Abstract

We report stochastic, spatiotemporal dynamics in stimulated Brillouin scattering from single-mode pump pulses propagating through a fiber that supports LP01 and LP11 modes. Comparison with experiments in single-mode fiber indicates that independent scattering from different modes plays a key role. We also investigate the role of transverse pump fluctuations in driving the observed spatiotemporal intensity dynamics in the scattered beam.

© 2013 Optical Society of America

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References

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  1. J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. 62, 1274–1277 (1989).
    [CrossRef]
  2. C. Gouedard, D. Husson, C. Sauteret, F. Auzel, and A. Migus, “Generation of spatially incoherent short pulses in laser-pumped neodymium stoichiometric crystals and powders,” J. Opt. Soc. Am. B 10, 2358–2363 (1993).
    [CrossRef]
  3. G. Anstett, M. Nittmann, A. Borsutzky, and R. Wallenstein, “Experimental investigation and numerical simulation of the spatiotemporal dynamics of nanosecond pulses in Q-switched Nd:YAG lasers,” Appl. Phys. B 76, 833–838 (2003).
    [CrossRef]
  4. H.-C. Liang, Y.-C. Lee, J.-C. Tung, K.-W. Su, K.-F. Huang, and Y.-F. Chen, “Exploring the spatio-temporal dynamics of an optically pumped semiconductor laser with intracavity second harmonic generation,” Opt. Lett. 37, 4609–4611 (2012).
    [CrossRef]
  5. S. Randel, R. Ryf, A. Sierrra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R.-J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle, “6×56 Gb/s mode-division multiplexed transmission over 33 km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19, 16697–16707 (2011).
    [CrossRef]
  6. A. A. Amin, A. Li, S. Chen, X. Chen, G. Gao, and W. Shieh, “Dual-LP11 mode 4×4 MIMO-OFDM transmission over a two-mode fiber,” Opt. Express 19, 16672–16678 (2011).
    [CrossRef]
  7. F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36, 4572–4574 (2011).
    [CrossRef]
  8. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, “Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers,” Opt. Express 20, 15710–15722 (2012).
    [CrossRef]
  9. E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Phase conjugation by SMBS in optical fibers,” in Optical Phase Conjugation, M. Gower and D. Proch, eds. (Springer-Verlag, 1994), pp. 75–96.
  10. M. P. Petrov and E. A. Kuzin, “Stimulated Brillouin scattering and phase conjugation in optical fibers,” Sov. Tech. Phys. Lett. 8, 316–317 (1982).
  11. E. A. Kuzin, M. P. Petrov, and B. E. Davydenko, “Phase conjugation in an optical fiber,” Opt. Quantum Electron. 17, 393–397 (1985).
    [CrossRef]
  12. A. Heuer and R. Menzel, “Phase-conjugating stimulated Brillouin scattering mirror for low powers and reflectivities above 90% in an internally tapered optical fiber,” Opt. Lett. 23, 834–836 (1998).
    [CrossRef]
  13. H. J. Eichler, A. Mocofanescu, Th. Riesbeck, E. Risse, and D. Bedau, “Stimulated Brillouin scattering in multimode fibers for optical phase conjugation,” Opt. Commun. 208, 427–431 (2002).
    [CrossRef]
  14. P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1998).
  15. V. I. Bespalov, A. A. Betin, G. A. Pasmanik, and A. A. Shilov, “Observation of transient field oscillations in the radiation of stimulated Mandel’shtam–Brillouin scattering,” JETP Lett. 31, 630–633 (1980).
  16. D. S. Lim, W. Lu, and R. G. Harrison, “Evidence of phase singularities and dynamic patterns in stimulated Brillouin scattering,” Opt. Commun. 113, 471–475 (1995).
    [CrossRef]
  17. W. Potter and J. Thompson, “Stochastic spatiotemporal dynamics of stimulated Brillouin scattering in an optical fiber,” in CLEO: Science and Innovations (Optical Society of America, 2012), paper JW4A.26.
  18. A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
    [CrossRef]
  19. J. Correa, E. Manzano, R. Tracy, and J. R. Thompson, “Correlations between intensity fluctuations within stimulated Brillouin waveforms generated by scattering of Q-switched pulses in optical fiber,” Opt. Commun. 242, 267–278 (2004).
    [CrossRef]
  20. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).
  21. D. C. Montgomery and G. C. Runger, Applied Statistics and Probability for Engineers (Wiley, 1994).
  22. F. Heslot, B. Castaing, and A. Libchaber, “Transitions to turbulence in helium gas,” Phys. Rev. A 36, 5870–5873 (1987).
    [CrossRef]
  23. J. A. Buck, Fundamentals of Optical Fibers (Wiley, 2004).

2012

2011

2004

J. Correa, E. Manzano, R. Tracy, and J. R. Thompson, “Correlations between intensity fluctuations within stimulated Brillouin waveforms generated by scattering of Q-switched pulses in optical fiber,” Opt. Commun. 242, 267–278 (2004).
[CrossRef]

2003

G. Anstett, M. Nittmann, A. Borsutzky, and R. Wallenstein, “Experimental investigation and numerical simulation of the spatiotemporal dynamics of nanosecond pulses in Q-switched Nd:YAG lasers,” Appl. Phys. B 76, 833–838 (2003).
[CrossRef]

2002

H. J. Eichler, A. Mocofanescu, Th. Riesbeck, E. Risse, and D. Bedau, “Stimulated Brillouin scattering in multimode fibers for optical phase conjugation,” Opt. Commun. 208, 427–431 (2002).
[CrossRef]

1998

1995

D. S. Lim, W. Lu, and R. G. Harrison, “Evidence of phase singularities and dynamic patterns in stimulated Brillouin scattering,” Opt. Commun. 113, 471–475 (1995).
[CrossRef]

1993

1991

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef]

1989

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. 62, 1274–1277 (1989).
[CrossRef]

1987

F. Heslot, B. Castaing, and A. Libchaber, “Transitions to turbulence in helium gas,” Phys. Rev. A 36, 5870–5873 (1987).
[CrossRef]

1985

E. A. Kuzin, M. P. Petrov, and B. E. Davydenko, “Phase conjugation in an optical fiber,” Opt. Quantum Electron. 17, 393–397 (1985).
[CrossRef]

1982

M. P. Petrov and E. A. Kuzin, “Stimulated Brillouin scattering and phase conjugation in optical fibers,” Sov. Tech. Phys. Lett. 8, 316–317 (1982).

1980

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, and A. A. Shilov, “Observation of transient field oscillations in the radiation of stimulated Mandel’shtam–Brillouin scattering,” JETP Lett. 31, 630–633 (1980).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).

Amin, A. A.

Anstett, G.

G. Anstett, M. Nittmann, A. Borsutzky, and R. Wallenstein, “Experimental investigation and numerical simulation of the spatiotemporal dynamics of nanosecond pulses in Q-switched Nd:YAG lasers,” Appl. Phys. B 76, 833–838 (2003).
[CrossRef]

Auzel, F.

Bedau, D.

H. J. Eichler, A. Mocofanescu, Th. Riesbeck, E. Risse, and D. Bedau, “Stimulated Brillouin scattering in multimode fibers for optical phase conjugation,” Opt. Commun. 208, 427–431 (2002).
[CrossRef]

Bespalov, V. I.

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, and A. A. Shilov, “Observation of transient field oscillations in the radiation of stimulated Mandel’shtam–Brillouin scattering,” JETP Lett. 31, 630–633 (1980).

Betin, A. A.

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, and A. A. Shilov, “Observation of transient field oscillations in the radiation of stimulated Mandel’shtam–Brillouin scattering,” JETP Lett. 31, 630–633 (1980).

Bolle, C. A.

Borsutzky, A.

G. Anstett, M. Nittmann, A. Borsutzky, and R. Wallenstein, “Experimental investigation and numerical simulation of the spatiotemporal dynamics of nanosecond pulses in Q-switched Nd:YAG lasers,” Appl. Phys. B 76, 833–838 (2003).
[CrossRef]

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef]

Buck, J. A.

J. A. Buck, Fundamentals of Optical Fibers (Wiley, 2004).

Castaing, B.

F. Heslot, B. Castaing, and A. Libchaber, “Transitions to turbulence in helium gas,” Phys. Rev. A 36, 5870–5873 (1987).
[CrossRef]

Chen, S.

Chen, X.

Chen, Y.-F.

Correa, J.

J. Correa, E. Manzano, R. Tracy, and J. R. Thompson, “Correlations between intensity fluctuations within stimulated Brillouin waveforms generated by scattering of Q-switched pulses in optical fiber,” Opt. Commun. 242, 267–278 (2004).
[CrossRef]

Davydenko, B. E.

E. A. Kuzin, M. P. Petrov, and B. E. Davydenko, “Phase conjugation in an optical fiber,” Opt. Quantum Electron. 17, 393–397 (1985).
[CrossRef]

Eberly, J. H.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1998).

Eichler, H. J.

H. J. Eichler, A. Mocofanescu, Th. Riesbeck, E. Risse, and D. Bedau, “Stimulated Brillouin scattering in multimode fibers for optical phase conjugation,” Opt. Commun. 208, 427–431 (2002).
[CrossRef]

Eidam, T.

Essiambre, R.-J.

Fotiadi, A. A.

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Phase conjugation by SMBS in optical fibers,” in Optical Phase Conjugation, M. Gower and D. Proch, eds. (Springer-Verlag, 1994), pp. 75–96.

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef]

Gaida, C.

Gao, G.

Ghazzawi, A. M.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. 62, 1274–1277 (1989).
[CrossRef]

Gnauck, A. H.

Gouedard, C.

Green, C.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. 62, 1274–1277 (1989).
[CrossRef]

Harrison, R. G.

D. S. Lim, W. Lu, and R. G. Harrison, “Evidence of phase singularities and dynamic patterns in stimulated Brillouin scattering,” Opt. Commun. 113, 471–475 (1995).
[CrossRef]

Heslot, F.

F. Heslot, B. Castaing, and A. Libchaber, “Transitions to turbulence in helium gas,” Phys. Rev. A 36, 5870–5873 (1987).
[CrossRef]

Heuer, A.

Huang, K.-F.

Husson, D.

Jansen, F.

Jauregui, C.

Kuzin, E. A.

E. A. Kuzin, M. P. Petrov, and B. E. Davydenko, “Phase conjugation in an optical fiber,” Opt. Quantum Electron. 17, 393–397 (1985).
[CrossRef]

M. P. Petrov and E. A. Kuzin, “Stimulated Brillouin scattering and phase conjugation in optical fibers,” Sov. Tech. Phys. Lett. 8, 316–317 (1982).

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Phase conjugation by SMBS in optical fibers,” in Optical Phase Conjugation, M. Gower and D. Proch, eds. (Springer-Verlag, 1994), pp. 75–96.

Lee, Y.-C.

Li, A.

Liang, H.-C.

Libchaber, A.

F. Heslot, B. Castaing, and A. Libchaber, “Transitions to turbulence in helium gas,” Phys. Rev. A 36, 5870–5873 (1987).
[CrossRef]

Lim, D. S.

D. S. Lim, W. Lu, and R. G. Harrison, “Evidence of phase singularities and dynamic patterns in stimulated Brillouin scattering,” Opt. Commun. 113, 471–475 (1995).
[CrossRef]

Limpert, J.

Lingle, R.

Lu, W.

D. S. Lim, W. Lu, and R. G. Harrison, “Evidence of phase singularities and dynamic patterns in stimulated Brillouin scattering,” Opt. Commun. 113, 471–475 (1995).
[CrossRef]

Lugiato, L. A.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. 62, 1274–1277 (1989).
[CrossRef]

Manzano, E.

J. Correa, E. Manzano, R. Tracy, and J. R. Thompson, “Correlations between intensity fluctuations within stimulated Brillouin waveforms generated by scattering of Q-switched pulses in optical fiber,” Opt. Commun. 242, 267–278 (2004).
[CrossRef]

McCurdy, A.

Menzel, R.

Migus, A.

Milonni, P. W.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1998).

Mocofanescu, A.

H. J. Eichler, A. Mocofanescu, Th. Riesbeck, E. Risse, and D. Bedau, “Stimulated Brillouin scattering in multimode fibers for optical phase conjugation,” Opt. Commun. 208, 427–431 (2002).
[CrossRef]

Montgomery, D. C.

D. C. Montgomery and G. C. Runger, Applied Statistics and Probability for Engineers (Wiley, 1994).

Narducci, L. M.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. 62, 1274–1277 (1989).
[CrossRef]

Nittmann, M.

G. Anstett, M. Nittmann, A. Borsutzky, and R. Wallenstein, “Experimental investigation and numerical simulation of the spatiotemporal dynamics of nanosecond pulses in Q-switched Nd:YAG lasers,” Appl. Phys. B 76, 833–838 (2003).
[CrossRef]

Otto, H.-J.

Pasmanik, G. A.

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, and A. A. Shilov, “Observation of transient field oscillations in the radiation of stimulated Mandel’shtam–Brillouin scattering,” JETP Lett. 31, 630–633 (1980).

Peckham, D. W.

Pernigo, M. A.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. 62, 1274–1277 (1989).
[CrossRef]

Petrov, M. P.

E. A. Kuzin, M. P. Petrov, and B. E. Davydenko, “Phase conjugation in an optical fiber,” Opt. Quantum Electron. 17, 393–397 (1985).
[CrossRef]

M. P. Petrov and E. A. Kuzin, “Stimulated Brillouin scattering and phase conjugation in optical fibers,” Sov. Tech. Phys. Lett. 8, 316–317 (1982).

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Phase conjugation by SMBS in optical fibers,” in Optical Phase Conjugation, M. Gower and D. Proch, eds. (Springer-Verlag, 1994), pp. 75–96.

Potter, W.

W. Potter and J. Thompson, “Stochastic spatiotemporal dynamics of stimulated Brillouin scattering in an optical fiber,” in CLEO: Science and Innovations (Optical Society of America, 2012), paper JW4A.26.

Quel, E. J.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. 62, 1274–1277 (1989).
[CrossRef]

Randel, S.

Riesbeck, Th.

H. J. Eichler, A. Mocofanescu, Th. Riesbeck, E. Risse, and D. Bedau, “Stimulated Brillouin scattering in multimode fibers for optical phase conjugation,” Opt. Commun. 208, 427–431 (2002).
[CrossRef]

Risse, E.

H. J. Eichler, A. Mocofanescu, Th. Riesbeck, E. Risse, and D. Bedau, “Stimulated Brillouin scattering in multimode fibers for optical phase conjugation,” Opt. Commun. 208, 427–431 (2002).
[CrossRef]

Runger, G. C.

D. C. Montgomery and G. C. Runger, Applied Statistics and Probability for Engineers (Wiley, 1994).

Ryf, R.

Sauteret, C.

Shieh, W.

Shilov, A. A.

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, and A. A. Shilov, “Observation of transient field oscillations in the radiation of stimulated Mandel’shtam–Brillouin scattering,” JETP Lett. 31, 630–633 (1980).

Sierrra, A.

Stutzki, F.

Su, K.-W.

Thompson, J.

W. Potter and J. Thompson, “Stochastic spatiotemporal dynamics of stimulated Brillouin scattering in an optical fiber,” in CLEO: Science and Innovations (Optical Society of America, 2012), paper JW4A.26.

Thompson, J. R.

J. Correa, E. Manzano, R. Tracy, and J. R. Thompson, “Correlations between intensity fluctuations within stimulated Brillouin waveforms generated by scattering of Q-switched pulses in optical fiber,” Opt. Commun. 242, 267–278 (2004).
[CrossRef]

Tracy, R.

J. Correa, E. Manzano, R. Tracy, and J. R. Thompson, “Correlations between intensity fluctuations within stimulated Brillouin waveforms generated by scattering of Q-switched pulses in optical fiber,” Opt. Commun. 242, 267–278 (2004).
[CrossRef]

Tredicce, J. R.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. 62, 1274–1277 (1989).
[CrossRef]

Tung, J.-C.

Tünnermann, A.

Wallenstein, R.

G. Anstett, M. Nittmann, A. Borsutzky, and R. Wallenstein, “Experimental investigation and numerical simulation of the spatiotemporal dynamics of nanosecond pulses in Q-switched Nd:YAG lasers,” Appl. Phys. B 76, 833–838 (2003).
[CrossRef]

Winzer, P. J.

Appl. Phys. B

G. Anstett, M. Nittmann, A. Borsutzky, and R. Wallenstein, “Experimental investigation and numerical simulation of the spatiotemporal dynamics of nanosecond pulses in Q-switched Nd:YAG lasers,” Appl. Phys. B 76, 833–838 (2003).
[CrossRef]

J. Opt. Soc. Am. B

JETP Lett.

V. I. Bespalov, A. A. Betin, G. A. Pasmanik, and A. A. Shilov, “Observation of transient field oscillations in the radiation of stimulated Mandel’shtam–Brillouin scattering,” JETP Lett. 31, 630–633 (1980).

Opt. Commun.

D. S. Lim, W. Lu, and R. G. Harrison, “Evidence of phase singularities and dynamic patterns in stimulated Brillouin scattering,” Opt. Commun. 113, 471–475 (1995).
[CrossRef]

H. J. Eichler, A. Mocofanescu, Th. Riesbeck, E. Risse, and D. Bedau, “Stimulated Brillouin scattering in multimode fibers for optical phase conjugation,” Opt. Commun. 208, 427–431 (2002).
[CrossRef]

J. Correa, E. Manzano, R. Tracy, and J. R. Thompson, “Correlations between intensity fluctuations within stimulated Brillouin waveforms generated by scattering of Q-switched pulses in optical fiber,” Opt. Commun. 242, 267–278 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

E. A. Kuzin, M. P. Petrov, and B. E. Davydenko, “Phase conjugation in an optical fiber,” Opt. Quantum Electron. 17, 393–397 (1985).
[CrossRef]

Phys. Rev. A

A. L. Gaeta and R. W. Boyd, “Stochastic dynamics of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[CrossRef]

F. Heslot, B. Castaing, and A. Libchaber, “Transitions to turbulence in helium gas,” Phys. Rev. A 36, 5870–5873 (1987).
[CrossRef]

Phys. Rev. Lett.

J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. 62, 1274–1277 (1989).
[CrossRef]

Sov. Tech. Phys. Lett.

M. P. Petrov and E. A. Kuzin, “Stimulated Brillouin scattering and phase conjugation in optical fibers,” Sov. Tech. Phys. Lett. 8, 316–317 (1982).

Other

E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Phase conjugation by SMBS in optical fibers,” in Optical Phase Conjugation, M. Gower and D. Proch, eds. (Springer-Verlag, 1994), pp. 75–96.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1998).

W. Potter and J. Thompson, “Stochastic spatiotemporal dynamics of stimulated Brillouin scattering in an optical fiber,” in CLEO: Science and Innovations (Optical Society of America, 2012), paper JW4A.26.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).

D. C. Montgomery and G. C. Runger, Applied Statistics and Probability for Engineers (Wiley, 1994).

J. A. Buck, Fundamentals of Optical Fibers (Wiley, 2004).

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Figures (12)

Fig. 1.
Fig. 1.

Diagram of two-point intensity correlation apparatus: BSC, beam-splitter cube; OBJ, microscope objective; AP, aperture; NDF, neutral density filter; VNDF, variable NDF; FPD, fast photodiode.

Fig. 2.
Fig. 2.

Ensemble-averaged two-point intensity correlation coefficient versus aperture separation for SBS in multimode fiber with bending losses in the horizontal plane. Input pump peak power is 87 W in frames (a) and (b).

Fig. 3.
Fig. 3.

Correlation coefficient time series for individual SBS waveform pairs for a vertical aperture separation of 2.5 mm. This time series corresponds to the minimum average correlation in Fig. 2(b).

Fig. 4.
Fig. 4.

Sample SBS waveform pairs with the minimum correlation coefficients from different sections of the ensemble of 1000 shown in Fig. 3. One waveform is represented by a heavier line for ease of distinguishing the waveforms in the two arms of the correlation apparatus. Waveform pair from (a) first 250 scattering events, (b) second 250, (c) third 250, and (d) final 250.

Fig. 5.
Fig. 5.

Ensemble-averaged two-point pulse energy correlation coefficient versus aperture separation for the input pump pulses. Note the significant decorrelation between transverse points of the pump pulses for vertical aperture displacements in frame (b).

Fig. 6.
Fig. 6.

Ensemble-averaged two-point intensity correlation coefficient versus aperture separation for SBS in multimode fiber with bending losses in the vertical plane. Input pump peak power is 90 W in frame (a) and 94 W in frame (b). Note the contrast with Fig. 2, particularly for vertical aperture displacements.

Fig. 7.
Fig. 7.

Correlation coefficient time series for individual SBS waveform pairs for the maximum vertical aperture separation in Fig. 6. Note the smaller range of correlation fluctuations when the bending losses are rotated to the vertical plane.

Fig. 8.
Fig. 8.

Ensemble-averaged two-point intensity correlation coefficient versus aperture separation for SBS in single-mode fiber. Input pump peak power is 29 W in frame (a) and 32 W in frame (b). Note the contrast with Fig. 2.

Fig. 9.
Fig. 9.

Correlation coefficient time series for individual SBS waveform pairs for the maximum vertical aperture separation in Fig. 8. In stark contrast to Fig. 3 and 7, there is virtually no variation in the intensity correlation from shot-to-shot.

Fig. 10.
Fig. 10.

Sample SBS waveform pairs with the minimum correlation coefficients from different sections of the ensemble of 1000 shown in Fig. 9. Waveform pair from (a) first 250 scattering events, (b) second 250, (c) third 250, and (d) final 250. Note the stark contrast with the waveform pairs in Fig. 4.

Fig. 11.
Fig. 11.

Persistence plots of the ensemble of 1000 waveform pairs in Fig. 3 for SBS in multimode fiber. Note the distinct structure of the ensembles from the two channels of the intensity correlation apparatus and the well-defined two-peaked structure of frame (b).

Fig. 12.
Fig. 12.

Persistence plots of the ensemble of 1000 waveform pairs in Fig. 9 for SBS in single-mode fiber. The ensembles from both channels have identical structure and only one intensity peak.

Equations (1)

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C12=(I1(t)I1(t))(I2(t)I2(t))σ1σ2,

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