Abstract

The effect of stimulated Raman and Brillouin scattering on the power handling capacity of optical fibers is considered and found to be important especially when low loss optical fibers are used. A critical power below which stimulated effects may be neglected is defined for forward and backward Raman scattering and for backward Brillouin scattering. This critical power is determined by the effective core area A, the small signal attenuation constant of the fiber α, and the gain coefficient for the stimulated scattering process γ0, by the approximate relation Pcrit ≈ 20Aα/γ0. For a fiber with 20-dB/km attenuation and an area of 10−7 cm2Pcrit ≈ 35 mW for stimulated Brillouin scattering. For stimulated Raman scattering Pcrit is approximately two orders of magnitude higher. It is concluded that these effects must be considered in the design of optical communication systems using low loss fibers.

© 1972 Optical Society of America

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References

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  1. E. P. Ippen, Appl. Phys. Lett. 16, 303 (1970).
    [Crossref]
  2. R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
    [Crossref]
  3. E. P. Ippen, R. H. Stolen, Paper F9, 7th International Quantum Electronics Conference, Montreal, May 1972.
  4. W. D. Johnston, I. P. Kaminow, J. G. Bergman, Appl. Phys. Lett. 13, 190 (1968).
    [Crossref]
  5. C. L. Tang, J. Appl. Phys. 37, 2945 (1966).
    [Crossref]
  6. D. A. Pinnow, in Handbook of Lasers, R. J. Pressley, Ed. (Chemical Rubber Co., Cleveland, 1972).
  7. A. S. Pine, Phys. Rev. 185, 1187 (1969).
    [Crossref]
  8. J. Walder, C. L. Tang, Phys. Rev. Lett. 19, 623 (1967).
    [Crossref]
  9. T. C. Rich, D. A. Pinnow, Appl. Phys. Lett. 20, 264 (1972).
    [Crossref]

1972 (2)

R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
[Crossref]

T. C. Rich, D. A. Pinnow, Appl. Phys. Lett. 20, 264 (1972).
[Crossref]

1970 (1)

E. P. Ippen, Appl. Phys. Lett. 16, 303 (1970).
[Crossref]

1969 (1)

A. S. Pine, Phys. Rev. 185, 1187 (1969).
[Crossref]

1968 (1)

W. D. Johnston, I. P. Kaminow, J. G. Bergman, Appl. Phys. Lett. 13, 190 (1968).
[Crossref]

1967 (1)

J. Walder, C. L. Tang, Phys. Rev. Lett. 19, 623 (1967).
[Crossref]

1966 (1)

C. L. Tang, J. Appl. Phys. 37, 2945 (1966).
[Crossref]

Bergman, J. G.

W. D. Johnston, I. P. Kaminow, J. G. Bergman, Appl. Phys. Lett. 13, 190 (1968).
[Crossref]

Ippen, E. P.

R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
[Crossref]

E. P. Ippen, Appl. Phys. Lett. 16, 303 (1970).
[Crossref]

E. P. Ippen, R. H. Stolen, Paper F9, 7th International Quantum Electronics Conference, Montreal, May 1972.

Johnston, W. D.

W. D. Johnston, I. P. Kaminow, J. G. Bergman, Appl. Phys. Lett. 13, 190 (1968).
[Crossref]

Kaminow, I. P.

W. D. Johnston, I. P. Kaminow, J. G. Bergman, Appl. Phys. Lett. 13, 190 (1968).
[Crossref]

Pine, A. S.

A. S. Pine, Phys. Rev. 185, 1187 (1969).
[Crossref]

Pinnow, D. A.

T. C. Rich, D. A. Pinnow, Appl. Phys. Lett. 20, 264 (1972).
[Crossref]

D. A. Pinnow, in Handbook of Lasers, R. J. Pressley, Ed. (Chemical Rubber Co., Cleveland, 1972).

Rich, T. C.

T. C. Rich, D. A. Pinnow, Appl. Phys. Lett. 20, 264 (1972).
[Crossref]

Stolen, R. H.

R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
[Crossref]

E. P. Ippen, R. H. Stolen, Paper F9, 7th International Quantum Electronics Conference, Montreal, May 1972.

Tang, C. L.

J. Walder, C. L. Tang, Phys. Rev. Lett. 19, 623 (1967).
[Crossref]

C. L. Tang, J. Appl. Phys. 37, 2945 (1966).
[Crossref]

Tynes, A. R.

R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
[Crossref]

Walder, J.

J. Walder, C. L. Tang, Phys. Rev. Lett. 19, 623 (1967).
[Crossref]

Appl. Phys. Lett. (4)

E. P. Ippen, Appl. Phys. Lett. 16, 303 (1970).
[Crossref]

R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
[Crossref]

W. D. Johnston, I. P. Kaminow, J. G. Bergman, Appl. Phys. Lett. 13, 190 (1968).
[Crossref]

T. C. Rich, D. A. Pinnow, Appl. Phys. Lett. 20, 264 (1972).
[Crossref]

J. Appl. Phys. (1)

C. L. Tang, J. Appl. Phys. 37, 2945 (1966).
[Crossref]

Phys. Rev. (1)

A. S. Pine, Phys. Rev. 185, 1187 (1969).
[Crossref]

Phys. Rev. Lett. (1)

J. Walder, C. L. Tang, Phys. Rev. Lett. 19, 623 (1967).
[Crossref]

Other (2)

D. A. Pinnow, in Handbook of Lasers, R. J. Pressley, Ed. (Chemical Rubber Co., Cleveland, 1972).

E. P. Ippen, R. H. Stolen, Paper F9, 7th International Quantum Electronics Conference, Montreal, May 1972.

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Equations (39)

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P p ( z ) = P p ( 0 )   exp ( - α p z ) ,
[ ( d / d z ) + α s ] P s ( z ) = γ S p ( z ) P s ( z ) ,
[ ( d / d z ) + α s ] P s ( z ) = γ P s ( z ) S p ( 0 )   exp ( - α p z ) ,
P s ( z ) = P s ( 0 )   exp   { - α s z + γ S p ( 0 ) α p [ 1 - exp ( - α p z ) ] } .
P s ( L ) ≃ P s ( 0 )   exp [ - α s L + γ S p ( 0 ) α p ] .
P s ( L ) = ∑ transverse modes ∫ d ν ( h ν )   exp [ - α s L + S p ( 0 ) α p γ ( ν ) , ] ,
P s ( L ) = { ∑ transverse modes ( h ν s )   exp [ - α s L + S p ( 0 ) γ 0 α p ] }   B eff ,
B eff = √ π 2 Δ ν f w h m [ S p ( 0 ) γ 0 / α p ] 1 2 ,
P s ( 0 ) ∣ eff = ( h ν s ) ( B eff ) ( number   of   transverse   modes . )
P s ( 0 ) ∣ eff exp [ - α s L + S p ( 0 ) γ 0 α p ] < P p ( 0 )   exp ( - α p L ) .
√ π 2 ( h ν s )   ( γ 0 A α p )   Δ ν f w h m = ( γ 0 P crit A α p ) / 2 3 exp ( - γ 0 P crit A α p ) .
exp ( 100 P crit ) = 2 × 10 8 P crit / 2 3 ,
P crit ≈ 16 ( A α p / γ 0 ) ,
G = exp { - α s z 0 + [ γ S p ( 0 ) / α p ] [ 1 - exp ( - α p z 0 ) ] } .
G eff ( ν ) = exp { [ S p ( 0 ) γ ( ν ) ] / α p } [ S p ( 0 ) γ ( ν ) / α p ] .
P s ( 0 ) = ∑ transverse modes ∫ d ν ( h ν ) · G eff ( ν ) .
√ π 2 ( h ν s )   ( γ 0 α p A )   Δ ν f w h m Raman = ( γ 0 P crit ′ A α p ) / 2 5   exp ( - γ 0 P crit ′ A α p ) ,       ( Raman )
√ π 2 ( ν s ν a )   ( k T )   ( γ 0 α p A )   Δ ν f w h m Brill . = ( γ 0 P crit ″ A α p ) / 2 5 exp ( - γ 0 P crit ″ A α p ) .       ( Brillouin )
P crit ′ = 20 ( A α p / γ 0 ) .
P crit ″ ≈ 21 ( A α p / γ 0 ) .
γ 0 = ( 2 π 2 ν s ν a M 2 ) / c 2 α a ,
M 2 = n 6 p 2 / ρ V a 3 .
ν a = ν p ( V a / c ) ( n m + n m ′ ) ,
[ ( d / d z ) + α s ] N s = γ S p ( z ) ( N s + 1 ) ,
( d / d z ) N s spontaneous = γ S p ( z ) .
N s ( z 2 ) N s ( z 1 ) = exp [ α s ( z 1 - z 2 ) + ∫ z 1 z 2 γ S p ( z ) d z ] .
N s ( z ) = ∫ 0 z d ξ γ S p ( ξ )   exp [ α s ( ξ - z ) + ∫ ξ z γ S p ( η ) d η ] + N s ( 0 )   exp   [ - α s z + ∫ 0 z γ S p ( η ) d η ] ,
N s ( z ) = ∫ 0 z d ξ γ S p ( 0 )   exp   { - α p ξ + α s ( ξ - z ) + γ S p ( 0 ) α p × [ exp ( - α p ξ ) - exp ( - α p z ) ] } + N s ( 0 ) × exp   { - α s z + γ S p ( 0 ) α p [ 1 - exp ( - α p z ) ] } .
N s ( L ) = exp ( - α s L )   ∫ 0 L γ S p ( 0 ) d ξ   exp   { γ S p ( 0 ) α p × [ exp ( - α p ξ ) - exp ( - α p L ) ] } .
N s ( L ) ≅ exp [ - α s L ˙ + γ S p ( 0 ) α p ]   ∫ 0 L γ S p ( 0 ) d ξ   exp [ - γ S p ( 0 ) ξ ] = exp [ - α s L + γ S p ( 0 ) α p ]   [ 1 - exp ( - γ S p L ) ] ≈ [ - α s L + γ S p ( 0 ) α p ] ,
[ ( d / d z ) - α s ] N s = - γ S p ( z ) ( N s + 1 ) .
N s ( z 2 ) N s ( z 1 ) = exp [ α s ( z 2 - z 1 ) + ∫ z 2 z 1 γ S p ( z ) d z ] .
N s ( z ) = ∫ z L d ξ γ S p ( ξ )   exp [ α s ( z - ξ ) + ∫ z ξ γ S p ( η ) d η ] + N s ( L )   exp [ α s ( z - L ) + ∫ z L γ S p ( η ) d η ] ,
N s ( z ) = ∫ z L d ξ γ S p ( 0 )   exp   { α s z - ( α s + α p ) ξ + γ S p ( 0 ) α p × [ exp ( - α p z ) - exp ( - α p ξ ) ] } + N s ( L )   exp   { α s ( z - L ) + γ S p ( 0 ) α p [ exp ( - α p z ) - exp ( - α p L ) ] } .
N s ( 0 ) = ∫ 0 L d ξ γ S p ( 0 )   exp   { - ( α s + α p ) ξ + γ S p ( 0 ) α p [ 1 - exp ( - α p ξ ) ] } .
N s ( 0 ) = exp [ γ S p ( 0 ) / α p ] [ γ S p ( 0 ) / α p ] ,
γ S p ( 0 )   exp ( - α p z 0 ) = α s
α p z 0 = ln [ γ S p ( 0 ) / α s ] .
N s ( 0 ) = 1 / [ γ S p ( 0 ) / α p ]   exp { [ γ S p ( 0 ) / α p ] - 1 } .

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