Turitsyn, T. Schäfer, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999). See for a review: S. K. Turitsyn, V. K. Mezentsev, and E. G. Shapiro, Opt. Fiber Technol. 4, 384 (1998), and references therein.
[CrossRef]

G. Fibich and G. C. Papanicolaou, SIAM J. Appl. Math. 60, 183 (1999).
[CrossRef]

1998 (1)

L. Bergé, Phys. Rep. 303, 259 (1998).
[CrossRef]

1997 (2)

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1727 (1997).
[CrossRef]

E. Esarey, P. Sprangle, J. Krall, and A. Ting, IEEE J. Quantum Electron. 33, 1879 (1997).
[CrossRef]

1991 (1)

1986 (2)

S. Manoeuf, A. Barthelemy, and C. Froehly, J. Opt. 17, 139 (1986); V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

J. J. Rasmussen and K. Rypdal, Phys. Scr. 33, 481 (1986).
[CrossRef]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Anderson, D.

Barthelemy, A.

S. Manoeuf, A. Barthelemy, and C. Froehly, J. Opt. 17, 139 (1986); V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Bergé, L.

L. Bergé, Phys. Rep. 303, 259 (1998).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Desaix, M.

Doran, N. J.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1727 (1997).
[CrossRef]

Esarey, E.

E. Esarey, P. Sprangle, J. Krall, and A. Ting, IEEE J. Quantum Electron. 33, 1879 (1997).
[CrossRef]

Fibich, G.

G. Fibich and G. C. Papanicolaou, SIAM J. Appl. Math. 60, 183 (1999).
[CrossRef]

Forysiak, W.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1727 (1997).
[CrossRef]

Froehly, C.

S. Manoeuf, A. Barthelemy, and C. Froehly, J. Opt. 17, 139 (1986); V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Knox, F. M.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1727 (1997).
[CrossRef]

Krall, J.

E. Esarey, P. Sprangle, J. Krall, and A. Ting, IEEE J. Quantum Electron. 33, 1879 (1997).
[CrossRef]

Lisak, M.

Manoeuf, S.

S. Manoeuf, A. Barthelemy, and C. Froehly, J. Opt. 17, 139 (1986); V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Mezentsev, V. K.

S. K. Turitsyn, T. Schäfer, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999). See for a review: S. K. Turitsyn, V. K. Mezentsev, and E. G. Shapiro, Opt. Fiber Technol. 4, 384 (1998), and references therein.
[CrossRef]

Moloney, J. V.

A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Reading, Mass., 1991).

Newell, A. C.

A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Reading, Mass., 1991).

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1727 (1997).
[CrossRef]

Papanicolaou, G. C.

G. Fibich and G. C. Papanicolaou, SIAM J. Appl. Math. 60, 183 (1999).
[CrossRef]

Rasmussen, J. J.

J. J. Rasmussen and K. Rypdal, Phys. Scr. 33, 481 (1986).
[CrossRef]

Rypdal, K.

J. J. Rasmussen and K. Rypdal, Phys. Scr. 33, 481 (1986).
[CrossRef]

Schäfer, T.

S. K. Turitsyn, T. Schäfer, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999). See for a review: S. K. Turitsyn, V. K. Mezentsev, and E. G. Shapiro, Opt. Fiber Technol. 4, 384 (1998), and references therein.
[CrossRef]

Spatschek, K. H.

S. K. Turitsyn, T. Schäfer, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999). See for a review: S. K. Turitsyn, V. K. Mezentsev, and E. G. Shapiro, Opt. Fiber Technol. 4, 384 (1998), and references therein.
[CrossRef]

Sprangle, P.

E. Esarey, P. Sprangle, J. Krall, and A. Ting, IEEE J. Quantum Electron. 33, 1879 (1997).
[CrossRef]

Ting, A.

E. Esarey, P. Sprangle, J. Krall, and A. Ting, IEEE J. Quantum Electron. 33, 1879 (1997).
[CrossRef]

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Turitsyn, S. K.

S. K. Turitsyn, T. Schäfer, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999). See for a review: S. K. Turitsyn, V. K. Mezentsev, and E. G. Shapiro, Opt. Fiber Technol. 4, 384 (1998), and references therein.
[CrossRef]

Electron. Lett. (1)

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, Electron. Lett. 33, 1727 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. Esarey, P. Sprangle, J. Krall, and A. Ting, IEEE J. Quantum Electron. 33, 1879 (1997).
[CrossRef]

J. Opt. (1)

S. Manoeuf, A. Barthelemy, and C. Froehly, J. Opt. 17, 139 (1986); V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

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

Opt. Commun. (1)

S. K. Turitsyn, T. Schäfer, K. H. Spatschek, and V. K. Mezentsev, Opt. Commun. 163, 122 (1999). See for a review: S. K. Turitsyn, V. K. Mezentsev, and E. G. Shapiro, Opt. Fiber Technol. 4, 384 (1998), and references therein.
[CrossRef]

Phys. Rep. (1)

L. Bergé, Phys. Rep. 303, 259 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Phys. Scr. (1)

J. J. Rasmussen and K. Rypdal, Phys. Scr. 33, 481 (1986).
[CrossRef]

SIAM J. Appl. Math. (1)

G. Fibich and G. C. Papanicolaou, SIAM J. Appl. Math. 60, 183 (1999).
[CrossRef]

Other (1)

A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Reading, Mass., 1991).

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Figures (1)

Fig. 1
Fig. 1

Evolution of the peak intensity Er=0,z2. Beam collapse and spreading in homogeneous media are illustrated by the dotted n=1+ and dashed n=1- curves, respectively. The curves between them show the almost constant peak intensity of beams for periodically varying nz with parameters =0.1 and a=b=0.1, as detailed in inset (b). The thick curve refers to the case in which the incident beam is the QP solution. The thin curve refers to the case in which the incident beam is the ground state g0. In inset (b), the evolution of the QP beam (thick curve) is compared with the variational solution found from Eq. (5), with trial function g0 (thin curve). Inset (a) represents the intensity versus x,y=0,z of the QP beam.

Equations (7)

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

iEz+12k0ΔE+ω0cFE2E=0,
iEz+ΔE+nzE2E=0.
S=dzdri2EEz*-E*Ez+E2-nz2E4.
Er,z=1RzQrRz,zexpiMzRzr2.
14R3d2Rdz2=C1-nzC2=fz,
C1=ξQ2dξξ2Q2dξ, C2=Q4dξ2ξ2Q2dξ.
Rz=Rmax2-αz-zmax21/20<z<aRmin2+αz-zmin21/2a<z<a+b,

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