Abstract

The nonlinear phase change accompanying the gain induced by stimulated Brillouin scattering is investigated in single-mode fiber. A frequency-modulated signal, when counterpropagated by a strong pump wave, is converted to an amplitude-modulated signal owing to this nonlinear phase change. The measured amplitude modulation is in good agreement with the theoretical predictions. It is at its maximum for a frequency difference between the pump and signal waves that corresponds to the Brillouin Stokes shift ±0.5 full width at half-maximum of the Brillouin-gain bandwidth (90 MHz at λ = 820 nm). This conversion may lead to distortion in coherent transmission systems and Brillouin amplifiers.

© 1988 Optical Society of America

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References

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  1. D. Cotter, J. Opt. Commun. 1, 10 (1983).
  2. R. G. Waarts, R. P. Braun, Electron. Lett. 21, 1114 (1985).
    [CrossRef]
  3. N. A. Olsson, J. P. van der Ziel, Appl. Phys. Lett. 48, 1329 (1986).
    [CrossRef]
  4. C. G. Atkins, D. Cotter, D. W. Smith, R. Wyatt, Electron. Lett. 22, 556 (1986).
    [CrossRef]
  5. D. Cotter, D. W. Smith, C. G. Atkins, R. Wyatt, Electron. Lett. 22, 671 (1986).
    [CrossRef]
  6. K. O. Hill, D. C. Johnson, B. S. Kawasaki, R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
    [CrossRef]
  7. S. Kabyashi, Y. Yamamoto, T. Kimura, Electron. Lett. 17, 350 (1981).
    [CrossRef]
  8. R. W. Tkach, A. R Chraplyvy, R. M. Derosier, Electron. Lett. 22, 1011 (1986).
    [CrossRef]
  9. N. Shibata, R. G. Waarts, R. P. Braun, Opt. Lett. 21, 269 (1987).
    [CrossRef]

1987 (1)

1986 (4)

N. A. Olsson, J. P. van der Ziel, Appl. Phys. Lett. 48, 1329 (1986).
[CrossRef]

C. G. Atkins, D. Cotter, D. W. Smith, R. Wyatt, Electron. Lett. 22, 556 (1986).
[CrossRef]

D. Cotter, D. W. Smith, C. G. Atkins, R. Wyatt, Electron. Lett. 22, 671 (1986).
[CrossRef]

R. W. Tkach, A. R Chraplyvy, R. M. Derosier, Electron. Lett. 22, 1011 (1986).
[CrossRef]

1985 (1)

R. G. Waarts, R. P. Braun, Electron. Lett. 21, 1114 (1985).
[CrossRef]

1983 (1)

D. Cotter, J. Opt. Commun. 1, 10 (1983).

1981 (1)

S. Kabyashi, Y. Yamamoto, T. Kimura, Electron. Lett. 17, 350 (1981).
[CrossRef]

1978 (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

Atkins, C. G.

C. G. Atkins, D. Cotter, D. W. Smith, R. Wyatt, Electron. Lett. 22, 556 (1986).
[CrossRef]

D. Cotter, D. W. Smith, C. G. Atkins, R. Wyatt, Electron. Lett. 22, 671 (1986).
[CrossRef]

Braun, R. P.

N. Shibata, R. G. Waarts, R. P. Braun, Opt. Lett. 21, 269 (1987).
[CrossRef]

R. G. Waarts, R. P. Braun, Electron. Lett. 21, 1114 (1985).
[CrossRef]

Chraplyvy, A. R

R. W. Tkach, A. R Chraplyvy, R. M. Derosier, Electron. Lett. 22, 1011 (1986).
[CrossRef]

Cotter, D.

C. G. Atkins, D. Cotter, D. W. Smith, R. Wyatt, Electron. Lett. 22, 556 (1986).
[CrossRef]

D. Cotter, D. W. Smith, C. G. Atkins, R. Wyatt, Electron. Lett. 22, 671 (1986).
[CrossRef]

D. Cotter, J. Opt. Commun. 1, 10 (1983).

Derosier, R. M.

R. W. Tkach, A. R Chraplyvy, R. M. Derosier, Electron. Lett. 22, 1011 (1986).
[CrossRef]

Hill, K. O.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

Johnson, D. C.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

Kabyashi, S.

S. Kabyashi, Y. Yamamoto, T. Kimura, Electron. Lett. 17, 350 (1981).
[CrossRef]

Kawasaki, B. S.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

Kimura, T.

S. Kabyashi, Y. Yamamoto, T. Kimura, Electron. Lett. 17, 350 (1981).
[CrossRef]

MacDonald, R. I.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

Olsson, N. A.

N. A. Olsson, J. P. van der Ziel, Appl. Phys. Lett. 48, 1329 (1986).
[CrossRef]

Shibata, N.

Smith, D. W.

C. G. Atkins, D. Cotter, D. W. Smith, R. Wyatt, Electron. Lett. 22, 556 (1986).
[CrossRef]

D. Cotter, D. W. Smith, C. G. Atkins, R. Wyatt, Electron. Lett. 22, 671 (1986).
[CrossRef]

Tkach, R. W.

R. W. Tkach, A. R Chraplyvy, R. M. Derosier, Electron. Lett. 22, 1011 (1986).
[CrossRef]

van der Ziel, J. P.

N. A. Olsson, J. P. van der Ziel, Appl. Phys. Lett. 48, 1329 (1986).
[CrossRef]

Waarts, R. G.

N. Shibata, R. G. Waarts, R. P. Braun, Opt. Lett. 21, 269 (1987).
[CrossRef]

R. G. Waarts, R. P. Braun, Electron. Lett. 21, 1114 (1985).
[CrossRef]

Wyatt, R.

C. G. Atkins, D. Cotter, D. W. Smith, R. Wyatt, Electron. Lett. 22, 556 (1986).
[CrossRef]

D. Cotter, D. W. Smith, C. G. Atkins, R. Wyatt, Electron. Lett. 22, 671 (1986).
[CrossRef]

Yamamoto, Y.

S. Kabyashi, Y. Yamamoto, T. Kimura, Electron. Lett. 17, 350 (1981).
[CrossRef]

Appl. Phys. Lett. (1)

N. A. Olsson, J. P. van der Ziel, Appl. Phys. Lett. 48, 1329 (1986).
[CrossRef]

Electron. Lett. (5)

C. G. Atkins, D. Cotter, D. W. Smith, R. Wyatt, Electron. Lett. 22, 556 (1986).
[CrossRef]

D. Cotter, D. W. Smith, C. G. Atkins, R. Wyatt, Electron. Lett. 22, 671 (1986).
[CrossRef]

R. G. Waarts, R. P. Braun, Electron. Lett. 21, 1114 (1985).
[CrossRef]

S. Kabyashi, Y. Yamamoto, T. Kimura, Electron. Lett. 17, 350 (1981).
[CrossRef]

R. W. Tkach, A. R Chraplyvy, R. M. Derosier, Electron. Lett. 22, 1011 (1986).
[CrossRef]

J. Appl. Phys. (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

J. Opt. Commun. (1)

D. Cotter, J. Opt. Commun. 1, 10 (1983).

Opt. Lett. (1)

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. The crossing of the fibers is a directional coupler (3 dB).

Fig. 2
Fig. 2

A, Experimental results of the Brillouin gain as a function of the detuning from the maximum Brillouin gain for the carrier wave, Δν0 = νPνsνa (output from lock-in amplifier 1). B, Experimental results for the detected AM signal as a function of the detuning Δν0 (signal from lock-in amplifier 2).

Fig. 3
Fig. 3

A, Computer simulation of the AM signal as a function of the detuning Δν0 according to relation (8). B, AM signal calculated from the full solution, Eq. (3), after convolution with the laser linewidth.

Equations (8)

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s ( z ) = E s ( z ) exp ( i 2 π ν s t i k s z α 2 z ) ,
˜ s ( 0 ) = s ( 0 ) exp [ i β sin ( 2 π ν m t ) ] = s ( 0 ) n = J n ( β ) exp ( i 2 π n ν m t ) ,
˜ s ( L ) = n = s ( L ) J n ( β ) exp [ ( g n + i n 2 π ν m t + i ϕ n ) ] .
g n = 1 2 ( G 0 L eff Δ ν b 2 4 Δ ν n 2 + Δ ν b 2 )
ϕ n = G 0 L eff Δ ν b Δ ν n 4 Δ ν n 2 + Δ ν b 2 + ϕ n ,
ϕ n = ( k ν n ν + 2 k ν 2 n 2 ν 2 ) L .
G 0 = 2 π n 7 p 12 2 γ c λ 2 ρ 0 υ a Δ ν b P p A eff ,
i ( t ) A 0 2 + A 1 2 + A 1 2 + A 0 [ A 1 2 + A 1 2 + 2 A 1 A 1 × cos ( 2 ϕ 0 ϕ 1 ϕ 1 ) ] 1 / 2 cos ( 2 π ν m t + ψ ) .

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