Abstract

On the basis of a simple analysis of the coupled nonlinear Schrödinger equations that govern pulse propagation in isotropic nonlinear dispersive media, we show the existence of a novel class of bound-vector solitary waves. These solitary waves are novel in exhibiting elliptical polarization that varies across the pulse and evolves periodically during propagation while the pulse intensity envelope remains unchanged. Simple physical arguments allow us to understand the existence and the features of these particular solutions.

© 1993 Optical Society of America

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References

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  1. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
    [Crossref]
  2. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  3. C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1987).
    [Crossref]
  4. S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).
  5. R. Sahadevan, K. M. Tamizhmani, M. Lakshmanan, J. Phys. A 19, 1783 (1986).
    [Crossref]
  6. Y. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
    [Crossref]
  7. C.-J. Chen, P. K. A. Wai, C. R. Menyuk, Opt. Lett. 15, 477 (1990).
    [Crossref] [PubMed]
  8. D. N. Christodoulides, R. I. Joseph, Opt. Lett. 13, 53 (1988).
    [Crossref] [PubMed]
  9. M. V. Tratnik, J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
    [Crossref] [PubMed]
  10. S. Wabnitz, Phys. Rev. A 38, 2018 (1988).
    [Crossref] [PubMed]
  11. P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1965).
  12. J. P. Gordon, Opt. Lett. 8, 596 (1983).
    [Crossref] [PubMed]
  13. J. Hietarinta, Phys. Lett. A 96, 273 (1983).
    [Crossref]

1990 (1)

1989 (1)

Y. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[Crossref]

1988 (3)

D. N. Christodoulides, R. I. Joseph, Opt. Lett. 13, 53 (1988).
[Crossref] [PubMed]

M. V. Tratnik, J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[Crossref] [PubMed]

S. Wabnitz, Phys. Rev. A 38, 2018 (1988).
[Crossref] [PubMed]

1987 (1)

C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1987).
[Crossref]

1986 (1)

R. Sahadevan, K. M. Tamizhmani, M. Lakshmanan, J. Phys. A 19, 1783 (1986).
[Crossref]

1983 (2)

J. P. Gordon, Opt. Lett. 8, 596 (1983).
[Crossref] [PubMed]

J. Hietarinta, Phys. Lett. A 96, 273 (1983).
[Crossref]

1974 (1)

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

1973 (1)

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

1972 (1)

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

1965 (1)

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1965).

Chen, C.-J.

Christodoulides, D. N.

Gordon, J. P.

Hasegawa, A.

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

Hietarinta, J.

J. Hietarinta, Phys. Lett. A 96, 273 (1983).
[Crossref]

Joseph, R. I.

Kivshar, Y. S.

Y. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[Crossref]

Lakshmanan, M.

R. Sahadevan, K. M. Tamizhmani, M. Lakshmanan, J. Phys. A 19, 1783 (1986).
[Crossref]

Maker, P. D.

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1965).

Malomed, B. A.

Y. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[Crossref]

Manakov, S. V.

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

Menyuk, C. R.

Sahadevan, R.

R. Sahadevan, K. M. Tamizhmani, M. Lakshmanan, J. Phys. A 19, 1783 (1986).
[Crossref]

Shabat, A. B.

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

Sipe, J. E.

M. V. Tratnik, J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[Crossref] [PubMed]

Tamizhmani, K. M.

R. Sahadevan, K. M. Tamizhmani, M. Lakshmanan, J. Phys. A 19, 1783 (1986).
[Crossref]

Tappert, F.

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

Terhune, R. W.

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1965).

Tratnik, M. V.

M. V. Tratnik, J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[Crossref] [PubMed]

Wabnitz, S.

S. Wabnitz, Phys. Rev. A 38, 2018 (1988).
[Crossref] [PubMed]

Wai, P. K. A.

Zakharov, V. E.

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

Appl. Phys. Lett. (1)

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

IEEE J. Quantum Electron. (1)

C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1987).
[Crossref]

J. Phys. A (1)

R. Sahadevan, K. M. Tamizhmani, M. Lakshmanan, J. Phys. A 19, 1783 (1986).
[Crossref]

Opt. Lett. (3)

Phys. Lett. A (1)

J. Hietarinta, Phys. Lett. A 96, 273 (1983).
[Crossref]

Phys. Rev. A (3)

M. V. Tratnik, J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[Crossref] [PubMed]

S. Wabnitz, Phys. Rev. A 38, 2018 (1988).
[Crossref] [PubMed]

P. D. Maker, R. W. Terhune, Phys. Rev. A 137, 801 (1965).

Rev. Mod. Phys. (1)

Y. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[Crossref]

Sov. Phys. JETP (2)

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

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

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Figures (3)

Fig. 1
Fig. 1

Examples of separatrices of the Hamiltonian H with B = 1/3, α = 1, and β = 1 − . Curves (a) and (b) correspond to the case of degeneracy = 0 and represent two π/2 out-of-phase NLS solitons with orthogonal linear polarizations. Curves (c), (d), and (e) are obtained with = 0.5, = 0.22, and = 0.05, respectively.

Fig. 2
Fig. 2

Envelopes of the solitary waves u and v corresponding to (a) = 0.22 [see curve (d) of Fig. 1] and (b) = 5 × 10−4. (c) and (d) are the total intensity profiles |u|2 + |v|2 corresponding to (a) and (b), respectively.

Fig. 3
Fig. 3

Contour plots representing the evolution of the solitary waves of Fig. 2(a) obtained by numerical integration of Eqs. (1). |Etot|2 = |Ex|2 + |Ey|2 is the total intensity, where |Ex|2 and |Ey|2 are the x- and y-component intensities.

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 ,
U = sech ( t + τ ) + sech ( t τ ) ,
V = sech ( t + τ ) sech ( t τ ) ,
U ( z , t ) = u ( t ) exp ( i α z ) , V ( z , t ) = v ( t ) exp ( i β z ) ,
u ¨ = 2 α u ( 1 B ) u 3 ( 1 + B ) v 2 u ,
v ¨ = 2 β v ( 1 B ) v 3 ( 1 + B ) u 2 v ,
H = 1 2 u ˙ 2 + 1 2 v ˙ 2 α u 2 β v 2 + 1 4 ( u 2 + v 2 ) 2 B 4 ( u 2 v 2 ) 2 .

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