Abstract

Analytic expressions are derived for the phase-conjugation fidelity loss for stimulated scattering in waveguides. Beginning from the perturbation result, one obtains three regimes for the fidelity for a rectangular mode distribution. For a broad waveguide, the result agrees with those obtained by other authors. For narrow waveguides, the fidelity is seen to improve, in qualitative agreement with experiments reported in the literature and in qualitative agreement with numerical results. This narrow-waveguide regime, along with an intermediate regime, gives a fidelity dependence similar to that obtained numerically.

© 1988 Optical Society of America

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References

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  1. B. Ya. Zel’dovich, T. V. Yakovleva, “Calculations of the accuracy of wavefront reversal utilizing pump radiation with one-dimensional transverse modulation,” Sov. J. Quantum Electron. 11, 186 (1981);B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985).
    [CrossRef]
  2. P. Suni, J. Falk, “Theory of phase conjugation by stimulated Brillouin scattering,” J. Opt. Soc. Am. B 3, 1681 (1986).
    [CrossRef]
  3. R. Mays, R. J. Lysiak, “Phase conjugated wavefronts by stimulated Brillouin and Raman scattering,” Opt. Commun. 31, 89 (1979).
    [CrossRef]
  4. R. H. Lehmberg, “Numerical study of phase conjugation in stimulated Brillouin scattering from an optical waveguide,” J. Opt. Soc. Am. 73, 558 (1983).
    [CrossRef]
  5. B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated MandePshtam–Brillouin scattering,” Sov. Phys. JETP 15, 109 (1972).
  6. B. Ya. Zel’dovich, T. V. Yakovleva, “Small-scale distortions in wavefront reversal of a beam with incomplete spatial modulation,” Sov. J. Quantum Electron. 10, 181 (1980).
    [CrossRef]
  7. G. G. Kochemasov, V. D. Nikolaev, “Investigation of the spatial characteristics of the Stokes radiation in stimulated scattering under saturation conditions,” Sov. J. Quantum Electron. 9, 1155 (1979).
    [CrossRef]
  8. I. M. Bel’dyugin, E. M. Zemskov, “Influence of changes in the pump field on the form of the field of a signal amplified under stimulated scattering conditions,” Sov. J. Quantum Electron 8, 1163 (1978).
    [CrossRef]
  9. R. W. Hellwarth, “Phase conjugation in stimulated backscattering,” in Optical Phase Conjugation, R. A. Fisher, ed.(Academic, New York, 1983).
    [CrossRef]
  10. R. H. Lehmberg, “Numerical study of phase conjugation in stimulated backscatter with pump depletion,” Opt. Commun. 43, 369 (1982).
    [CrossRef]

1986 (1)

1983 (1)

1982 (1)

R. H. Lehmberg, “Numerical study of phase conjugation in stimulated backscatter with pump depletion,” Opt. Commun. 43, 369 (1982).
[CrossRef]

1981 (1)

B. Ya. Zel’dovich, T. V. Yakovleva, “Calculations of the accuracy of wavefront reversal utilizing pump radiation with one-dimensional transverse modulation,” Sov. J. Quantum Electron. 11, 186 (1981);B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985).
[CrossRef]

1980 (1)

B. Ya. Zel’dovich, T. V. Yakovleva, “Small-scale distortions in wavefront reversal of a beam with incomplete spatial modulation,” Sov. J. Quantum Electron. 10, 181 (1980).
[CrossRef]

1979 (2)

G. G. Kochemasov, V. D. Nikolaev, “Investigation of the spatial characteristics of the Stokes radiation in stimulated scattering under saturation conditions,” Sov. J. Quantum Electron. 9, 1155 (1979).
[CrossRef]

R. Mays, R. J. Lysiak, “Phase conjugated wavefronts by stimulated Brillouin and Raman scattering,” Opt. Commun. 31, 89 (1979).
[CrossRef]

1978 (1)

I. M. Bel’dyugin, E. M. Zemskov, “Influence of changes in the pump field on the form of the field of a signal amplified under stimulated scattering conditions,” Sov. J. Quantum Electron 8, 1163 (1978).
[CrossRef]

1972 (1)

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated MandePshtam–Brillouin scattering,” Sov. Phys. JETP 15, 109 (1972).

Bel’dyugin, I. M.

I. M. Bel’dyugin, E. M. Zemskov, “Influence of changes in the pump field on the form of the field of a signal amplified under stimulated scattering conditions,” Sov. J. Quantum Electron 8, 1163 (1978).
[CrossRef]

Faizullov, F. S.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated MandePshtam–Brillouin scattering,” Sov. Phys. JETP 15, 109 (1972).

Falk, J.

Hellwarth, R. W.

R. W. Hellwarth, “Phase conjugation in stimulated backscattering,” in Optical Phase Conjugation, R. A. Fisher, ed.(Academic, New York, 1983).
[CrossRef]

Kochemasov, G. G.

G. G. Kochemasov, V. D. Nikolaev, “Investigation of the spatial characteristics of the Stokes radiation in stimulated scattering under saturation conditions,” Sov. J. Quantum Electron. 9, 1155 (1979).
[CrossRef]

Lehmberg, R. H.

R. H. Lehmberg, “Numerical study of phase conjugation in stimulated Brillouin scattering from an optical waveguide,” J. Opt. Soc. Am. 73, 558 (1983).
[CrossRef]

R. H. Lehmberg, “Numerical study of phase conjugation in stimulated backscatter with pump depletion,” Opt. Commun. 43, 369 (1982).
[CrossRef]

Lysiak, R. J.

R. Mays, R. J. Lysiak, “Phase conjugated wavefronts by stimulated Brillouin and Raman scattering,” Opt. Commun. 31, 89 (1979).
[CrossRef]

Mays, R.

R. Mays, R. J. Lysiak, “Phase conjugated wavefronts by stimulated Brillouin and Raman scattering,” Opt. Commun. 31, 89 (1979).
[CrossRef]

Nikolaev, V. D.

G. G. Kochemasov, V. D. Nikolaev, “Investigation of the spatial characteristics of the Stokes radiation in stimulated scattering under saturation conditions,” Sov. J. Quantum Electron. 9, 1155 (1979).
[CrossRef]

Popovichev, V. I.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated MandePshtam–Brillouin scattering,” Sov. Phys. JETP 15, 109 (1972).

Ragul’skii, V. V.

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated MandePshtam–Brillouin scattering,” Sov. Phys. JETP 15, 109 (1972).

Suni, P.

Yakovleva, T. V.

B. Ya. Zel’dovich, T. V. Yakovleva, “Calculations of the accuracy of wavefront reversal utilizing pump radiation with one-dimensional transverse modulation,” Sov. J. Quantum Electron. 11, 186 (1981);B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985).
[CrossRef]

B. Ya. Zel’dovich, T. V. Yakovleva, “Small-scale distortions in wavefront reversal of a beam with incomplete spatial modulation,” Sov. J. Quantum Electron. 10, 181 (1980).
[CrossRef]

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, T. V. Yakovleva, “Calculations of the accuracy of wavefront reversal utilizing pump radiation with one-dimensional transverse modulation,” Sov. J. Quantum Electron. 11, 186 (1981);B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985).
[CrossRef]

B. Ya. Zel’dovich, T. V. Yakovleva, “Small-scale distortions in wavefront reversal of a beam with incomplete spatial modulation,” Sov. J. Quantum Electron. 10, 181 (1980).
[CrossRef]

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated MandePshtam–Brillouin scattering,” Sov. Phys. JETP 15, 109 (1972).

Zemskov, E. M.

I. M. Bel’dyugin, E. M. Zemskov, “Influence of changes in the pump field on the form of the field of a signal amplified under stimulated scattering conditions,” Sov. J. Quantum Electron 8, 1163 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (2)

R. Mays, R. J. Lysiak, “Phase conjugated wavefronts by stimulated Brillouin and Raman scattering,” Opt. Commun. 31, 89 (1979).
[CrossRef]

R. H. Lehmberg, “Numerical study of phase conjugation in stimulated backscatter with pump depletion,” Opt. Commun. 43, 369 (1982).
[CrossRef]

Sov. J. Quantum Electron (1)

I. M. Bel’dyugin, E. M. Zemskov, “Influence of changes in the pump field on the form of the field of a signal amplified under stimulated scattering conditions,” Sov. J. Quantum Electron 8, 1163 (1978).
[CrossRef]

Sov. J. Quantum Electron. (3)

B. Ya. Zel’dovich, T. V. Yakovleva, “Calculations of the accuracy of wavefront reversal utilizing pump radiation with one-dimensional transverse modulation,” Sov. J. Quantum Electron. 11, 186 (1981);B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985).
[CrossRef]

B. Ya. Zel’dovich, T. V. Yakovleva, “Small-scale distortions in wavefront reversal of a beam with incomplete spatial modulation,” Sov. J. Quantum Electron. 10, 181 (1980).
[CrossRef]

G. G. Kochemasov, V. D. Nikolaev, “Investigation of the spatial characteristics of the Stokes radiation in stimulated scattering under saturation conditions,” Sov. J. Quantum Electron. 9, 1155 (1979).
[CrossRef]

Sov. Phys. JETP (1)

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated MandePshtam–Brillouin scattering,” Sov. Phys. JETP 15, 109 (1972).

Other (1)

R. W. Hellwarth, “Phase conjugation in stimulated backscattering,” in Optical Phase Conjugation, R. A. Fisher, ed.(Academic, New York, 1983).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Fidelity versus u/2. Solid and open diamonds, numerical calculations for backscattered light from Ref. 4; crosses, our numerical calculations; solid curves, fits of the analytic expression described in the text corresponding to the intermediate-width waveguide regime [expression (20)]; dashed curve, quoted by Ref. 4 from Ref. 1.

Equations (37)

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u = 2 k ( Θ L ) 2 / g I 1 ,
υ = 2 k ( Θ A ) 2 / g I ,
N = Θ L / Θ A .
1 H = 2 Θ 1 Θ 2 Θ 3 j ( Θ 1 ) j ( Θ 2 ) j ( Θ 3 ) 1 + ( Δ Θ 12 Δ Θ 13 a ) 2 ,
| Δ Θ 12 Δ Θ 13 a | 1 .
ϕ L a Θ L | Δ Θ 13 | a Θ A ϕ A .
ϕ L < ϕ A < Θ A < Θ L ,
ϕ L < Θ A < ϕ A < Θ L ,
ϕ L < Θ A < Θ L < ϕ A ,
Θ A < ϕ L < ϕ A < Θ L ,
Θ A < ϕ L < Θ L < ϕ A ,
Θ A < Θ L < ϕ L < ϕ A .
u > N ,
υ > 1 .
| Δ Θ 13 Θ A | = g I 2 k Θ A 2 1 .
2 j ( Θ 1 ) j ( Θ 1 ± Θ A ) j ( Θ 3 ) / [ 1 + ( Θ A 2 / a ) 2 ] .
1 H = 2 1 + ( Θ A 2 a ) 2 Θ 1 j ( Θ 1 ) j ( Θ 1 ± Θ A ) j ( Θ 1 ± Θ A ) .
j ( Θ ) = Θ A / Θ L = 1 / N .
1 H = 8 N 2 ( 1 + υ 2 ) ,
1 H = 8 / ( u υ ) .
u > N ,
1 < υ 1 < N .
| Δ Θ 13 Θ A | = max ( N / n , 1 ) ,
j ( Θ 1 ) j ( Θ 1 + n Θ A ) j ( Θ 3 ) ( 2 N / n ) .
1 H = 4 N | n θ 1 | = 1 N 1 n j ( Θ 1 ) j ( Θ 1 + n Θ A ) j ( Θ 3 ) + 2 | n θ 1 | = N N j ( Θ 1 ) j ( Θ 1 + n Θ A ) j ( Θ 1 ± Θ A ) 1 + ( n Θ A 2 a ) 2 .
Θ 1 j ( Θ 1 ) j ( Θ 1 + n Θ A ) = ( Θ L Θ A n ) ( Θ A Θ L ) 2 ,
j ( Θ 3 ) = Θ A / Θ L .
1 H ( 8 / u ) [ B ( N , 1 ) N / N ] + ( 8 / u υ ) × { 1 / N 1 / N [ 1 + B ( N , N ) ] } + 0 ( u 1 ) ( 8 / u ) { In ( u ) + 1 + C + In ( N 2 ) ( N / u ) × [ 2 ln ( N / u ) ] } + 0 ( u 1 ) ,
B ( N , N ) N N 1 n
C = Euler’s constant .
u > 1 ,
υ 1 > N .
| Δ Θ 13 Θ A | = min ( N / n , N ) ,
j ( Θ 1 ) j ( Θ 1 + n Θ A ) j ( Θ 3 ) ( 2 N / n ) if n > N / N , j ( Θ 1 ) j ( Θ 1 + n Θ A ) j ( Θ 3 ) ( 2 N ) if n < N / N .
N = integer part of N / N .
1 H = 4 N | n | = 1 Θ 1 N j ( Θ 1 ) j ( Θ 1 + n Θ A ) j ( Θ 3 ) + 4 N | n | = N Θ 1 N ( 1 n ) j ( Θ 1 ) j ( Θ 1 + n Θ A ) j ( Θ 3 ) .
1 H ( 8 / u ) ln ( u ) + 0 ( u 1 ) .

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