Abstract

A model incorporating noise and pump depletion in a Brillouin amplifier (BA) predicts a fundamental limitation on attainable pump-to-signal-ratio extraction efficiency. Experimental data supporting this model are also presented. In spite of the limitation, an experimental technique is shown that results in a factor-of-7 increase in extraction efficiency. We accomplish this by noise suppressing and subsequently double passing a BA. We report an overall power efficiency of 37% and phase-conjugate amplification of 3.75 × 1010 for a signal input power near the noise level. This performance, which is the best to our knowledge recorded to date, is accomplished without requiring additional input energy.

© 1995 Optical Society of America

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  1. P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484 (1989), and references therein.
    [CrossRef]
  2. Y. Yamamoto and T. Mukai, "Fundamentals of optical amplifiers," Opt. Quantum Electron. 21, S1 (1989).
    [CrossRef]
  3. K. D. Ridley and A. M. Scott, "High-reflectivity phase conjugation using Brillouin preamplification," Opt. Lett. 15, 777 (1990).
    [CrossRef] [PubMed]
  4. B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985).
    [CrossRef]
  5. S. Sternklar, Y. Glick, and S. Jackel, "Noise limitations of Brillouin two-beam coupling: theory and experiment," J. Opt. Soc. Am. B 9, 391 (1992).
    [CrossRef]
  6. D. Rogovin, R. McGraw, and A. Gavrielides, "Role of thermal fluctuations in nondegenerate two-wave mixing," Appl. Phys. Lett. 55, 1937 (1989).
    [CrossRef]
  7. I. L. Fabelinskii, Molecular Scattering of Light (Plenum, New York, 1968).
    [CrossRef]
  8. R. McGraw and D. Rogovin, "Noise in nonlinear optics," in Nonlinear Optics, R. A. Fisher and J. F. Reintjes, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1220, 100 (1990).
    [CrossRef]
  9. Y. Glick and S. Sternklar, "Noise limitations to Brillouin amplifier efficiency," in Digest of Conference on Lasers and Electro-Optics (Europe) (Optical Society of America, Washington, D.C., 1994), paper CWF52.
  10. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 11, p. 190.
  11. Y. Glick and S. Sternklar, "Reducing the noise in Brillouin amplification by mode-selective phase conjugation," Opt. Lett. 17, 862 (1992).
    [CrossRef] [PubMed]
  12. D. T. Hon, "Pulse compression by stimulated Brillouin scattering," Opt. Lett. 5, 516 (1980).
    [CrossRef] [PubMed]
  13. J. R. Ackerman and P. S. Lebow, "Optimization of the field of view of a Brillouin-enhanced four-wave mixing phase conjugator," Opt. Lett. 19, 2015 (1994).
    [CrossRef] [PubMed]
  14. Y. Glick and S. Sternklar, "High efficiency in a double pass Brillouin amplifier with noise suppression," in Digest of Conference on Lasers and Electro-Optics (Europe) (Optical Society of America, Washington, D.C., 1994), paper CMC6.
  15. A. M. Scott and K. D. Ridley, "A review of Brillouin-enhanced four wave mixing," IEEE J. Quantum Electron. 25, 438 (1989).
    [CrossRef]
  16. J. R. Ackerman and P. S. Lebow, "Observation and compensation of frequency detuning in high-reflectivity Brillouinenhanced four-wave mixing," J. Opt. Soc. Am B 8, 1028 (1991).
    [CrossRef]

1994 (1)

1992 (2)

1991 (1)

J. R. Ackerman and P. S. Lebow, "Observation and compensation of frequency detuning in high-reflectivity Brillouinenhanced four-wave mixing," J. Opt. Soc. Am B 8, 1028 (1991).
[CrossRef]

1990 (1)

1989 (4)

D. Rogovin, R. McGraw, and A. Gavrielides, "Role of thermal fluctuations in nondegenerate two-wave mixing," Appl. Phys. Lett. 55, 1937 (1989).
[CrossRef]

P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484 (1989), and references therein.
[CrossRef]

Y. Yamamoto and T. Mukai, "Fundamentals of optical amplifiers," Opt. Quantum Electron. 21, S1 (1989).
[CrossRef]

A. M. Scott and K. D. Ridley, "A review of Brillouin-enhanced four wave mixing," IEEE J. Quantum Electron. 25, 438 (1989).
[CrossRef]

1980 (1)

Ackerman, J. R.

J. R. Ackerman and P. S. Lebow, "Optimization of the field of view of a Brillouin-enhanced four-wave mixing phase conjugator," Opt. Lett. 19, 2015 (1994).
[CrossRef] [PubMed]

J. R. Ackerman and P. S. Lebow, "Observation and compensation of frequency detuning in high-reflectivity Brillouinenhanced four-wave mixing," J. Opt. Soc. Am B 8, 1028 (1991).
[CrossRef]

Fabelinskii, I. L.

I. L. Fabelinskii, Molecular Scattering of Light (Plenum, New York, 1968).
[CrossRef]

Gavrielides, A.

D. Rogovin, R. McGraw, and A. Gavrielides, "Role of thermal fluctuations in nondegenerate two-wave mixing," Appl. Phys. Lett. 55, 1937 (1989).
[CrossRef]

Glick, Y.

S. Sternklar, Y. Glick, and S. Jackel, "Noise limitations of Brillouin two-beam coupling: theory and experiment," J. Opt. Soc. Am. B 9, 391 (1992).
[CrossRef]

Y. Glick and S. Sternklar, "Reducing the noise in Brillouin amplification by mode-selective phase conjugation," Opt. Lett. 17, 862 (1992).
[CrossRef] [PubMed]

Y. Glick and S. Sternklar, "Noise limitations to Brillouin amplifier efficiency," in Digest of Conference on Lasers and Electro-Optics (Europe) (Optical Society of America, Washington, D.C., 1994), paper CWF52.

Y. Glick and S. Sternklar, "High efficiency in a double pass Brillouin amplifier with noise suppression," in Digest of Conference on Lasers and Electro-Optics (Europe) (Optical Society of America, Washington, D.C., 1994), paper CMC6.

Hon, D. T.

Jackel, S.

Lebow, P. S.

J. R. Ackerman and P. S. Lebow, "Optimization of the field of view of a Brillouin-enhanced four-wave mixing phase conjugator," Opt. Lett. 19, 2015 (1994).
[CrossRef] [PubMed]

J. R. Ackerman and P. S. Lebow, "Observation and compensation of frequency detuning in high-reflectivity Brillouinenhanced four-wave mixing," J. Opt. Soc. Am B 8, 1028 (1991).
[CrossRef]

McGraw, R.

D. Rogovin, R. McGraw, and A. Gavrielides, "Role of thermal fluctuations in nondegenerate two-wave mixing," Appl. Phys. Lett. 55, 1937 (1989).
[CrossRef]

R. McGraw and D. Rogovin, "Noise in nonlinear optics," in Nonlinear Optics, R. A. Fisher and J. F. Reintjes, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1220, 100 (1990).
[CrossRef]

Mukai, T.

Y. Yamamoto and T. Mukai, "Fundamentals of optical amplifiers," Opt. Quantum Electron. 21, S1 (1989).
[CrossRef]

Pilipetsky, N. F.

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985).
[CrossRef]

Ridley, K. D.

K. D. Ridley and A. M. Scott, "High-reflectivity phase conjugation using Brillouin preamplification," Opt. Lett. 15, 777 (1990).
[CrossRef] [PubMed]

A. M. Scott and K. D. Ridley, "A review of Brillouin-enhanced four wave mixing," IEEE J. Quantum Electron. 25, 438 (1989).
[CrossRef]

Rogovin, D.

D. Rogovin, R. McGraw, and A. Gavrielides, "Role of thermal fluctuations in nondegenerate two-wave mixing," Appl. Phys. Lett. 55, 1937 (1989).
[CrossRef]

R. McGraw and D. Rogovin, "Noise in nonlinear optics," in Nonlinear Optics, R. A. Fisher and J. F. Reintjes, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1220, 100 (1990).
[CrossRef]

Scott, A. M.

K. D. Ridley and A. M. Scott, "High-reflectivity phase conjugation using Brillouin preamplification," Opt. Lett. 15, 777 (1990).
[CrossRef] [PubMed]

A. M. Scott and K. D. Ridley, "A review of Brillouin-enhanced four wave mixing," IEEE J. Quantum Electron. 25, 438 (1989).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 11, p. 190.

Shkunov, V. V.

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985).
[CrossRef]

Sternklar, S.

Y. Glick and S. Sternklar, "Reducing the noise in Brillouin amplification by mode-selective phase conjugation," Opt. Lett. 17, 862 (1992).
[CrossRef] [PubMed]

S. Sternklar, Y. Glick, and S. Jackel, "Noise limitations of Brillouin two-beam coupling: theory and experiment," J. Opt. Soc. Am. B 9, 391 (1992).
[CrossRef]

Y. Glick and S. Sternklar, "Noise limitations to Brillouin amplifier efficiency," in Digest of Conference on Lasers and Electro-Optics (Europe) (Optical Society of America, Washington, D.C., 1994), paper CWF52.

Y. Glick and S. Sternklar, "High efficiency in a double pass Brillouin amplifier with noise suppression," in Digest of Conference on Lasers and Electro-Optics (Europe) (Optical Society of America, Washington, D.C., 1994), paper CMC6.

Yamamoto, Y.

Y. Yamamoto and T. Mukai, "Fundamentals of optical amplifiers," Opt. Quantum Electron. 21, S1 (1989).
[CrossRef]

Yeh, P.

P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484 (1989), and references therein.
[CrossRef]

Zeldovich, B. Y.

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985).
[CrossRef]

Appl. Phys. Lett. (1)

D. Rogovin, R. McGraw, and A. Gavrielides, "Role of thermal fluctuations in nondegenerate two-wave mixing," Appl. Phys. Lett. 55, 1937 (1989).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. M. Scott and K. D. Ridley, "A review of Brillouin-enhanced four wave mixing," IEEE J. Quantum Electron. 25, 438 (1989).
[CrossRef]

P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484 (1989), and references therein.
[CrossRef]

J. Opt. Soc. Am B (1)

J. R. Ackerman and P. S. Lebow, "Observation and compensation of frequency detuning in high-reflectivity Brillouinenhanced four-wave mixing," J. Opt. Soc. Am B 8, 1028 (1991).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (4)

Opt. Quantum Electron. (1)

Y. Yamamoto and T. Mukai, "Fundamentals of optical amplifiers," Opt. Quantum Electron. 21, S1 (1989).
[CrossRef]

Other (6)

B. Y. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985).
[CrossRef]

I. L. Fabelinskii, Molecular Scattering of Light (Plenum, New York, 1968).
[CrossRef]

R. McGraw and D. Rogovin, "Noise in nonlinear optics," in Nonlinear Optics, R. A. Fisher and J. F. Reintjes, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1220, 100 (1990).
[CrossRef]

Y. Glick and S. Sternklar, "Noise limitations to Brillouin amplifier efficiency," in Digest of Conference on Lasers and Electro-Optics (Europe) (Optical Society of America, Washington, D.C., 1994), paper CWF52.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 11, p. 190.

Y. Glick and S. Sternklar, "High efficiency in a double pass Brillouin amplifier with noise suppression," in Digest of Conference on Lasers and Electro-Optics (Europe) (Optical Society of America, Washington, D.C., 1994), paper CMC6.

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Figures (9)

Fig. 1
Fig. 1

Predicted efficiency versus G for various pump powers; results from our model, the previous model, and experimental data, all at PSin = 0.2 mW. Dashed curve, Pp = 200 MW; thick solid curve, Pp = 2 MW; thin solid curve, Pp = 0.02 MW; dotted curve, previous model with Pp = 2 MW; crosses, experiment.

Fig. 2
Fig. 2

Schematic of Brillouin two-beam coupling with counterpropagating circularly polarized beams Ip (pump) and Is (signal). The signal has been frequency downshifted in a Brillouin PCM filled with the same medium as is the BA. D, detector; pol’s, dielectric polarizing beam splitters; VBS, variable beam splitter.

Fig. 3
Fig. 3

Gopt for maximum efficiency versus signal power for various pump powers. Dashed curve, Pp = 200 MW; thick solid curve, Pp = 2 MW; thin solid curve, Pp = 0.02 MW.

Fig. 4
Fig. 4

Maximum achievable efficiency for varying signal and pump powers. (a) Present model and experimental results. Dashed curve, Pp = 200 MW; thick solid curve, Pp = 2 MW; thin solid curve, Pp = 0.02 MW; crosses, experiment at Pp = 10 MW; triangles, experiment at Pp = 1.6 MW (Ref. 3); squares, experiment at Pp = 30 MW. (b) Thick curves, present model; thin curves, previous model. Dashed curves, Pp = 200 MW; dotted curves, Pp = 2 MW; solid curves, Pp = 0.02 MW. (c) Solid curve, at 1064 nm (w); dashed curve, at 532 nm (2w), Pp = 2 MW.

Fig. 5
Fig. 5

Maximum achievable efficiency as a function of pump power at PSin = 0.2 mW. Solid curve, previous model at G = Gopt of the present model; dashed curve, present model; crosses, experiment.

Fig. 6
Fig. 6

Temporal behavior of pulse taken with a fast detector (<150-ps rise time) and a fast scope (5-GHz bandwidth). (a) Pump pulse; Dt = 8.8 ns. (b) Signal pulse before the amplifier; Dt = 4.9 ns. (c) Signal pulse after amplification; Dt = 2.9 ns.

Fig. 7
Fig. 7

Schematic of double-pass Brillouin amplification. The beam is split at the first polarizer. The signal is downshifted in PCM1, is attenuated, and meets the pump beam in the BA cell for the first-pass gain. The amplified signal plus noise enters PCM2, where noise suppression occurs. The phase-conjugate signal meets the pump beam, which has been phase conjugated in PCM3 for a second gain. The first- and the second-pass gains are measured by D1 and D2, respectively. PCM’s, Brillouin PCM’s; pol’s, dielectric polarizing beam splitters; ND, neutral-density filter; M’s, mirrors; BS’s, beam splitters; D’s, photodetectors or power meters.

Fig. 8
Fig. 8

BA efficiency versus pump power for the first and the second passes at PSin = 0.2 mW. Crosses, first pass; squares, second pass.

Fig. 9
Fig. 9

BA noise output from the second pass (a) for the setup shown in Fig. 7 and (b) when PCM2 and PCM3 were replaced with conventional 0° mirrors. Squares, noise; curve, linear average.

Equations (15)

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2 E z 2 μ 0 LIN 2 t 2 E = 2 z 2 ( NL + δ ) E
E = A s ( z ) exp [ i ( k s z ω s t ) ] + A p ( z ) exp [ i ( k p z ω p t ) ] + c . c .
= 0 [ 1 + χ ( 1 ) + χ B E · E ] + δ
LIN = 0 [ 1 + χ ( 1 ) ] , NL = 0 χ B E · E 2 E · E
δ ( k g , ω g ) = δ g exp [ i ( k g z + ω g t ) ] + c . c .
( k g , ω g ) = g exp [ i ( k g z + ω g t ) ] + c . c . ,
d I s d z = d I p d z = g B I p I s + 2 β I p 1 / 2 I s 1 / 2 ,
β = k s 2 r δ g 0 , 0 r ; g B = 4 0 n c k s 2 r | χ B |
| δ | 2 = 8 π k T V s 2 ,
C = I p ( L ) ( 1 I s 2 ( 0 ) exp ( C g B L ) { [ γ 2 + C I s ( 0 ) ] 1 / 2 γ } 2 ) ,
ξ P out P p = I p ( L ) C I p ( L ) , q P Sin P p = I s ( 0 ) I p ( L ) , R P P 4 π ω k T = I p 2 ( L ) G γ 2 ,
ξ = exp [ G ( 1 ξ ) ] q 2 G R { [ 1 + q G R ( 1 ξ ) ] 1 / 2 1 } 2 .
η = ξ ( P Sin 0 ) ξ ( P Sin = 0 ) .
Amp P out ( P Sin 0 ) P out ( P Sin = 0 ) P Sin ,
Amp = η ( P Sin ) P p P Sin .

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