Abstract

We report results on the appearance of temporally stable Stokes emission in stimulated Brillouin scattering (SBS) excited by continuous-wave pump radiation in optical fiber. With increasing pump strength the stable component emerges from stochastic emission slightly above the SBS threshold to become the dominant contribution, independent of fiber characteristics. These findings are shown to be a manifestation of spectral self-phase conjugation, providing what is to our knowledge the first experimental evidence of this phenomenon in optics.

© 2005 Optical Society of America

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  1. R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, Phys. Rev. Lett. 12, 592 (1964).
    [CrossRef]
  2. C. L. Tang, J. Appl. Phys. 37, 2945 (1966).
    [CrossRef]
  3. A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
    [CrossRef] [PubMed]
  4. V. I. Kovalev and R. G. Harrison, Phys. Rev. Lett. 85, 1879 (2000).
    [CrossRef] [PubMed]
  5. N. F. Andreev, V. I. Bespalov, A. M. Kiselev, A. M. Kubarev, and G. A. Pasmanik, Sov. J. Quantum Electron. 6, 1223 (1976).
    [CrossRef]
  6. V. I. Bespalov, E. L. Bubis, O. V. Kulagin, G. A. Pasmanik, and A. A. Shilov, Sov. J. Quantum Electron. 16, 1348 (1986).
    [CrossRef]
  7. E. P. Ippen and R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
    [CrossRef]
  8. I. Bar-Joseph, A. A. Friesem, E. Lichtman, and R. G. Waarts, J. Opt. Soc. Am. B 2, 1606 (1985).
    [CrossRef]
  9. E. M. Dianov, A. Ya. Karasik, A. V. Lutchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
    [CrossRef]
  10. R. G. Harrison, J. S. Uppal, A. Johnston, and J. V. Moloney, Phys. Rev. Lett. 65, 167 (1990).
    [CrossRef] [PubMed]
  11. M. Dammig, G. Zinner, F. Mitschke, and H. Welling, Phys. Rev. A 48, 3301 (1993).
    [CrossRef]
  12. A. A. Fotiadi and R. V. Kiyan, Opt. Lett. 23, 1805 (1998).
    [CrossRef]
  13. V. I. Kovalev, R. G. Harrison, and A. M. Scott, Opt. Commun. 185, 185 (2000).
    [CrossRef]
  14. V. I. Kovalev and R. G. Harrison, Opt. Lett. 27, 2022 (2002).
    [CrossRef]
  15. V. I. Kovalev and R. G. Harrison, Opt. Lett. 29, 379 (2004).
    [CrossRef] [PubMed]
  16. B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).
  17. B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).
    [CrossRef]
  18. I. Yu. Anikeev, I. G. Zubarev, and S. I. Mikhailov, Sov. Phys. JETP 57, 978 (1983).
  19. J. H. Marburger, Appl. Phys. Lett. 32, 372 (1978).
    [CrossRef]
  20. A. Yariv, D. Fekete, and D. M. Pepper, Opt. Lett. 4, 52 (1979).
    [CrossRef]
  21. A. L. Gaeta and R. W. Boyd, Int. J. Nonlinear Opt. Phys. 1, 581 (1992).
    [CrossRef]

2004

2002

2000

V. I. Kovalev and R. G. Harrison, Phys. Rev. Lett. 85, 1879 (2000).
[CrossRef] [PubMed]

V. I. Kovalev, R. G. Harrison, and A. M. Scott, Opt. Commun. 185, 185 (2000).
[CrossRef]

1998

1993

M. Dammig, G. Zinner, F. Mitschke, and H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

1992

A. L. Gaeta and R. W. Boyd, Int. J. Nonlinear Opt. Phys. 1, 581 (1992).
[CrossRef]

1991

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

1990

R. G. Harrison, J. S. Uppal, A. Johnston, and J. V. Moloney, Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

1989

E. M. Dianov, A. Ya. Karasik, A. V. Lutchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

1986

V. I. Bespalov, E. L. Bubis, O. V. Kulagin, G. A. Pasmanik, and A. A. Shilov, Sov. J. Quantum Electron. 16, 1348 (1986).
[CrossRef]

1985

1983

I. Yu. Anikeev, I. G. Zubarev, and S. I. Mikhailov, Sov. Phys. JETP 57, 978 (1983).

1979

1978

J. H. Marburger, Appl. Phys. Lett. 32, 372 (1978).
[CrossRef]

1976

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, A. M. Kubarev, and G. A. Pasmanik, Sov. J. Quantum Electron. 6, 1223 (1976).
[CrossRef]

1972

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

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

1966

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

1964

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, Phys. Rev. Lett. 12, 592 (1964).
[CrossRef]

Andreev, N. F.

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, A. M. Kubarev, and G. A. Pasmanik, Sov. J. Quantum Electron. 6, 1223 (1976).
[CrossRef]

Anikeev, I. Yu.

I. Yu. Anikeev, I. G. Zubarev, and S. I. Mikhailov, Sov. Phys. JETP 57, 978 (1983).

Bar-Joseph, I.

Bespalov, V. I.

V. I. Bespalov, E. L. Bubis, O. V. Kulagin, G. A. Pasmanik, and A. A. Shilov, Sov. J. Quantum Electron. 16, 1348 (1986).
[CrossRef]

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, A. M. Kubarev, and G. A. Pasmanik, Sov. J. Quantum Electron. 6, 1223 (1976).
[CrossRef]

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, Int. J. Nonlinear Opt. Phys. 1, 581 (1992).
[CrossRef]

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

Bubis, E. L.

V. I. Bespalov, E. L. Bubis, O. V. Kulagin, G. A. Pasmanik, and A. A. Shilov, Sov. J. Quantum Electron. 16, 1348 (1986).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, Phys. Rev. Lett. 12, 592 (1964).
[CrossRef]

Dammig, M.

M. Dammig, G. Zinner, F. Mitschke, and H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

Dianov, E. M.

E. M. Dianov, A. Ya. Karasik, A. V. Lutchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

Faizullov, F. S.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

Fekete, D.

Fotiadi, A. A.

Friesem, A. A.

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, Int. J. Nonlinear Opt. Phys. 1, 581 (1992).
[CrossRef]

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

Harrison, R. G.

V. I. Kovalev and R. G. Harrison, Opt. Lett. 29, 379 (2004).
[CrossRef] [PubMed]

V. I. Kovalev and R. G. Harrison, Opt. Lett. 27, 2022 (2002).
[CrossRef]

V. I. Kovalev, R. G. Harrison, and A. M. Scott, Opt. Commun. 185, 185 (2000).
[CrossRef]

V. I. Kovalev and R. G. Harrison, Phys. Rev. Lett. 85, 1879 (2000).
[CrossRef] [PubMed]

R. G. Harrison, J. S. Uppal, A. Johnston, and J. V. Moloney, Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

Ippen, E. P.

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

Johnston, A.

R. G. Harrison, J. S. Uppal, A. Johnston, and J. V. Moloney, Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

Karasik, A. Ya.

E. M. Dianov, A. Ya. Karasik, A. V. Lutchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

Kiselev, A. M.

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, A. M. Kubarev, and G. A. Pasmanik, Sov. J. Quantum Electron. 6, 1223 (1976).
[CrossRef]

Kiyan, R. V.

Kovalev, V. I.

V. I. Kovalev and R. G. Harrison, Opt. Lett. 29, 379 (2004).
[CrossRef] [PubMed]

V. I. Kovalev and R. G. Harrison, Opt. Lett. 27, 2022 (2002).
[CrossRef]

V. I. Kovalev, R. G. Harrison, and A. M. Scott, Opt. Commun. 185, 185 (2000).
[CrossRef]

V. I. Kovalev and R. G. Harrison, Phys. Rev. Lett. 85, 1879 (2000).
[CrossRef] [PubMed]

Kubarev, A. M.

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, A. M. Kubarev, and G. A. Pasmanik, Sov. J. Quantum Electron. 6, 1223 (1976).
[CrossRef]

Kulagin, O. V.

V. I. Bespalov, E. L. Bubis, O. V. Kulagin, G. A. Pasmanik, and A. A. Shilov, Sov. J. Quantum Electron. 16, 1348 (1986).
[CrossRef]

Lichtman, E.

Lutchnikov, A. V.

E. M. Dianov, A. Ya. Karasik, A. V. Lutchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

Marburger, J. H.

J. H. Marburger, Appl. Phys. Lett. 32, 372 (1978).
[CrossRef]

Mikhailov, S. I.

I. Yu. Anikeev, I. G. Zubarev, and S. I. Mikhailov, Sov. Phys. JETP 57, 978 (1983).

Mitschke, F.

M. Dammig, G. Zinner, F. Mitschke, and H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

Moloney, J. V.

R. G. Harrison, J. S. Uppal, A. Johnston, and J. V. Moloney, Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

Pasmanik, G. A.

V. I. Bespalov, E. L. Bubis, O. V. Kulagin, G. A. Pasmanik, and A. A. Shilov, Sov. J. Quantum Electron. 16, 1348 (1986).
[CrossRef]

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, A. M. Kubarev, and G. A. Pasmanik, Sov. J. Quantum Electron. 6, 1223 (1976).
[CrossRef]

Pepper, D. M.

Pilipetskii, A. N.

E. M. Dianov, A. Ya. Karasik, A. V. Lutchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).
[CrossRef]

Popovichev, V. I.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

Ragul’skii, V. V.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

Scott, A. M.

V. I. Kovalev, R. G. Harrison, and A. M. Scott, Opt. Commun. 185, 185 (2000).
[CrossRef]

Shilov, A. A.

V. I. Bespalov, E. L. Bubis, O. V. Kulagin, G. A. Pasmanik, and A. A. Shilov, Sov. J. Quantum Electron. 16, 1348 (1986).
[CrossRef]

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).
[CrossRef]

Stoicheff, B. P.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, Phys. Rev. Lett. 12, 592 (1964).
[CrossRef]

Stolen, R. H.

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

Tang, C. L.

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

Townes, C. H.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, Phys. Rev. Lett. 12, 592 (1964).
[CrossRef]

Uppal, J. S.

R. G. Harrison, J. S. Uppal, A. Johnston, and J. V. Moloney, Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

Waarts, R. G.

Welling, H.

M. Dammig, G. Zinner, F. Mitschke, and H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

Yariv, A.

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).
[CrossRef]

Zinner, G.

M. Dammig, G. Zinner, F. Mitschke, and H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

Zubarev, I. G.

I. Yu. Anikeev, I. G. Zubarev, and S. I. Mikhailov, Sov. Phys. JETP 57, 978 (1983).

Appl. Phys. Lett.

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

J. H. Marburger, Appl. Phys. Lett. 32, 372 (1978).
[CrossRef]

Int. J. Nonlinear Opt. Phys.

A. L. Gaeta and R. W. Boyd, Int. J. Nonlinear Opt. Phys. 1, 581 (1992).
[CrossRef]

J. Appl. Phys.

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

J. Opt. Soc. Am. B

JETP Lett.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

Opt. Commun.

V. I. Kovalev, R. G. Harrison, and A. M. Scott, Opt. Commun. 185, 185 (2000).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

E. M. Dianov, A. Ya. Karasik, A. V. Lutchnikov, and A. N. Pilipetskii, Opt. Quantum Electron. 21, 381 (1989).
[CrossRef]

Phys. Rev. A

M. Dammig, G. Zinner, F. Mitschke, and H. Welling, Phys. Rev. A 48, 3301 (1993).
[CrossRef]

A. L. Gaeta and R. W. Boyd, Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett.

V. I. Kovalev and R. G. Harrison, Phys. Rev. Lett. 85, 1879 (2000).
[CrossRef] [PubMed]

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, Phys. Rev. Lett. 12, 592 (1964).
[CrossRef]

R. G. Harrison, J. S. Uppal, A. Johnston, and J. V. Moloney, Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

Sov. J. Quantum Electron.

N. F. Andreev, V. I. Bespalov, A. M. Kiselev, A. M. Kubarev, and G. A. Pasmanik, Sov. J. Quantum Electron. 6, 1223 (1976).
[CrossRef]

V. I. Bespalov, E. L. Bubis, O. V. Kulagin, G. A. Pasmanik, and A. A. Shilov, Sov. J. Quantum Electron. 16, 1348 (1986).
[CrossRef]

Sov. Phys. JETP

I. Yu. Anikeev, I. G. Zubarev, and S. I. Mikhailov, Sov. Phys. JETP 57, 978 (1983).

Other

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, 1985).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Time recordings of the Stokes emission in two-mode fiber of 650 m length with d c = 9 μ m at (a) N = 1.1 , (b) N = 1.5 , (c) N = 2 , (d) N = 9 . The time scale is 2 μ s div . Traces (b)–(d) demonstrate the appearance and growth of a DC component that is temporally stable, on top of which an irregular spiking component rides.

Fig. 2
Fig. 2

Spiking + stable (solid symbols) and stable (open symbols) amplitudes of Stokes (solid lines) and transmitted pump (dashed lines) signals versus N for two single-mode fibers, one with NA = 0.24 and L 200 m and one with NA = 0.13 and L 100 m . As can be seen, the temporally stable Stokes component and the spiking component in the pump both appear above the SBS threshold, at N 1.2 .

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

E p = 1 2 { E p 0 exp [ i ( ω p 0 t k p 0 z ) ] + E p 1 exp [ i ( ω p 1 t k p 1 z ) ] + c.c. } ,
E S = 1 2 { E S 0 exp [ i ( ω S 0 t + k S 0 z ) ] + E S 1 exp [ i ( ω S 1 t + k S 1 z ) ] + c.c. }
d E S 0 d z = g 2 [ ( E p 0 2 + 1 i δ 1 + δ 2 E p 1 2 ) E S 0 + 1 i δ 1 + δ 2 E p 1 E p 0 * E S 1 exp ( i 2 Δ k z ) ] ,
d E S 1 d z = g 2 [ ( 1 i δ 1 + δ 2 E p 0 2 + 1 i 2 δ 1 + 4 δ 2 E p 1 2 ) E S 1 + 1 i δ 1 + δ 2 E p 0 E p 1 * E S 0 exp ( i 2 Δ k z ) ] ,
E S 0 ( 0 ) = E S 0 ( L ) e G + g L 2 γ E p 1 E p 0 * E S 1 ( 0 ) ( L ) ,
E S 1 ( 0 ) = E S 1 ( L ) exp ( G 1 + δ 2 ) exp ( i G δ 1 + δ 2 ) + g L 2 γ E p 0 E p 1 * E S 0 ( 0 ) ( L ) ,
γ = ( 1 i δ ) ( 1 + δ 2 ) 1 exp [ ( a + i b ) ( 1 z L ) ] a + i b exp [ G ( 1 z L ) ] ,
a = G δ 2 ( 1 + δ 2 ) , b = G δ ( 1 + δ 2 ) + 2 Δ k L ,

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