Abstract

A theory for Raman fiber laser oscillators is presented. The Stokes output and the residual pump power are shown to be calculable from a knowledge of the input pump power and the fiber characteristics. The evolution of the pump and the Stokes waves along the fiber are also obtained. The threshold pump power and the oscillation condition are considered. Pump depletion is incorporated in the analysis and is shown to be the dominant saturation effect present in a Raman fiber laser.

© 1979 Optical Society of America

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  1. E. P. Ippen, Appl. Phys. Lett. 16, 303 (1970).
    [CrossRef]
  2. E. P. Ippen and R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
    [CrossRef]
  3. J. Stone, Appl. Phys. Lett. 26, 163 (1975).
    [CrossRef]
  4. K. O. Hill, B. S. Kawasaki, and D. C. Johnson, Appl. Phys. Lett. 29, 181 (1976).
    [CrossRef]
  5. C. Lin, R. K. Jain, and R. H. Stolen, J. Opt. Soc. Am. 67, 250A (1977);R. K. Jain, C. Lin, R. H. Stolen, W. Pleibel, and P. Kaiser, Appl. Phys. Lett. 30, 162, (1977).
    [CrossRef]
  6. K. O. Hill, B. S. Kawasaki, and D. C. Johnson, J. Opt. Soc. Am. 66, 1114A (1976);D. C. Johnson, K. O. Hill, B. S. Kawasaki, and D. Kato, Electron. Lett. 13, 53 (1977).
    [CrossRef]
  7. R. K. Jain, C. Lin, R. H. Stolen, and A. Ashkin, Appl. Phys. Lett. 31, 89 (1977).
    [CrossRef]
  8. C. Lin, R. H. Stolen, W. G. French, and T. G. Malone, Opt. Lett. 1, 96 (1977).
    [CrossRef] [PubMed]
  9. R. H. Stolen, C. Lin, and R. K. Jain, Appl. Phys. Lett. 30, 340 (1977).
    [CrossRef]
  10. C. Lin, R. H. Stolen, and L. G. Cohen, Appl. Phys. Lett. 31, 97 (1977).
    [CrossRef]
  11. L. G. Cohen and C. Lin, Appl. Opt. 16, 3136 (1977).
    [CrossRef] [PubMed]
  12. R. G. Smith, Appl. Opt. 11, 2489 (1972).
    [CrossRef] [PubMed]
  13. F. Capasso and P. D. Porto, J. Appl. Phys. 47, 1472 (1976).
    [CrossRef]
  14. J. AuYeung and A. Yariv, IEEE J. Quantum Electron. QE-14, 347 (1978).
    [CrossRef]
  15. D. C. Johnson, K. O. Hill, and B. S. Kawasaki, Radio Sci. 12, 519 (1977).
    [CrossRef]
  16. A. Yariv, Quantum Electronics, 2nd ed. (New York, Wiley, 1975).

1978 (1)

J. AuYeung and A. Yariv, IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

1977 (7)

D. C. Johnson, K. O. Hill, and B. S. Kawasaki, Radio Sci. 12, 519 (1977).
[CrossRef]

C. Lin, R. H. Stolen, W. G. French, and T. G. Malone, Opt. Lett. 1, 96 (1977).
[CrossRef] [PubMed]

C. Lin, R. K. Jain, and R. H. Stolen, J. Opt. Soc. Am. 67, 250A (1977);R. K. Jain, C. Lin, R. H. Stolen, W. Pleibel, and P. Kaiser, Appl. Phys. Lett. 30, 162, (1977).
[CrossRef]

L. G. Cohen and C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

R. K. Jain, C. Lin, R. H. Stolen, and A. Ashkin, Appl. Phys. Lett. 31, 89 (1977).
[CrossRef]

R. H. Stolen, C. Lin, and R. K. Jain, Appl. Phys. Lett. 30, 340 (1977).
[CrossRef]

C. Lin, R. H. Stolen, and L. G. Cohen, Appl. Phys. Lett. 31, 97 (1977).
[CrossRef]

1976 (3)

F. Capasso and P. D. Porto, J. Appl. Phys. 47, 1472 (1976).
[CrossRef]

K. O. Hill, B. S. Kawasaki, and D. C. Johnson, Appl. Phys. Lett. 29, 181 (1976).
[CrossRef]

K. O. Hill, B. S. Kawasaki, and D. C. Johnson, J. Opt. Soc. Am. 66, 1114A (1976);D. C. Johnson, K. O. Hill, B. S. Kawasaki, and D. Kato, Electron. Lett. 13, 53 (1977).
[CrossRef]

1975 (1)

J. Stone, Appl. Phys. Lett. 26, 163 (1975).
[CrossRef]

1972 (2)

E. P. Ippen and R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[CrossRef]

R. G. Smith, Appl. Opt. 11, 2489 (1972).
[CrossRef] [PubMed]

1970 (1)

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

Ashkin, A.

R. K. Jain, C. Lin, R. H. Stolen, and A. Ashkin, Appl. Phys. Lett. 31, 89 (1977).
[CrossRef]

AuYeung, J.

J. AuYeung and A. Yariv, IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

Capasso, F.

F. Capasso and P. D. Porto, J. Appl. Phys. 47, 1472 (1976).
[CrossRef]

Cohen, L. G.

L. G. Cohen and C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

C. Lin, R. H. Stolen, and L. G. Cohen, Appl. Phys. Lett. 31, 97 (1977).
[CrossRef]

French, W. G.

Hill, K. O.

D. C. Johnson, K. O. Hill, and B. S. Kawasaki, Radio Sci. 12, 519 (1977).
[CrossRef]

K. O. Hill, B. S. Kawasaki, and D. C. Johnson, J. Opt. Soc. Am. 66, 1114A (1976);D. C. Johnson, K. O. Hill, B. S. Kawasaki, and D. Kato, Electron. Lett. 13, 53 (1977).
[CrossRef]

K. O. Hill, B. S. Kawasaki, and D. C. Johnson, Appl. Phys. Lett. 29, 181 (1976).
[CrossRef]

Ippen, E. P.

E. P. Ippen and R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[CrossRef]

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

Jain, R. K.

R. H. Stolen, C. Lin, and R. K. Jain, Appl. Phys. Lett. 30, 340 (1977).
[CrossRef]

R. K. Jain, C. Lin, R. H. Stolen, and A. Ashkin, Appl. Phys. Lett. 31, 89 (1977).
[CrossRef]

C. Lin, R. K. Jain, and R. H. Stolen, J. Opt. Soc. Am. 67, 250A (1977);R. K. Jain, C. Lin, R. H. Stolen, W. Pleibel, and P. Kaiser, Appl. Phys. Lett. 30, 162, (1977).
[CrossRef]

Johnson, D. C.

D. C. Johnson, K. O. Hill, and B. S. Kawasaki, Radio Sci. 12, 519 (1977).
[CrossRef]

K. O. Hill, B. S. Kawasaki, and D. C. Johnson, J. Opt. Soc. Am. 66, 1114A (1976);D. C. Johnson, K. O. Hill, B. S. Kawasaki, and D. Kato, Electron. Lett. 13, 53 (1977).
[CrossRef]

K. O. Hill, B. S. Kawasaki, and D. C. Johnson, Appl. Phys. Lett. 29, 181 (1976).
[CrossRef]

Kawasaki, B. S.

D. C. Johnson, K. O. Hill, and B. S. Kawasaki, Radio Sci. 12, 519 (1977).
[CrossRef]

K. O. Hill, B. S. Kawasaki, and D. C. Johnson, J. Opt. Soc. Am. 66, 1114A (1976);D. C. Johnson, K. O. Hill, B. S. Kawasaki, and D. Kato, Electron. Lett. 13, 53 (1977).
[CrossRef]

K. O. Hill, B. S. Kawasaki, and D. C. Johnson, Appl. Phys. Lett. 29, 181 (1976).
[CrossRef]

Lin, C.

L. G. Cohen and C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

C. Lin, R. H. Stolen, W. G. French, and T. G. Malone, Opt. Lett. 1, 96 (1977).
[CrossRef] [PubMed]

C. Lin, R. H. Stolen, and L. G. Cohen, Appl. Phys. Lett. 31, 97 (1977).
[CrossRef]

R. H. Stolen, C. Lin, and R. K. Jain, Appl. Phys. Lett. 30, 340 (1977).
[CrossRef]

R. K. Jain, C. Lin, R. H. Stolen, and A. Ashkin, Appl. Phys. Lett. 31, 89 (1977).
[CrossRef]

C. Lin, R. K. Jain, and R. H. Stolen, J. Opt. Soc. Am. 67, 250A (1977);R. K. Jain, C. Lin, R. H. Stolen, W. Pleibel, and P. Kaiser, Appl. Phys. Lett. 30, 162, (1977).
[CrossRef]

Malone, T. G.

Porto, P. D.

F. Capasso and P. D. Porto, J. Appl. Phys. 47, 1472 (1976).
[CrossRef]

Smith, R. G.

Stolen, R. H.

C. Lin, R. H. Stolen, W. G. French, and T. G. Malone, Opt. Lett. 1, 96 (1977).
[CrossRef] [PubMed]

R. H. Stolen, C. Lin, and R. K. Jain, Appl. Phys. Lett. 30, 340 (1977).
[CrossRef]

C. Lin, R. H. Stolen, and L. G. Cohen, Appl. Phys. Lett. 31, 97 (1977).
[CrossRef]

C. Lin, R. K. Jain, and R. H. Stolen, J. Opt. Soc. Am. 67, 250A (1977);R. K. Jain, C. Lin, R. H. Stolen, W. Pleibel, and P. Kaiser, Appl. Phys. Lett. 30, 162, (1977).
[CrossRef]

R. K. Jain, C. Lin, R. H. Stolen, and A. Ashkin, Appl. Phys. Lett. 31, 89 (1977).
[CrossRef]

E. P. Ippen and R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[CrossRef]

Stone, J.

J. Stone, Appl. Phys. Lett. 26, 163 (1975).
[CrossRef]

Yariv, A.

J. AuYeung and A. Yariv, IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

A. Yariv, Quantum Electronics, 2nd ed. (New York, Wiley, 1975).

Appl. Opt. (2)

Appl. Phys. Lett. (7)

R. H. Stolen, C. Lin, and R. K. Jain, Appl. Phys. Lett. 30, 340 (1977).
[CrossRef]

C. Lin, R. H. Stolen, and L. G. Cohen, Appl. Phys. Lett. 31, 97 (1977).
[CrossRef]

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

E. P. Ippen and R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[CrossRef]

J. Stone, Appl. Phys. Lett. 26, 163 (1975).
[CrossRef]

K. O. Hill, B. S. Kawasaki, and D. C. Johnson, Appl. Phys. Lett. 29, 181 (1976).
[CrossRef]

R. K. Jain, C. Lin, R. H. Stolen, and A. Ashkin, Appl. Phys. Lett. 31, 89 (1977).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. AuYeung and A. Yariv, IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

J. Appl. Phys. (1)

F. Capasso and P. D. Porto, J. Appl. Phys. 47, 1472 (1976).
[CrossRef]

J. Opt. Soc. Am. (2)

C. Lin, R. K. Jain, and R. H. Stolen, J. Opt. Soc. Am. 67, 250A (1977);R. K. Jain, C. Lin, R. H. Stolen, W. Pleibel, and P. Kaiser, Appl. Phys. Lett. 30, 162, (1977).
[CrossRef]

K. O. Hill, B. S. Kawasaki, and D. C. Johnson, J. Opt. Soc. Am. 66, 1114A (1976);D. C. Johnson, K. O. Hill, B. S. Kawasaki, and D. Kato, Electron. Lett. 13, 53 (1977).
[CrossRef]

Opt. Lett. (1)

Radio Sci. (1)

D. C. Johnson, K. O. Hill, and B. S. Kawasaki, Radio Sci. 12, 519 (1977).
[CrossRef]

Other (1)

A. Yariv, Quantum Electronics, 2nd ed. (New York, Wiley, 1975).

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Figures (3)

FIG. 1
FIG. 1

Typical experimental setup.

FIG. 2
FIG. 2

Solid lines are the Stokes output powers and the broken lines are the residual pump powers. The input pump powers are (a) 5 W (b) 4 W (c) 3 W, and (d) 2 W.

FIG. 3
FIG. 3

The pump and the Stokes powers inside the 100-m long fiber at a 4 W pump power input.

Equations (23)

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d P p d z = α P p ν p ν s g A P p ( P f + P b ) ,
d P f d z = α P f + g A P p P f ,
d P b d z = α P b g A P p P b .
P p ( z = 0 ) P p o ,
P f ( z = 0 ) P f o = R 1 P b ( z = 0 ) R 1 P b o ,
P b ( z = L ) P b L = R 2 P f ( z = L ) R 2 P f L .
P f ( z ) P b ( z ) = P f o P b o = P f L P b L = K ,
P f o / P f L = P b L / P b o = ( R 1 R 2 ) 1 / 2 .
P f o P f L = P b L P b o = exp [ α L g A 0 L P p ( z ) d z ] .
( R 1 R 2 ) 1 / 2 exp [ α L + g A 0 L P p ( z ) d z ] = 1 .
P p ( z ) P b ( z ) exp { g ν p α A ν s [ ν s ν p P p ( z ) + P f ( z ) P b ( z ) ] } = P p o P b o exp { g ν p α A ν s [ ν s ν p P p o + P f o P b o ( z ) ] } = C .
P f L = ln [ ( R 1 R 2 ) 1 / 2 P p L / P p o ] + ( g / α A ) ( P p o P p L ) ( g / α A ) ( ν p / ν s ) { 1 R 2 ( R 1 R 2 ) 1 / 2 [ 1 ( 1 / R 1 ) ] } .
d υ d z = α u ,
d υ d z = { α 2 υ 2 + 4 α 2 K + 4 α 2 ν s ν p P p o P b o × exp [ g ν p α A ν s ( υ o υ ) ] } 1 / 2 ,
υ ( z ) υ o d υ { α 2 υ 2 + 4 α 2 K + 4 α 2 ν s ν p P p o P b o × exp [ g ν p α A ν s ( υ o υ ) ] } 1 / 2 = z .
υ L υ o d υ { α 2 υ 2 + 4 α 2 K + 4 α 2 ν s ν p P p o P b o × exp [ g ν p α A ν s ( υ o υ ) ] } 1 / 2 = L ,
P f L ( max ) = ln [ ( R 1 R 2 ) 1 / 2 ( α A / g P p o ) ] + ( g / α A ) P p o 1 ( g / α A ) ( ν p / ν s ) { 1 R 2 ( R 1 R 2 ) 1 / 2 [ 1 ( 1 / R 1 ) ] } .
P p t = α A g [ α L ( 1 / 2 ) ln ( R 1 R 2 ) 1 exp ( α L ) ] .
α 0 L P p ( z ) d z = P p t [ 1 exp ( α L ) ] .
d P f d z = α P f + g A P f ( P f + P b ) ,
P f L = P f o exp { α L + g A 0 L [ P f ( z ) + P b ( z ) ] d z } .
0 L [ P f ( z ) + P b ( z ) ] d z = 0 L u ( z ) d z ν s ν p 0 L P p ( z ) d z .
0 L [ P f ( z ) + P b ( z ) ] d z = 1 α [ υ o υ L ] ν s ν p A g [ α L 1 2 ln ( R 1 R 2 ) ] ,