Abstract

We apply a local two-photon bleaching model to describe polarization grating formation in birefringent optical fibers. We show that the dynamics of the grating formation at each point in the fiber follows a universal growth history and study how the dynamics of the grating development can shed light on the underlying material parameters characterizing the two-photon photosensitivity.

© 1992 Optical Society of America

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References

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  1. K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
    [CrossRef]
  2. V. Mizrahi, S. LaRochelle, G. I. Stegeman, J. E. Sipe, Phys. Rev. A 43, 433 (1991).
    [CrossRef] [PubMed]
  3. C. M. de Sterke, S. An, J. E. Sipe, Opt. Commun. 83, 315 (1991).
    [CrossRef]
  4. S. An, J. E. Sipe, Opt. Lett. 16, 1478 (1991).
    [CrossRef] [PubMed]
  5. M. Parent, J. Bures, S. Lacroix, J. Lapierre, Appl. Opt. 24, 354 (1985).
    [CrossRef] [PubMed]
  6. D. P. Hand, P. St. J. Russell, Electron. Lett. 26, 1846 (1990).
    [CrossRef]
  7. F. Ouellette, D. Gagnon, M. Poirier, Appl. Phys. Lett. 58, 1813 (1991).
    [CrossRef]

1991

V. Mizrahi, S. LaRochelle, G. I. Stegeman, J. E. Sipe, Phys. Rev. A 43, 433 (1991).
[CrossRef] [PubMed]

C. M. de Sterke, S. An, J. E. Sipe, Opt. Commun. 83, 315 (1991).
[CrossRef]

S. An, J. E. Sipe, Opt. Lett. 16, 1478 (1991).
[CrossRef] [PubMed]

F. Ouellette, D. Gagnon, M. Poirier, Appl. Phys. Lett. 58, 1813 (1991).
[CrossRef]

1990

D. P. Hand, P. St. J. Russell, Electron. Lett. 26, 1846 (1990).
[CrossRef]

1985

1978

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

An, S.

C. M. de Sterke, S. An, J. E. Sipe, Opt. Commun. 83, 315 (1991).
[CrossRef]

S. An, J. E. Sipe, Opt. Lett. 16, 1478 (1991).
[CrossRef] [PubMed]

Bures, J.

de Sterke, C. M.

C. M. de Sterke, S. An, J. E. Sipe, Opt. Commun. 83, 315 (1991).
[CrossRef]

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

Gagnon, D.

F. Ouellette, D. Gagnon, M. Poirier, Appl. Phys. Lett. 58, 1813 (1991).
[CrossRef]

Hand, D. P.

D. P. Hand, P. St. J. Russell, Electron. Lett. 26, 1846 (1990).
[CrossRef]

Hill, K. O.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

Johnson, D. C.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

Lacroix, S.

Lapierre, J.

LaRochelle, S.

V. Mizrahi, S. LaRochelle, G. I. Stegeman, J. E. Sipe, Phys. Rev. A 43, 433 (1991).
[CrossRef] [PubMed]

Mizrahi, V.

V. Mizrahi, S. LaRochelle, G. I. Stegeman, J. E. Sipe, Phys. Rev. A 43, 433 (1991).
[CrossRef] [PubMed]

Ouellette, F.

F. Ouellette, D. Gagnon, M. Poirier, Appl. Phys. Lett. 58, 1813 (1991).
[CrossRef]

Parent, M.

Poirier, M.

F. Ouellette, D. Gagnon, M. Poirier, Appl. Phys. Lett. 58, 1813 (1991).
[CrossRef]

Russell, P. St. J.

D. P. Hand, P. St. J. Russell, Electron. Lett. 26, 1846 (1990).
[CrossRef]

Sipe, J. E.

S. An, J. E. Sipe, Opt. Lett. 16, 1478 (1991).
[CrossRef] [PubMed]

C. M. de Sterke, S. An, J. E. Sipe, Opt. Commun. 83, 315 (1991).
[CrossRef]

V. Mizrahi, S. LaRochelle, G. I. Stegeman, J. E. Sipe, Phys. Rev. A 43, 433 (1991).
[CrossRef] [PubMed]

Stegeman, G. I.

V. Mizrahi, S. LaRochelle, G. I. Stegeman, J. E. Sipe, Phys. Rev. A 43, 433 (1991).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

F. Ouellette, D. Gagnon, M. Poirier, Appl. Phys. Lett. 58, 1813 (1991).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
[CrossRef]

Electron. Lett.

D. P. Hand, P. St. J. Russell, Electron. Lett. 26, 1846 (1990).
[CrossRef]

Opt. Commun.

C. M. de Sterke, S. An, J. E. Sipe, Opt. Commun. 83, 315 (1991).
[CrossRef]

Opt. Lett.

Phys. Rev. A

V. Mizrahi, S. LaRochelle, G. I. Stegeman, J. E. Sipe, Phys. Rev. A 43, 433 (1991).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the geometry that we consider. We choose the x axis (or the y axis) as the slow (or fast) principal axis of the birefringence fiber. The indices of refraction are given by n1 for z < 0, n2 for 0 < z < L, and n3 for z > L. Note that the light enters from z = 0 and we neglect the Fresnel reflection from the back surface (z = L) of the fiber.

Fig. 2
Fig. 2

Trajectory of (1, 2, 3) as x increases from 0 to ∞ for (a) ψ = 30° and (b) ψ = 60° in the case of θ = 0. The arrows denote the direction of increasing x.

Fig. 3
Fig. 3

Plot of Ty versus time t for χ = 0, ψ = 20°, and θ = 0, π /4, π/3, and π/2. Note that as t → ∞, Ty → 0 for θπ/2 and Ty, → 1/2 for θ = π/2.

Equations (15)

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( z , t ) = 0 σ 0 + δ σ 3 + [ Δ 11 ( z , t ) Δ 12 ( z , t ) Δ 21 ( z , t ) Δ 22 ( z , t ) ] ,
1 k U 1 ( z , t ) z = i [ a 1 ( z , t ) U 1 ( z , t ) + b ( z , t ) U 2 ( z , t ) ] , 1 k U 2 ( z , t ) z = i [ b * ( z , t ) U 1 ( z , t ) - a 2 ( z , t ) U 2 ( z , t ) ] ,
1 2 0 Δ i i ( z , t ) = a i ( z , t ) , 1 2 0 Δ 12 ( z , t ) = b ( z , t ) exp ( 2 i K z ) + c . c . ,
t i j ( z , t ) = k , l , m , n = 1 2 A i j k l m n E k ( z , t ) × E l ( z , t ) E m * ( z , t ) E n * ( z , t ) ,
i j t = [ r 1 ( E · E ) ( E * · E * ) + r 2 ( E · E * ) 2 ] δ i j + r 3 ( E i E j * + E i * E j ) ( E · E * ) + c E i E j ( E * · E * ) + c * E i * E j * ( E · E ) ,
1 B a ( z , t ) t = [ U 1 ( z , t ) 4 - U 2 ( z , t ) 4 ] cos θ , 1 B b ( z , t ) t = [ U 1 ( z , t ) 2 + U 2 ( z , t ) 2 ] × U 1 ( z , t ) U 2 * ( z , t ) cos θ + i [ U 1 ( z , t ) 2 - U 2 ( z , t ) 2 ] × U 1 ( z , t ) U 2 * ( z , t ) sin θ ,
a ( z , 0 ) = b ( z , 0 ) = 0.
1 ( 0 , t ) = U 1 ( 0 , t ) = cos ψ , 2 ( 0 , t ) = U 2 ( 0 , t ) = exp ( i χ ) sin ψ ,
s 1 ( z , t ) = 2 Re { U 1 * ( z , t ) U 2 ( z , t ) exp [ i ϕ ( z , t ) ] } , s 2 ( z , t ) = 2 Im { U 1 * ( z , t ) U 2 ( z , t ) exp [ i ϕ ( z , t ) ] } , s 3 ( z , t ) = U 1 ( z , t ) 2 - U 2 ( z , t ) 2 .
1 κ s 1 z = 2 η s 2 , 1 κ s 2 z = - 2 η s 1 + 2 s 3 , 1 κ s 3 z = - 2 s 2 ,
η ( z , t ) = 1 κ ( z , t ) [ a ( z , t ) - 1 2 ϕ ( z , t ) z ] ,
a t = s 3 cos θ , κ t = 1 2 s 1 cos θ + 1 2 s 2 s 3 sin θ , 1 κ ϕ t = - 1 2 s 2 cos θ + 1 2 s 1 s 3 sin θ .
1 κ ¯ ( x ) d s ¯ 1 ( x ) d x = 2 η ¯ ( x ) s ¯ 2 ( x ) , 1 κ ¯ ( x ) d s ¯ 2 ( x ) d x = - 2 η ¯ ( x ) s ¯ 1 ( x ) + 2 s ¯ 3 ( x ) , 1 κ ¯ ( x ) d s ¯ 3 ( x ) d x = - 2 s ¯ 2 ( x ) .
a ¯ ( x ) = 1 x 0 x s ¯ 3 ( x ) cos θ d x , κ ¯ ( x ) = 1 x 0 x 1 2 [ s ¯ 1 ( x ) cos θ + s ¯ 2 ( x ) s ¯ 3 ( x ) sin θ ] d x ,
d ϕ ¯ ( x ) d x = 1 2 x κ ¯ ( x ) [ - s ¯ 2 ( x ) cos θ + s ¯ 1 ( x ) s ¯ 3 ( x ) sin θ ] .

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