Abstract

Numerical simulations show that, because of the spatiotemporal coupling implied by the multidimensional nonlinear Schrödinger equation, self-focusing of ultrashort optical pulses can lead to pulse compression even in the normal-dispersion regime of a nonlinear Kerr medium. We show how this coupling can be further exploited to control the compression by use of spatial phase modulation. Both the compression factor and the position at which the minimum pulse width is realized change with the amplitude of the phase modulation.

© 1995 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 1995), Chaps. 2 and 6.
  2. A. T. Ryan, G. P. Agrawal, Opt. Lett. 18, 1795 (1992).
    [CrossRef]
  3. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  4. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  5. R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [CrossRef]
  6. P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
    [CrossRef]
  7. W. G. Wagner, H. A. Haus, J. H. Marburger, Phys. Rev. 175, 256 (1968).
    [CrossRef]
  8. J. H. Marburger, IEEE J. Quantum Electron. QE-3, 415 (1967).
    [CrossRef]
  9. Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 17.
  10. N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986), and references therein.
  11. P. Chernev, V. Petrov, Opt. Lett. 17, 72 (1992).
    [CrossRef]
  12. J. E. Rothenberg, Opt. Lett. 17, 583 (1992).
    [CrossRef] [PubMed]
  13. G. G. Luther, A. C. Newell, J. V. Moloney, Physica D 74, 59 (1994).
    [CrossRef]
  14. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Chaps. 6 and 7.

1994

G. G. Luther, A. C. Newell, J. V. Moloney, Physica D 74, 59 (1994).
[CrossRef]

1992

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Chaps. 6 and 7.

P. Chernev, V. Petrov, Opt. Lett. 17, 72 (1992).
[CrossRef]

J. E. Rothenberg, Opt. Lett. 17, 583 (1992).
[CrossRef] [PubMed]

A. T. Ryan, G. P. Agrawal, Opt. Lett. 18, 1795 (1992).
[CrossRef]

1986

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986), and references therein.

1973

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

1972

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

1968

W. G. Wagner, H. A. Haus, J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

1967

J. H. Marburger, IEEE J. Quantum Electron. QE-3, 415 (1967).
[CrossRef]

1965

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

1964

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

Agrawal, G. P.

A. T. Ryan, G. P. Agrawal, Opt. Lett. 18, 1795 (1992).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 1995), Chaps. 2 and 6.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Chaps. 6 and 7.

Chernev, P.

P. Chernev, V. Petrov, Opt. Lett. 17, 72 (1992).
[CrossRef]

Chiao, R. Y.

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

Garmire, E.

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

Hasegawa, A.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Haus, H. A.

W. G. Wagner, H. A. Haus, J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

Kelley, P. L.

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Litvak, A. G.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986), and references therein.

Luther, G. G.

G. G. Luther, A. C. Newell, J. V. Moloney, Physica D 74, 59 (1994).
[CrossRef]

Marburger, J. H.

W. G. Wagner, H. A. Haus, J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

J. H. Marburger, IEEE J. Quantum Electron. QE-3, 415 (1967).
[CrossRef]

Moloney, J. V.

G. G. Luther, A. C. Newell, J. V. Moloney, Physica D 74, 59 (1994).
[CrossRef]

Newell, A. C.

G. G. Luther, A. C. Newell, J. V. Moloney, Physica D 74, 59 (1994).
[CrossRef]

Petrov, V.

P. Chernev, V. Petrov, Opt. Lett. 17, 72 (1992).
[CrossRef]

Petrova, T. A.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986), and references therein.

Rothenberg, J. E.

Ryan, A. T.

Sergeev, A. M.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986), and references therein.

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Shen, Y. R.

Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 17.

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Townes, C. H.

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

Wagner, W. G.

W. G. Wagner, H. A. Haus, J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

Yunakovskii, A. D.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986), and references therein.

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Zharova, N. A.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986), and references therein.

Appl. Phys. Lett.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

IEEE J. Quantum Electron.

J. H. Marburger, IEEE J. Quantum Electron. QE-3, 415 (1967).
[CrossRef]

JETP Lett.

N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, A. D. Yunakovskii, JETP Lett. 44, 13 (1986), and references therein.

Nonlinear Optics

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Chaps. 6 and 7.

Opt. Lett.

Phys. Rev.

W. G. Wagner, H. A. Haus, J. H. Marburger, Phys. Rev. 175, 256 (1968).
[CrossRef]

Phys. Rev. Lett.

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

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Physica D

G. G. Luther, A. C. Newell, J. V. Moloney, Physica D 74, 59 (1994).
[CrossRef]

Sov. Phys. JETP

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Other

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, Boston, Mass., 1995), Chaps. 2 and 6.

Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 17.

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Figures (4)

Fig. 1
Fig. 1

Input Gaussian pulse evolution in a normally dispersive nonlinear medium for N = 3 nonlinearity and the pulse traveling in (a) a fiber and (b) a waveguide such that s = 0.5 [see Eq. (1)].

Fig. 2
Fig. 2

Normalized pulse FWHM at beam center for fields initially Gaussian in space and time, traveling in a dispersive nonlinear waveguide such that s = 0.5 and with input nonlinearities as indicated.

Fig. 3
Fig. 3

(a) Minimum normalized pulse FWHM and (b) the position of the minimum as a function of the nonlinearity at input for s = 1.0 (diamonds), s = 0.5 (squares), and s = 0.1 (triangles). The dashed curve in (b) is the position of the minimum beam width of a (cw) spatial soliton of order N.

Fig. 4
Fig. 4

Effects of spatial phase modulation on (a) the minimum normalized pulse FWHM and (b) the position of the minimum for s = 1.0; (c) the minimum FWHM and (d) the position of the minimum for s = 0.1. The phase is modulated at input according to Eq. (3) with p = 0.2, δ = π/2, and ϕ0 = 1.0 (filled triangles), ϕ0 = −1.0 (filled squares), and unmodulated or ϕ0 = 0.0 (open triangles). There are only two curves in (b) because there is no compression for the case of defocusing phase modulation and s = 1.0.

Equations (3)

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i u ζ + 1 2 2 u ξ 2 - s 2 2 u τ 2 + N 2 u 2 u = 0.
u ( ξ , τ , 0 ) = exp ( - ξ 2 2 - τ 2 2 ) exp [ i ϕ ( ξ ) ] .
ϕ ( ξ ) = ϕ 0 sin ( 2 π p ξ + δ ) ,

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