Abstract

Continuous wave (CW) stimulated Brillouin scattering (SBS) phase conjugation in step-index optical fibers was studied experimentally and modeled as a function of fiber length. A phase conjugate fidelity over 80% was measured from SBS in a 40 m fiber using a pinhole technique. Fidelity decreases with fiber length, and a fiber with a numerical aperture (NA) of 0.06 was found to generate good phase conjugation fidelity over longer lengths than a fiber with 0.13 NA. Modeling and experiment support previous work showing the maximum interaction length which yields a high fidelity phase conjugate beam is inversely proportional to the fiber NA2, but find that fidelity remains high over much longer fiber lengths than previous models calculated. Conditions for SBS beam cleanup in step-index fibers are discussed.

©2008 Optical Society of America

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References

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  1. E. A. Kuzin, M. P. Petrov, and B. E. Davydenko, “Phase conjugation in an optical fibre,” Opt. Quantum Electron. 17, 393–397 (1985).
    [Crossref]
  2. Y. P. Vasil’ev, P. S. Razenshtein, and E. I. Shklovskii, “Stimulated Brillouin scattering mirror in the form of a multimode optical fiber in a four-pass neodymium phosphate glass laser amplifier,” Quantum Electron. 15, 1417–1418 (1985).
    [Crossref]
  3. A. Heuer, C. Hänisch, and R. Menzel, “Low-power phase conjugation based on stimulated Brillouin scattering in fiber amplifiers,” Opt. Lett. 28, 34–36 (2003).
    [Crossref] [PubMed]
  4. H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
    [Crossref]
  5. V. I. Kovalev and R. G. Harrison, “Continuous wave stimulated Brillouin scattering in optical fibers: new results and applications for high power lasers,” Proceedings of SPIE 5975, 59750L (2006).
    [Crossref]
  6. A. Mocofanescu and K. D. Shaw, “Stimulated Brillouin scattering phase conjugating properties of long multimode optical fibers,” Opt. Commun. 266, 307–316 (2006).
    [Crossref]
  7. L. Lombard, A. Brignon, J. P. Huignard, E. Lallier, and P. Georges, “Beam cleanup in a self-aligned gradient-index Brillouin cavity for high-power multimode fiber amplifiers,” Opt. Lett. 31, 158–160 (2006).
    [Crossref] [PubMed]
  8. B. C. Rodgers, T. H. Russell, and W. B. Roh, “Laser beam combining and cleanup by stimulated Brillouin scattering in a multimode optical fiber,” Opt. Lett. 24, 1124–1126 (1999).
    [Crossref]
  9. T. Russell, W. Roh, and J. Marciante, “Incoherent beam combining using stimulated Brillouin scattering in multimode fibers,” Opt. Express 8, 246–254 (2001).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  21. I. 11146-1, “Lasers and laser-related equipment - Test methods for laser beam widths, divergence angles, and beam propagation ratios - Part 1: Stigmatic and simple astigmatic beams,” (International Organization for Standardization, 2005).
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    [Crossref]
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    [Crossref] [PubMed]

2007 (1)

S. Meister, T. Riesbeck, and H. J. Eichler, “Glass fibers for stimulated Brillouin scattering and phase conjugation,” Laser and Particle Beams 25, 15–21 (2007).
[Crossref]

2006 (4)

V. I. Kovalev and R. G. Harrison, “Suppression of stimulated Brillouin scattering in high-power singlefrequency fiber amplifiers,” Opt. Lett. 31, 161–163 (2006).
[Crossref] [PubMed]

V. I. Kovalev and R. G. Harrison, “Continuous wave stimulated Brillouin scattering in optical fibers: new results and applications for high power lasers,” Proceedings of SPIE 5975, 59750L (2006).
[Crossref]

A. Mocofanescu and K. D. Shaw, “Stimulated Brillouin scattering phase conjugating properties of long multimode optical fibers,” Opt. Commun. 266, 307–316 (2006).
[Crossref]

L. Lombard, A. Brignon, J. P. Huignard, E. Lallier, and P. Georges, “Beam cleanup in a self-aligned gradient-index Brillouin cavity for high-power multimode fiber amplifiers,” Opt. Lett. 31, 158–160 (2006).
[Crossref] [PubMed]

2003 (1)

2001 (1)

1999 (1)

1997 (1)

H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
[Crossref]

1985 (2)

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

Y. P. Vasil’ev, P. S. Razenshtein, and E. I. Shklovskii, “Stimulated Brillouin scattering mirror in the form of a multimode optical fiber in a four-pass neodymium phosphate glass laser amplifier,” Quantum Electron. 15, 1417–1418 (1985).
[Crossref]

1978 (1)

1977 (1)

B. Y. Zel’dovich and V.V. Shkunov, Sov. J. Quantum Electron. 4, 610–615 (1977).
[Crossref]

1972 (1)

1971 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

Alley, T. G.

T. H. Russell, B. W. Grime, T. G. Alley, and W. B. Roh, “Stimulated Brillouin scattering beam cleanup and combining in optical fiber,” in Nonlinear Optics and Applications, H. A. Abdeldayem and D. O. Frazier, ed. (Research Signpost, Kerala, India, 2007), pp. 179–206.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 2003).

Brignon, A.

Bruesselbach, H.

H. Bruesselbach, “Beam cleanup using stimulated Brillouin scattering in multimode fibers,” in Conference on Lasers and Electro-Optics (OSA, 1993), pp. 424–426.

Davydenko, B. E.

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

Eichler, H. J.

S. Meister, T. Riesbeck, and H. J. Eichler, “Glass fibers for stimulated Brillouin scattering and phase conjugation,” Laser and Particle Beams 25, 15–21 (2007).
[Crossref]

H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
[Crossref]

Georges, P.

Gloge, D.

Gower, M.

M. Gower and D. Proch, Optical Phase Conjugation (Springer, 1994).

Grime, B. W.

T. H. Russell, B. W. Grime, T. G. Alley, and W. B. Roh, “Stimulated Brillouin scattering beam cleanup and combining in optical fiber,” in Nonlinear Optics and Applications, H. A. Abdeldayem and D. O. Frazier, ed. (Research Signpost, Kerala, India, 2007), pp. 179–206.

Hänisch, C.

Harrison, R. G.

V. I. Kovalev and R. G. Harrison, “Suppression of stimulated Brillouin scattering in high-power singlefrequency fiber amplifiers,” Opt. Lett. 31, 161–163 (2006).
[Crossref] [PubMed]

V. I. Kovalev and R. G. Harrison, “Continuous wave stimulated Brillouin scattering in optical fibers: new results and applications for high power lasers,” Proceedings of SPIE 5975, 59750L (2006).
[Crossref]

Hellwarth, R. W.

Heuer, A.

Huignard, J. P.

Kovalev, V. I.

V. I. Kovalev and R. G. Harrison, “Suppression of stimulated Brillouin scattering in high-power singlefrequency fiber amplifiers,” Opt. Lett. 31, 161–163 (2006).
[Crossref] [PubMed]

V. I. Kovalev and R. G. Harrison, “Continuous wave stimulated Brillouin scattering in optical fibers: new results and applications for high power lasers,” Proceedings of SPIE 5975, 59750L (2006).
[Crossref]

Kunde, J.

H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
[Crossref]

Kuzin, E. A.

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

Lallier, E.

Lehmberg, R. H.

R. H. Lehmberg, “Numerical study of phase conjugation in stimulated Brillouin scattering from an optical waveguide,” (NRL-MR-4985, Naval Research Lab., Washington, DC (USA), 1982).

Liu, B.

H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
[Crossref]

Lombard, L.

Marciante, J.

Meister, S.

S. Meister, T. Riesbeck, and H. J. Eichler, “Glass fibers for stimulated Brillouin scattering and phase conjugation,” Laser and Particle Beams 25, 15–21 (2007).
[Crossref]

Menzel, R.

Mocofanescu, A.

A. Mocofanescu and K. D. Shaw, “Stimulated Brillouin scattering phase conjugating properties of long multimode optical fibers,” Opt. Commun. 266, 307–316 (2006).
[Crossref]

Petrov, M. P.

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

Proch, D.

M. Gower and D. Proch, Optical Phase Conjugation (Springer, 1994).

Razenshtein, P. S.

Y. P. Vasil’ev, P. S. Razenshtein, and E. I. Shklovskii, “Stimulated Brillouin scattering mirror in the form of a multimode optical fiber in a four-pass neodymium phosphate glass laser amplifier,” Quantum Electron. 15, 1417–1418 (1985).
[Crossref]

Riesbeck, T.

S. Meister, T. Riesbeck, and H. J. Eichler, “Glass fibers for stimulated Brillouin scattering and phase conjugation,” Laser and Particle Beams 25, 15–21 (2007).
[Crossref]

Rodgers, B. C.

Roh, W.

Roh, W. B.

B. C. Rodgers, T. H. Russell, and W. B. Roh, “Laser beam combining and cleanup by stimulated Brillouin scattering in a multimode optical fiber,” Opt. Lett. 24, 1124–1126 (1999).
[Crossref]

T. H. Russell, B. W. Grime, T. G. Alley, and W. B. Roh, “Stimulated Brillouin scattering beam cleanup and combining in optical fiber,” in Nonlinear Optics and Applications, H. A. Abdeldayem and D. O. Frazier, ed. (Research Signpost, Kerala, India, 2007), pp. 179–206.

Russell, T.

Russell, T. H.

B. C. Rodgers, T. H. Russell, and W. B. Roh, “Laser beam combining and cleanup by stimulated Brillouin scattering in a multimode optical fiber,” Opt. Lett. 24, 1124–1126 (1999).
[Crossref]

T. H. Russell, B. W. Grime, T. G. Alley, and W. B. Roh, “Stimulated Brillouin scattering beam cleanup and combining in optical fiber,” in Nonlinear Optics and Applications, H. A. Abdeldayem and D. O. Frazier, ed. (Research Signpost, Kerala, India, 2007), pp. 179–206.

Shaw, K. D.

A. Mocofanescu and K. D. Shaw, “Stimulated Brillouin scattering phase conjugating properties of long multimode optical fibers,” Opt. Commun. 266, 307–316 (2006).
[Crossref]

Shklovskii, E. I.

Y. P. Vasil’ev, P. S. Razenshtein, and E. I. Shklovskii, “Stimulated Brillouin scattering mirror in the form of a multimode optical fiber in a four-pass neodymium phosphate glass laser amplifier,” Quantum Electron. 15, 1417–1418 (1985).
[Crossref]

Shkunov, V.V.

B. Y. Zel’dovich and V.V. Shkunov, Sov. J. Quantum Electron. 4, 610–615 (1977).
[Crossref]

Smith, R. G.

Spring, J.

J. Spring, “Modeling of SBS Phase Conjugation in Multimode Step Index Fibers,” in Dept of Engineering Physics (Air Force Institute of Technology, Air University, 2008), pp. 40–89.

Vasil’ev, Y. P.

Y. P. Vasil’ev, P. S. Razenshtein, and E. I. Shklovskii, “Stimulated Brillouin scattering mirror in the form of a multimode optical fiber in a four-pass neodymium phosphate glass laser amplifier,” Quantum Electron. 15, 1417–1418 (1985).
[Crossref]

Zel’dovich, B. Y.

B. Y. Zel’dovich and V.V. Shkunov, Sov. J. Quantum Electron. 4, 610–615 (1977).
[Crossref]

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Laser and Particle Beams (1)

S. Meister, T. Riesbeck, and H. J. Eichler, “Glass fibers for stimulated Brillouin scattering and phase conjugation,” Laser and Particle Beams 25, 15–21 (2007).
[Crossref]

Opt. Commun. (2)

H. J. Eichler, J. Kunde, and B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
[Crossref]

A. Mocofanescu and K. D. Shaw, “Stimulated Brillouin scattering phase conjugating properties of long multimode optical fibers,” Opt. Commun. 266, 307–316 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Opt. Quantum Electron. (1)

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

Proceedings of SPIE (1)

V. I. Kovalev and R. G. Harrison, “Continuous wave stimulated Brillouin scattering in optical fibers: new results and applications for high power lasers,” Proceedings of SPIE 5975, 59750L (2006).
[Crossref]

Quantum Electron. (1)

Y. P. Vasil’ev, P. S. Razenshtein, and E. I. Shklovskii, “Stimulated Brillouin scattering mirror in the form of a multimode optical fiber in a four-pass neodymium phosphate glass laser amplifier,” Quantum Electron. 15, 1417–1418 (1985).
[Crossref]

Sov. J. Quantum Electron. (1)

B. Y. Zel’dovich and V.V. Shkunov, Sov. J. Quantum Electron. 4, 610–615 (1977).
[Crossref]

Other (8)

M. Gower and D. Proch, Optical Phase Conjugation (Springer, 1994).

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

J. Spring, “Modeling of SBS Phase Conjugation in Multimode Step Index Fibers,” in Dept of Engineering Physics (Air Force Institute of Technology, Air University, 2008), pp. 40–89.

R. W. Boyd, Nonlinear Optics (Academic Press, 2003).

H. Bruesselbach, “Beam cleanup using stimulated Brillouin scattering in multimode fibers,” in Conference on Lasers and Electro-Optics (OSA, 1993), pp. 424–426.

T. H. Russell, B. W. Grime, T. G. Alley, and W. B. Roh, “Stimulated Brillouin scattering beam cleanup and combining in optical fiber,” in Nonlinear Optics and Applications, H. A. Abdeldayem and D. O. Frazier, ed. (Research Signpost, Kerala, India, 2007), pp. 179–206.

R. H. Lehmberg, “Numerical study of phase conjugation in stimulated Brillouin scattering from an optical waveguide,” (NRL-MR-4985, Naval Research Lab., Washington, DC (USA), 1982).

I. 11146-1, “Lasers and laser-related equipment - Test methods for laser beam widths, divergence angles, and beam propagation ratios - Part 1: Stigmatic and simple astigmatic beams,” (International Organization for Standardization, 2005).

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Figures (9)

Fig. 1.
Fig. 1. Apparatus used to test phase conjugation fidelity of silicate fibers at 1064 nm wavelength.
Fig. 2.
Fig. 2. Phase conjugation fidelity vs. fiber length for a 20 μm core, 0.13 NA silicate fiber. The experimental data is compared to this work’s model and Hellwarth’s model (red dotted line).
Fig. 3.
Fig. 3. Phase conjugation fidelity vs. fiber length with a 40 μm core diameter, 0.06 NA fiber. The experimental data is plotted along with the results of this work’s model and Hellwarth’s model (red dashed line).
Fig. 4.
Fig. 4. Clockwise from top left: Incident beam, test fiber transmitted beam, and Stokes reflection from 40/400, 0.06 NA fiber at (a) 100 m length and (b) 40 m length.
Fig. 5.
Fig. 5. Clockwise from top left: Incident, transmitted, and Stokes reflection from 20/125, 0.13NA fiber at (a) 40 m length, (b) 30 m, and (c) 15 m length. Without changing the coupling, the Stokes reflection is 2-lobed at 40m length and converts to single transverse mode as the fiber length is decreased.
Fig. 6.
Fig. 6. Model results showing phase conjugation and beam cleanup to the LP11 mode in a 20 micron core diameter, 0.13 NA fiber with pump irradiance (a). The resulting Stokes irradiance patterns are shown from a fiber with lengths (b) 1 m, (c) 5 m, (d) 20 m, and (e) 250 m.
Fig. 7.
Fig. 7. Fidelity vs. fiber length for the 0.06 NA and 0.13 NA fibers, including both modeling and experiment.
Fig. 8.
Fig. 8. The fidelity from both modeling and experiment is plotted against a scaled fiber length.
Fig. 9.
Fig. 9. SBS threshold power of a silicate fiber expected to generate a fidelity higher than 0.7, 0.8, and 0.9 as a function of the beam quality accepted by the fiber.

Tables (1)

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Table 1. SBS test fiber and coupling characteristics

Equations (26)

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I p ( r , z ) z = g ( r ) ω p ω s I p ( r , z ) I s ( r , z ) α p I p ( r , z )
I s ( r , z ) z = g I s ( r , z ) I p ( r , z ) + α s I s ( r , z )
E p , s ( r , z , t ) = f A p , s f ( r ) ψ p , s f ( r ) cos ( β p , s f z ω p , s t + ϕ p , s f )
I p , s ( r , z ) = 2 ε 0 cn E p , s ( r , z , t ) 2
= ε 0 cn f , q A p , s f ( r ) A p , s q ( r ) ψ p , s f ( r ) ψ p , s q ( r ) cos ( Δ β p , s fq z + Δ ϕ p , s fq ) ,
A p , s f ( z ) = κ p , s ( z ) A p , s f ( 0 ) .
P s ( z ) z = g ( ε 0 cn ) 2 f , q , j , v A ppss fqjv γ ppss fqjv κ s ( z ) 2 κ p ( z ) 2 cos ( Δ β p fq z + Δ ϕ p fq ) cos ( Δ β s jv z + Δ ϕ s jv )
A ppss fqjv = A p f ( 0 ) A p q ( 0 ) A s j ( 0 ) A s v ( 0 )
γ ppss fqjv = ψ p f ( r ) ψ p q ( r ) ψ s j ( r ) ψ s v ( r ) d r
P s ( z ) = exp [ g ( ε 0 cn ) 2 P s ( 0 ) f , q , j , v A ppss fqjv γ ppss fqjv κ p ( z ) 2 cos ( Δ β p fq z + Δ ϕ p fq ) cos ( Δ β s jv z + Δ ϕ s jv ) dz ]
I p ( z ) z = g I p ( z ) I s ( z )
I s ( z ) z = g I s ( z ) I p ( z )
κ p ( z ) 2 = I s ( 0 ) [ I p ( 0 ) I s ( 0 ) ] I p ( 0 ) 2 exp { gz [ I p ( 0 ) I s ( 0 ) ] } I s ( 0 ) I p ( 0 ) + 1 I s ( 0 ) I p ( 0 )
2 cos ( Δ β p fq z + Δ ϕ p fq ) cos ( Δ β s jv z + Δ ϕ s jv )
= cos [ ( Δ β p fq Δ β s jv ) z + Δ ϕ p fq Δ ϕ s jv ] + cos [ ( Δ β p fq + Δ β s jv ) z + Δ ϕ p fq + Δ ϕ s jv ]
cos ( Δ β p fq z + Δ ϕ p fq ) cos ( Δ β s jv z + Δ ϕ s jv )
{ 1 2 cos [ ( Δ β p fq Δ β s jv ) z + Δ ϕ p fq Δ ϕ s jv ] , if f = j and q = v f 1 2 cos [ ( Δ β p fq + Δ β s jv ) z + Δ ϕ p fq + Δ ϕ s jv ] , if f = v and q = j f 1 , if f = q and j = v 0 , otherwise
L 6 ( 1 F ) A N w Δ λ
L 6 ( 1 F ) c N A 2 Ω B
L 3 1 F Mc n Ω B N A 2
L = 2 nc Δ ϕ Ω B N A 2
L s L Ω B N A 2 .
P th = 21 A gL
P th = 21 A Ω B ( NA ) 2 g L s
M 2 = π λ d o θ 4
P th 21 Ω B λ 2 M 4 πg L s

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