Abstract

The growth of optical radiation, scattered transverse to the pump axis by stimulated Brillouin scattering (SBS) in optical windows, is considered. Basic equations are presented, and an analytic expression that determines the parasitic buildup time is derived for a transverse SBS geometry. Losses suffered by the scattered optical radiation are included in a bulk-loss term. Calculations are performed for fused-silica windows and compared with a numerical model. This parasitic process may affect the design of laser systems that will generate multinanosecond, multikilojoule, narrow-band pulses in the ultraviolet region.

© 1987 Optical Society of America

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References

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  1. W. Kaiser, M. Maier, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150, and references therein.
  2. A. Yariv, Quantum Electronics (Wiley, New York, 1975).
  3. C. Yu, M. F. Haw, H. Hsu, Electron. Lett. 13, 240 (1977), and references therein.
    [Crossref]
  4. D. B. Harris, J. H. Pendergrass, Fusion Technol. 8, 1868 (1985).
  5. G. B. Benedek, K. Fritsch, Phys. Rev. 149, 647 (1966).
    [Crossref]
  6. E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
    [Crossref]
  7. R. Vacher, J. Pelous, Phys. Rev. B 14, 823 (1976).
    [Crossref]
  8. N. L. Rowell, P. J. Thomas, H. M. Van Driel, G. I. Stegeman, Appl. Phys. Lett. 34, 139 (1979).
    [Crossref]
  9. S. A. Akhmanov, Yu. E. D'yakov, L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).

1985 (1)

D. B. Harris, J. H. Pendergrass, Fusion Technol. 8, 1868 (1985).

1979 (1)

N. L. Rowell, P. J. Thomas, H. M. Van Driel, G. I. Stegeman, Appl. Phys. Lett. 34, 139 (1979).
[Crossref]

1977 (1)

C. Yu, M. F. Haw, H. Hsu, Electron. Lett. 13, 240 (1977), and references therein.
[Crossref]

1976 (1)

R. Vacher, J. Pelous, Phys. Rev. B 14, 823 (1976).
[Crossref]

1974 (1)

S. A. Akhmanov, Yu. E. D'yakov, L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).

1972 (1)

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[Crossref]

1966 (1)

G. B. Benedek, K. Fritsch, Phys. Rev. 149, 647 (1966).
[Crossref]

Akhmanov, S. A.

S. A. Akhmanov, Yu. E. D'yakov, L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).

Benedek, G. B.

G. B. Benedek, K. Fritsch, Phys. Rev. 149, 647 (1966).
[Crossref]

D'yakov, Yu. E.

S. A. Akhmanov, Yu. E. D'yakov, L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).

Fritsch, K.

G. B. Benedek, K. Fritsch, Phys. Rev. 149, 647 (1966).
[Crossref]

Harris, D. B.

D. B. Harris, J. H. Pendergrass, Fusion Technol. 8, 1868 (1985).

Haw, M. F.

C. Yu, M. F. Haw, H. Hsu, Electron. Lett. 13, 240 (1977), and references therein.
[Crossref]

Hsu, H.

C. Yu, M. F. Haw, H. Hsu, Electron. Lett. 13, 240 (1977), and references therein.
[Crossref]

Ippen, E. P.

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[Crossref]

Kaiser, W.

W. Kaiser, M. Maier, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150, and references therein.

Maier, M.

W. Kaiser, M. Maier, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150, and references therein.

Pavlov, L. I.

S. A. Akhmanov, Yu. E. D'yakov, L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).

Pelous, J.

R. Vacher, J. Pelous, Phys. Rev. B 14, 823 (1976).
[Crossref]

Pendergrass, J. H.

D. B. Harris, J. H. Pendergrass, Fusion Technol. 8, 1868 (1985).

Rowell, N. L.

N. L. Rowell, P. J. Thomas, H. M. Van Driel, G. I. Stegeman, Appl. Phys. Lett. 34, 139 (1979).
[Crossref]

Stegeman, G. I.

N. L. Rowell, P. J. Thomas, H. M. Van Driel, G. I. Stegeman, Appl. Phys. Lett. 34, 139 (1979).
[Crossref]

Stolen, R. H.

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[Crossref]

Thomas, P. J.

N. L. Rowell, P. J. Thomas, H. M. Van Driel, G. I. Stegeman, Appl. Phys. Lett. 34, 139 (1979).
[Crossref]

Vacher, R.

R. Vacher, J. Pelous, Phys. Rev. B 14, 823 (1976).
[Crossref]

Van Driel, H. M.

N. L. Rowell, P. J. Thomas, H. M. Van Driel, G. I. Stegeman, Appl. Phys. Lett. 34, 139 (1979).
[Crossref]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

Yu, C.

C. Yu, M. F. Haw, H. Hsu, Electron. Lett. 13, 240 (1977), and references therein.
[Crossref]

Appl. Phys. Lett. (2)

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[Crossref]

N. L. Rowell, P. J. Thomas, H. M. Van Driel, G. I. Stegeman, Appl. Phys. Lett. 34, 139 (1979).
[Crossref]

Electron. Lett. (1)

C. Yu, M. F. Haw, H. Hsu, Electron. Lett. 13, 240 (1977), and references therein.
[Crossref]

Fusion Technol. (1)

D. B. Harris, J. H. Pendergrass, Fusion Technol. 8, 1868 (1985).

Phys. Rev. (1)

G. B. Benedek, K. Fritsch, Phys. Rev. 149, 647 (1966).
[Crossref]

Phys. Rev. B (1)

R. Vacher, J. Pelous, Phys. Rev. B 14, 823 (1976).
[Crossref]

Sov. Phys. JETP (1)

S. A. Akhmanov, Yu. E. D'yakov, L. I. Pavlov, Sov. Phys. JETP 39, 249 (1974).

Other (2)

W. Kaiser, M. Maier, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150, and references therein.

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

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Figures (3)

Fig. 1
Fig. 1

Phase-matching diagram for SBS showing the pump, Stokes, and acoustic wave vectors.

Fig. 2
Fig. 2

Transverse SBS geometry. A uniform pump field in time and space is normally incident upon a window. A Stokes field propagating normal to the pump field builds up, reflecting off the sides of the windows with reflection coefficient R, and eventually depletes the pump field.

Fig. 3
Fig. 3

Comparison of analytic results with a numerical model. Plotted is the buildup time (f = 0.1) to depletion threshold versus the KrF pump intensity in a uniformly filled fused-silica optical window. The first case is for a very wide window or one with perfectly reflecting edges. The second and third cases are for 40-cm- and 20-cm-wide windows, respectively, with a reflectivity of 0.001 at their edges. All curves assume a width-to-thickness ratio of 10.

Equations (18)

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ω a = 2 ω p n υ a c sin ( θ / 2 ) ,
ω s = ω p ω a ,
θ a = ( θ / 2 ) 90 ° ,
E s = ( π / c ) 1 / 2 S exp [ i ( ω s t K s r ) ] + c.c. ,
E p = ( π / c ) 1 / 2 P exp [ i ( ω p t K p r ) ] + c.c. ,
( δ δ t + c n δ δ x p ) P = S ρ * α p 2 P ,
( δ δ t + c n δ δ x s ) S = P ρ α p 2 S ,
( 2 τ b δ δ t + 1 ) ρ = g 0 c 4 n S P * ,
g 0 = 2 π n 7 P 12 2 c ρ 0 λ s 2 υ a Δ ν b 1 sin θ / 2 ,
Δ ν = ( ω a ω a 0 ) 2 Δ ν b 0 ,
1 / τ b = 2 π Δ ν .
[ δ δ t 2 + ( 1 2 τ b + α s s ) δ δ t + ( α s 4 τ b g 0 I p c 4 τ b n ) ] S = 0 .
κ ± = ± [ ( 1 α s τ b 4 τ b ) 2 + g 0 I p c 4 τ b n ] 1 / 2 1 + α s τ b 4 τ b .
I s ( t ) I s ( 0 ) exp ( 2 κ + t ) .
T = 1 2 κ + ln ( f I p t I n w ) ,
α s = [ c ln ( R ) ] / ( n w ) .
I p = ( α s n ) / ( g 0 c ) .
I th b = I th m + I cr , I cr = ( 4 Δ ν p ) / g ,

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