Abstract

The properties of elliptically polarized solitary waves in isotropic optical fibers are investigated. Two families of polarized solitary pulses are identified, but only one of them is shown to be stable. These pulses are characterized by a fixed polarization pattern that rotates at a constant rate as the pulse propagates down the fiber. The evolution of the polarization of these pulses is important for the operation of short-pulse fiber lasers and other nonlinear devices.

© 1995 Optical Society of America

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References

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  1. C. R. Menyuk, IEEE J. Quantum Electron. QE-25, 174 (1987).
    [CrossRef]
  2. C. R. Menyuk, Opt. Lett. 12, 614 (1987); J. Opt. Soc. Am. B 5, 392 (1988).
    [CrossRef] [PubMed]
  3. D. N. Christodoulides, R. I. Joseph, Opt. Lett. 13, 53 (1988).
    [CrossRef] [PubMed]
  4. K. J. Blow, N. J. Doran, D. Wood, Opt. Lett. 12, 202 (1988).
    [CrossRef]
  5. M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, A. M. Weiner, Appl. Phys. Lett. 62, 910 (1993).
    [CrossRef]
  6. K. Tamura, E. P. Ippen, H. A. Haus, L. E. Nelson, Opt. Lett. 18, 1080 (1993).
    [CrossRef] [PubMed]
  7. M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, New York, 1992).
  8. A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).
  9. S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).
  10. M. Haelterman, A. P. Sheppard, A. W. Snyder, Opt. Lett. 18, 1406 (1993); M. Haelterman, A. Sheppard, Phys. Rev. E 49, 3376 (1994).
    [CrossRef] [PubMed]
  11. P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
    [CrossRef]
  12. A. W. Snyder, S. J. Hewlett, D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
    [CrossRef] [PubMed]
  13. A. W. Snyder, Optical Sciences Center, Australian National University, Canberra, Australia (personal communication, 1994).
  14. L. Landau, E. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1958), p. 70.
  15. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 268.

1994 (1)

A. W. Snyder, S. J. Hewlett, D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

1993 (3)

1988 (2)

1987 (2)

1974 (1)

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

1970 (1)

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

1964 (1)

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Andrejco, M. J.

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, A. M. Weiner, Appl. Phys. Lett. 62, 910 (1993).
[CrossRef]

Berkhoer, A. L.

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

Blow, K. J.

Christodoulides, D. N.

Doran, N. J.

Fermann, M. E.

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, A. M. Weiner, Appl. Phys. Lett. 62, 910 (1993).
[CrossRef]

Haelterman, M.

Haus, H. A.

Hewlett, S. J.

A. W. Snyder, S. J. Hewlett, D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

Ippen, E. P.

Islam, M. N.

M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, New York, 1992).

Joseph, R. I.

Landau, L.

L. Landau, E. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1958), p. 70.

Lifshitz, E.

L. Landau, E. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1958), p. 70.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 268.

Maker, P. D.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Manakov, S. V.

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Menyuk, C. R.

Mitchell, D. J.

A. W. Snyder, S. J. Hewlett, D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

Nelson, L. E.

Savage, C. M.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Sheppard, A. P.

Silberberg, Y.

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, A. M. Weiner, Appl. Phys. Lett. 62, 910 (1993).
[CrossRef]

Snyder, A. W.

A. W. Snyder, S. J. Hewlett, D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

M. Haelterman, A. P. Sheppard, A. W. Snyder, Opt. Lett. 18, 1406 (1993); M. Haelterman, A. Sheppard, Phys. Rev. E 49, 3376 (1994).
[CrossRef] [PubMed]

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 268.

A. W. Snyder, Optical Sciences Center, Australian National University, Canberra, Australia (personal communication, 1994).

Stock, M. L.

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, A. M. Weiner, Appl. Phys. Lett. 62, 910 (1993).
[CrossRef]

Tamura, K.

Terhune, R. W.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Weiner, A. M.

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, A. M. Weiner, Appl. Phys. Lett. 62, 910 (1993).
[CrossRef]

Wood, D.

Zakharov, V. E.

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

Appl. Phys. Lett. (1)

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, A. M. Weiner, Appl. Phys. Lett. 62, 910 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. R. Menyuk, IEEE J. Quantum Electron. QE-25, 174 (1987).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. Lett. (2)

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

A. W. Snyder, S. J. Hewlett, D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

Sov. Phys. JETP (2)

A. L. Berkhoer, V. E. Zakharov, Sov. Phys. JETP 31, 486 (1970).

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Other (4)

M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, New York, 1992).

A. W. Snyder, Optical Sciences Center, Australian National University, Canberra, Australia (personal communication, 1994).

L. Landau, E. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1958), p. 70.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 268.

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Figures (3)

Fig. 1
Fig. 1

A circularly polarized soliton field [Eq. (3), solid curve] can support, through cross-phase modulation, two kinds of weak pulse in the orthogonal polarization mode: a symmetric pulse [Eq. (5), dotted–dashed curve) and an antisymmetric pulse [Eq. (6), dashed curve]. All pulses have been calculated with α = 1 and normalized to v0 = 1 for ease of viewing.

Fig. 2
Fig. 2

Rate of ellipse rotation, βα, for elliptically polarized solitary waves as a function of the ellipticity (ratio of the two ellipse axes) at the center of the pulse. Calculated with α = 1. Also shown (dashed curve) is the ellipse rotation for a cw wave with intensity equal to the peak intensity of the soliton.

Fig. 3
Fig. 3

Simulation of propagation of a solitary wave from the antisymmetric branch with α = 1, β = 0.7572, u ( 0 ) = 2, and v ( 0 ) = 8 / 3. The intensity of the two polarization modes is shown along the propagation distance from z = 0 (bottom) to z = 50 (top). An instability appears, as a symmetric perturbation grows from noise, that eventually transforms the pulse into a simple elliptically polarized soliton.

Equations (8)

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i U z + 1 2 2 U t 2 + ( 1 - B 2 U 2 + 1 + B 2 V 2 ) U = 0 ,
i V z + 1 2 2 V t 2 + ( 1 - B 2 V 2 + 1 + B 2 U 2 ) V = 0.
d 2 u d t 2 = 2 α u - u 3 - / 3 4 v 2 u ,
d 2 v d t 2 = 2 β v - v 3 - / 3 4 u 2 v ,
u ( t ) = 6 α sech ( 2 α t ) ,             v ( t ) = 0 ,
u ( t ) = v ( t ) = 2 α sech ( 2 α t ) .
v s ( t ) = v 0 sech s ( 2 α t ) ,             β s / α = 4 - s ,
v a ( t ) = v 0 sech s - 1 ( 2 α t ) tanh ( 2 α t ) , β a / α = 5 - 3 s ,

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