Abstract

In this paper, we study the optical Kerr effect theoretically in multimode birefringent optical fibers in connection with the characteristics of the fiber and excitation conditions. We observe experimentally, for a pump power 2 W in the fundamental mode, 70% modulation depth for the probe light with multimodal coupling.

© 1983 Optical Society of America

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References

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  1. J. M. Dziedzic, R. H. Stolen, A. Ashkin, Appl. Opt. 20, 1403 (1981).
    [CrossRef] [PubMed]
  2. R. H. Stolen, J. Botineau, A. Ashkin, Opt. Lett. 10, 512 (1982).
    [CrossRef]
  3. D. Gloge, Appl. Opt. 10, 2252 (1971).
    [CrossRef] [PubMed]
  4. A. J. Snyder, W. R. Young, J. Opt. Soc. Am. 68, 297 (1978).
    [CrossRef]
  5. R. E. Wagner, R. H. Stolen, W. Pleibel, Electron. Lett. 17, 177 (1981).
    [CrossRef]
  6. A. Saissy, J. Botineau, D. B. Ostrowsky, Colloque Horizons de l'optique 82, Institut National Polytechnique de Grenoble, E.N.S.I.E.G. BP46 38402, St Martin d'Heres.

1982

R. H. Stolen, J. Botineau, A. Ashkin, Opt. Lett. 10, 512 (1982).
[CrossRef]

1981

R. E. Wagner, R. H. Stolen, W. Pleibel, Electron. Lett. 17, 177 (1981).
[CrossRef]

J. M. Dziedzic, R. H. Stolen, A. Ashkin, Appl. Opt. 20, 1403 (1981).
[CrossRef] [PubMed]

1978

1971

Ashkin, A.

R. H. Stolen, J. Botineau, A. Ashkin, Opt. Lett. 10, 512 (1982).
[CrossRef]

J. M. Dziedzic, R. H. Stolen, A. Ashkin, Appl. Opt. 20, 1403 (1981).
[CrossRef] [PubMed]

Botineau, J.

R. H. Stolen, J. Botineau, A. Ashkin, Opt. Lett. 10, 512 (1982).
[CrossRef]

A. Saissy, J. Botineau, D. B. Ostrowsky, Colloque Horizons de l'optique 82, Institut National Polytechnique de Grenoble, E.N.S.I.E.G. BP46 38402, St Martin d'Heres.

Dziedzic, J. M.

Gloge, D.

Ostrowsky, D. B.

A. Saissy, J. Botineau, D. B. Ostrowsky, Colloque Horizons de l'optique 82, Institut National Polytechnique de Grenoble, E.N.S.I.E.G. BP46 38402, St Martin d'Heres.

Pleibel, W.

R. E. Wagner, R. H. Stolen, W. Pleibel, Electron. Lett. 17, 177 (1981).
[CrossRef]

Saissy, A.

A. Saissy, J. Botineau, D. B. Ostrowsky, Colloque Horizons de l'optique 82, Institut National Polytechnique de Grenoble, E.N.S.I.E.G. BP46 38402, St Martin d'Heres.

Snyder, A. J.

Stolen, R. H.

R. H. Stolen, J. Botineau, A. Ashkin, Opt. Lett. 10, 512 (1982).
[CrossRef]

R. E. Wagner, R. H. Stolen, W. Pleibel, Electron. Lett. 17, 177 (1981).
[CrossRef]

J. M. Dziedzic, R. H. Stolen, A. Ashkin, Appl. Opt. 20, 1403 (1981).
[CrossRef] [PubMed]

Wagner, R. E.

R. E. Wagner, R. H. Stolen, W. Pleibel, Electron. Lett. 17, 177 (1981).
[CrossRef]

Young, W. R.

Appl. Opt.

Electron. Lett.

R. E. Wagner, R. H. Stolen, W. Pleibel, Electron. Lett. 17, 177 (1981).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

R. H. Stolen, J. Botineau, A. Ashkin, Opt. Lett. 10, 512 (1982).
[CrossRef]

Other

A. Saissy, J. Botineau, D. B. Ostrowsky, Colloque Horizons de l'optique 82, Institut National Polytechnique de Grenoble, E.N.S.I.E.G. BP46 38402, St Martin d'Heres.

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Figures (7)

Fig. 1
Fig. 1

Positions respectives des axes de la fibre, de la lame quart d'onde et du polariseur.

Fig. 2
Fig. 2

Variation de la transmission T au cours du temps pour δφ( M ) = π et différentes valeurs de η.

Fig. 3
Fig. 3

Idem fig. 2 mais pour δφ( M ) = 2π.

Fig. 4
Fig. 4

Idem fig. 2 mais pour δφ( M ) = 3π.

Fig. 5
Fig. 5

Variations du maximum et du minimum de T pour δφ( M ) = π ou 2π, η = 0.5 en fonction du rapport des intégrales de recouvrement.

Fig. 6
Fig. 6

Dispositif expérimental.

Fig. 7
Fig. 7

Modulations de l'onde sonde pour des puissances excitatrices croissantes de haut en bas (échelle temporelle: 20 nsec/div.).

Equations (22)

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P N L ( ω S ) = X ( 3 ) : E ( ω P ) E ( ω p * ) E ( ω S ) ,
rot rot E ( ω S C ) 2 : E = μ 0 ω S 2 P N L .
E ( ω ) = ν A ( ν ) ( z ) exp j β ( ν ) z E t , ( ν ) ( x , y ) ,
E t ( ρ ) E t ( ν ) * dxdy = 2 μ 0 ω β ν δ ρ , ν .
d d z A ( ν ) ( z ) = j ω 4 P N L E ( ν ) * dxdy exp ( j β ( ν ) z ) .
E t 1 = E X ( 0 ) e ̂ x , E t 2 = E Y ( 0 ) E t 3 = E X ( 1 ) e ̂ x , E t 4 = E Y ( 1 ) e ̂ y ,
E X ( 0 ) = E Y ( 0 ) = E t ( 0 ) ( r ) et E X ( 1 ) = E Y ( 1 ) = E t ( 1 ) ( r , φ ) .
d d z A ( 1 ) ( ω S ) = j ω S 4 χ X X | A ( ω p ) | 2 R ( 0 ) A ( 1 ) ( ω S ) , d d z A ( 2 ) ( ω S ) = j ω S 4 χ X Y | A ( ω p ) | 2 R ( 0 ) A ( 2 ) ( ω S ) , d d z A ( 3 ) ( ω S ) = j ω S 4 χ X X | A ( ω p ) | 2 R ( 1 ) A ( 3 ) ( ω S ) , d d z A ( 4 ) ( ω S ) = j ω S 4 χ X Y | A ( ω p ) | 2 R ( 1 ) A ( 4 ) ( ω S ) .
R ( 0 ) = | E t ( 0 ) ( ω p ) | 2 | E t ( 0 ) ( ω S ) | 2 r d r , R ( 1 ) = | E t ( 1 ) ( ω p ) | 2 | E t ( 1 ) ( ω S ) | 2 rdrd φ .
A ( 1 ) ( z ) = B ( 1 ) exp j [ ω S 4 χ X X R ( 0 ) | A ( ω p ) | 2 z ] , A ( 2 ) ( z ) = B ( 1 ) exp j [ ω S 4 χ X Y R ( 0 ) | A ( ω p ) | 2 z ] , A ( 3 ) ( z ) = B ( 2 ) exp j [ ω S 4 χ X X R ( 1 ) | A ( ω p ) | 2 z ] , A ( 4 ) ( z ) = B ( 2 ) exp j [ ω S 4 χ X Y R ( 1 ) | A ( ω p ) | 2 z ] .
E ( ω S ) = E t ( 0 ) exp j φ ( 0 ) B ( 1 ) [ exp j Δ φ ( 0 ) e ̂ x + e ̂ y ] + E t ( 1 ) exp j φ ( 1 ) B ( 2 ) [ exp j Δ φ ( 1 ) e ̂ x + e ̂ y ] ,
Δ φ ( 0 ) = [ β y ( 0 ) + ω S 4 χ X Y | A ( ω p ) | 2 R ( 0 ) ] z , Δ φ ( 0 ) = [ β x ( 0 ) β y ( 0 ) + ω S 4 ( χ X X χ X Y ) | A ( ω p ) | 2 R ( 0 ) ] z , φ ( 1 ) = [ β y ( 1 ) + ω S 4 χ X Y | A ( ω p ) | 2 R ( 1 ) ] z , Δ φ ( 1 ) = [ β x ( 1 ) β y ( 1 ) ω S 4 ( χ X X χ X Y ) | A ( ω p ) | 2 R ( 1 ) ] z .
r ̂ ( i ) = cos ψ ( i ) l ̂ x + sin ψ ( i ) l ̂ y , i = 0 , 1.
E ( ω S ) P ̂ = E t ( 0 ) 2 B ( 1 ) exp j [ φ ( 0 ) + Δ φ ( 0 ) 2 ] sin [ ψ ( 0 ) θ ] + E t ( 1 ) 2 B ( 2 ) exp j [ φ ( 1 ) + Δ φ ( 1 ) 2 ] sin [ ψ ( 1 ) θ ] .
I = I ( 0 ) ( 0 ) sin 2 [ ψ ( 0 ) θ ] + I ( 0 ) ( 0 ) sin 2 [ ψ ( 1 ) θ ] ,
T = 1 1 + η { sin 2 [ δ φ ( 0 ) 2 ] η sin 2 [ δ φ ( 1 ) 2 ] } ,
η = I ( 1 ) / I ( 0 ) , δ φ ( i ) = ω S 4 ( χ X X χ X Y ) | A ( ω p ) | 2 R ( i ) z , i = 0 , 1 .
E ( 0 ) ( ω p ) = exp ( r W 1 ) 2 , E ( 0 ) ( ω S ) = exp ( r V 1 ) 2 , E ( 1 ) ( ω S ) = r W 3 exp ( r W 3 ) 2 cos φ ,
R ( 0 ) = 4 μ 2 ω S ω p β S ( 0 ) β p ( 0 ) 1 S eff ( 0 ) , S eff ( 0 ) = π 2 ( W 1 2 + V 1 2 ) , R ( 1 ) = 4 μ 2 ω S ω p β S ( 1 ) β p ( 0 ) 1 S eff ( 1 ) , S eff ( 1 ) = π 2 W 1 2 [ 1 + ( W 3 W 1 ) 2 ] 2 ;
δ φ ( 1 ) δ φ ( 0 ) = β S ( 0 ) β S ( 1 ) 1 + ( V 1 W 1 ) 2 [ 1 + ( W 3 W 1 ) 2 ] 2 .
T = 1 1 + η { sin 2 [ δ φ ( M ) 2 exp ( t / τ ) 2 ] + η sin 2 [ δ φ ( M ) 4 exp ( t / τ ) 2 ] } ,
N 2 B = N C λ S 8 π 2 S eff δ φ ( M ) l eff P 10 7 ues .

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