Abstract

The angular bandwidth (ABW) of a Brillouin amplifier is shown to be dependent on the spectral bandwidth of the interacting beams in a counterpropagating geometry. Theory and experiment reveal that the actual ABW for typical lasers is much larger than monochromatic theory suggests. For single-longitudinal-mode pulses of a 8.5-ns duration interacting in CS2 the ABW is equal to ±320 mrad (±18°), corresponding to an external angle of ±29°. However, to permit us to take advantage of the full ABW afforded by the Brillouin interaction, proper design of the amplifier is necessary to ensure that angular walk-off loss does not occur.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, and G. A. Pasmanik, "Phase conjugation and amplification of weak space-inhomogeneous fields," Rev. Roum. Phys. 31, 951–955 (1986); V. I. Bespalov, A. Z. Matveev, and G. A. Pasmanik, "Limiting sensitivity of a stimulated-Brillouin-scattering amplifier and a four-wave hypersonic phase-conjugating mirror," Radiophys. Quantum Electron. 29, 818–830 (1987).
    [CrossRef]
  2. D. Rogovin, R. McGraw, and A. Gavrielides, "Role of thermal fluctuations in nondegenerate two-wave mixing," Appl. Phys. Lett. 55, 1937–1939 (1989).
    [CrossRef]
  3. A. M. Scott, D. E. Watkins, and P. Tapster, "Gain and noise characteristics of a Brillouin amplifier and their dependence on the spatial structure of the pump beam," J. Opt. Soc. Am. B 7, 929–935 (1990).
    [CrossRef]
  4. S. Sternklar, Y. Glick, and S. Jackel, "Noise limitations of Brillouin two-beam coupling: theory and experiment," J. Opt. Soc. Am. B 9, 391–397 (1992).
    [CrossRef]
  5. A. M. Scott and M. S. Hazell, "High-efficiency scattering in transient Brillouin enhanced four-wave mixing," IEEE J. Quantum Electron. 22, 1248–1257 (1986).
    [CrossRef]
  6. B. Ya. Zel'dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
    [CrossRef]
  7. I. L. Fabelinski, Molecular Scattering of Light (Plenum, New York, 1968).
    [CrossRef]
  8. D. Pohl and W. Kaiser, "Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetimes," Phys. Rev. B 1, 31–43 (1970).
    [CrossRef]
  9. F. Barocchi, M. Mancini, and R. Vallauri, "Stimulated Brillouin scattering in liquid mixtures," Nuovo Cimento 49B, 223–236 (1967).

1992 (1)

1990 (1)

1989 (1)

D. Rogovin, R. McGraw, and A. Gavrielides, "Role of thermal fluctuations in nondegenerate two-wave mixing," Appl. Phys. Lett. 55, 1937–1939 (1989).
[CrossRef]

1986 (2)

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, and G. A. Pasmanik, "Phase conjugation and amplification of weak space-inhomogeneous fields," Rev. Roum. Phys. 31, 951–955 (1986); V. I. Bespalov, A. Z. Matveev, and G. A. Pasmanik, "Limiting sensitivity of a stimulated-Brillouin-scattering amplifier and a four-wave hypersonic phase-conjugating mirror," Radiophys. Quantum Electron. 29, 818–830 (1987).
[CrossRef]

A. M. Scott and M. S. Hazell, "High-efficiency scattering in transient Brillouin enhanced four-wave mixing," IEEE J. Quantum Electron. 22, 1248–1257 (1986).
[CrossRef]

1970 (1)

D. Pohl and W. Kaiser, "Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetimes," Phys. Rev. B 1, 31–43 (1970).
[CrossRef]

1967 (1)

F. Barocchi, M. Mancini, and R. Vallauri, "Stimulated Brillouin scattering in liquid mixtures," Nuovo Cimento 49B, 223–236 (1967).

Andreev, N. F.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, and G. A. Pasmanik, "Phase conjugation and amplification of weak space-inhomogeneous fields," Rev. Roum. Phys. 31, 951–955 (1986); V. I. Bespalov, A. Z. Matveev, and G. A. Pasmanik, "Limiting sensitivity of a stimulated-Brillouin-scattering amplifier and a four-wave hypersonic phase-conjugating mirror," Radiophys. Quantum Electron. 29, 818–830 (1987).
[CrossRef]

Barocchi, F.

F. Barocchi, M. Mancini, and R. Vallauri, "Stimulated Brillouin scattering in liquid mixtures," Nuovo Cimento 49B, 223–236 (1967).

Bespalov, V. I.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, and G. A. Pasmanik, "Phase conjugation and amplification of weak space-inhomogeneous fields," Rev. Roum. Phys. 31, 951–955 (1986); V. I. Bespalov, A. Z. Matveev, and G. A. Pasmanik, "Limiting sensitivity of a stimulated-Brillouin-scattering amplifier and a four-wave hypersonic phase-conjugating mirror," Radiophys. Quantum Electron. 29, 818–830 (1987).
[CrossRef]

Dvoretsky, M. A.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, and G. A. Pasmanik, "Phase conjugation and amplification of weak space-inhomogeneous fields," Rev. Roum. Phys. 31, 951–955 (1986); V. I. Bespalov, A. Z. Matveev, and G. A. Pasmanik, "Limiting sensitivity of a stimulated-Brillouin-scattering amplifier and a four-wave hypersonic phase-conjugating mirror," Radiophys. Quantum Electron. 29, 818–830 (1987).
[CrossRef]

Fabelinski, I. L.

I. L. Fabelinski, 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, 1937–1939 (1989).
[CrossRef]

Glick, Y.

Hazell, M. S.

A. M. Scott and M. S. Hazell, "High-efficiency scattering in transient Brillouin enhanced four-wave mixing," IEEE J. Quantum Electron. 22, 1248–1257 (1986).
[CrossRef]

Jackel, S.

Kaiser, W.

D. Pohl and W. Kaiser, "Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetimes," Phys. Rev. B 1, 31–43 (1970).
[CrossRef]

Katin, E. V.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, and G. A. Pasmanik, "Phase conjugation and amplification of weak space-inhomogeneous fields," Rev. Roum. Phys. 31, 951–955 (1986); V. I. Bespalov, A. Z. Matveev, and G. A. Pasmanik, "Limiting sensitivity of a stimulated-Brillouin-scattering amplifier and a four-wave hypersonic phase-conjugating mirror," Radiophys. Quantum Electron. 29, 818–830 (1987).
[CrossRef]

Mancini, M.

F. Barocchi, M. Mancini, and R. Vallauri, "Stimulated Brillouin scattering in liquid mixtures," Nuovo Cimento 49B, 223–236 (1967).

Matveev, A. Z.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, and G. A. Pasmanik, "Phase conjugation and amplification of weak space-inhomogeneous fields," Rev. Roum. Phys. 31, 951–955 (1986); V. I. Bespalov, A. Z. Matveev, and G. A. Pasmanik, "Limiting sensitivity of a stimulated-Brillouin-scattering amplifier and a four-wave hypersonic phase-conjugating mirror," Radiophys. Quantum Electron. 29, 818–830 (1987).
[CrossRef]

McGraw, R.

D. Rogovin, R. McGraw, and A. Gavrielides, "Role of thermal fluctuations in nondegenerate two-wave mixing," Appl. Phys. Lett. 55, 1937–1939 (1989).
[CrossRef]

Pasmanik, G. A.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, and G. A. Pasmanik, "Phase conjugation and amplification of weak space-inhomogeneous fields," Rev. Roum. Phys. 31, 951–955 (1986); V. I. Bespalov, A. Z. Matveev, and G. A. Pasmanik, "Limiting sensitivity of a stimulated-Brillouin-scattering amplifier and a four-wave hypersonic phase-conjugating mirror," Radiophys. Quantum Electron. 29, 818–830 (1987).
[CrossRef]

Pilipetsky, N. F.

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

Pohl, D.

D. Pohl and W. Kaiser, "Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetimes," Phys. Rev. B 1, 31–43 (1970).
[CrossRef]

Rogovin, D.

D. Rogovin, R. McGraw, and A. Gavrielides, "Role of thermal fluctuations in nondegenerate two-wave mixing," Appl. Phys. Lett. 55, 1937–1939 (1989).
[CrossRef]

Scott, A. M.

A. M. Scott, D. E. Watkins, and P. Tapster, "Gain and noise characteristics of a Brillouin amplifier and their dependence on the spatial structure of the pump beam," J. Opt. Soc. Am. B 7, 929–935 (1990).
[CrossRef]

A. M. Scott and M. S. Hazell, "High-efficiency scattering in transient Brillouin enhanced four-wave mixing," IEEE J. Quantum Electron. 22, 1248–1257 (1986).
[CrossRef]

Shkunov, V. V.

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

Sternklar, S.

Tapster, P.

Vallauri, R.

F. Barocchi, M. Mancini, and R. Vallauri, "Stimulated Brillouin scattering in liquid mixtures," Nuovo Cimento 49B, 223–236 (1967).

Watkins, D. E.

Zel’dovich, B. Ya.

B. Ya. Zel'dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 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, 1937–1939 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. M. Scott and M. S. Hazell, "High-efficiency scattering in transient Brillouin enhanced four-wave mixing," IEEE J. Quantum Electron. 22, 1248–1257 (1986).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nuovo Cimento (1)

F. Barocchi, M. Mancini, and R. Vallauri, "Stimulated Brillouin scattering in liquid mixtures," Nuovo Cimento 49B, 223–236 (1967).

Phys. Rev. B (1)

D. Pohl and W. Kaiser, "Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonon lifetimes," Phys. Rev. B 1, 31–43 (1970).
[CrossRef]

Rev. Roum. Phys. (1)

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, and G. A. Pasmanik, "Phase conjugation and amplification of weak space-inhomogeneous fields," Rev. Roum. Phys. 31, 951–955 (1986); V. I. Bespalov, A. Z. Matveev, and G. A. Pasmanik, "Limiting sensitivity of a stimulated-Brillouin-scattering amplifier and a four-wave hypersonic phase-conjugating mirror," Radiophys. Quantum Electron. 29, 818–830 (1987).
[CrossRef]

Other (2)

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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Schematic of Brillouin two-wave mixing. Is and Ip are the signal- and the pump-beam intensities interacting in the Brillouin medium.

Fig. 2
Fig. 2

Monochromatic theory of the normalized gain coefficient and amplification as a function of offset angle. These graphs show the dependence of the gain coefficient on, curve a, Fkg; b, FΩ; c, Ftp and the dependence of the amplification on, curve d, FkgFΩFtp; e, FkgFtp.

Fig. 3
Fig. 3

(a) Normalized amplification and (b) normalized gain coefficient as functions of θ for various pulse lengths.

Fig. 4
Fig. 4

Pump-beam structure in the amplifier cell.

Fig. 5
Fig. 5

Data of normalized gain coefficient as a function of θ for the pump shown in Fig. 4, after the interaction intensity is normalized out. Solid curve, theory from Fig. 3(b).

Fig. 6
Fig. 6

Data of normalized gain coefficient as a function of θ for a Gaussian beam.

Fig. 7
Fig. 7

Normalized amplification as a function of frequency shift from the Brillouin resonance frequency for a number of pulse lengths.

Fig. 8
Fig. 8

Data of normalized amplification as a function of frequency shift from the Brillouin resonance frequency, with the appropriate theoretical curve.

Equations (13)

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

A I s out / I s in = exp ( g I p L ) ,
g ( θ ) = g ( ) F k g F Ω F t p .
F k g = 1 / cos ( θ / 2 ) .
F Ω = 1 1 + x 2 ,
F t p = { [ ( g I p L / 2 ) + Γ B ( ) t p ] 2 cos 2 ( θ / 2 ) [ ( g I p L / 2 ) + Γ B ( ) t p cos 2 ( θ / 2 ) ] 2 t p < g I p L 2 t o ( θ = 0 ) 1 t p > g I p L 2 t o ( θ ) 2 g I p L Γ B ( ) t p cos 2 ( θ / 2 ) [ ( g I p L / 2 ) + Γ B ( ) t p cos 2 ( θ / 2 ) ] 2 g I p L 2 t o ( θ = 0 ) < t p < g I p L 2 t o ( θ ) .
A = exp [ g ( θ f ) I p L ] = μ exp [ g ( ) I p L ] .
cos ( θ f / 2 ) = 1 - Γ B ( ) Ω B ( ) [ g ( ) I p L ln ( μ ) - 1 ] - 1 / 2 .
I p ( ω p ) = I p ( ω p o ) 1 + t p 2 ( ω p - ω p o ) 2 / π 2
I s ( ω s ) = I s ( ω s o ) 1 + t p 2 ( ω s - ω s o ) 2 / π 2
I s out ( θ ) = - - I s in ( ω s ) exp [ g ( θ , ω s , ω p ) I p ( ω p ) L ] × d ω s d ω p .
θ f = 2 arccos [ 1 - Γ s Ω ( ) ] .
I s out = - - I s in ( ω s ) exp [ g ( Ω , ω s , ω p ) I p ( ω p ) L ] d ω s d ω p ,
Ω = 2 n λ L { E 1 E 2 [ x E 2 + ( 1 - x ) E 1 ] [ x ρ 1 + ( 1 - x ) ρ 2 ] } 1 / 2 ,

Metrics