Abstract

A theoretical and experimental study of noise in Brillouin two-beam coupling is presented, which includes both the nondepleted and the depleted pump regimes. The signal-to-noise ratio (SNR) is shown to be proportional to the weak signal input power as well as to the pump intensity in the nondepleted regime. Pump depletion causes both the SNR and the gain to degrade significantly, leading to an optimum working point of gBIpL ≃ 20. The minimum detectable signal power per mode of noise, predicted and measured to be approximately 5 μW at λ = 1.06 μm, is dependent on frequency and temperature, while the peak gain is also dependent on the Brillouin coupling coefficient gB, interaction length, and cross-sectional area of the amplifier.

© 1992 Optical Society of America

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References

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  1. P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989), and references therein.
    [CrossRef]
  2. Y. Yamamoto, T. Mukai, Opt. Quantum Electron. 21, S1 (1989).
    [CrossRef]
  3. V. I. Bespalov, A. Z. Matveev, G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 29, 1080 (1986); Radiophys. Quantum Electron. 14, 818 (1987).
  4. R. McGraw, D. Rogovin, A. Gavrielides, Appl. Phys. Lett. 54, 199 (1989).
    [CrossRef]
  5. D. Rogovin, R. McGraw, A. Gavrielides, Appl. Phys. Lett. 55, 1937 (1989).
    [CrossRef]
  6. A. M. Scott, D. E. Watkins, P. Tapster, J. Opt. Soc. Am. B 7, 929 (1990).
    [CrossRef]
  7. I. L. Fabelinskii, Molecular Scattering of Light(Plenum, New York, 1968).
    [CrossRef]
  8. B. Ya. Zeldovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation(Springer-Verlag, New York, 1985).
    [CrossRef]
  9. R. McGraw, D. Rogovin, in Nonlinear Optics, R. A. Fisher, J. F. Reintjes, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1220, 100 (1990).
    [CrossRef]
  10. S. Sternklar, Y. Glick, S. Jackel, A. Zigler, “Signal to noise ratio in Brillouin two-beam coupling,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 52, paper CMG5.

1990 (1)

1989 (4)

P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989), and references therein.
[CrossRef]

Y. Yamamoto, T. Mukai, Opt. Quantum Electron. 21, S1 (1989).
[CrossRef]

R. McGraw, D. Rogovin, A. Gavrielides, Appl. Phys. Lett. 54, 199 (1989).
[CrossRef]

D. Rogovin, R. McGraw, A. Gavrielides, Appl. Phys. Lett. 55, 1937 (1989).
[CrossRef]

1986 (1)

V. I. Bespalov, A. Z. Matveev, G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 29, 1080 (1986); Radiophys. Quantum Electron. 14, 818 (1987).

Bespalov, V. I.

V. I. Bespalov, A. Z. Matveev, G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 29, 1080 (1986); Radiophys. Quantum Electron. 14, 818 (1987).

Fabelinskii, I. L.

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

Gavrielides, A.

D. Rogovin, R. McGraw, A. Gavrielides, Appl. Phys. Lett. 55, 1937 (1989).
[CrossRef]

R. McGraw, D. Rogovin, A. Gavrielides, Appl. Phys. Lett. 54, 199 (1989).
[CrossRef]

Glick, Y.

S. Sternklar, Y. Glick, S. Jackel, A. Zigler, “Signal to noise ratio in Brillouin two-beam coupling,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 52, paper CMG5.

Jackel, S.

S. Sternklar, Y. Glick, S. Jackel, A. Zigler, “Signal to noise ratio in Brillouin two-beam coupling,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 52, paper CMG5.

Matveev, A. Z.

V. I. Bespalov, A. Z. Matveev, G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 29, 1080 (1986); Radiophys. Quantum Electron. 14, 818 (1987).

McGraw, R.

R. McGraw, D. Rogovin, A. Gavrielides, Appl. Phys. Lett. 54, 199 (1989).
[CrossRef]

D. Rogovin, R. McGraw, A. Gavrielides, Appl. Phys. Lett. 55, 1937 (1989).
[CrossRef]

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

Mukai, T.

Y. Yamamoto, T. Mukai, Opt. Quantum Electron. 21, S1 (1989).
[CrossRef]

Pasmanik, G. A.

V. I. Bespalov, A. Z. Matveev, G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 29, 1080 (1986); Radiophys. Quantum Electron. 14, 818 (1987).

Pilipetsky, N. F.

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

Rogovin, D.

R. McGraw, D. Rogovin, A. Gavrielides, Appl. Phys. Lett. 54, 199 (1989).
[CrossRef]

D. Rogovin, R. McGraw, A. Gavrielides, Appl. Phys. Lett. 55, 1937 (1989).
[CrossRef]

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

Scott, A. M.

Shkunov, V. V.

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

Sternklar, S.

S. Sternklar, Y. Glick, S. Jackel, A. Zigler, “Signal to noise ratio in Brillouin two-beam coupling,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 52, paper CMG5.

Tapster, P.

Watkins, D. E.

Yamamoto, Y.

Y. Yamamoto, T. Mukai, Opt. Quantum Electron. 21, S1 (1989).
[CrossRef]

Yeh, P.

P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989), and references therein.
[CrossRef]

Zeldovich, B. Ya.

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

Zigler, A.

S. Sternklar, Y. Glick, S. Jackel, A. Zigler, “Signal to noise ratio in Brillouin two-beam coupling,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 52, paper CMG5.

Appl. Phys. Lett. (2)

R. McGraw, D. Rogovin, A. Gavrielides, Appl. Phys. Lett. 54, 199 (1989).
[CrossRef]

D. Rogovin, R. McGraw, A. Gavrielides, Appl. Phys. Lett. 55, 1937 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989), and references therein.
[CrossRef]

Izv. Vyssh. Uchebn. Zaved. Radiofiz. (1)

V. I. Bespalov, A. Z. Matveev, G. A. Pasmanik, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 29, 1080 (1986); Radiophys. Quantum Electron. 14, 818 (1987).

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

Opt. Quantum Electron. (1)

Y. Yamamoto, T. Mukai, Opt. Quantum Electron. 21, S1 (1989).
[CrossRef]

Other (4)

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

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

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

S. Sternklar, Y. Glick, S. Jackel, A. Zigler, “Signal to noise ratio in Brillouin two-beam coupling,” in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 52, paper CMG5.

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Figures (9)

Fig. 1
Fig. 1

Schematic of Brillouin TBC in a CS2 cell with counterpropagating, circularly polarized beams Ip (pump) and Is (signal). The signal has been frequency downshifted in a SBS phase-conjugate mirror (PCM) filled with CS2. D, detector; pol’s polarizers; VBS, variable beam splitter.

Fig. 2
Fig. 2

Experimental data of SNR versus input signal energy, at a pump intensity of approximately 4 MW/cm2. Each data point in this and the following figures represents an average over 10 laser shots, with an error of ±30%. The main source of error is variation in the pump intensity from shot to shot.

Fig. 3
Fig. 3

Amplified signal and noise as a function of pump energy. The top curve is the output signal plus noise, with an input signal of 1 pJ; the bottom curve is just output noise (no input signal). (a) 50-cm cell, (b) 100-cm cell.

Fig. 4
Fig. 4

SNR for the two cell lengths, determined from the data in Fig. 3.

Fig. 5
Fig. 5

Theoretical prediction of signal and noise output of a 50-cm cell versus pump intensity. Top curve, output signal plus noise for an input signal intensity of 20 W/m2; bottom curve, just noise.

Fig. 6
Fig. 6

Theoretical prediction of SNR versus pump intensity in CS2, calculated from Fig. 5, for cell lengths of 50 and 100 cm.

Fig. 7
Fig. 7

Theoretical prediction of the minimum detectable input signal intensity (normalized to pump input) versus G = gBIpL for various values of β ^ in the region of CS2.

Fig. 8
Fig. 8

Theoretical prediction of Brillouin gain at SNR = 1 versus G, for varying β ^. Note that the gain actually degrades in the depletion regime.

Fig. 9
Fig. 9

Optimum G to achieve best sensitivity (lowest NEP) versus β ^. The four points were taken from the minimum of the four curves of Fig. 7. The curve through the points is an interpolation function.

Equations (38)

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2 E z 2 - μ 0 ɛ LIN 2 t 2 E = μ 0 2 t 2 ( ɛ NL + δ ɛ ) 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 .
ɛ = ɛ o [ 1 + χ ( 1 ) + χ B E · E ] + δ ɛ
ɛ LIN = ɛ o ( 1 + χ ( 1 ) ) ,             ɛ NL = ɛ o χ B E · E ɛ 2 E · E
δ ɛ ( k g , ω g ) = δ ɛ g exp [ - i ( k g z + ω g t ) ] + c . c .
ɛ ( k g , ω g ) = ɛ g ( z ) exp [ - i ( k g z + ω g t ) ] + c . c .
d A s d z = α A p 2 A s + β A p ,
α = k s 2 ɛ r χ B ,             β = k s 2 ɛ r δ ɛ g ɛ o ,             ɛ ɛ o ɛ r .
A s ( z ) = A s ( o ) exp ( α A p 2 z ) + β α A p * [ exp ( α A p 2 z ) - 1 ] ,
A s ( z ) 2 = A s ( o ) 2 exp ( 2 α A p 2 z ) + β 2 α 2 A p 2 × [ exp ( α A p 2 z ) - 1 ] 2 + 2 Re [ A s ( o ) · β α A p * ] × exp ( α A p 2 z ) [ exp ( α A p 2 z ) - 1 ] .
I s ( L ) = I s ( o ) exp ( g B I p L ) + 4 β 2 g B 2 I p exp ( g B I p L ) ,
SNR = I p ( L ) I s ( o ) g B 2 4 β 2 .
δ ɛ 2 = ( 8 π k B T V s ɛ 2 )
β 2 = ( π ω k B T V s g B ) .
SNR = P s 4 π ω k B T g B I p L ,
SNR = I s ( L ) - I n ( L ) I n ( L ) ,
d I s d z = d I p d z = g B I p I s + β I p 1 / 2 I s 1 / 2 .
I s ( z ) = - C 2 { 1 - ( 4 γ 2 + C 2 ) 1 / 2 cosh [ * ] 2 γ - C sinh [ * ] } ,
C = [ 2 γ - 2 I s ( o ) sinh ( H ) + 4 γ I s ( o ) C ] e - H ,
4 γ I p ( L ) - 2 C I p ( L ) sinh ( C g B L 2 + H ) - 2 γ C - C 2 exp [ - ( C g B L 2 + H ) ] .
β ^ = β L = ( π ω k B T g B L A ) 1 / 2 ,             G = g B I p ( L ) L , C ^ = C I p ( L ) ,             q = I s ( o ) I p ( L ) ;
q min = 32 C ^ ( β ^ G ) 2 exp [ G 2 ( 1 - C ^ ) ] × [ 2 C ^ - 1 C ^ exp [ G 2 ( 1 - C ^ ) ] - 1 2 ] ,
1 - C ^ - 16 C ^ 2 ( β ^ G ) 2 e G C ^ = o .
G opt = 5.85 ( β ^ ) 0.108 .
SNR max = I s A 4 π k B T ω G opt ,
I s min = 4 π k B T ω G opt A ,
I s A = P s min = 2.3 ( ω k B T ) 1.054 ( g B L A ) 0.054
r r o = [ - ln ( 1 - 1 g B I p ( max ) L ) ] 1 / 2
( G opt ) max gain = 8.1 ( β ^ ) 0.092 .
A max = 0.26 exp ( 8.1 / β ^ 0.092 ) .
C = [ 2 γ - 2 I s ( o ) sinh ( H ) ] e - H ,
2 C I p ( L ) sinh ( C g B L 2 + H ) + C 2 exp [ - ( C g B L 2 + H ) ] = o ,
e - H = - γ + γ 2 + C I s ( o ) I s ( o ) .
C = I p ( L ) ( 1 - I s 2 ( o ) exp ( C g B L ) { [ γ 2 + C I s ( o ) ] 1 / 2 - γ } 2 ) .
I s ( L ) = I p ( L ) I s 2 ( o ) exp ( C g B L ) { [ γ 2 + C I s ( o ) ] 1 / 2 - γ } 2 .
I s min = 8 γ 2 C exp [ ( C - C ) g B L / 2 ] × { C C exp [ ( C - C ) g B L / 2 ] - 1 2 } ,
C = I p ( L ) [ 1 - 4 γ 2 C 2 exp ( C g B L ) ] .
C = 2 C - I p ( L ) .

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