Abstract

The theory of the growth of the total first-order Raman stokes power with the corresponding depletion of the laser pump power in optical fibers is examined. Numerical solutions are given for circumstances where the losses at the pump and Stokes wavelengths are unequal. The nature of the power-coupling process and the depletion of the total power at all wavelengths can be described without a full analytical solution. The variation of the output power with respect to input power when the fiber length is a constant is also studied.

© 1986 Optical Society of America

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References

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  1. Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single-Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
    [CrossRef]
  2. R. H. Stolen, “Fibre Raman Lasers,” in Fibre and Integrated Optics, D. B. Ostrowsky, ed. (Plenum, New York, 1979), pp. 157–182.
    [CrossRef]
  3. R. H. Stolen, E. P. Ippen, A. R. Tynes, “Raman Oscillation in Glass Optical Waveguides,” Appl. Phys. Lett. 20, 62 (1972).
    [CrossRef]
  4. Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
    [CrossRef]
  5. R. G. Smith, “Critical Power Handling Capacity of Low-Loss Optical Fibers as Determined by Stimulated Raman and Bril-louin Scattering,” Appl. Opt. 11, 2489 (1972).
    [CrossRef] [PubMed]
  6. J. Au Yeung, A. Yariv, “Spontaneous and Stimulated Raman Scattering in Long Low Loss Fibers,” IEEE J. Quantum Electron. QE-14, 347 (1978).
    [CrossRef]
  7. W. P. Urquhart, P. J. R. Laybourn, “Stimulated Raman Scattering in Optical Fibers with Nonconstant Losses: A Multiwavelength Model.” To be published in Appl. Opt. (Month 1986).
    [PubMed]
  8. M. M. von der Linde, W. Kaiser, “Quantitative Investigations of the Simulated Raman Effect Using Subnanosecond Light Pulses,” Phys. Rev. 178, 11 (1969).
    [CrossRef]
  9. D. Gloge, “Weakly Guiding Fibers,” Appl. Opt. 10, 2252 (1971).
    [CrossRef] [PubMed]
  10. W. P. Urquhart, P. J. R. Laybourn, “The Effective Core Area for Stimulated Raman Scattering in Single-Mode Optical Fibres,” Proc. IEE (J) Optoelectron. 132, 201 (1985).
    [CrossRef]
  11. Numerical Algorithms Group (NAG): Fortran Library Mark 10 Implementation (1983) Routines D02BBF, D02BAF, and D01GAF used (NAG Central Office, Mayfield House, 256 Banbury Road, Oxford OY2 7DE, U.K.).

1985

W. P. Urquhart, P. J. R. Laybourn, “The Effective Core Area for Stimulated Raman Scattering in Single-Mode Optical Fibres,” Proc. IEE (J) Optoelectron. 132, 201 (1985).
[CrossRef]

1981

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single-Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

1978

J. Au Yeung, A. Yariv, “Spontaneous and Stimulated Raman Scattering in Long Low Loss Fibers,” IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

1972

1971

1969

M. M. von der Linde, W. Kaiser, “Quantitative Investigations of the Simulated Raman Effect Using Subnanosecond Light Pulses,” Phys. Rev. 178, 11 (1969).
[CrossRef]

Au Yeung, J.

J. Au Yeung, A. Yariv, “Spontaneous and Stimulated Raman Scattering in Long Low Loss Fibers,” IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

Edahiro, T.

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single-Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

Gloge, D.

Ippen, E. P.

R. H. Stolen, E. P. Ippen, A. R. Tynes, “Raman Oscillation in Glass Optical Waveguides,” Appl. Phys. Lett. 20, 62 (1972).
[CrossRef]

Kaiser, W.

M. M. von der Linde, W. Kaiser, “Quantitative Investigations of the Simulated Raman Effect Using Subnanosecond Light Pulses,” Phys. Rev. 178, 11 (1969).
[CrossRef]

Kawachi, M.

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single-Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

Laybourn, P. J. R.

W. P. Urquhart, P. J. R. Laybourn, “The Effective Core Area for Stimulated Raman Scattering in Single-Mode Optical Fibres,” Proc. IEE (J) Optoelectron. 132, 201 (1985).
[CrossRef]

W. P. Urquhart, P. J. R. Laybourn, “Stimulated Raman Scattering in Optical Fibers with Nonconstant Losses: A Multiwavelength Model.” To be published in Appl. Opt. (Month 1986).
[PubMed]

Ohmori, Y.

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single-Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

Sasaki, Y.

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single-Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

Smith, R. G.

Stolen, R. H.

R. H. Stolen, E. P. Ippen, A. R. Tynes, “Raman Oscillation in Glass Optical Waveguides,” Appl. Phys. Lett. 20, 62 (1972).
[CrossRef]

R. H. Stolen, “Fibre Raman Lasers,” in Fibre and Integrated Optics, D. B. Ostrowsky, ed. (Plenum, New York, 1979), pp. 157–182.
[CrossRef]

Tynes, A. R.

R. H. Stolen, E. P. Ippen, A. R. Tynes, “Raman Oscillation in Glass Optical Waveguides,” Appl. Phys. Lett. 20, 62 (1972).
[CrossRef]

Urquhart, W. P.

W. P. Urquhart, P. J. R. Laybourn, “The Effective Core Area for Stimulated Raman Scattering in Single-Mode Optical Fibres,” Proc. IEE (J) Optoelectron. 132, 201 (1985).
[CrossRef]

W. P. Urquhart, P. J. R. Laybourn, “Stimulated Raman Scattering in Optical Fibers with Nonconstant Losses: A Multiwavelength Model.” To be published in Appl. Opt. (Month 1986).
[PubMed]

von der Linde, M. M.

M. M. von der Linde, W. Kaiser, “Quantitative Investigations of the Simulated Raman Effect Using Subnanosecond Light Pulses,” Phys. Rev. 178, 11 (1969).
[CrossRef]

Yariv, A.

J. Au Yeung, A. Yariv, “Spontaneous and Stimulated Raman Scattering in Long Low Loss Fibers,” IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

R. H. Stolen, E. P. Ippen, A. R. Tynes, “Raman Oscillation in Glass Optical Waveguides,” Appl. Phys. Lett. 20, 62 (1972).
[CrossRef]

Electron. Lett.

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

Y. Sasaki, Y. Ohmori, M. Kawachi, T. Edahiro, “CW Single-Pass Raman Generation in Optical Fibres,” Electron. Lett. 17, 315 (1981).
[CrossRef]

IEEE J. Quantum Electron.

J. Au Yeung, A. Yariv, “Spontaneous and Stimulated Raman Scattering in Long Low Loss Fibers,” IEEE J. Quantum Electron. QE-14, 347 (1978).
[CrossRef]

Phys. Rev.

M. M. von der Linde, W. Kaiser, “Quantitative Investigations of the Simulated Raman Effect Using Subnanosecond Light Pulses,” Phys. Rev. 178, 11 (1969).
[CrossRef]

Proc. IEE (J) Optoelectron.

W. P. Urquhart, P. J. R. Laybourn, “The Effective Core Area for Stimulated Raman Scattering in Single-Mode Optical Fibres,” Proc. IEE (J) Optoelectron. 132, 201 (1985).
[CrossRef]

Other

Numerical Algorithms Group (NAG): Fortran Library Mark 10 Implementation (1983) Routines D02BBF, D02BAF, and D01GAF used (NAG Central Office, Mayfield House, 256 Banbury Road, Oxford OY2 7DE, U.K.).

R. H. Stolen, “Fibre Raman Lasers,” in Fibre and Integrated Optics, D. B. Ostrowsky, ed. (Plenum, New York, 1979), pp. 157–182.
[CrossRef]

W. P. Urquhart, P. J. R. Laybourn, “Stimulated Raman Scattering in Optical Fibers with Nonconstant Losses: A Multiwavelength Model.” To be published in Appl. Opt. (Month 1986).
[PubMed]

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Figures (7)

Fig. 1
Fig. 1

Growth of the Stokes power and corresponding depletion of the pump power. Ratio of losses; Stokes to pump: (A) 1.0; (B) 20.0; (C) 30.0; (D) 40.0. Other data used in computations are in Table I.

Fig. 2
Fig. 2

Growth of the Stokes power and corresponding depletion of the pump power. Ratio of losses; Stokes to pump: (A) 1.0; (B) 0.6; (C) 0.4; (D) 0.2. Other data used in computations are in Table I.

Fig. 3
Fig. 3

Variation of the normalized power coupling parameter (1 − ) with respect to length. Ratio of losses; Stokes to pump: (A) 1.0; (B) 20.0; (C) 30.0; (D) 40.0. Other data used in computations are in Table I.

Fig. 4
Fig. 4

Variation of the total power in the fiber with respect to length. Ratio of losses; Stokes to pump: (A) 1.0; (B) 20.0; (C) 30.0; (D) 40.0. Other data used in computations are in Table I.

Fig. 5
Fig. 5

Comparison of the total power in the fiber with the pump power in the fiber for the case where the ratio of Stokes to pump loss is 40.0. The broken line is the total power calculated by the direct addition of the pump and Stokes power. Other data used in computations are in Table I.

Fig. 6
Fig. 6

Output pump and Stokes power as a function of the input pump power. The fiber length is a constant. Fiber length = 12,000 m. Ratio of losses; Stokes to pump: (A) 1.0; (B) 2.0; (C) 4.0; (D) 6.0. Other data used in computations are in Table I.

Fig. 7
Fig. 7

Dimensionless output pump and Stokes power as a function of the input pump power. The fiber parameters are the same as those of Fig. 6.

Tables (1)

Tables Icon

Table I Values of Constants for the Numerical Examples used Throughout a

Equations (44)

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p i = h c ν s i n e L .
d P l d z + α l P l = g 0 A P l ( P S + p q ) ;
d P S d z + α S P S = λ l λ S g 0 A P l ( P S + p q ) .
p = 1 q i = 1 q p s i .
P l ( z = 0 ) = P 0 ;
P s ( z = 0 ) = p q .
R l = P l / P 0 ,
R S = P S / P 0 .
Q = p q P 0 .
Z = z P 0 g 0 A ,
β l = α l A g 0 P 0 ,
β s = α s A g 0 P 0 .
Λ = λ l / λ S = ν S / ν l .
d R l d Z + β l R l = R l ( R S + Q ) ;
d R s d Z + β S R S = + Λ R l ( R S + Q ) .
R l ( Z = 0 ) = 1 ,
R S ( Z = 0 ) = Q .
0.9 < Λ < 1.0 ; 5 × 10 3 < β < 10 1 ; 10 9 < Q < 10 6 .
B eff = δ ν { π β 4 Λ [ 1 exp ( β Z ) ] } 1 / 2 δ ν π β 4 Λ .
q = ( n e L B eff ) / c .
Q = h ν S B eff P 0 .
d d Z ( Λ R l + R S ) + β l Λ R l + β S R S = 0.
γ ( Z ) = β l Λ R l + β S R S Λ R l + R S .
d d Z ( Λ R l + R S ) + γ ( Z ) ( Λ R l + R S ) = 0 ,
Λ R l + R S = Λ exp [ 0 Z γ ( Z ) d Z ] .
if β S > β l , then β l γ ( Z ) β S ,
if β S < β l , then β S γ ( Z ) β l ,
if β S = β l = β , then γ = β .
if β S > β l ; exp ( β l Z ) Λ R l + R S exp ( β S Z ) , if β l > β S ; exp ( β S Z ) Λ R l + R S exp ( β l Z ) .
γ ( 0 ) = Λ β l + Q β S Λ + Q β l
γ th = y R S β l + R S β S y R S + R S = y β l + β S y + 1 .
( Z ) = β S γ β S β l ,
1 = γ β l β S β l .
P l ( z ) P 0 exp ( α z ) / [ 1 + η ( P 0 ) ] ,
P S ( z ) Λ η ( P 0 exp ( α z ) / [ 1 + η ( P 0 ) ] ,
η ( P 0 ) = [ Q ( P 0 ) / Λ ] exp ( b P 0 ) .
b = λ l λ S g 0 α A [ 1 exp ( α z ) ] .
P l ( P 0 ) = P 0 exp ( α z ) 1 + Q Λ exp ( b P 0 ) .
P S ( P 0 ) = P 0 Q exp ( b P 0 ) exp ( α z ) 1 + ( Q / Λ ) exp ( b P 0 ) .
P l ( P 0 ) P 0 exp ( α z ) ,
P S ( P 0 ) 0.
P l ( P 0 ) 0 ,
P S ( P 0 ) Λ P 0 exp ( α z ) .
P S ( P 0 ) = Λ P 0 exp ( α S z ) .

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