Abstract

We investigate the process of Brillouin amplification when the pump beam has a TEM00 Gaussian spatial profile. We show that the fidelity of amplification is a function of the ratio of the signal-beam diameter to the pump-beam diameter, the signal-beam intensity, and the small-signal gain of the Brillouin amplifier. We have verified these results experimentally by amplifying weak 1.06-μm laser pulses in CCl2FCClF2.

© 1991 Optical Society of America

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References

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  1. N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, G. A. Pasmanik, Rev. Roum. Phys. 31, 951 (1986).
  2. R. Fedosejevs, I. V. Tomov, D. C. D. McKen, A. A. Offenberger, Appl. Phys. Lett. 45, 340 (1984).
    [CrossRef]
  3. S. Sternklar, S. Jackel, D. Chomsky, A. Zigler, Opt. Lett. 15, 616 (1990).
    [CrossRef]
  4. K. D. Ridley, A. M. Scott, Opt. Lett. 15, 777 (1990).
    [CrossRef] [PubMed]
  5. A. M. Scott, D. E. Watkins, P. Tapster, J. Opt. Soc. Am. B 7, 929 (1990).
    [CrossRef]
  6. W. Kaiser, M. Maier, inLaser Handbook,F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland,Amsterdam, (1972), Vol.2, p.1078.
  7. E. J. Miller, M. D. Skeldon, R. W. Boyd, Appl. Opt. 28, 92 (1989).
    [CrossRef] [PubMed]
  8. B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).
  9. B. Ya. Zel’dovich, N. F. Pilipetskii, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag,Berlin, 1985).
    [CrossRef]
  10. A. A. Betin, G. A. Pasmanik, Kvantovaya Elektron. (Moscow) 4, 60 (1973) [Sov. J. Quantum Electron. 3, 312 (1974)].
  11. A. Yariv, Quantum Electronics,3rd ed. (Wiley,New York,1989), Sec. 6.6.
  12. D. Cotter, D. C. Hanna, R. Wyatt, Appl. Phys. 8, 333 (1975).
    [CrossRef]

1990 (3)

1989 (1)

1986 (1)

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, G. A. Pasmanik, Rev. Roum. Phys. 31, 951 (1986).

1984 (1)

R. Fedosejevs, I. V. Tomov, D. C. D. McKen, A. A. Offenberger, Appl. Phys. Lett. 45, 340 (1984).
[CrossRef]

1975 (1)

D. Cotter, D. C. Hanna, R. Wyatt, Appl. Phys. 8, 333 (1975).
[CrossRef]

1973 (1)

A. A. Betin, G. A. Pasmanik, Kvantovaya Elektron. (Moscow) 4, 60 (1973) [Sov. J. Quantum Electron. 3, 312 (1974)].

1972 (1)

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

Andreev, N. F.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, G. A. Pasmanik, Rev. Roum. Phys. 31, 951 (1986).

Bespalov, V. I.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, G. A. Pasmanik, Rev. Roum. Phys. 31, 951 (1986).

Betin, A. A.

A. A. Betin, G. A. Pasmanik, Kvantovaya Elektron. (Moscow) 4, 60 (1973) [Sov. J. Quantum Electron. 3, 312 (1974)].

Boyd, R. W.

Chomsky, D.

Cotter, D.

D. Cotter, D. C. Hanna, R. Wyatt, Appl. Phys. 8, 333 (1975).
[CrossRef]

Dvoretsky, M. A.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, G. A. Pasmanik, Rev. Roum. Phys. 31, 951 (1986).

Faizullov, F. S.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

Fedosejevs, R.

R. Fedosejevs, I. V. Tomov, D. C. D. McKen, A. A. Offenberger, Appl. Phys. Lett. 45, 340 (1984).
[CrossRef]

Hanna, D. C.

D. Cotter, D. C. Hanna, R. Wyatt, Appl. Phys. 8, 333 (1975).
[CrossRef]

Jackel, S.

Kaiser, W.

W. Kaiser, M. Maier, inLaser Handbook,F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland,Amsterdam, (1972), Vol.2, p.1078.

Katin, E. V.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, G. A. Pasmanik, Rev. Roum. Phys. 31, 951 (1986).

Maier, M.

W. Kaiser, M. Maier, inLaser Handbook,F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland,Amsterdam, (1972), Vol.2, p.1078.

Matveev, A. Z.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, G. A. Pasmanik, Rev. Roum. Phys. 31, 951 (1986).

McKen, D. C. D.

R. Fedosejevs, I. V. Tomov, D. C. D. McKen, A. A. Offenberger, Appl. Phys. Lett. 45, 340 (1984).
[CrossRef]

Miller, E. J.

Offenberger, A. A.

R. Fedosejevs, I. V. Tomov, D. C. D. McKen, A. A. Offenberger, Appl. Phys. Lett. 45, 340 (1984).
[CrossRef]

Pasmanik, G. A.

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, G. A. Pasmanik, Rev. Roum. Phys. 31, 951 (1986).

A. A. Betin, G. A. Pasmanik, Kvantovaya Elektron. (Moscow) 4, 60 (1973) [Sov. J. Quantum Electron. 3, 312 (1974)].

Pilipetskii, N. F.

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

Popovichev, V. I.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

Ragul’skii, V. V.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

Ridley, K. D.

Scott, A. M.

Shkunov, V. V.

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

Skeldon, M. D.

Sternklar, S.

Tapster, P.

Tomov, I. V.

R. Fedosejevs, I. V. Tomov, D. C. D. McKen, A. A. Offenberger, Appl. Phys. Lett. 45, 340 (1984).
[CrossRef]

Watkins, D. E.

Wyatt, R.

D. Cotter, D. C. Hanna, R. Wyatt, Appl. Phys. 8, 333 (1975).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics,3rd ed. (Wiley,New York,1989), Sec. 6.6.

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

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

Zigler, A.

Appl. Opt. (1)

Appl. Phys. (1)

D. Cotter, D. C. Hanna, R. Wyatt, Appl. Phys. 8, 333 (1975).
[CrossRef]

Appl. Phys. Lett. (1)

R. Fedosejevs, I. V. Tomov, D. C. D. McKen, A. A. Offenberger, Appl. Phys. Lett. 45, 340 (1984).
[CrossRef]

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

JETP Lett. (1)

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, JETP Lett. 15, 109 (1972).

Kvantovaya Elektron. (Moscow) (1)

A. A. Betin, G. A. Pasmanik, Kvantovaya Elektron. (Moscow) 4, 60 (1973) [Sov. J. Quantum Electron. 3, 312 (1974)].

Opt. Lett. (2)

Rev. Roum. Phys. (1)

N. F. Andreev, V. I. Bespalov, M. A. Dvoretsky, E. V. Katin, A. Z. Matveev, G. A. Pasmanik, Rev. Roum. Phys. 31, 951 (1986).

Other (3)

W. Kaiser, M. Maier, inLaser Handbook,F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland,Amsterdam, (1972), Vol.2, p.1078.

A. Yariv, Quantum Electronics,3rd ed. (Wiley,New York,1989), Sec. 6.6.

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

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Figures (7)

Fig. 1
Fig. 1

Schematic showing Brillouin amplification geometry.

Fig. 2
Fig. 2

Relative change in signal-beam spot sizeωs(0)/ωs(L) versus signal-beam peak gain. The input pump- to signal-beam spot size ratiosωp/ωs(L) are a, 4.0; b, 2.0; c, 1.0; d, 0.5; e, 0.25.

Fig. 3
Fig. 3

Relative change in signal-beam spot sizeωs(0)/ωs(L) versus signal-beam peak intensity gain for equal input signal- and pump-beam spot sizesωp(0) =ωs(L). The peak normalized input signal intensitiesgL|Es(L, 0)|2 are a, 10.0; b, 1.0; c, 0.1; d, 10−2; e, 10−3; f, 10−4.

Fig. 4
Fig. 4

Schematic of experimental setup; A’s, apertures.

Fig. 5
Fig. 5

Undepleted-pump regime: output signal-beam diameter (1/e) versus signal-beam peak gain. The input pump-beam diameter is 1.4 mm. a, Input signal-beam diameter, 1.8 mm; b, input signal-beam diameter, 0.78 mm. The solid curves are the theoretical predictions.

Fig. 6
Fig. 6

Depleted-pump regime: output signal-beam diameter versus signal-beam peak gain. The input pump diameter is 1.4 mm; the input signal diameter is 0.78 mm. The input signal-beam energies are a, 1μJ; b, 10μJ; c, 100μJ; d, 5 mJ.

Fig. 7
Fig. 7

Depleted-pump regime: output signal-beam diameter versus signal-beam peak gain. The input pump diameter is 1.4 mm; the input signal diameter is 1.8 mm. The input signal-beam energies are a, 10μJ; b, 100μJ; c, 5 mJ.

Equations (15)

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E p z - i 2 k E p = - g 2 E s 2 E p ,
E s z - i 2 k E s = - g 2 E p 2 E s ,
E s z + i 2 k r r ( r E s r ) = - g 2 I p E s ,
E s ( r , z ) = E s 0 exp [ - ( i / 2 ) Q r 2 ] ,
Q ( z ) = k R ( z ) - 2 i ω s ( z ) 2 .
1 E s 0 d E s 0 d z + Q k = - g 2 I p 0 ,
d Q d z + Q 2 k = 2 i g I p 0 ω p 2 .
Q ( z ) = A 1 / 2 tan [ A 1 / 2 k ( z - L ) + α ] .
E s 0 ( z ) = E s 0 ( L ) { cos [ ( A 1 / 2 / k ) ( z - L ) + α ] cos α } × exp [ g 2 I p 0 ( L - z ) ] .
ω s ( z ) = ω s ( L ) { 1 + g I p 0 ( L - z ) [ ω s ( L ) / ω p ] 2 } 1 / 2 .
1 + i ( z - L ) k [ 2 ω s ( L ) 2 - 2 g I p 0 ( z - L ) ω p 2 ] ,
M s ( 0 ) [ M s ( L ) + M p ( 0 ) - M s ( 0 ) ] = M s ( L ) M p ( 0 ) exp [ M p ( 0 ) - M s ( 0 ) ] ,
M p ( 0 , r ) = M p ( 0 , 0 ) exp ( - 2 r 2 ω p ( 0 ) 2 ) ,
M s ( L , r ) = M s ( L , 0 ) exp ( - 2 r 2 ω s ( L ) 2 ) ,
M s ( 0 , 0 ) e 2 { M s ( L , 0 ) exp [ - 2 ω s ( 0 ) 2 ω s ( L ) 2 ] + M p ( 0 , 0 ) exp [ - 2 ω s ( 0 ) 2 ω p ( 0 ) 2 ] - M s ( 0 , 0 ) e 2 } = M s ( L , 0 ) exp [ - 2 ω s ( 0 ) ω s ( L ) 2 ] M p ( 0 , 0 ) exp [ - 2 ω s ( 0 ) 2 ω p ( 0 ) 2 ] × exp { M p ( 0 , 0 ) exp [ - 2 ω s ( 0 ) 2 ω p ( 0 ) 2 ] - M s ( 0 , 0 ) e 2 } .

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