Abstract

Spatial solitons of Maxwell’s equations propagating in an isotropic Kerr material differ significantly from the classical soliton of the nonlinear Schrödinger equation unless the electric field is linearly polarized along a geometric axis of the soliton intensity pattern. In general the polarization state changes continuously as the beam propagates, with a period of millimeters for highly nonlinear materials. This effect is due to the form birefringence of the soliton-induced waveguide. Equivalently, a soliton of Maxwell’s equations is composed of both the TE and TM modes of the axially uniform waveguide it induces. Modal beating leads to the polarization dynamics.

© 1994 Optical Society of America

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References

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  1. R. Chaio, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [CrossRef]
  2. A. W. Snyder, W. R. Young, J. Opt. Soc. Am. 68, 297 (1978).
    [CrossRef]
  3. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 32.
  4. P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964). Their case of B = 0 applies for materials with zero nonlinear intrinsic birefringence.
    [CrossRef]
  5. A. W. Snyder, D. J. Mitchell, L. Poladian, F. Ladouceur, Opt. Lett. 16, 21 (1991); A. W. Snyder, D. J. Mitchell, Opt. Lett. 18, 101 (1993).
    [CrossRef] [PubMed]
  6. D. Pohl, Opt. Commun. 2, 305 (1970). This paper suggests that TM solitons do not exist, but their existence is established in Ref. 7.
    [CrossRef]
  7. Y. Chen, A. W. Snyder, Electron. Lett. 27, 565 (1991).
    [CrossRef]
  8. Beam propagation is accomplished with the pair of equations Lψy = 0 andLψx=-∂∂x(ψx∂ ln n2∂x),where L = i2kn0(∂/∂z) + ∇t2 + k2δn2, with n2 = n02 + δn2(|E|2) and E = (x̂ψx + ŷψy)exp(ikn0z).
  9. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  10. A. W. Snyder, S. J. Hewlett, D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
    [CrossRef] [PubMed]

1994 (1)

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

1991 (2)

1978 (1)

1972 (1)

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

1970 (1)

D. Pohl, Opt. Commun. 2, 305 (1970). This paper suggests that TM solitons do not exist, but their existence is established in Ref. 7.
[CrossRef]

1964 (2)

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

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964). Their case of B = 0 applies for materials with zero nonlinear intrinsic birefringence.
[CrossRef]

Chaio, R.

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

Chen, Y.

Y. Chen, A. W. Snyder, Electron. Lett. 27, 565 (1991).
[CrossRef]

Garmire, E.

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

Hewlett, S. J.

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

Ladouceur, F.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 32.

Maker, P. D.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964). Their case of B = 0 applies for materials with zero nonlinear intrinsic birefringence.
[CrossRef]

Mitchell, D. J.

Pohl, D.

D. Pohl, Opt. Commun. 2, 305 (1970). This paper suggests that TM solitons do not exist, but their existence is established in Ref. 7.
[CrossRef]

Poladian, L.

Savage, C. M.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964). Their case of B = 0 applies for materials with zero nonlinear intrinsic birefringence.
[CrossRef]

Shabat, A. B.

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

Snyder, A. W.

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

Y. Chen, A. W. Snyder, Electron. Lett. 27, 565 (1991).
[CrossRef]

A. W. Snyder, D. J. Mitchell, L. Poladian, F. Ladouceur, Opt. Lett. 16, 21 (1991); A. W. Snyder, D. J. Mitchell, Opt. Lett. 18, 101 (1993).
[CrossRef] [PubMed]

A. W. Snyder, W. R. Young, J. Opt. Soc. Am. 68, 297 (1978).
[CrossRef]

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 32.

Terhune, R. W.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964). Their case of B = 0 applies for materials with zero nonlinear intrinsic birefringence.
[CrossRef]

Townes, C. H.

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

Young, W. R.

Zakharov, V. E.

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

Electron. Lett. (1)

Y. Chen, A. W. Snyder, Electron. Lett. 27, 565 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

D. Pohl, Opt. Commun. 2, 305 (1970). This paper suggests that TM solitons do not exist, but their existence is established in Ref. 7.
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (3)

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964). Their case of B = 0 applies for materials with zero nonlinear intrinsic birefringence.
[CrossRef]

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

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

Sov. Phys. JETP (1)

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

Other (2)

Beam propagation is accomplished with the pair of equations Lψy = 0 andLψx=-∂∂x(ψx∂ ln n2∂x),where L = i2kn0(∂/∂z) + ∇t2 + k2δn2, with n2 = n02 + δn2(|E|2) and E = (x̂ψx + ŷψy)exp(ikn0z).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chaps. 13 and 32.

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Equations (12)

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[ 2 + k 2 n 2 ( E 2 ) ] E = - [ E · ln n 2 ( E 2 ) ] ,
E ( x , z ) = e y ( x ) exp ( i β y z ) ,
( d 2 d x 2 + k 2 n 2 - β y 2 ) e y = 0 ,
( d 2 d x 2 + k 2 n 2 - β x 2 ) e x = - d d x ( e x d ln n 2 d x ) ,
( d 2 d x 2 + k 2 n 2 - β x 2 ) e z = - i β x e x d ln n 2 d x ,
E ( x , z ) = a x [ x ^ e x ( x ) + z ^ e z ( x ) ] exp ( i β x z ) + y ^ a y e y ( x ) exp ( i β y z ) ,
E = x ^ e y ( x ) exp [ i ( β y + δ β ) z ] ,
δ β = - - e y ( d e y d x ) ( d d x ln n 2 ) d x 2 k n 0 - e y 2 d x ,
E ( x , z ) = e ^ ( z ) E CS ( x , z ) ,
e ^ ( z ) = [ a x x ^ exp ( i z δ β ) + a y y ^ ] / ( a x 2 + a y 2 ) 1 / 2 .
z = α ρ / ( δ n / n 0 ) 3 / 2 ,
L ψ x = - x ( ψ x ln n 2 x ) ,

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