Abstract

Phase conjugation in stimulated Brillouin scattering (SBS) from an optical waveguide is studied numerically, using a Cartesian two-dimensional propagation code (bounce) that includes pump depletion. The simulations show that light scattered back through a phase aberrator produces a far-field profile closely matching that of the incident beam; however, the near-field intensity exhibits large and rapid spatial inhomogeneities across the entire aberrator, even for conjugation fidelities H as high as 98%. This effect can be only partially removed by spatial-filtering techniques. The dependence of H on SBS gain, scattering length L, and the average intensity Ī and angular divergence θD of the pump beam is first studied in the low-reflectivity regime (i.e., ignoring pump depletion). For amplitude gains ≳e10, H decreases monotonically with the factor Ī/θD that is due to a small-scale intensity pulling effect. This result appears to be independent of whether θD arises entirely from the aberrator or from a combination of the aberrator plus curvature introduced by a lens. In all cases, pump depletion is found to enhance the fidelity by inhibiting the small-scale pulling effect. Under appropriate conditions, this can actually reverse the intensity dependence of H seen in the absence of pump depletion.

© 1983 Optical Society of America

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  1. R. W. Hellwarth, “Optical beam phase conjugation by stimulated backscattering,” Opt. Eng. 21, 257–262 (1982), and references therein.
    [CrossRef]
  2. V. G. Sidorovich, “Theory of the Brillouin mirror,” Zh. Tekh. Fiz. 46, 2168–2174 (1976) [Sov. Phys. Tech. Phys. 21, 1270–1274 (1976)].
  3. I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, and V. I. Mandrosov, “Complex conjugation of fields in stimulated Brillouin scattering.” Kvantovaya Elektron. 3, 2467–2470 (1976) [Sov. J. Quantum Electron. 6, 1349–1351 (1976)].
  4. B. Ya. Zel’dovich and V. V. Shkunov, “Limits of existence of wavefront reversal in stimulated light scattering,” Kvantovaya Elektron. 5, 36–43 (1978) [Sov. J. Quantum Electron. 8, 15–20 (1978)].
  5. B. Ya. Zel’dovich and T. V. Yakovlea, “Calculations of the accuracy of wavefront reversal utilizing pump radiation with one-dimensional transverse modulation,” Kvantovaya Elektron. 8, 314–321 (1981) [Sov. J. Quantum Electron. 11, 186–189 (1981)].
  6. R. W. Hellwarth, “Theory of phase conjugation by stimulated scattering in a waveguide,” J. Opt. Soc. Am. 68, 1050–1056 (1978).
    [CrossRef]
  7. R. H. Lehmberg, “Theory of optical ray retracing in laser-plasma backscatter,” Phys. Rev. Lett. 41, 863–866 (1978).
    [CrossRef]
  8. N. B. Baranova, B. Ya. Zel’dovich, and V. V. Shkunov, “Wavefront reversal in stimulated light scattering in a focused spatially inhomogeneous pump beam,” Kvantovaya Elektron. 5, 973–985 (1978) [Sov. J. Quantum Electron. 8, 559–566 (1978)].
  9. N. B. Baranova and B. Ya. Zel’dovich, “Wavefront reversal of focused beams (theory of stimulated Brillouin backscattering),” Kvantovaya Elektron. 7, 973–982 (1980) [Sov. J. Quantum Electron. 10, 555–560 (1980)].
  10. G. G. Kochemasov and V. D. Nikolaev, “Investigation of the spatial characteristics of Stokes radiation in stimulated scattering under saturation conditions,” Kvantovaya Elektron. 6, 1960–1965 (1979) [Sov. J. Quantum Electron. 9, 1155–1157 (1979)].
  11. R. H. Lehmberg, “Numerical study of phase conjugation in stimulated backscatter with pump depletion,” Opt. Commun. 43, 369–374 (1982).
    [CrossRef]
  12. B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel’shtam–Brillouin scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 15, 160–164 (1972) [JETP Lett. 15, 109–112 (1972)].
  13. O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Cancellation of phase distortions in an amplifying medium with a Brillouin mirror,” Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617–621 (1972) [Sov. Phys. JETP Lett. 16, 435–438 (1972)].
  14. V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Melnikov, N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Wavefront inversion in stimulated scattering of focused light beams,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 211–215 (1977) [Sov. Tech. Phys. Lett. 3, 83–85 (1977)].
  15. V. Wang and C. R. Guiliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2, 4–6 (1978).
    [CrossRef] [PubMed]
  16. C. R. Guiliano, R. W. Hellwarth, R. K. Jain, R. C. Lind, T. R. O’Meara, S. M. Wandzura, and V. Wang, “Correction of phase distortion by nonlinear optical techniques” (Hughes Research Laboratories Interim Tech. Rep. for period 15 July 1977–30 September 1978 (March1979).
  17. N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, A. B. Mironov, S. I. Mikhailov, and M. G. Smirnov, “Influence of certain radiation parameters on wavefront reversal of a pump wave in a Brillouin mirror,” Kvantovaya Elektron,  6, 765–771 (1979) [Sov. J. Quantum Electron. 9, 455–458 (1979)].
  18. R. Mays and R. J. Lysiak, “Phase conjugated wavefronts by stimulated Brillouin and Raman scattering,” Opt. Commun. 31, 89–92 (1979).
    [CrossRef]
  19. R. Mays and R. J. Lysiak,„ Observations of wavefront reproduction by stimulated Brillouin and Raman scattering as a function of pump power and waveguide dimensions,” Opt. Commun. 32, 334–338 (1980).
    [CrossRef]
  20. N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Comparison of the amplification coefficients of conjugate and nonconjugate waves in stimulated light scattering,” Opt. Commun. 40, 73–76 (1981).
    [CrossRef]
  21. M. C. Gower and R. G. Caro, “KrF laser with a phase-conjugate Brillouin mirror,” Opt. Lett. 7, 162–164 (1982).
    [CrossRef] [PubMed]
  22. V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, “Reconstruction effects in stimulated scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 215–220 (1977) [Sov. Tech. Phys. Lett. 3, 85–87 (1977)].
  23. A. I. Sokolovskyaya, G. L. Blekhovskikh, and A. D. Kudryavtseva, “Light beam wavefront reconstruction and real volume image reconstruction of the object in stimulated Raman scattering,” Opt. Commun. 24, 74–76 (1978).
    [CrossRef]
  24. M. Slatkine, I. J. Bigio, B. J. Feldman, and R. A. Fisher, “Efficient phase conjugation of an ultraviolet XeF laser beam by stimulated Brillouin scattering,” Opt. Lett. 7, 108–110 (1982).
    [CrossRef] [PubMed]
  25. R. H. Lehmberg and K. A. Holder, “Numerical study of optical ray retracing in laser-plasma backscatter,” Phys. Rev. 22, 2156–2170 (1980).
    [CrossRef]
  26. J. A. Fleck, J. R. Morris, and M. D. Feit, “Time dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–139 (1976); Appl. Phys. 14, 99–115 (1977).
    [CrossRef]

1982 (4)

R. W. Hellwarth, “Optical beam phase conjugation by stimulated backscattering,” Opt. Eng. 21, 257–262 (1982), and references therein.
[CrossRef]

R. H. Lehmberg, “Numerical study of phase conjugation in stimulated backscatter with pump depletion,” Opt. Commun. 43, 369–374 (1982).
[CrossRef]

M. C. Gower and R. G. Caro, “KrF laser with a phase-conjugate Brillouin mirror,” Opt. Lett. 7, 162–164 (1982).
[CrossRef] [PubMed]

M. Slatkine, I. J. Bigio, B. J. Feldman, and R. A. Fisher, “Efficient phase conjugation of an ultraviolet XeF laser beam by stimulated Brillouin scattering,” Opt. Lett. 7, 108–110 (1982).
[CrossRef] [PubMed]

1981 (2)

N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Comparison of the amplification coefficients of conjugate and nonconjugate waves in stimulated light scattering,” Opt. Commun. 40, 73–76 (1981).
[CrossRef]

B. Ya. Zel’dovich and T. V. Yakovlea, “Calculations of the accuracy of wavefront reversal utilizing pump radiation with one-dimensional transverse modulation,” Kvantovaya Elektron. 8, 314–321 (1981) [Sov. J. Quantum Electron. 11, 186–189 (1981)].

1980 (3)

N. B. Baranova and B. Ya. Zel’dovich, “Wavefront reversal of focused beams (theory of stimulated Brillouin backscattering),” Kvantovaya Elektron. 7, 973–982 (1980) [Sov. J. Quantum Electron. 10, 555–560 (1980)].

R. Mays and R. J. Lysiak,„ Observations of wavefront reproduction by stimulated Brillouin and Raman scattering as a function of pump power and waveguide dimensions,” Opt. Commun. 32, 334–338 (1980).
[CrossRef]

R. H. Lehmberg and K. A. Holder, “Numerical study of optical ray retracing in laser-plasma backscatter,” Phys. Rev. 22, 2156–2170 (1980).
[CrossRef]

1979 (3)

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, A. B. Mironov, S. I. Mikhailov, and M. G. Smirnov, “Influence of certain radiation parameters on wavefront reversal of a pump wave in a Brillouin mirror,” Kvantovaya Elektron,  6, 765–771 (1979) [Sov. J. Quantum Electron. 9, 455–458 (1979)].

R. Mays and R. J. Lysiak, “Phase conjugated wavefronts by stimulated Brillouin and Raman scattering,” Opt. Commun. 31, 89–92 (1979).
[CrossRef]

G. G. Kochemasov and V. D. Nikolaev, “Investigation of the spatial characteristics of Stokes radiation in stimulated scattering under saturation conditions,” Kvantovaya Elektron. 6, 1960–1965 (1979) [Sov. J. Quantum Electron. 9, 1155–1157 (1979)].

1978 (6)

R. W. Hellwarth, “Theory of phase conjugation by stimulated scattering in a waveguide,” J. Opt. Soc. Am. 68, 1050–1056 (1978).
[CrossRef]

R. H. Lehmberg, “Theory of optical ray retracing in laser-plasma backscatter,” Phys. Rev. Lett. 41, 863–866 (1978).
[CrossRef]

N. B. Baranova, B. Ya. Zel’dovich, and V. V. Shkunov, “Wavefront reversal in stimulated light scattering in a focused spatially inhomogeneous pump beam,” Kvantovaya Elektron. 5, 973–985 (1978) [Sov. J. Quantum Electron. 8, 559–566 (1978)].

V. Wang and C. R. Guiliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2, 4–6 (1978).
[CrossRef] [PubMed]

B. Ya. Zel’dovich and V. V. Shkunov, “Limits of existence of wavefront reversal in stimulated light scattering,” Kvantovaya Elektron. 5, 36–43 (1978) [Sov. J. Quantum Electron. 8, 15–20 (1978)].

A. I. Sokolovskyaya, G. L. Blekhovskikh, and A. D. Kudryavtseva, “Light beam wavefront reconstruction and real volume image reconstruction of the object in stimulated Raman scattering,” Opt. Commun. 24, 74–76 (1978).
[CrossRef]

1977 (2)

V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, “Reconstruction effects in stimulated scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 215–220 (1977) [Sov. Tech. Phys. Lett. 3, 85–87 (1977)].

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Melnikov, N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Wavefront inversion in stimulated scattering of focused light beams,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 211–215 (1977) [Sov. Tech. Phys. Lett. 3, 83–85 (1977)].

1976 (3)

V. G. Sidorovich, “Theory of the Brillouin mirror,” Zh. Tekh. Fiz. 46, 2168–2174 (1976) [Sov. Phys. Tech. Phys. 21, 1270–1274 (1976)].

I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, and V. I. Mandrosov, “Complex conjugation of fields in stimulated Brillouin scattering.” Kvantovaya Elektron. 3, 2467–2470 (1976) [Sov. J. Quantum Electron. 6, 1349–1351 (1976)].

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–139 (1976); Appl. Phys. 14, 99–115 (1977).
[CrossRef]

1972 (2)

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel’shtam–Brillouin scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 15, 160–164 (1972) [JETP Lett. 15, 109–112 (1972)].

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Cancellation of phase distortions in an amplifying medium with a Brillouin mirror,” Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617–621 (1972) [Sov. Phys. JETP Lett. 16, 435–438 (1972)].

Baranova, N. B.

N. B. Baranova and B. Ya. Zel’dovich, “Wavefront reversal of focused beams (theory of stimulated Brillouin backscattering),” Kvantovaya Elektron. 7, 973–982 (1980) [Sov. J. Quantum Electron. 10, 555–560 (1980)].

N. B. Baranova, B. Ya. Zel’dovich, and V. V. Shkunov, “Wavefront reversal in stimulated light scattering in a focused spatially inhomogeneous pump beam,” Kvantovaya Elektron. 5, 973–985 (1978) [Sov. J. Quantum Electron. 8, 559–566 (1978)].

Basov, N. G.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, A. B. Mironov, S. I. Mikhailov, and M. G. Smirnov, “Influence of certain radiation parameters on wavefront reversal of a pump wave in a Brillouin mirror,” Kvantovaya Elektron,  6, 765–771 (1979) [Sov. J. Quantum Electron. 9, 455–458 (1979)].

Bel’dyugin, I. M.

I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, and V. I. Mandrosov, “Complex conjugation of fields in stimulated Brillouin scattering.” Kvantovaya Elektron. 3, 2467–2470 (1976) [Sov. J. Quantum Electron. 6, 1349–1351 (1976)].

Bespalov, V. I.

V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, “Reconstruction effects in stimulated scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 215–220 (1977) [Sov. Tech. Phys. Lett. 3, 85–87 (1977)].

Betin, A. A.

V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, “Reconstruction effects in stimulated scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 215–220 (1977) [Sov. Tech. Phys. Lett. 3, 85–87 (1977)].

Bigio, I. J.

Blashchuk, V. N.

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Melnikov, N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Wavefront inversion in stimulated scattering of focused light beams,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 211–215 (1977) [Sov. Tech. Phys. Lett. 3, 83–85 (1977)].

Blekhovskikh, G. L.

A. I. Sokolovskyaya, G. L. Blekhovskikh, and A. D. Kudryavtseva, “Light beam wavefront reconstruction and real volume image reconstruction of the object in stimulated Raman scattering,” Opt. Commun. 24, 74–76 (1978).
[CrossRef]

Caro, R. G.

Efimkov, V. F.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, A. B. Mironov, S. I. Mikhailov, and M. G. Smirnov, “Influence of certain radiation parameters on wavefront reversal of a pump wave in a Brillouin mirror,” Kvantovaya Elektron,  6, 765–771 (1979) [Sov. J. Quantum Electron. 9, 455–458 (1979)].

Faizullov, F. S.

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Cancellation of phase distortions in an amplifying medium with a Brillouin mirror,” Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617–621 (1972) [Sov. Phys. JETP Lett. 16, 435–438 (1972)].

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel’shtam–Brillouin scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 15, 160–164 (1972) [JETP Lett. 15, 109–112 (1972)].

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–139 (1976); Appl. Phys. 14, 99–115 (1977).
[CrossRef]

Feldman, B. J.

Fisher, R. A.

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–139 (1976); Appl. Phys. 14, 99–115 (1977).
[CrossRef]

Galushkin, M. G.

I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, and V. I. Mandrosov, “Complex conjugation of fields in stimulated Brillouin scattering.” Kvantovaya Elektron. 3, 2467–2470 (1976) [Sov. J. Quantum Electron. 6, 1349–1351 (1976)].

Gower, M. C.

Guiliano, C. R.

V. Wang and C. R. Guiliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2, 4–6 (1978).
[CrossRef] [PubMed]

C. R. Guiliano, R. W. Hellwarth, R. K. Jain, R. C. Lind, T. R. O’Meara, S. M. Wandzura, and V. Wang, “Correction of phase distortion by nonlinear optical techniques” (Hughes Research Laboratories Interim Tech. Rep. for period 15 July 1977–30 September 1978 (March1979).

Hellwarth, R. W.

R. W. Hellwarth, “Optical beam phase conjugation by stimulated backscattering,” Opt. Eng. 21, 257–262 (1982), and references therein.
[CrossRef]

R. W. Hellwarth, “Theory of phase conjugation by stimulated scattering in a waveguide,” J. Opt. Soc. Am. 68, 1050–1056 (1978).
[CrossRef]

C. R. Guiliano, R. W. Hellwarth, R. K. Jain, R. C. Lind, T. R. O’Meara, S. M. Wandzura, and V. Wang, “Correction of phase distortion by nonlinear optical techniques” (Hughes Research Laboratories Interim Tech. Rep. for period 15 July 1977–30 September 1978 (March1979).

Holder, K. A.

R. H. Lehmberg and K. A. Holder, “Numerical study of optical ray retracing in laser-plasma backscatter,” Phys. Rev. 22, 2156–2170 (1980).
[CrossRef]

Jain, R. K.

C. R. Guiliano, R. W. Hellwarth, R. K. Jain, R. C. Lind, T. R. O’Meara, S. M. Wandzura, and V. Wang, “Correction of phase distortion by nonlinear optical techniques” (Hughes Research Laboratories Interim Tech. Rep. for period 15 July 1977–30 September 1978 (March1979).

Kochemasov, G. G.

G. G. Kochemasov and V. D. Nikolaev, “Investigation of the spatial characteristics of Stokes radiation in stimulated scattering under saturation conditions,” Kvantovaya Elektron. 6, 1960–1965 (1979) [Sov. J. Quantum Electron. 9, 1155–1157 (1979)].

Kotov, A. V.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, A. B. Mironov, S. I. Mikhailov, and M. G. Smirnov, “Influence of certain radiation parameters on wavefront reversal of a pump wave in a Brillouin mirror,” Kvantovaya Elektron,  6, 765–771 (1979) [Sov. J. Quantum Electron. 9, 455–458 (1979)].

Kudryavtseva, A. D.

A. I. Sokolovskyaya, G. L. Blekhovskikh, and A. D. Kudryavtseva, “Light beam wavefront reconstruction and real volume image reconstruction of the object in stimulated Raman scattering,” Opt. Commun. 24, 74–76 (1978).
[CrossRef]

Lehmberg, R. H.

R. H. Lehmberg, “Numerical study of phase conjugation in stimulated backscatter with pump depletion,” Opt. Commun. 43, 369–374 (1982).
[CrossRef]

R. H. Lehmberg and K. A. Holder, “Numerical study of optical ray retracing in laser-plasma backscatter,” Phys. Rev. 22, 2156–2170 (1980).
[CrossRef]

R. H. Lehmberg, “Theory of optical ray retracing in laser-plasma backscatter,” Phys. Rev. Lett. 41, 863–866 (1978).
[CrossRef]

Lind, R. C.

C. R. Guiliano, R. W. Hellwarth, R. K. Jain, R. C. Lind, T. R. O’Meara, S. M. Wandzura, and V. Wang, “Correction of phase distortion by nonlinear optical techniques” (Hughes Research Laboratories Interim Tech. Rep. for period 15 July 1977–30 September 1978 (March1979).

Lysiak, R. J.

R. Mays and R. J. Lysiak,„ Observations of wavefront reproduction by stimulated Brillouin and Raman scattering as a function of pump power and waveguide dimensions,” Opt. Commun. 32, 334–338 (1980).
[CrossRef]

R. Mays and R. J. Lysiak, “Phase conjugated wavefronts by stimulated Brillouin and Raman scattering,” Opt. Commun. 31, 89–92 (1979).
[CrossRef]

Mandrosov, V. I.

I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, and V. I. Mandrosov, “Complex conjugation of fields in stimulated Brillouin scattering.” Kvantovaya Elektron. 3, 2467–2470 (1976) [Sov. J. Quantum Electron. 6, 1349–1351 (1976)].

Mays, R.

R. Mays and R. J. Lysiak,„ Observations of wavefront reproduction by stimulated Brillouin and Raman scattering as a function of pump power and waveguide dimensions,” Opt. Commun. 32, 334–338 (1980).
[CrossRef]

R. Mays and R. J. Lysiak, “Phase conjugated wavefronts by stimulated Brillouin and Raman scattering,” Opt. Commun. 31, 89–92 (1979).
[CrossRef]

Melnikov, N. A.

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Melnikov, N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Wavefront inversion in stimulated scattering of focused light beams,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 211–215 (1977) [Sov. Tech. Phys. Lett. 3, 83–85 (1977)].

Mikhailov, S. I.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, A. B. Mironov, S. I. Mikhailov, and M. G. Smirnov, “Influence of certain radiation parameters on wavefront reversal of a pump wave in a Brillouin mirror,” Kvantovaya Elektron,  6, 765–771 (1979) [Sov. J. Quantum Electron. 9, 455–458 (1979)].

Mironov, A. B.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, A. B. Mironov, S. I. Mikhailov, and M. G. Smirnov, “Influence of certain radiation parameters on wavefront reversal of a pump wave in a Brillouin mirror,” Kvantovaya Elektron,  6, 765–771 (1979) [Sov. J. Quantum Electron. 9, 455–458 (1979)].

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–139 (1976); Appl. Phys. 14, 99–115 (1977).
[CrossRef]

Nikolaev, V. D.

G. G. Kochemasov and V. D. Nikolaev, “Investigation of the spatial characteristics of Stokes radiation in stimulated scattering under saturation conditions,” Kvantovaya Elektron. 6, 1960–1965 (1979) [Sov. J. Quantum Electron. 9, 1155–1157 (1979)].

Nosach, O. Yu.

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Cancellation of phase distortions in an amplifying medium with a Brillouin mirror,” Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617–621 (1972) [Sov. Phys. JETP Lett. 16, 435–438 (1972)].

O’Meara, T. R.

C. R. Guiliano, R. W. Hellwarth, R. K. Jain, R. C. Lind, T. R. O’Meara, S. M. Wandzura, and V. Wang, “Correction of phase distortion by nonlinear optical techniques” (Hughes Research Laboratories Interim Tech. Rep. for period 15 July 1977–30 September 1978 (March1979).

Pasmanik, G. A.

V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, “Reconstruction effects in stimulated scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 215–220 (1977) [Sov. Tech. Phys. Lett. 3, 85–87 (1977)].

Pilipetskii, N. F.

N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Comparison of the amplification coefficients of conjugate and nonconjugate waves in stimulated light scattering,” Opt. Commun. 40, 73–76 (1981).
[CrossRef]

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Melnikov, N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Wavefront inversion in stimulated scattering of focused light beams,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 211–215 (1977) [Sov. Tech. Phys. Lett. 3, 83–85 (1977)].

Popovichev, V. I.

N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Comparison of the amplification coefficients of conjugate and nonconjugate waves in stimulated light scattering,” Opt. Commun. 40, 73–76 (1981).
[CrossRef]

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Melnikov, N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Wavefront inversion in stimulated scattering of focused light beams,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 211–215 (1977) [Sov. Tech. Phys. Lett. 3, 83–85 (1977)].

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel’shtam–Brillouin scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 15, 160–164 (1972) [JETP Lett. 15, 109–112 (1972)].

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Cancellation of phase distortions in an amplifying medium with a Brillouin mirror,” Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617–621 (1972) [Sov. Phys. JETP Lett. 16, 435–438 (1972)].

Ragul’skii, V. V.

N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Comparison of the amplification coefficients of conjugate and nonconjugate waves in stimulated light scattering,” Opt. Commun. 40, 73–76 (1981).
[CrossRef]

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Melnikov, N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Wavefront inversion in stimulated scattering of focused light beams,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 211–215 (1977) [Sov. Tech. Phys. Lett. 3, 83–85 (1977)].

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel’shtam–Brillouin scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 15, 160–164 (1972) [JETP Lett. 15, 109–112 (1972)].

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Cancellation of phase distortions in an amplifying medium with a Brillouin mirror,” Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617–621 (1972) [Sov. Phys. JETP Lett. 16, 435–438 (1972)].

Shkunov, V. V.

B. Ya. Zel’dovich and V. V. Shkunov, “Limits of existence of wavefront reversal in stimulated light scattering,” Kvantovaya Elektron. 5, 36–43 (1978) [Sov. J. Quantum Electron. 8, 15–20 (1978)].

N. B. Baranova, B. Ya. Zel’dovich, and V. V. Shkunov, “Wavefront reversal in stimulated light scattering in a focused spatially inhomogeneous pump beam,” Kvantovaya Elektron. 5, 973–985 (1978) [Sov. J. Quantum Electron. 8, 559–566 (1978)].

Sidorovich, V. G.

V. G. Sidorovich, “Theory of the Brillouin mirror,” Zh. Tekh. Fiz. 46, 2168–2174 (1976) [Sov. Phys. Tech. Phys. 21, 1270–1274 (1976)].

Slatkine, M.

Smirnov, M. G.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, A. B. Mironov, S. I. Mikhailov, and M. G. Smirnov, “Influence of certain radiation parameters on wavefront reversal of a pump wave in a Brillouin mirror,” Kvantovaya Elektron,  6, 765–771 (1979) [Sov. J. Quantum Electron. 9, 455–458 (1979)].

Sokolovskyaya, A. I.

A. I. Sokolovskyaya, G. L. Blekhovskikh, and A. D. Kudryavtseva, “Light beam wavefront reconstruction and real volume image reconstruction of the object in stimulated Raman scattering,” Opt. Commun. 24, 74–76 (1978).
[CrossRef]

Wandzura, S. M.

C. R. Guiliano, R. W. Hellwarth, R. K. Jain, R. C. Lind, T. R. O’Meara, S. M. Wandzura, and V. Wang, “Correction of phase distortion by nonlinear optical techniques” (Hughes Research Laboratories Interim Tech. Rep. for period 15 July 1977–30 September 1978 (March1979).

Wang, V.

V. Wang and C. R. Guiliano, “Correction of phase aberrations via stimulated Brillouin scattering,” Opt. Lett. 2, 4–6 (1978).
[CrossRef] [PubMed]

C. R. Guiliano, R. W. Hellwarth, R. K. Jain, R. C. Lind, T. R. O’Meara, S. M. Wandzura, and V. Wang, “Correction of phase distortion by nonlinear optical techniques” (Hughes Research Laboratories Interim Tech. Rep. for period 15 July 1977–30 September 1978 (March1979).

Yakovlea, T. V.

B. Ya. Zel’dovich and T. V. Yakovlea, “Calculations of the accuracy of wavefront reversal utilizing pump radiation with one-dimensional transverse modulation,” Kvantovaya Elektron. 8, 314–321 (1981) [Sov. J. Quantum Electron. 11, 186–189 (1981)].

Zel’dovich, B. Ya.

B. Ya. Zel’dovich and T. V. Yakovlea, “Calculations of the accuracy of wavefront reversal utilizing pump radiation with one-dimensional transverse modulation,” Kvantovaya Elektron. 8, 314–321 (1981) [Sov. J. Quantum Electron. 11, 186–189 (1981)].

N. B. Baranova and B. Ya. Zel’dovich, “Wavefront reversal of focused beams (theory of stimulated Brillouin backscattering),” Kvantovaya Elektron. 7, 973–982 (1980) [Sov. J. Quantum Electron. 10, 555–560 (1980)].

N. B. Baranova, B. Ya. Zel’dovich, and V. V. Shkunov, “Wavefront reversal in stimulated light scattering in a focused spatially inhomogeneous pump beam,” Kvantovaya Elektron. 5, 973–985 (1978) [Sov. J. Quantum Electron. 8, 559–566 (1978)].

B. Ya. Zel’dovich and V. V. Shkunov, “Limits of existence of wavefront reversal in stimulated light scattering,” Kvantovaya Elektron. 5, 36–43 (1978) [Sov. J. Quantum Electron. 8, 15–20 (1978)].

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Melnikov, N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Wavefront inversion in stimulated scattering of focused light beams,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 211–215 (1977) [Sov. Tech. Phys. Lett. 3, 83–85 (1977)].

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel’shtam–Brillouin scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 15, 160–164 (1972) [JETP Lett. 15, 109–112 (1972)].

Zemskov, E. M.

I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, and V. I. Mandrosov, “Complex conjugation of fields in stimulated Brillouin scattering.” Kvantovaya Elektron. 3, 2467–2470 (1976) [Sov. J. Quantum Electron. 6, 1349–1351 (1976)].

Zubarev, I. G.

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, A. B. Mironov, S. I. Mikhailov, and M. G. Smirnov, “Influence of certain radiation parameters on wavefront reversal of a pump wave in a Brillouin mirror,” Kvantovaya Elektron,  6, 765–771 (1979) [Sov. J. Quantum Electron. 9, 455–458 (1979)].

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, “Time dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–139 (1976); Appl. Phys. 14, 99–115 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

Kvantovaya Elektron (1)

N. G. Basov, V. F. Efimkov, I. G. Zubarev, A. V. Kotov, A. B. Mironov, S. I. Mikhailov, and M. G. Smirnov, “Influence of certain radiation parameters on wavefront reversal of a pump wave in a Brillouin mirror,” Kvantovaya Elektron,  6, 765–771 (1979) [Sov. J. Quantum Electron. 9, 455–458 (1979)].

Kvantovaya Elektron. (6)

I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, and V. I. Mandrosov, “Complex conjugation of fields in stimulated Brillouin scattering.” Kvantovaya Elektron. 3, 2467–2470 (1976) [Sov. J. Quantum Electron. 6, 1349–1351 (1976)].

B. Ya. Zel’dovich and V. V. Shkunov, “Limits of existence of wavefront reversal in stimulated light scattering,” Kvantovaya Elektron. 5, 36–43 (1978) [Sov. J. Quantum Electron. 8, 15–20 (1978)].

B. Ya. Zel’dovich and T. V. Yakovlea, “Calculations of the accuracy of wavefront reversal utilizing pump radiation with one-dimensional transverse modulation,” Kvantovaya Elektron. 8, 314–321 (1981) [Sov. J. Quantum Electron. 11, 186–189 (1981)].

N. B. Baranova, B. Ya. Zel’dovich, and V. V. Shkunov, “Wavefront reversal in stimulated light scattering in a focused spatially inhomogeneous pump beam,” Kvantovaya Elektron. 5, 973–985 (1978) [Sov. J. Quantum Electron. 8, 559–566 (1978)].

N. B. Baranova and B. Ya. Zel’dovich, “Wavefront reversal of focused beams (theory of stimulated Brillouin backscattering),” Kvantovaya Elektron. 7, 973–982 (1980) [Sov. J. Quantum Electron. 10, 555–560 (1980)].

G. G. Kochemasov and V. D. Nikolaev, “Investigation of the spatial characteristics of Stokes radiation in stimulated scattering under saturation conditions,” Kvantovaya Elektron. 6, 1960–1965 (1979) [Sov. J. Quantum Electron. 9, 1155–1157 (1979)].

Opt. Commun. (5)

R. H. Lehmberg, “Numerical study of phase conjugation in stimulated backscatter with pump depletion,” Opt. Commun. 43, 369–374 (1982).
[CrossRef]

R. Mays and R. J. Lysiak, “Phase conjugated wavefronts by stimulated Brillouin and Raman scattering,” Opt. Commun. 31, 89–92 (1979).
[CrossRef]

R. Mays and R. J. Lysiak,„ Observations of wavefront reproduction by stimulated Brillouin and Raman scattering as a function of pump power and waveguide dimensions,” Opt. Commun. 32, 334–338 (1980).
[CrossRef]

N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Comparison of the amplification coefficients of conjugate and nonconjugate waves in stimulated light scattering,” Opt. Commun. 40, 73–76 (1981).
[CrossRef]

A. I. Sokolovskyaya, G. L. Blekhovskikh, and A. D. Kudryavtseva, “Light beam wavefront reconstruction and real volume image reconstruction of the object in stimulated Raman scattering,” Opt. Commun. 24, 74–76 (1978).
[CrossRef]

Opt. Eng. (1)

R. W. Hellwarth, “Optical beam phase conjugation by stimulated backscattering,” Opt. Eng. 21, 257–262 (1982), and references therein.
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (1)

R. H. Lehmberg and K. A. Holder, “Numerical study of optical ray retracing in laser-plasma backscatter,” Phys. Rev. 22, 2156–2170 (1980).
[CrossRef]

Phys. Rev. Lett. (1)

R. H. Lehmberg, “Theory of optical ray retracing in laser-plasma backscatter,” Phys. Rev. Lett. 41, 863–866 (1978).
[CrossRef]

Pis’ma Zh. Eksp. Teor. Fiz. (3)

V. I. Bespalov, A. A. Betin, and G. A. Pasmanik, “Reconstruction effects in stimulated scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 215–220 (1977) [Sov. Tech. Phys. Lett. 3, 85–87 (1977)].

B. Ya. Zel’dovich, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Connection between the wave fronts of the reflected and exciting light in stimulated Mandel’shtam–Brillouin scattering,” Pis’ma Zh. Eksp. Teor. Fiz. 15, 160–164 (1972) [JETP Lett. 15, 109–112 (1972)].

V. N. Blashchuk, B. Ya. Zel’dovich, N. A. Melnikov, N. F. Pilipetskii, V. I. Popovichev, and V. V. Ragul’skii, “Wavefront inversion in stimulated scattering of focused light beams,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 211–215 (1977) [Sov. Tech. Phys. Lett. 3, 83–85 (1977)].

Zh. Eksp. Teor. Fiz. Pis’ma Red. (1)

O. Yu. Nosach, V. I. Popovichev, V. V. Ragul’skii, and F. S. Faizullov, “Cancellation of phase distortions in an amplifying medium with a Brillouin mirror,” Zh. Eksp. Teor. Fiz. Pis’ma Red. 16, 617–621 (1972) [Sov. Phys. JETP Lett. 16, 435–438 (1972)].

Zh. Tekh. Fiz. (1)

V. G. Sidorovich, “Theory of the Brillouin mirror,” Zh. Tekh. Fiz. 46, 2168–2174 (1976) [Sov. Phys. Tech. Phys. 21, 1270–1274 (1976)].

Other (1)

C. R. Guiliano, R. W. Hellwarth, R. K. Jain, R. C. Lind, T. R. O’Meara, S. M. Wandzura, and V. Wang, “Correction of phase distortion by nonlinear optical techniques” (Hughes Research Laboratories Interim Tech. Rep. for period 15 July 1977–30 September 1978 (March1979).

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Figures (12)

Fig. 1
Fig. 1

Intensity profiles of a nonaxially propagating wave in a linear medium, calculated with (a)–(c) the conventional DFT and (d)–(f) the waveguide modes.

Fig. 2
Fig. 2

Simulation of SBS wave-front conjugation in an optical waveguide with a 75-cm gain length, showing intensity profiles of the incident light (solid lines) and backscatter (dashed lines) with negligible pump depletion. (The incident intensity is uniform across the aberrator.)

Fig. 3
Fig. 3

Far-field intensity profile of the incident light after traversing an aberrator of 20-mrad (full 1/e) angular divergence.

Fig. 4
Fig. 4

Conjugation fidelity H (as calculated directly by the code), HM given by the mode approximation [Eqs. (18) and (19)], and conjugate mode enhancement factor ln ρ [Eq. (18)] versus average (amplitude) gain exponent for the same aberrator and gain length used in Fig. 2.

Fig. 5
Fig. 5

Same as Fig. 2, except for a shorter gain length (L = 20 cm).

Fig. 6
Fig. 6

Conjugation fidelity versus D2/, as calculated from Ref. 5 (dashed curve) and simulations with aberrators of 10-mrad (solid diamonds) and 20-mrad (open diamonds) far-field divergence. Each point shows the average and mean deviation of five simulations using independent aberrators.

Fig. 7
Fig. 7

Conjugation fidelity versus D/ from simulations with aberrators of 5-mrad (open squares), 10-mrad (solid diamonds), and 20-mrad (open diamonds) far-field divergence.

Fig. 8
Fig. 8

SBS wave-front conjugation geometry, where aberrator A is imaged onto the entrance face of the optical waveguide.

Fig. 9
Fig. 9

Comparison between the fidelity versus D/ data of Fig. 7 and simulations of the geometry shown in Fig. 8 (asterisks), using θD = 20.6 mrad.

Fig. 10
Fig. 10

Conjugation fidelity H and reflectivity R versus incident intensity from simulations of the model shown in Fig. 8 (L = 75 cm, θD′ = 5 mrad, θF = 20 mrad). The dashed line shows the fidelity in the absence of pump depletion.

Fig. 11
Fig. 11

Simulation of SBS wave-front conjugation in an optical waveguide with pump depletion (corresponding to the R = 41% point of Fig. 10). The intensity profiles have the same meaning as in Figs. 2 and 5. The horizontal line in the near-field plot is the phase of the backscattered field after it traverses the aberrator.

Fig. 12
Fig. 12

Comparisons between the top-hat incident pump profile and an image of the backscatter at the aberrator, using spatial filtering with far-field apertures of (a) 10× diffraction limit and (b) 4× diffraction limit.

Equations (37)

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( z + i 2 k 2 x 2 ) E L = 1 2 g E S 2 E L ,
( z - i 2 k 2 x 2 ) E S = 1 2 g E L 2 E S
E ( J ) = K = 0 N - 1 E ˜ ( K ) exp ( i 2 π J K / N ) ,
x ( J ) = ( W / N ) J - W / 2 ,             J = 0 , 1 , , N - 1.
E L , S ( W / 2 , z ) = E L , S ( - W / 2 , z ) = 0
E ( J ) = K = 1 N - 1 E ˜ ( K ) sin ( π J K / N ) ,             J = 0 , 1 , , N - 1 ,
E ( 2 N - 1 ) = - E ( I ) ,             I = 1 , 2 , , N - 1 ,
E ( N ) = E ( 0 ) = 0.
G P S ( z 2 ) / P S ( z 1 ) ,
R P S ( z 2 ) / P L ( z 2 ) ,
P L , S ( z ) - W / 2 W / 2 E L , S ( x , z ) 2 d x
P L ( z ) - P S ( z ) = constant
H ( z ) 1 P L ( z ) P S ( z ) | - W / 2 W / 2 E L ( x , z ) E S ( x , z ) d x | 2 .
1 - H background hash total backscatter power .
( z - i 2 k 2 x 2 ) E L * ( x , z ) = 0
E S ( x , z ) = C E L * ( x , z ) exp [ 1 2 σ g Ī ( z - z 1 ) ] + E N C ( x , z ) exp [ 1 2 g Ī ( z - z 1 ) ] ,
- W / 2 W / 2 E L ( x , z ) E N C ( x , z ) d x = 0.
H 1 P S ( z 1 ) = C 2 P L ,
H P S ( z 2 ) = C 2 P L exp ( σ g Ī L ) ,
σ = ln ( G H / H 1 ) g Ī L .
ρ C 2 P L exp ( σ g Ī L ) P N C exp ( g Ī L ) ,
P N C - W / 2 W / 2 E N C ( x , z 1 ) 2 d x .
P N C = P S ( z 1 ) - C 2 P L = ( 1 - H 1 ) P S ( z 1 ) P S ( z 1 ) ;
ρ = G H / exp ( g Ī L ) .
H M = ρ / ( 1 + ρ ) .
θ F = W M / f = W A / f ,
max ( θ F , θ A ) < θ D < θ F + θ A .
γ g L z 1 z 2 Ī ( z ) d z ( 1 - R ) g Ī ( z 2 ) ,
exp [ i ( K m 2 + K m 2 - K n 2 - K n 2 ) z / 2 k ] ,
k - 1 ( K max - K min ) Δ K Δ z > π ,
θ D / g Ī > W
θ D > ( g Ī L ) W / L 10 W / L .
E S ( x ) R 1 / 2 E L * [ 1 + N 0 α N exp ( i 2 π N x / W A ) ] ,
E S ( x ) 2 R E L 2 [ 1 + N 0 α N exp ( i 2 π N x / W A ) + c . c ] ,
H ( 1 + N 0 α N 2 ) - 1 .
E S max 2 / E S min 2 ( 1 + 2 N M 1 / 2 α r m s ) / ( 1 - 2 N M 1 / 2 α rms ) ,
H 1 - N M α rms 2 .