Abstract

A novel type of vector dark solitary wave is shown to exist in Kerr materials. These solitary waves consist of localized structures separating adjacent regions (or domains) of different polarization eigenstates of the Kerr medium.

© 1994 Optical Society of America

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References

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  1. See, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), Chap. 7, p. 172.
  2. D. N. Christodoulides, R. I. Joseph, Opt. Lett. 13, 53 (1988).
    [Crossref] [PubMed]
  3. M. V. Tratnik, J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
    [Crossref] [PubMed]
  4. D. N. Christodoulides, Phys. Lett. A 132, 451 (1988).
    [Crossref]
  5. M. Haelterman, A. P. Sheppard, Electron. Lett. 29, 1176 (1993).
    [Crossref]
  6. M. Haelterman, A. P. Sheppard, A. W. Snyder, Opt. Lett. 18, 1406 (1993).
    [Crossref] [PubMed]
  7. Yu. S. Kivshar, S. K. Turitsyn, Opt. Lett. 18, 337 (1993).
    [Crossref] [PubMed]
  8. S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 6415 (1990).
    [Crossref] [PubMed]
  9. V. E. Zakharov, A. V. Mikhailov, JETP Lett. 45, 348 (1987).

1993 (3)

1990 (1)

S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 6415 (1990).
[Crossref] [PubMed]

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]

D. N. Christodoulides, Phys. Lett. A 132, 451 (1988).
[Crossref]

1987 (1)

V. E. Zakharov, A. V. Mikhailov, JETP Lett. 45, 348 (1987).

Agrawal, G. P.

See, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), Chap. 7, p. 172.

Christodoulides, D. N.

Haelterman, M.

Joseph, R. I.

Kivshar, Yu. S.

Mikhailov, A. V.

V. E. Zakharov, A. V. Mikhailov, JETP Lett. 45, 348 (1987).

Sheppard, A. P.

Sipe, J. E.

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

Snyder, A. W.

Stegeman, G. I.

S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 6415 (1990).
[Crossref] [PubMed]

Tratnik, M. V.

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

Turitsyn, S. K.

Wabnitz, S.

S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 6415 (1990).
[Crossref] [PubMed]

Wright, E. M.

S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 6415 (1990).
[Crossref] [PubMed]

Zakharov, V. E.

V. E. Zakharov, A. V. Mikhailov, JETP Lett. 45, 348 (1987).

Electron. Lett. (1)

M. Haelterman, A. P. Sheppard, Electron. Lett. 29, 1176 (1993).
[Crossref]

JETP Lett. (1)

V. E. Zakharov, A. V. Mikhailov, JETP Lett. 45, 348 (1987).

Opt. Lett. (3)

Phys. Lett. A (1)

D. N. Christodoulides, Phys. Lett. A 132, 451 (1988).
[Crossref]

Phys. Rev. A (2)

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

S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 6415 (1990).
[Crossref] [PubMed]

Other (1)

See, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), Chap. 7, p. 172.

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Figures (3)

Fig. 1
Fig. 1

(a) Contour plot of the potential V in the plane (u, υ) for β = 1. The thick solid lines and dashed lines correspond to the linearly and the circularly polarized NLS dark solitons, respectively. The dotted curves that connect adjacent maxima correspond to the polarization domain walls, (b) The envelopes u and υ of the domain walls, (c) Intensity profile I and ellipticity degree q of the domain wall.

Fig. 2
Fig. 2

(a) Contour plot of the potential V for a birefringent medium characterized by κ = 0.2 (β = 1). The thick solid lines represent the linearly polarized NLS dark solitons. The dashed curve shows the separatrix of the elliptically polarized dark soliton. The dotted–dashed curve corresponds to the polarization domain wall, (b) The elliptically polarized dark soliton. (c) The polarization domain wall.

Fig. 3
Fig. 3

Numerical simulation of the propagation in an isotropic medium of the polarization domain wall inscribed onto a broader square-shaped pulse. The curves show the intensity profiles of the circular polarization components E± at (a) z = 0, i.e., initial conditions, (b) z = 16, (c) z = 32.

Equations (7)

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i U z + 1 2 2 U x 2 [ | U | 2 + ( 1 B ) | V | 2 ] U B V 2 U * + κ U = 0 ,
i V z + 1 2 2 V x 2 [ | V | 2 + ( 1 B ) | U | 2 ] V BU 2 V * κ V = 0 ,
U ( x , z ) = u ( x ) exp ( i β z ) , V ( x , z ) = i υ ( x ) exp ( i β z ) .
1 2 u ¨ + β u u 3 ( 1 2 B ) υ 2 u + κ u = 0 ,
1 2 υ ¨ + β υ υ 3 ( 1 2 B ) u 2 υ κ υ = 0 ,
V ( u , υ ) = β ( u 2 + υ 2 ) 1 2 ( u 2 + υ 2 ) 2 + 2 Bu 2 υ 2 + κ ( u 2 υ 2 ) .
u = ± [ 1 2 ( β 1 B + κ B ) ] 1 / 2 , υ = ± [ 1 2 ( β 1 B κ B ) ] 1 / 2 .

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